ExEcutivE summary
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
organisations. score recommends that there is a review
of the mathematical requirements for each of the sciences
at a-level and that a framework is developed to regulate
the way mathematics is assessed within the sciences to
ensure parity across the system.
FULL REPORT FROM SCORE
aims
MATHEMATICS WITHIN A-LEVEL
SCIENCE 2010 EXAMINATIONS
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
score’s ov
gather evide
mathematic
a-level spec
was being a
work did no
between ph
these will dif
the findings
inform the d
and difficult
assessment
physics. th
how the exa
CONTENTS
CHAPTER 1:
INTRODUCTION
ExEcutivE
summary
1.1 Background
mathematics
enables students to understand and
describe many scientific phenomena yet there is concern
1.2 Research aims
that science assessments at a-level are not reflecting the
1.3 Overview
of findings
subject’s
analytical
nature. to explore whether there was
any
evidence
for
this
concern,
score investigated the
1.4 Related literature
and research
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical
requirements listed in the biology, chemistry
CHAPTER 2:
and physics specifications are not assessed. those that
2.1 Research design – overview
are assessed are covered repeatedly and often at a lower
level
than required.
this is
to 1
have an impact on
2.2 Research
design
– likely
Phase
the way that the subjects are taught and therefore on
2.3 Research design – Phase 2
students’ ability to have the necessary skills to progress
2.4 Research
design
– Phase
3 and employment.
effectively
to stem
higher
education
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
CHAPTER 3:score recommends that there is a review
organisations.
of
mathematical requirements for each of the sciences
3.1thePhysics
at a-level and that a framework is developed to regulate
way3.1.1
Phase is
1:assessed
A-level papers
the
mathematics
within the sciences to
ensure
theExtent
system.
parity across
3.1.1.1
3.1.1.2 Type
Background
4
4
4
4
4
7
7
7
10
aims
11
score’s overall objective for this project was to
gather evidence on the type, extent and difficulty of 13
mathematics required to access the sciences in current
13
a-level specifications and to establish whether this
13
was being appropriately met by the assessments. the
13
work did not compare the mathematical requirements
between physics, chemistry and biology as it is accepted
15
these will differ between the disciplines.
16
there
has been3.1.1.3
growingDifficulty
concern across the science
the findings aim to provide score with evidence to
community
the mathematical
demand of science
about
3.1.1.4
Appropriateness
23
inform the development of policy on the type, extent
qualifications, specifically that Gcse and a-level science
and
difficulty of the mathematics in the criteria and
3.1.2 Phase 2 – Physics A-level in comparison with
GCSE
qualifications are not meeting the needs of students in
assessments
for a-levels in biology, chemistry and 25
mathematics and National Curriculum
Level Descriptors
the way they assess the analytical nature of science.
physics. the project also supports score’s work on
3.1.3 Phase 3 – Survey findings
31
how the examinations system should operate to ensure
in 2009 score published evidence on Gcse science
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
work on improving the coherence between the sciences
the
amount
of
mathematics
assessed
across
awarding
3.2 Chemistry
33
and mathematics.
organisations and confirmed that the use of mathematics
3.2.1 Phase 1: A-level papers
within the context of science was examined in a very
limited
organisations
felt that this was
way. score
3.2.1.1
Extent
unacceptable. mathematics is integral to the teaching
3.1.1.2 Type
and learning of the sciences, and offers a valuable aid
3.2.1.3
Difficulty scientific phenomena;
in
understanding
and describing
as such it should be appropriately represented in the
3.2.1.4 Appropriateness
biology, chemistry and physics curricula and their
3.2.2 Phase 2 – Chemistry A-level in comparison
assessments.
with GCSE
mathematics and National Curriculum Level Descriptors
to provide further evidence to support these
3.2.3 Phase 3 – Survey findings
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
2
SCORE Maths
report
score
mathsininscience
science
report
33
in the project, we looked across all assessments at
33
a-level for a given year, including both experimental and
practical examination papers.
36
37
43
45
49
3.3
Biology
mEthodology
designed
in three
phases. the
the project
3.3.1was
Phase
1: A-level
papers
first was to establish the nature of the mathematics
3.3.1.1 Extent
assessed within the biology, chemistry and physics
a-level examinations
2010. the full suite of
3.3.1.2inType
examinations papers from aQa, ccea, edexcel,
3.3.1.3 Difficulty
ocr and WJec were analysed using the four
measures that3.3.1.4
follow: Appropriateness
the groups comprised practising a-level teachers, 52
teachers with experience in curriculum research and
52
development and individuals working for awarding
52
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout
the
54
analysis to verify the reliability of judgements within and
55
across the subject expert groups.
the second phase aimed to measure the coherence 61
between
1. the
3.3.2
2 – Biology
in comparison
GCSE the teaching and learning of mathematics
typePhase
of mathematics.
theA-level
mathematical
areas with
and
the
sciences.
there is an assumption that the 63
mathematics
and
National
Curriculum
Level
Descriptors
assessed were categorised against the stated
mathematical
concepts
used to access the sciences
mathematical requirements for biology, chemistry
3.3.3 Phase 3 – Survey findings
67
1
are
first
taught
within
a
mathematical
context, i.e. within
and physics respectively .
the mathematics curriculum. the project compared the
2. the extent of the mathematics. the proportion
mathematical requirements for the sciences at a-level
3.4 Views
industry
70
of the from
question
parts within a paper that
with the mathematics curriculum prior to Key stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
APPENDICES
72
that required mathematics.
was carried out by a researcher and by a mathematics
3. the
Appendix
Summer 2010
A-level
papers analysed
72
teacher.
difficulty 1:
of mathematics.
this
was measured
against
3 criteria:
the number ofrequirements
steps in a
Appendix
2: Mathematical
for physics
71
theA-level
aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics
Appendix 3: Mathematical requirements for chemistry
A-level that the community would like to see
72
the complexity of the question. each category
in a-level science assessments. this was achieved
Appendix
4: Mathematical
requirements
75
had
varying levels
of difficulty and
each was for biology A-level
through an online survey for stakeholders in the science
measured as a proportion of the total number of
Appendix 5a: Examples of mathematical questionscommunity.
within Depending on their expertise, participants
question parts containing mathematics. it was not
answered the survey for biology, chemistry or physics
a science A-level of a single step calculation, a multiple
measured against the number of marks.
step calculation and an extended step calculation a-level assessment. the participants were chosen in 76
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
Appendix 5b: Examples of mathematical questions within a science
professional bodies. an online survey was completed by
looked at whether the answer required scientific
A-level of a Level 1, Level 2, Level 3 and Level 4 complexity
81
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Appendix
5c: Examples
of mathematical
a science
38within
for chemistry;
and 32 for physics). participants from
this
was measured
as a proportion
of the total questions
A-level
of
a
Level
1,
Level
2
and
Level
3
context
83
industry
were
also
consulted more generally but as most
number of question parts containing mathematics.
science-related industries employ at a graduate level
Appendix
5d: Examples
of mathematical
questions within a science
a subject
expert group
was established
for each
their comments tended to focus more on the outcomes
A-level
where each
all marks,
of the
marks, none of marks require
of the three
sciences.
groupsome
analysed
the full
at graduate level rather than directly referring to a-level.
comprehension
to mathematical skill
85
suite ofscientific
2010 examinations
papers in
of addition
aQa, ccea,
edexcel,
ocr and6:WJec
for their for
respective
subjects
Appendix
Framework
analysing
A-level theory and practical papers
88
at a two-day workshop. examination papers included
all the theory
Appendix
7: Acknowledgements
90
papers
(Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
CHAPTER 1: INTRODUCTION
1.1 BACKGROUND
ExEcutivE
summary
1.3 OVERVIEW OF FINDINGS
There has been
growing
concern
acrossand
the
mathematics
enables
students
to understand
science many
community
the use
mathematical
describe
scientificabout
phenomena
yetofthere
is concern
assessments
in scienceatqualifications.
that
science assessments
a-level are not reflecting the
subject’s analytical nature. to explore whether there was
In 2009
SCORE
published
research
on GCSEthe
any
evidence
for this
concern, score
investigated
science
examination
The report
showed
type,
extent
and difficultypapers.
of mathematical
questions
within
a wide a-levels.
variationthe
in the
amount
mathematics
science
findings
showofthat
a large number of
assessed across
awarding
organisations
mathematical
requirements
listed
in the biology,and
chemistry
confirmed
that
the
use
of
mathematics
and physics specifications are not assessed. within
those that
theassessed
context of
examined
in a at
very
are
arescience
covered was
repeatedly
and often
a lower
limited
SCORE
that this
level
thanway.
required.
thisorganisations
is likely to have felt
an impact
on
was
unacceptable.
Mathematics
is
integral
to
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teaching ability
and learning
of necessary
the sciences,
offers
students’
to have the
skills and
to progress
a valuabletoaid
in understanding
effectively
stem
higher educationand
and describing
employment.
scientific
as such
it should
in
addition,phenomena;
the findings show
a disparity
in thebe
way
appropriately
represented
in
the
biology,
chemistry
mathematics is assessed across the different awarding
and physics curricula
and their assessments.
organisations.
score recommends
that there is a review
of the mathematical requirements for each of the sciences
Toa-level
provide
further
these
at
and
that a evidence
frameworkto
is support
developed
to regulate
concerns,
SCORE
set
up
this
project
to
investigate
the way mathematics is assessed within the sciences to
the mathematics
in the summer 2010 science
ensure
parity acrossfound
the system.
The main findings of the research were as follows:
assessments for the biology, chemistry and physics
A-levels across the unitary awarding organisations in
Background
England, Wales and Northern Ireland.
there has been growing concern across the science
community
about the
mathematical demand of science
1.2 RESEARCH
AIMS
qualifications, specifically that Gcse and a-level science
SCORE’s overall
objective
this
project
was to in
qualifications
are not
meetingfor
the
needs
of students
gather
on the
the analytical
type, extent
andofdifficulty
the
wayevidence
they assess
nature
science.of
mathematics assessed in science A-levels and to
in
2009 score
published
evidence
on Gcse reflected
science
establish
whether
the current
assessments
examination
papersrequirements
which reported
wide
variationThe
in
the mathematical
of athe
sciences.
the
amount
of
mathematics
assessed
across
awarding
work did not compare the mathematical requirements
organisations
and confirmed
use ofas
mathematics
between biology,
chemistrythat
andthe
physics
it is
within
the context
of science
was examined
in a very
accepted
these will
differ between
the disciplines.
limited way. score organisations felt that this was
The findings aim
to provideisSCORE
unacceptable.
mathematics
integral with
to theevidence
teaching
to inform
theofdevelopment
policy
type,aid
and
learning
the sciences,of
and
offersona the
valuable
extent
and difficulty
the mathematics
in the
in
understanding
andof
describing
scientific phenomena;
specifications
and
for A-levels in the
biology,
as
such it should
beassessments
appropriately represented
chemistry
and physics.
The project
also
supports
biology,
chemistry
and physics
curricula
and
their
SCORE’s work on how the examinations system
assessments.
should operate to ensure science qualifications are
to
provide
further
evidence
support
these
fit for
purpose
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also its to
work
on improving
the
concerns,
score
set
up
this
project
to
the
coherence between the sciences and investigate
mathematics.
mathematics found in the 2010 science assessments
at
acrosswe
thelooked
unitary awarding
in
In a-level
the project,
across allorganisations
assessments
england,
Wales
and
northern
ireland.
at A-level for 2010, including theory and practical
examination papers.
2
4
SCORE Maths
report
score
mathsininscience
science
report
• A large number of the mathematical requirements
listed in the 2010 biology, chemistry and physics
AS and A2 specifications were assessed in a limited
way or not at all within the examination papers.
• There is a measurable variation between awarding
organisations in terms of the amount and difficulty
of the mathematics that is assessed in biology,
chemistry and physics AS and A2 examination
papers. Participants in our survey felt that in some
cases the amount of mathematics assessed in
A-level science examinations was too low.
aims
• The examination questions that did require
score’s overall objective for this project was to
mathematics were felt to be of insufficient difficulty;
gather evidence on the type, extent and difficulty of
too many involved only single step questions,
mathematics required to access the sciences in current
require only simple recall, and
a-level specifications and to establish whether this
were set only in familiar contexts.
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
• There were many mathematical requirements
between physics, chemistry and biology as it is accepted
identified in biology, chemistry and physics A-levels
these will differ between the disciplines.
that go beyond the current GCSE mathematics.
the findings aim to provide score with evidence to
1.4 RELATED LITERATURE AND RESEARCH
inform the development of policy on the type, extent
and
difficulty
of the and
mathematics
the criteria
and are
Relevant
literature
previousinresearch
findings
assessments
for a-levels in biology, chemistry and
presented below.
physics. the project also supports score’s work on
SCORE:
GCSE science
2008
examinations
how
the examinations
system
should
operate to ensure
This
project
explored
the
fitness
for
purpose
ofits
GCSE
science qualifications are fit for purpose
and also
science
examination
papers,
focusing
on
how
the
work on improving the coherence between the sciences
examination
papers assessed particular aspects
and
mathematics.
of GCSE science. One aspect was the extent and
in
theof
project,
we looked
across all
at and
type
mathematics
required
byassessments
the questions
a-level
forthis
a given
both experimental
whether
wasyear,
the including
same across
the awardingand
practical
examination
papers.
organisations. Findings showed that the demand and
type of the mathematics within the GCSE science
papers was limited. The assessed mathematical
content, in some cases, did not correspond with the
mathematics found in the science specifications.
This was particularly true for the more advanced
mathematics. The mathematics found was judged
to be limited in terms of both the type and extent
of mathematics required by students. The project
considered only the examinations themselves and not
the internal assessment/coursework; it was accepted
that this may account for discrepancies across
awarding organisations.
SCORE:
GCSE science examinations 2008,
mEthodology
2009
and
the project2010
was designed in three phases. the
The
SCORE
research
to
first was
to establish
theabove
nature was
of theextended
mathematics
include
similar
analyses
of
the
2009
and
2010
assessed within the biology, chemistry and physics
science
GCSEs. While
therethe
hadfullbeen
a-level examinations
in 2010.
suite modest
of
increases
in
the
amount
of
mathematics
required in
examinations papers from aQa, ccea, edexcel,
the
GCSEs
overwere
the three
cycles
assessments,
ocr
and WJec
analysed
usingofthe
four
much
of
the
mathematics
was
found
to
be at Key
measures that follow:
Stage 2 level of difficulty with the demand and type
type of mathematics.
areas
of 1.
thethe
mathematics
still foundthe
to mathematical
be limited when
assessed
were
categorised
against the
stated
compared
to the
lists
of mathematical
requirements
mathematical
requirements
for
biology,
chemistry
provided by some awarding organisations in their
and physics respectively1.
specifications.
2. the extent of the mathematics. the proportion
IOP: of
Mind
the Gap,
July
2011
the question
parts
within
a paper that
The Institute
of
Physics
had
included mathematics wasconcerns,
measured borne
as wasout
the of
anecdotal
evidence,
the
current
and
proportion
of the that
marks
within
thesephysics
questions
mathematics
A-levels
were
not
preparing
students
that required mathematics.
sufficiently for studying physics or engineering as
the difficulty of This
mathematics.
measured
an3.undergraduate.
concernthis
waswas
two-fold:
that
against
3
criteria:
the
number
of
steps
in
a
first-year undergraduates were not proficient in
calculation, theskills
familiarity
of the
context
and lack
the mathematical
needed,
and
that the
the
complexity
of
the
question.
each
category
of mathematical content in the physics A-levels
hadmotivating
varying levels
of difficulty
and
each was
was not
students
who
enjoyed
solving
measured
as
a
proportion
of
the
total
number
of
mathematical problems from to take further related
question
parts
containing
mathematics.
it
was
study. 55% of the academics surveyed in the not
measured
the number
marks.
project
felt thatagainst
the students
wereofnot
very, or not
at 4.
all the
wellappropriateness
prepared to cope
with
the
mathematical
of mathematics. We
content
of undergraduate
study. required
92% feltscientific
that a
looked
at whether the answer
lack of
fluency in mathematics
a barrier to
comprehension
in addition towas
mathematical
skill.
students
achieving
their
potential.
this was measured as a proportion of the total
number of question parts containing mathematics.
In the IOP research, integration, identifying particular
a subject expert
group wasto
established
each and
equations
and techniques
deal with for
problems,
of the three
each group
analysed
the full
vectors
andsciences.
scalars were
identified
by academics
suite
of
2010
examinations
papers
of
aQa,
ccea,
and students as being more difficult content areas.
edexcel,
ocr andalso
WJec
for theirhow
respective
subjects
The
IOP research
showed
academics
were
at
a
two-day
workshop.
examination
papers
included
concerned that in the physics A-level there was not
all the theory
papersof(Units
1, 2, 4 understanding
and 5) and the of
enough
promotion
contextual
experimental
and
practical
papers
(Units 3 and 6).
the topic.
Royal
Statistical
Society:
The
Future
of
the groups
comprised
practising
a-level
teachers,
Statistics
inexperience
our Schools
and Colleges,
teachers with
in curriculum
research and
January
2012
development
and individuals working for awarding
This
report analysed
thequestion
current writers
provision
in
organisations
as markers,
or examiners.
statistics
in schools
andwere
colleges.
There
are threethe
standardisation
exercises
employed
throughout
recommendations
theofreport
that are
relevant
analysis to verify the from
reliability
judgements
within
and
to
the current
discussion:
across
the subject
expert groups.
1. Recommendation 3: national education policy
the second phase aimed to measure the coherence
should ensure that all students are equipped
between the teaching and learning of mathematics
with a working knowledge of basic statistics,
and the sciences. there is an assumption that the
including the necessary associated mathematical
mathematical concepts used to access the sciences
competence
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
2. Recommendation 8: the curriculum should be
mathematical requirements for the sciences at a-level
designed so that, wherever possible, students
with the mathematics curriculum prior to Key stage 5
have met statistical techniques in mathematics
using the current national curriculum level descriptions
before they need to use them in other subjects
and a 2012 mathematics Gcse specification3. this work
was
carried out by a researcher
and by a mathematics
3.
Recommendation
15: the statistics
content
teacher.
within mathematics, up to GCSE, should include
thatphase
are either
currently
thesome
aim oftopics
the third
was tonot
determine
thecovered
nature
or are only treated
of mathematics
that thelightly
community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
5
Dr. Jenny Koenig
for the UK Centre for
ExEcutivE
summary
Bioscience and the HEA: A survey of the
mathematics enables students to understand and
mathematics landscape within bioscience
describe many scientific phenomena yet there is concern
undergraduate and postgraduate UK higher
that science assessments at a-level are not reflecting the
education, June 2011
subject’s analytical nature. to explore whether there was
This report was prompted in part by the
any evidence for this concern, score investigated the
understanding that biology was becoming a
type, extent and difficulty of mathematical questions within
more quantitative science with greater of levels
science a-levels. the findings show that a large number of
of mathematics and so the mathematics skills of
mathematical requirements listed in the biology, chemistry
biologists needed to increase to meet this demand.
and physics specifications are not assessed. those that
The report explained how amongst bioscience
are assessed are covered repeatedly and often at a lower
undergraduates, there was a wide variety in their
level than required. this is likely to have an impact on
mathematics qualifications. There were specific
the way that the subjects are taught and therefore on
concerns about undergraduate students’ abilities
students’ ability to have the necessary skills to progress
to rearrange simple equations and reliably use ratio
effectively to stem higher education and employment.
and proportion.
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
Advisory Committee on Mathematics
organisations. score recommends that there is a review
Education (ACME): Mathematical Needs,
of the mathematical requirements for each of the sciences
Mathematics in the workplace and in Higher
at a-level and that a framework is developed to regulate
Education, June 2011
the way mathematics is assessed within the sciences to
The report outlines the mathematical needs from
ensure parity across the system.
the perspective of higher education and employers.
ACME’s first recommendation in the report is that a
Background
large majority of young people should continue with
there
growing concern
acrossACME’s
the science
some has
formbeen
of mathematics
post-16.
third
community
about the
mathematical
science
recommendation
refers
to how, in demand
a revisedofNational
qualifications,
specifically
a-level science
Curriculum, there
shouldthat
be Gcse
greaterand
emphasis
on
qualifications
are
not
meeting
the
needs
of
students
in
essential mathematics techniques and the application
the
way they assess
the analytical
nature of science.
of mathematics.
ACME’s
recommendation
10 refers
to using mathematics in a range of familiar and
in 2009 score published evidence on Gcse science
unfamiliar contexts. ACME’s recommendation 14
examination papers which reported a wide variation in
is that universities should make clear the level and
the amount of mathematics assessed across awarding
extent of mathematics within their degrees.
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
6
SCORE Maths
report
score
mathsininscience
science
report
The Nuffield Foundation: Mathematics in other
subjects at A-level, 2012
The Nuffield Foundation has completed a project
which analysed the mathematical content of other
A-levels: business studies, computer science,
economics, geography, psychology and sociology.
The same methodology was used as in the first
phase of the SCORE research, that is, the A-level
assessments were analysed against a framework
of measures of type, extent and difficulty of the
mathematical content. The same method of
analysis of data was also utilised. The results
from the Nuffield research (due April 2012) should
determine whether there are common areas among
a wider spread of subjects at A-level that would
benefit from changes to the mathematics GCSE
aims
or future mathematics for post-16.
score’s overall objective for this project was to
gather evidence on the type, extent and difficulty of
mathematics required to access the sciences in current
a-level specifications and to establish whether this
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
CHAPTER 2: METHODOLOGY
2.1
RESEARCH DESIGN – OVERVIEW
mEthodology
2.2
DESIGN
– PHASE
1
the RESEARCH
groups comprised
practising
a-level teachers,
the project
project was
in three
phases.
theThe first
The
wasdesigned
designed
in three
stages.
first
was
to
establish
the
nature
of
the
mathematics
was to establish the nature of the mathematics
assessed assessed
within the biology,
chemistryA-level
and physics
currently
within science
papers.
a-level
examinations
in
2010.
the
full
suite
of
The second compared the current mathematical
examinations papers
from aQa,
ccea,and
edexcel,
requirements
for biology,
chemistry
physics
ocr
and
WJec
were
analysed
using
the
fourto identify
A-level with GCSE mathematics in order
measures
follow:
overlap
orthat
gaps
in mathematical content. The
third
findings with
fromareas
the
1. reviewed
the type ofthe
mathematics.
themembers
mathematical
science
community
and
focused
on
the
nature
assessed were categorised against the stated
of mathematics
that
the community
would
like to
mathematical
requirements
for biology,
chemistry
1
see inand
A-level
science
assessments.
Views
were
physics respectively .
gathered from teachers, professional bodies, higher
2. the extent
of the mathematics. the proportion
education
and industry.
Phase 1 aimed to establish the nature of the
development and individuals working for awarding
mathematics assessed within the biology, chemistry
organisations as markers, question writers or examiners.
and physics A-level summer 2010 examinations1.
standardisation exercises were employed throughout the
Papers from the five awarding organisations that
analysis to verify the reliability of judgements within and
offered single science A-levels in England, Wales
across the subject expert groups.
and Northern Ireland were analysed: AQA, CCEA,
Edexcel,
OCR
andaimed
WJEC
.
the second
phase
to 2measure
the coherence
of the question parts within a paper that
included
mathematics
was measured
as wasthe
the
A working
group
was established
to oversee
proportion
of
the
marks
within
these
questions
research project and to inform the methodology
that required
mathematics.
and policy
implications.
The group comprised
representatives
3. the difficultyfrom:
of mathematics. this was measured
• Theagainst
Institute
of
Physics
3 criteria:
the number of steps in a
• Society
of
Biology
calculation, the familiarity of the context and
• Royal
of Chemistry
the Society
complexity
of the question. each category
• Thehad
Royal
Society
varying
levels of difficulty and each was
• AQA
measured as a proportion of the total number of
• ACME
question parts containing mathematics. it was not
• Institute
of Education
measured
against the number of marks.
• Institute of Mathematics and its Applications
4. the
appropriateness
• Sixth
Form
College of mathematics. We
looked
at
whether the answer required scientific
• Industry
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
1
teachers with experience in curriculum research and
between the teaching and learning of mathematics
The
analysis
did not
compare
the mathematical
and the
sciences.
there
is an assumption
that the
content
across
the sciences
it is accepted
there
mathematical
concepts
used to as
access
the sciences
are
different
requirements
are first
taughtmathematical
within a mathematical
context,fori.e.biology,
within
chemistry
and physics.
the mathematics
curriculum. the project compared the
mathematical requirements for the sciences at a-level
A
framework
was developed
order
to make
with
the mathematics
curriculuminprior
to Key
stage 5
judgements
about
the
type,
extent,
difficulty
using the current national curriculum level descriptions
and
of Gcse
the mathematics
and aappropriateness
2012 mathematics
specification3within
. this work
each
of
the
examination
papers
was carried out by a researcher andfor
bybiology,
a mathematics
chemistry
teacher. and physics A-level. The framework
incorporated measures used in previous research
the aim
of the thirdfrom
phase
to determine
and
suggestions
thewas
working
group.the
A nature
pilot
of
mathematics
that
the
community
would
like
exercise was carried out to test the validitytoofsee
the
in a-level science
assessments.
thisof
was
framework
and the
effectiveness
theachieved
analysis
through an
3 online survey for stakeholders in the science
. Figure 1 outlines the measures of the
process
community.
their expertise,
participants
framework Depending
used in theonanalysis
of science
A-level
answered
the
survey
for
biology,
chemistry
or physics
examination papers.
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
ummer 2010 papers were analysed to represent an A-level rather than AS 2009 and A2 2010 papers. This was because awarding
S
organisations usually commission a group of examiners who are responsible for all the assessments for a single examining session;
it is unlikely that any comparison would be made with papers for other sessions during the course of that process.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
2
Whereand
awarding
offered
more than
specification
for a science A-level, the one with the highest uptake was
chemistry
physics.organisations
the mathematical
requirements
are one
available
in the full report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
chosen. Where there were options questions, or sections within an A-level, the awarding organisations were contacted and asked
a-level
assessment
andthe
the highest
marks from
the practical
and
experimental
papers
(Unitfinal
3 and
6) makefor
up example,
the remaining
the analysis,
which
option had
uptake
and that
option
was used
in the
analysis,
for 20%.
AQA inPhysics
A, paper 5,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
option
C
was
used
in
the
analysis.
Appendix
1
details
the
summer
2010
A-level
papers
analysed
in
the
research.
3
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
theThe
revised
mathematics
3
report
from theGcses.
pilot exercise testing the validity of the framework is available from the SCORE Secretariat.
SCORE
Mathsininscience
science report
report
score
maths
3
7
Figure 1: Measures
used to analyse the mathematics assessed within science A-level examinations
ExEcutivE
summary
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
EXTENT
that science assessments at a-level are not reflecting the
1. Question number and part: This allowed for
subject’s analytical nature. to explore whether there was
the number of questions and question parts
any evidence for this concern, score investigated the
with mathematical content to be worked
type, extent and difficulty of mathematical questions within
out as a proportion of the total number of
science a-levels. the findings show that a large number of
questions parts, giving a measure of the
mathematical requirements listed in the biology, chemistry
extent of the mathematical content. A
and physics specifications are not assessed. those that
question part was the smallest division that
are assessed are covered repeatedly and often at a lower
a question was divided into which may be a
level than required. this is likely to have an impact on
whole question, as in most multiple choice
the way that the subjects are taught and therefore on
question or it may be, for example, Q3aii.
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
2. The number of marks that required
in addition, the findings show a disparity in the way
mathematics: The percentage of marks
mathematics is assessed across the different awarding
awarded for mathematical comprehension
organisations. score recommends that there is a review
was calculated as a proportion of overall
of the mathematical requirements for each of the sciences
marks available in the paper. This provided
at a-level and that a framework is developed to regulate
a second measure of the extent of the
the way mathematics is assessed within the sciences to
mathematical content. Whole marks were
ensure parity across the system.
counted rather than parts of marks.
Background
TYPE
there
been of
growing
concern across
the science
3. Thas
he type
mathematics:
The mathematical
community
about thefor
mathematical
demand and
of science
requirements
biology, chemistry
4
qualifications,
Gcse
and a-level
physics,specifically
as set by that
Ofqual
, were
used science
qualifications
are the
not type
meeting
the needs of students in
to identify
of mathematics
the way
they assess
analytical
nature
of science.
assessed
andthe
how
frequently
they
occur
in assessments. The mathematical
in 2009 score published evidence on Gcse science
requirements for physics are stated in
examination papers which reported a wide variation in
Appendix 2, for chemistry in Appendix 3
the amount of mathematics assessed across awarding
and for biology in Appendix 4. All of the
organisations and confirmed that the use of mathematics
requirements needed for each question
within the context of science was examined in a very
part were recorded. The mathematical
limited way. score organisations felt that this was
requirements for the three subjects are
unacceptable. mathematics is integral to the teaching
different so comparisons across subjects
and learning of the sciences, and offers a valuable aid
are not straightforward, for example, ratios,
in understanding and describing scientific phenomena;
fractions and percentages is listed under 1c)
as such it should be appropriately represented in the
in the physics requirements and under 1b)
biology, chemistry and physics curricula and their
in the chemistry requirements.
assessments.
DIFFICULTY
4. The number of steps in a calculation: This
aspect of difficulty discriminated between
mathematical questions where only one step
was needed to gain the solution to a problem
(single step), where more than one step was
needed in one calculation to gain the solution
to a problem (multiple step) and where a
value, for example x, had to be found
and that value, x, used in a subsequent
calculation in order to find the solution to the
problem, y (extended calculation). Appendix
5a gives an example at A-level of single,
aims
multiple and extended type questions.
score’s overall objective for this project was to
gather evidence on the type, extent and difficulty of
5. The complexity of the task: This aspect
mathematics required to access the sciences in current
of difficulty established the complexity
a-level specifications and to establish whether this
of the mathematical question as defined
was being appropriately
met by the assessments. the
by Geoff Wake’s5 four
descriptions of
work did not compare the mathematical requirements
increasing difficulty. Level 1 complexity
between physics, chemistry and biology as it is accepted
is defined as straightforward or routine,
these will differ between the disciplines.
which requires recall of procedures and
straightforward
application.
Levelto
the relatively
findings aim
to provide score
with evidence
2
requires
application
and
understanding
of
inform the development of policy on the type, extent
one domain.
Level
3 requires
and mathematics
difficulty of the in
mathematics
in the
criteria
and
understanding
and
use
of
mathematics
assessments for a-levels in biology, chemistry and
across
and
necessitates
a decision
physics.
thedomains
project also
supports
score’s
work on
about
the
direction
in
which
to
proceed.
Level
how the examinations system should operate to ensure
4 involves
complex
activity
requiring
synthesis
science
qualifications
are fit
for purpose
and also
its
and
application
across
a
number
of
domains
work on improving the coherence between the sciences
structuring or decision making being
and with
mathematics.
necessary. Appendix 5b gives an example at
in the
project,
across all assessments at
A-level
ofwe
thelooked
four categories.
a-level for a given year, including both experimental and
6. Familiarity
of context:
practical
examination
papers.It is generally accepted
that if a context is more familiar it is easier
to apply mathematics than if the context
is unfamiliar. Three categories were used
to judge the familiarity of the mathematical
question, in relation to recognising which
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
continues 
4Mathematical requirements form part of the Criteria set by Ofqual for biology, chemistry and physics A-level.
5Drake, P., Wake, G. and Noyes, A. Assessing ‘functionality’ in school mathematics examinations: what does being human have to
do with it? Research in Mathematics Education, 2012
2
8
SCORE Maths
report
score
mathsininscience
science
report
mEthodology
Figure
1: continued
the project was designed in three phases. the
first was to establish the nature of the mathematics
mathematics
to apply,
aschemistry
defined by
assessed
within the
biology,
andGeoff
physics
Wake’s
work
referenced
above.
These
a-level examinations in 2010. the full suite oflevels
were: Levelpapers
1 – typically
met ccea,
through
the learning
examinations
from aQa,
edexcel,
programme;
– someusing
novelthe
aspects;
and
ocr
and WJecLevel
were 2
analysed
four
Level
3
–
situation
unlikely
to
have
been
met
measures that follow:
before. Appendix 5c gives an example at A-level
1. the type of mathematics. the mathematical areas
of the three levels of familiarity.
assessed were categorised against the stated
mathematical requirements for biology, chemistry
APPROPRIATENESS
1
physics respectively
. was made on
7. Aand
pplication:
A judgement
the
of the question
part
2. whether
the extent
of content
the mathematics.
the proportion
reflected
how
mathematics
is
used
in
of the question parts within a paper that the
real
world
in a scientific
This
wasthe
included
mathematics
wascontext.
measured
as was
identified
GCSE
review
as
proportioninofthe
the SCORE
marks within
these
questions
athat
particular
issue
for
biology
and
one
that
required mathematics.
merited investigation at A-level.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
A subject
expert
grouptheofnumber
6-8 participants
measured
against
of marks. was
established for each of the three sciences. The
4. the appropriateness of mathematics. We
groups comprised practising A-level teachers,
looked at whether the answer required scientific
teachers with experience in curriculum research
comprehension in addition to mathematical skill.
and development and individuals working for
this was measured as a proportion of the total
awarding organisations as markers, question
number of question parts containing mathematics.
writers or examiners. Each group took part in a
a subject expert
group was
for full
each
dedicated
workshop,
and established
analysed the
suite
of 2010
the three
sciences. each
groupforanalysed
the full
of
examinations
papers
their respective
suite of 2010
examinations
papersabove.
of aQa,A ccea,
subjects,
using
the framework
different
edexcel, ocr
and
WJec
their respective
subjects
framework
was
used
forfor
A-level
theory papers
and
at
a
two-day
workshop.
examination
papers
included
A-level practical papers (see Appendix 6 for the
all the theorytemplates).
papers (Units 1, 2, 4 and 5) and the
framework
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
the groups comprised practising a-level teachers,
teachers with experience in curriculum research and
development and individuals working for awarding
organisations
as markers,
question
writers or examiners.
8. Relationship
to question:
A judgement
was
standardisation
employed throughout
made as toexercises
whetherwere
the mathematics
was a the
analysis
to verify
the of
reliability
of judgements
withinitand
structural
part
the question
or whether
across
subject
expert
wasthejust
tagged
on.groups.
This was identified in the
SCORE GCSE review as an issue across the
the second phase aimed to measure the coherence
sciences at GCSE.
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
9.Mathematics skill or scientific comprehension:
mathematical concepts used to access the sciences
This measure differentiates between marks
are first taught within a mathematical context, i.e. within
within a mathematical question part that
the mathematics curriculum. the project compared the
require scientific comprehension and marks
mathematical requirements for the sciences at a-level
which are given purely based on mathematics
with the mathematics curriculum prior to Key stage 5
skills. Analysts made a judgement between
using the current national curriculum level descriptions
three categories: whether all the marks in
and a 2012 mathematics Gcse specification3. this work
a question part required mathematics skill
was carried out by a researcher and by a mathematics
only, whether the marks included a mixture of
teacher.
scientific comprehension and mathematical skill
theoraim
of the third
was torequired
determine
the nature
whether
all ofphase
the marks
scientific
of mathematics
that
the
community
would
like
comprehension. Appendix 5d provides to
ansee
in a-level
science
assessments.
this
was
achieved
example at A-level of this measure.
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
In the analysis of the science A-levels, all six units
a-level assessment. the participants were chosen in
which make up a complete A-level were analysed.
three groups; teaching profession; higher education; and
Units 1, 2, 4 and 5 are the theory papers. Units
professional bodies. an online survey was completed by
3 and 6 are referred to in this research as the
97 participants across the three groups (27 for biology;
practical papers6. Subject expert groups were given
38 for chemistry; and 32 for physics). participants from
the A-level papers and associated mark schemes,
industry were also consulted more generally but as most
the A-level specifications, data sheets and any
science-related industries employ at a graduate level
other necessary materials from the awarding
their comments tended to focus more on the outcomes
organisations needed to fully comprehend the
at graduate level rather than directly referring to a-level.
demand and scope of the complete A-level.
The data was analysed for single papers and an
average was calculated for the theory papers
(Units 1, 2, 4 and 5) and the practical papers (Units
3 and 6). These averages were then recalibrated
to provide an average for the complete A-level
where theory papers make 80% contribution of the
complete A-level and practical papers make up
20% contribution7.
1
theThe
five nature
awarding
the mathematical
defined by ofqual
developing
their specifications
forreferred
biology, to in the
6
oforganisations
units 3 and use
6 varied
across the requirements
awarding organisations
andinacross
the subjects.
They are
chemistry and physics. the mathematical requirements are available in the full report.
specifications as experimental and practical papers, experimental tasks, laboratory tasks, practical skills, practical tasks and
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
investigations, project work, controlled assessments or coursework. Following a pilot exercise, it was accepted that in these units
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
we were
comparing
likewere
withused
like,inbut
judgements
about the the
mathematics
expected to be met and used by an average
question
partsnot
rather
than marks
the that
calculation
but we maintained
80:20 weighting.
3 thestudent
made. The
analysts
most
challenging
in these cases
to be content
identifying
thein number of
edexcel could
2012 abe
specification
was
used forconsidered
the purposethe
of the
analysis
as it was judgement
considered representative
of typical
found
themarks
revisedthat
mathematics
Gcses.mathematics, however, in their groups they did feel that reliable judgements could be made.
would require
SCORE
Mathsininscience
science report
report
score
maths
3
9
Standardisation
exercises were employed
ExEcutivE
summary
throughout the analysis to verify the reliability of
mathematics enables students to understand and
judgements within and across the subject expert
describe many scientific phenomena yet there is concern
groups. These included:
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
• An individual sample analysis prior to the two-day
any evidence for this concern, score investigated the
group workshop. Each analyst on the subject
type, extent and difficulty of mathematical questions within
expert groups was sent a sample of A-level
science a-levels. the findings show that a large number of
questions, along with instructions for analysing
mathematical requirements listed in the biology, chemistry
the questions. The results from the exercise were
and physics specifications are not assessed. those that
compared at the workshop in order to reach
are assessed are covered repeatedly and often at a lower
agreement on the meaning of the measures.
level than required. this is likely to have an impact on
the
that the
are of
taught
and therefore
on
• Cway
hanging
thesubjects
make-up
the subject
expert
students’
ability
to
have
the
necessary
skills
to
progress
groups throughout the analysis to verify the
effectively
to of
stem
higher education
reliability
judgements
acrossand
the employment.
groups.
in addition, the findings show a disparity in the way
mathematics
is assessed
acrosstothe
different
awarding
• Whole group
discussions
clarify
issues
as they
organisations.
score
recommends
there is a review
arose to ensure
all groups
werethat
in agreement
with
of existing
the mathematical
requirements
for
each
of
the
sciences
measures.
at a-level and that a framework is developed to regulate
the
mathematics
assessed
within the sciences
to
• Gway
roups
checking istheir
final judgements
against
ensure
across
thestart
system.
thoseparity
made
at the
of the analysis session
to check that they had not slipped throughout
Background
the process.
there has been growing concern across the science
Students’ scripts were not analysed in this
community about the mathematical demand of science
research; if they had been there may have
qualifications, specifically that Gcse and a-level science
been instances of students using higher level
qualifications are not meeting the needs of students in
mathematics in their responses to Units 3 and 6.
the way they assess the analytical nature of science.
For the purpose of this project, however, analysts
considered
more
typical evidence
responses
by
in
2009 score
published
on expected
Gcse science
teachers and
markers,
those
givenvariation
in the mark
examination
papers
whichboth
reported
a wide
in
schemes
what they would
expect
from
their
the
amountand
of mathematics
assessed
across
awarding
own professional
experience.
was
that
organisations
and confirmed
that Itthe
useaccepted
of mathematics
mathematics
of higher
complexities
andina agreater
within
the context
of science
was examined
very
number
of score
extended
calculations
in
limited
way.
organisations
feltmay
that be
thispresent
was
such scripts, mathematics
although they
may not
unacceptable.
is integral
to be
therewarded
teaching
withlearning
a greater
number
of marks
thana were
possible
and
of the
sciences,
and offers
valuable
aid
tounderstanding
be given in the
scheme.
in
andmark
describing
scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2.3 RESEARCH DESIGN – PHASE 2
In Phase 2 we measured the extent to which the
mathematical requirements of biology, chemistry
and physics A-level had been previously taught
in the mathematics curriculum. This provided an
indication of coherence between the sciences
and mathematics. Two comparisons were used
to compare the coherence of science A-levels
and the mathematics accessed up to Key Stage
4: comparison with National Curriculum level
descriptors and comparison with the 2012
mathematics GCSE specification.
The National Curriculum level descriptors go
from Level 1, the easiest level, up to Level 8.
aims
Mathematics beyond Level 8 is classified as EP,
exceptional
performance.
areas
score’s
overall
objective forThe
this content
project was
to from
the
mathematical
requirements
were
levelled
gather evidence on the type, extent and difficulty of
against the National
Curriculum
descriptors
mathematics
required to
access thelevel
sciences
in current
by
two
mathematicians
with
experience
in
teaching
a-level specifications and to establish whether this
and
research.
Their
responses
were
collated
was being appropriately met by the assessments. and
the
considered.
As the mathematical
requirements
work
did not compare
the mathematical
requirements
were notphysics,
set in achemistry
context of
expectations,
between
and
biology as it issome
accepted
of
the
areas
were
open
to
interpretation.
In
these
these will differ between the disciplines.
cases the mathematics experts gave a range of
the
findings
aimmathematics
to provide score
evidence to
levels
that the
couldwith
correspond
inform
the
development
of
policy
on
the
type,
extent
to depending on the actual expectations of
an
and
difficulty ofitem.
the mathematics in the criteria and
assessment
assessments for a-levels in biology, chemistry and
The collated
levels also
weresupports
then further
analysed
by
physics.
the project
score’s
work on
the lead
researcher and
subject
specialists
how
the examinations
system
should
operate towho
ensure
had been
involved with
1 and
analysis
of the
science
qualifications
are fitthe
forPhase
purpose
also its
papers.
This allowed
the levels between
to be considered
in
work
on improving
the coherence
the sciences
terms
of the contexts that the items were set in and
and
mathematics.
the levels could be refined.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
7The 80:20 ratio of theory and practical papers refers to the weighting of marks in a complete A-level. In the analysis the
averages were taken as a proportion of question parts containing mathematics rather than as a proportion of marks awarded
for mathematics but we maintained the 80:20 weighting. The results are not dissimilar but a more accurate measure would have
been obtained with averages based on proportion of marks awarded for mathematics.
2
10
SCORE Maths
report
score
mathsininscience
science
report
Secondly,
the mathematical requirements found
mEthodology
in
the
A-level
specifications
werephases.
analysed
the project was
designed in three
theagainst
the
specification
to see
first GCSE
was to mathematics
establish the nature
of the mathematics
whether
or
not
the
mathematical
requirements
assessed within the biology, chemistry and physics that
featured
in the science
A-level
were
a-level examinations
in 2010.
thespecifications
full suite of
covered
in
the
GCSE
mathematics
specification.
examinations papers from aQa, ccea, edexcel,
This
indicates
theusing
mathematics
ocrcomparison
and WJec were
analysed
the four that
students
who
are
not
studying
mathematics
measures that follow:
beyond GCSE will need to be taught within the
1. thecurriculum
type of mathematics.
mathematical
areas
science
in order tothe
access
all content
were categorised
against
the are
stated
areasassessed
of the science
A-level. The
results
shown
mathematical
requirements
for
biology,
chemistry
for students studying GCSE mathematics at both
1
and physics
respectively
Foundation
and Higher
level.. The Edexcel 2012
‘A’2.specification
used for the purpose
of the
the extent ofwas
the mathematics.
the proportion
analysis
asquestion
it was considered
of
of the
parts within representative
a paper that
typical
content
found in the
revised
mathematics
included
mathematics
was
measured
as was the
GCSEs.
proportion of the marks within these questions
that required mathematics.
The analysis was carried out by the lead researcher
3. athe
difficulty of mathematics.
measured
and
mathematics
teacher whothis
hadwas
taught
3 criteria:
the number of
steps
a
GCSEagainst
and A-level
mathematics
and
hadintaught
calculation,
the
familiarity
of
the
context
and
mathematics sessions for students taking all three
complexity
of theHis
question.
each category
of thethe
A-level
sciences.
experience
over time
had
varying
levels
of
difficulty
and
was
meant that further comments could each
be added,
measured
as a proportion
of thearea
total had
number
of
for example,
whether
the content
been
question
parts
containing
mathematics.
it
was
not
removed from GCSE specifications.
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
8
2.4
DESIGN
– PHASE
3
the RESEARCH
groups comprised
practising
a-level teachers,
teachers with experience in curriculum research and
The aim of the third phase of the research was
development and individuals working for awarding
to gather the opinions of the science community
organisations as markers, question writers or examiners.
on the findings from Phase 1 and 2. In order
standardisation exercises were employed throughout the
to do so, a survey was sent to members of the
analysis to verify the reliability of judgements within and
science community and focused on the nature
across the subject expert groups.
of the mathematics that they would like to see in
the
assessments.
participant
the A-level
second science
phase aimed
to measureFour
the coherence
groups
identified:
betweenwere
the teaching
and learning of mathematics
•and
A-level
sciencethere
teachers
the sciences.
is an assumption that the
•mathematical
Higher education
representatives
concepts
used to access the sciences
•are
Representatives
professional
bodies
first taught withinfrom
a mathematical
context,
i.e. within
•the
Industry
representatives.
mathematics
curriculum. the project compared the
mathematical requirements for the sciences at a-level
The
three of these
groups prior
responded
to an5
with first
the mathematics
curriculum
to Key stage
8
. The
online
survey
in national
order tocurriculum
give their opinions
using the
current
level descriptions
3
industry
representatives
responded
to
a
short
and a 2012 mathematics Gcse specification . this work
questionnaire
over the telephone
or in writing.
was carried outeither
by a researcher
and by a mathematics
teacher.
The online survey was taken in two parts to avoid
the aim of the
phasePart
wasAtoasked
determine
the nature
prejudicing
thethird
results.
respondents
of
mathematics
that
the
community
would
like
to see
for general comments about the mathematics
in
in
a-level
science
assessments.
this
was
achieved
the current science A-levels. These comments were
throughon
an previous
online survey
for stakeholders
in the
science
based
experience
of science
A-levels,
community.
their expertise,
9
and onparticipants
reviewing a
on
viewing Depending
a completeonA-level
answered
the
survey
for
biology,
chemistry
or content
physics 10.
selection of questions with mathematical
a-level
assessment.
the
participants
were
chosen
in
In Part B respondents were asked for their views
three
groups;
teaching
profession;
higher
education;
and
on the way mathematics is assessed within A-level
professional
bodies.
an online
was completed
Sciences
having
been
givensurvey
the findings
from theby
97
participants
across
the
three
groups
(27
for
biology;
first phase of the research.
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
The online survey and responses are available from the SCORE Secretariat.
9
complete
theoryuse
paper
for their subject.
The papers
that
sat in their
the specifications
middle of thefordata
range from the first
1 theAfive
awardingA-level
organisations
the mathematical
requirements
defined
by were
ofqualchosen
in developing
biology,
phase and
of the
research,
i.e. they satrequirements
in mid-range
the extent
paper involving mathematics, the mid-range in terms of
chemistry
physics.
the mathematical
arefor
available
in theof
fullthe
report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
difficulty and included a typical range of mathematical content.
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
10
A set parts
of questions
with
mathematical
The questions
were chosen
to weighting.
cover the range of mathematical requirements
question
rather than
marks
were used incontent.
the calculation
but we maintained
the 80:20
3 thethat
were2012
assessed
in the A-level
papers
wereofchosen
so that
was an even
spread from
across
all offound
the awarding
edexcel
a specification
was used
for theand
purpose
the analysis
as itthere
was considered
representative
of typical
content
in
and from
the AS and A2 papers.
theorganisations
revised mathematics
Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
11
The online survey
was completed by nearly 100
ExEcutivE
summary
participants, with the breakdown for each subject
mathematics enables students to understand and
in Table 1. This represents a very small proportion
describe many scientific phenomena yet there is concern
of the science community and, in some participant
that science assessments at a-level are not reflecting the
groups, numbers were so small that findings can
subject’s analytical nature. to explore whether there was
only offer guidance on how mathematics should be
any evidence for this concern, score investigated the
assessed within the sciences at A-level and should
type, extent and difficulty of mathematical questions within
not be regarded as strong evidence.
online survey data, basic statistics were generated.
Where questions were open-ended, responses
were coded and categorised. Similar codes were
used to report the responses from the industry
questionnaire.
For industry, the most effective means of gathering
opinions on the mathematical element of the
science A-levels was through written or telephone
questionnaire. Six representatives in total took part
in the questionnaire.
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
Data was analysed separately for the different
and physics specifications are not assessed. those that
participant groups so that similarities and
are assessed are covered repeatedly and often at a lower
differences of opinion could be identified. The
level than required. this is likely to have an impact on
results were reported for the whole group apart
the way that the subjects are taught and therefore on
from where there were significant differences
students’ ability to have the necessary skills to progress
of opinion between the groups. A variety of
effectively to stem higher education and employment.
question types were used in the survey to elicit
aims
in addition, the findings show a disparity in the way
data relevant to the research questions. From the
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at
a-level
and
that
a
framework
is
developed
to
regulate
Table 1: Number of participants completing the online
survey
for Phase
a-level
specifications
and 3
to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure
parity across NUMBER
the system. OF PARTICIPANTS
work did not compare the mathematical requirements
SUBJECT
between physics, chemistry and biology as it is accepted
Higher education
Professional Bodies Total
Background Teachers
these will differ between the disciplines.
Biology
21 concern across the science
3
there
has been growing
community about the mathematical demand of science
Chemistry
20
11
qualifications, specifically that Gcse and a-level science
Physics are not21
7 in
qualifications
meeting the needs of students
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
12
SCORE Maths
report
score
mathsininscience
science
report
3
27
the findings aim to provide score with evidence to
7
inform the development
of policy on the38
type, extent
and difficulty of the mathematics in the criteria and
4
32
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
CHAPTER 3: DETAILED FINDINGS
average
percentage
questiona-level
parts teachers,
containing
the groups
comprisedofpractising
mathematics
in a complete
A-level. research
Figure 2and
teachers with experience
in curriculum
illustrates
theand
percentage
question
parts in
development
individualsof
working
for awarding
aorganisations
complete A-level
containing
mathematics
for
as markers,
question
writers or examiners.
the
five awarding
organisations.
standardisation
exercises
were employed throughout the
The
detailed findings from Phases 1, 2 and 3 are
mEthodology
separated
chemistry
and physics.
the projectinto
wasbiology,
designed
in three phases.
the The
awarding
are not
named
and are
first was toorganisations
establish the nature
of the
mathematics
represented
by
A-E.
These
representations
are
assessed within the biology, chemistry and physics
the
same
throughout.
a-level examinations in 2010. the full suite of
analysis to verify the reliability of judgements within and
across the subject expert groups.
examinations papers from aQa, ccea, edexcel,
3.1
PHYSICS
ocr and WJec were analysed using the four
Figure 2: Percentage of question parts
the second phase aimed to measure the coherence
containing
mathematics in a complete physics
between the teaching and learning of mathematics
A-level
for the five awarding organisations
measures
that follow:
3.1.1
PHASE
1: A-LEVEL PAPERS
1. theEXTENT
type of mathematics. the mathematical areas
3.1.1.1
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within
a mathematical
context, i.e. within
Theory
Practical
Contribution
(80%)
Contribution
(20%)
the mathematics curriculum. the project compared
the
70
mathematical
requirements for the sciences at a-level
60
with the mathematics
curriculum prior to Key stage 5
50
using the current
national curriculum level descriptions
40
and a 2012
mathematics Gcse specification3. this work
30
was carried out by a researcher and by a mathematics
20
teacher.
assessed were categorised against the stated
Percentage of question parts
in a complete A level
This measure seeks to capture how much of
mathematical requirements for biology, chemistry
the A-level physics assessment
is mathematical
and physics respectively1.
(independent of the type, appropriateness or
2. the extent
of the mathematics.
the proportion
difficulty).
It is quantified
by the proportion
of
of the or
question
parts
within
a paper
that
questions
question
parts
within
a complete
included
mathematics
was measured
was the
A-level
that require
mathematics
and theas
proportion
proportion
of
the
marks
within
these
questions
of marks requiring mathematics. Table 2a shows
that requiredofmathematics.
the percentage
question parts containing
mathematics
within
each unit and the percentage
3. the difficulty of mathematics. this was measured
of question
parts
containing
mathematics for
against 3 criteria: the number of steps in a
theorycalculation,
only and the
practical
only papers. Table 2b
familiarity of the context and
takesthe
intocomplexity
account the
weighting
of theory papers
of the question. each category
(80%)had
andvarying
practical
papers
(20%)
to calculate the
levels of difficulty and each was
10
the aim of 0the third phase was to determine the nature
A
B
C
D
E
of mathematics that the community would like to see
Awarding Organisations
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
measured as a proportion of the total number of
community. Depending on their expertise, participants
question parts containing mathematics. it was not
answered the survey for biology, chemistry or physics
Tablemeasured
2a: Percentage
question
parts containing mathematics within each unit and within the
against theofnumber
of marks.
a-level assessment. the participants were chosen in
set of theory and practical papers across the five awarding organisations
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
professional bodies. an online survey was completed by
looked at whether the answer required scientific
comprehension in addition to mathematical
A
B 97 participants
C across the D
three groups (27Efor biology;
skill.
from
this was
measured
as a proportion of
AS units
1 and
2
49the total
57 38 for chemistry;
68 and 32 for
42physics). participants
51
industry
were
also
consulted
more
generally
but
as
most
number of question parts containing mathematics.
AS unit 3
56
15
33
38
76
science-related industries employ at a graduate level
aA2
subject
unitsexpert
4 andgroup
5 was established for
62each
48 their comments
63 tended to 46
63 outcomes
focus more on the
of the three sciences. each group analysed the full
at
graduate
level
rather
than
directly
referring
A2 unit
6 examinations papers of aQa,
58ccea,
31
33
82
58to a-level.
suite
of 2010
edexcel,
andonly
WJec for their respective
Theory ocr
papers
56 subjects 53
66
44
57
at a two-day workshop. examination papers included
Practical papers only
57
23
33
60
67
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers2b:
make
up 80% of the
the
Table
Percentage
of complete
questiona-level
partsand
weighted
to take account of the theory component (80%)
experimental
andcomponent
practical papers
the remaining
20%2. assessments
and
practical
(20%)
of the A-level
A
B
C
D
E
Theory contribution (80%)
45
42
53
35
46
1
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry andcontribution
physics. the mathematical
Practical
(20%) requirements
11 are available in the
5 full report.
7
12
13
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level A-level
assessment and the marks from the practical
make up the remaining
Total
56and experimental papers
47 (Unit 3 and 6)60
47 20%. in the analysis,
59
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
13
Table 3a shows
the percentage of marks requiring
ExEcutivE
summary
Figure 3: Percentage of marks requiring
mathematics in a complete physics A-level for
the five awarding organisations
mathematics for each unit and for theory only and
mathematics enables students to understand and
practical only papers. Table 3b takes into account
describe many scientific phenomena yet there is concern
the weighting of theory papers (80%) and practical
that science assessments at a-level are not reflecting the
papers (20%) to calculate the average percentage
subject’s analytical nature. to explore whether there was
of marks requiring mathematics in a complete
any evidence for this concern, score investigated the
A-level. Figure 3 illustrates this as a graph.
Theory
Contribution (80%)
Practical
Contribution (20%)
A
Background
AS units 1 and 2
45
there
has 3
been growing concern across the
AS unit
44 science
community about the mathematical demand of science
A2 units 4 and 5
53
qualifications, specifically that Gcse and a-level science
A2 unit 6 are not meeting the needs of50
qualifications
students in
the
way they
assessonly
the analytical nature of
Theory
papers
49science.
Percentage of question parts
in a complete A level
type, extent and difficulty of mathematical questions within
60
science a-levels. the findings show that a large number of
50
mathematical requirements listed in the biology, chemistry
40
and physics specifications are not assessed. those that
30
are assessed are covered repeatedly and often at a lower
20
level than required. this is likely to have an impact on
10
the way that the subjects are taught and therefore on
0
students’ ability to have the necessary skills to progress
A
B
C
D
E
effectively to stem higher education and employment.
Awarding Organisations
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each
of
the
sciences
mathematics required to access the sciences in current
Table 3a: Percentage of marks11 that require mathematics within each unit and within the set of
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
theory and practical papers across the five awarding organisations
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
B
C
between physics,
chemistryDand biology asEit is accepted
60 these will differ
66 between the40disciplines. 49
15 the findings33aim to provide55
74
score with evidence
to
inform
the
development
of
policy
on
the
type,
extent
49
62
45
66
and difficulty of the mathematics in the criteria and
27
70
25
assessments for a-levels in biology, chemistry and
55 physics. the
64project also supports
43
58work on
score’s
system
papers
only evidence on Gcse
47 science 23 how the examinations
30
63 should operate
50 to ensure
inPractical
2009 score
published
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
work on improving the coherence between the sciences
the amount of mathematics assessed across awarding
and mathematics.
organisations and confirmed that the use of mathematics
Table
3b:
Percentage
of
marks
requiring
mathematics
within a total A-level, weighted to take account
within the context of science was examined in a very
in the project, we looked across all assessments at
of the way.
theory
component
(80%)
limited
score
organisations
feltand
that practical
this was component (20%) of the A-level assessments
a-level for a given year, including both experimental and
unacceptable. mathematics is integral to the teaching
practical examination papers.
and learning of the sciences, and offers a A
valuable aid
B
C
D
E
in understanding and describing scientific phenomena;
Theory contribution (80%)
39
44
51
34
46
as such it should be appropriately represented in the
Practical
contribution
(20%)
9 their
5
6
13
10
biology,
chemistry
and physics
curricula and
assessments.
Total A-level
48
49
57
47
56
30
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
11 A mark was judged to require mathematics if part or all of the mark could not be achieved without mathematics.
2
14
SCORE Maths
report
score
mathsininscience
science
report
3.1.1.2
TYPE
mEthodology
the groups comprised practising a-level teachers,
teachers with experience in curriculum research and
the number
project was
designed in three
phases.
the
The
of occurrences
of each
mathematical
requirement listed in Physics A-level was measured to
development and individuals working for awarding
first wasthe
to establish
the nature of the
mathematics
identify
type of mathematics
assessed
and the frequency of each type of mathematics assessed. The
organisations as markers, question writers or examiners.
assessed
the biology,
chemistry
results
arewithin
displayed
in Figure
4. and physics
standardisation exercises were employed throughout the
a-level examinations in 2010. the full suite of
analysis to verify the reliability of judgements within and
examinations papers from aQa, ccea, edexcel,
across the subject expert groups.
ocr
and WJecrequirements
were analysed
using
the four
Mathematical
listed
in x-axis
on Figure 4
measures that follow:
1. Arithmetic and Computation
(a)
use atype
calculator
for addition, subtraction,
multiplication
1. the
of mathematics.
the mathematical
areas
and
division;
assessed were categorised against the stated
(b)recognise and use expressions in decimal form;
mathematical requirements for biology, chemistry
(‘standard from’ deleted from
this requirement and
and
physics respectively1.
recorded separately as 1(h) to illustrate how commonly
eachextent
occurred.)
2. the
of the mathematics. the proportion
(c)use ratios, fractions and percentages;
of the question parts within a npaper 2that
(d)use calculators to find and use x , 1/x, x , √x, logl0x , e x,
included
mathematics was measured as was the
log ex;
proportion
of the
markssinѲ,
within
these
questions
(e)use calculators
to handle
cosѲ,
tanѲ,
sin-1Ѳ, cos1
-1
Ѳ, tan
Ѳ when
Ѳ is expressed in degrees or radians.
that
required
mathematics.
(f)recognise and use SI prefixes 10-12, 10-9, 10-6, 10-3, 103,
3. the
difficulty
106 and
109 of mathematics. this was measured
3 criteria: the
number
of steps
in are
a neither
(g)against
handle calculations
so that
significant
figures
lost or carriedthe
beyond
what is
calculation,
familiarity
ofjustified;
the context and
(h)the
standard
form. of the question. each category
complexity
had varying
2. Handling
datalevels of difficulty and each was
(a)measured
show an awareness
of the order
of magnitude
of physical
as a proportion
of the
total number
of
quantities
and
make
order
of
magnitude
calculations;
question parts containing mathematics. it was not
(b)use an appropriate number of significant figures;
measured against the number of marks.
(c)find arithmetic means and medians;
(d)
express
changes as percentages
and vice We
versa;
4. the
appropriateness
of mathematics.
(e)understand and use logarithmic scales in relation to
looked at whether the answer required scientific
quantities which range over several orders of magnitude.
comprehension in addition to mathematical skill.
3. Algebra
this was measured as a proportion of the total
(a)change the subject of an equation by manipulation of
number of question parts containing mathematics.
the terms, including positive and negative, integer and
fractional
indices
andwas
square
roots
a subject
expert
group
established
for each
(b)
s
ubstitute
numerical
values
into
algebraic
of the three sciences. each group analysedequations
the full using
appropriate units for physical quantities
suite of 2010 examinations papers of aQa, ccea,
(c)check the dimensional consistency of physical equations
edexcel,
and numerical
WJec forvalues
their into
respective
subjects
and ocr
substitute
such equations
using
at a two-day
workshop.
examination
papers
included
appropriate units for physical quantities;
simple
algebraic
including
y=k/x,
all(d)
thesolve
theory
papers
(Unitsequations
1, 2, 4 and
5) and
the y=k/x2
(e)
formulate
and
use
simple
algebraic
equations
experimental and practical papers (Units 3 andas6).
mathematical models of physical situations, and identify
calculations
were based on the assumption that theory
the inadequacy of such models
papers make up 80% of the complete a-level and the
(f)understand and use the symbols: <, <<, >>, >, ~, , ∑,
experimental
and practical papers the remaining 20%2.
∆x, x, dx/dt
1
2
3
the second phase aimed to measure the coherence
4. Geometry and Trigonometry
between
theareas
teaching
and learning
of mathematics
(a)
calculate
of triangles,
circumferences
and areas of
andcircles,
the sciences.
thereand
is an
assumption
that the
surface areas
volumes
of rectangular
blocks,
cylinders and
spheres; used to access the sciences
mathematical
concepts
(b)
theorem,
similarity of context,
triangles and
are use
firstPythagoras’
taught within
a mathematical
i.e. the
within
angle sum of a triangle;
the mathematics curriculum. the project compared the
(c)use sines, cosines and tangents in physical problems;
mathematical
requirements
forѲthe
at a-level
(d)
use sinѲ ≈ tanѲ
≈ Ѳ and cos
≈ 1sciences
for small Ѳ;
withunderstand
the mathematics
curriculum
priordegrees
to Keyand
stage
5
(e)
the relationship
between
radians
andthe
translate
one to curriculum
the other. level descriptions
using
currentfrom
national
and
a 2012 mathematics Gcse specification . this work
5.
Graphs
wastranslate
carried information
out by a researcher
and by a
mathematics
(a)
between graphical,
numerical
and
algebraic forms;
teacher.
(b)plot two variables from experimental or other data using
theappropriate
aim of thescales
third phase
was
to determine the nature
for graph
plotting;
of mathematics
the community
would like
to see
(c)
plot data on a that
log-linear
graph and determine
whether
they change
exponentially
and determine
exponent;
in a-level
science
assessments.
this wasthe
achieved
(d)
plot data
on a log-log
graph
and decide whether
through
an online
survey
for stakeholders
in thedata
science
obey a power law and determine the exponent;
community. Depending on their expertise, participants
(e)select appropriate variables for graph plotting;
answered
the survey
chemistry
or physics
(f)
understand
that y = for
mx biology,
+ c represents
a linear
a-level
assessment.
the
participants
were
chosen
relationship and rearrange relationships into this form in
where
appropriate;
three
groups;
teaching profession; higher education; and
(g)
determine
the
slopean
/ gradient
and intercept
of a linear by
professional bodies.
online survey
was completed
graph in the appropriate physical units;
97 participants across the three groups (27 for biology;
(h)determine the gradient of a tangent to a non-linear
38 for
chemistry; and 32 for physics). participants from
graph by drawing and use the slope of the tangent as a
industry
were
consulted
measure
of also
rate of
change; more generally but as most
science-related
industries
employ
graduate
level
(i)
choose by inspection
a straight
lineatoracurved
line which
serve as the
best straight
linemore
through
set outcomes
of data
theirwill
comments
tended
to focus
onathe
points presented
graphically;
at graduate
level rather
than directly referring to a-level.
(j)understand the possible physical significance of the area
between a curve and the x axis and be able to calculate it
or measure it by counting squares as appropriate;
(k)understand and use the slope of a tangent to a curve as
a means to obtain the gradient. Understand and use the
notation d/dt for a rate of change;
(l)understand and use multiplicative scales (1, 10, 100...);
(m)use logarithmic plots to test exponential and power law
variations;
(n)sketch simple functions including y = k/x, y = kx2 y = k/x2,
y = sinѲ, y = cosѲ, y = e-kx.
(o)understand or recognise the physical significance of a
straight line passing or not passing through the origin.
3
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
15
Figure 4: The
number of occurrences for each mathematical requirement in a full suite of
ExEcutivE
summary
examination papers for a complete physics A-level in each of the awarding organisations.
Number of Occurrences
mathematics enables students to understand and
It has no relation to the number of marks awarded for each mathematical requirement.
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
subject’s analytical
nature. to explore whether there was
Awarding Organisations
any evidence for Athis concern,
score
investigated
the
B
C
D
E
type, extent
and
difficulty
of
mathematical
questions
within
120
science a-levels. the findings show that a large number of
100
mathematical
requirements listed in the biology, chemistry
and physics80specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
60
level than required.
this is likely to have an impact on
the way that
the subjects are taught and therefore on
40
students’ ability to have the necessary skills to progress
20stem higher education and employment.
effectively to
aims
in addition, the
findings show a disparity in the way
0
1b 1c 1d 1eacross
1f 1g 1h
2b 2c 2d awarding
2e 3a 3b 3c 3d 3e 3f 4a 4b 4c 4d 4e 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n
mathematics is1aassessed
the2adifferent
score’s overall objective for this project was to
Arithmetic and
Handling Data
Algebra
Geometry and
Graphs
organisations. score
recommends that there is a review
gather
evidence on the type, extent and difficulty of
Computation
Trigonometry
of the mathematical requirements for eachMathematical
of the sciences
mathematics
Requirements
for Physicsrequired
A-Level to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
3.1.1.3 DIFFICULTY
Background
For each of the following measures, percentages
are stated
as agrowing
proportion
of the
number
of
there
has been
concern
across
the science
question parts.
percentagesdemand
do not relate
community
aboutThe
the mathematical
of science
in any way tospecifically
the number
marks
awarded
for
qualifications,
thatofGcse
and
a-level science
mathematical
qualifications
areunderstanding.
not meeting the needs of students in
the way they assess the analytical nature of science.
NUMBER OF STEPS
in
2009
score
evidence
Gcse science
The
number
of published
steps involved
in aoncalculation
was
examination
papers
which
reported
a
wide
variation
used as one measure of difficulty, based on thein
the
amount ofthat
mathematics
assessed
across
awarding
assumption
questions
containing
mathematics
organisations
confirmed
the use of calculation
mathematics
that requiredand
multiple
stepthat
or extended
within
the context
wasand
examined
in aa very
(e.g. value
x hadoftoscience
be found
used in
limited
way.
score
organisations
felt
that
this
subsequent calculation in order to find thewas
solution
unacceptable.
mathematics
is integral
to the
teaching
to the problem,
y) were more
difficult
than
single
and
of the sciences,
and offers
a valuable
steplearning
calculations,
as they require
students
to aid
in
understanding
describing
scientificreasoning.
phenomena;
use
higher orderand
skills
and extended
as
such it should
be appropriately
represented
in the
Appendix
5a shows
an example
of each type
of
biology,
chemistry
and
physics
curricula
and
their
calculation.
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
16
SCORE Maths
report
score
mathsininscience
science
report
Table 4aphysics,
shows the
percentage
of mathematical
between
chemistry
and biology
as it is accepted
question
parts
classified
as
containing
single
these will differ between the disciplines.
step (S), multiple step (M) or extended step (E)
the
findings aim
to provide
scoreunit
withand
evidence
calculations
within
each A-level
as anto
inform
thefor
development
policy
on the type,
average
theory onlyofand
practical
only extent
papers.
and
difficulty
of are
the mathematics
criteria and
These
figures
calculated asin athe
percentage
assessments
for a-levels
in biology,aschemistry
and
of the question
parts identified
containing
physics.
the project
score’s
work on
mathematics.
Tablealso
4b supports
shows these
percentages
how
thetotal
examinations
system
should
operate
ensure
of the
number of
question
parts
and to
Table
4c
science
qualifications
are weighting
fit for purpose
and also
its
takes into
account the
of theory
papers
work
improving
thepapers
coherence
between
the sciences
(80%)onand
practical
(20%)
to calculate
the
and
mathematics.
average
percentage of single step, multiple step
and extended step calculations in a complete
in the project, we looked across all assessments at
A-level. Figure 5a illustrates the percentage of
a-level for a given year, including both experimental and
single, multiple and extended step calculations in
practical examination papers.
a complete A-level for each of the five awarding
organisations. Figures 5b and 5c illustrate these
percentages for theory only and practical only
papers respectively.
mEthodology
the step
groups
comprised practising
a-level
teachers,
Table
4a: Percentage of single, multiple and extended
calculations
in physics
A-level,
teachers
with
experience
in
curriculum
research
and
calculated
as a
percentage
question
the project was
designed
in threeof
phases.
the parts identified as containing mathematics
first was to establish the nature of the mathematics
assessed within the biology, A
chemistry and physics
B
a-level examinations in 2010. the full suite of
Number of steps
E
M S
E
M
examinations papers from aQa, ccea, edexcel,
AS units
1 andwere
2 analysed
16 using
63 the22
65
ocr
and WJec
four 5
measures
AS unit 3that follow:
0
21 79 0
17
development and individuals working for awarding
organisations as markers, question writers or examiners.
C
D
E
standardisation exercises were employed throughout the
S analysis
E to
MverifySthe reliability
E
Mof judgements
S
E within
M and
S
31 across
19 the55subject
27 expert
9 groups.
48 44 13 74 14
1. units
the type
of mathematics.
mathematical
A2
4 and
5
30the37
34 5 areas
63
the teaching and learning of mathematics
33 between
0
60
41 5
38 57 28 69 4
assessed were categorised against the stated
0
20 80 0
50
mathematical requirements for biology, chemistry
1
Theory
only
23
50 28 5
64
and papers
physics respectively
.
A2 unit 6
measure
83 the0second
31 phase
69 aimed
0 to50
50 the
2 coherence
13 85
and the sciences. there is an assumption that the
50mathematical
0
20 concepts
80 0 used
39to access
61 0the sciences
50 50
first taught
a mathematical
i.e. within
32are10
58 within
34 7
43 51 context,
21 72
9
the mathematics curriculum. the project compared the
0
26 75 0
45 56 1
32 68
mathematical requirements for the sciences at a-level
of the question parts within a paper that
with the mathematics curriculum prior to Key stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
Tablethat
4b:required
Percentage
of single, multiple and extended step calculations in physics A-level,
mathematics.
was carried out by a researcher and by a mathematics
calculated as a percentage of the total number of question parts in a complete A-level
teacher.
3. the difficulty of mathematics. this was measured
Practical
papers
only
0
21the80
0
34
2. the extent
of the
mathematics.
proportion
67
against 3 criteria: the number of steps in a
A
B
calculation, the familiarity of the context and
the complexity
Number
of stepsof the question.
E
MeachScategory
E
M
had varying levels of difficulty and each was
AS units 1 and 2
8
31 11 3
37
measured as a proportion of the total number of
AS unit
3 parts containing
0 mathematics.
12 44 it 0was not
3
question
measured
against
of marks.
A2 units
4 and
5 the number
19 23
21 2
30
theCaim of the third phase
D was to determine
E the nature
of mathematics that the community would like to see
S in a-level
E
M
S
E
M S
E
M S
science assessments. this was achieved
stakeholders
18 through
13 an
37online
18survey
4 for20
18 7 in the
38science
7
community. Depending on their expertise, participants
12 0
10 23 0
19 19 2
10 65
answered the survey for biology, chemistry or physics
16 a-level
0 assessment.
38 26 the
2 participants
17 26 were
18 chosen
43 in3
higher
and
A2
6
4. unit
the appropriateness
of 0mathematics.
12 46We 0
16 16three
0 groups;
7 teaching
26 0 profession;
32 50
0 education;
29 29
professional bodies. an online survey was completed by
looked at whether the answer required scientific
Theory
papers only
14 27 16 3
34 17 7
38 22 3
19 22 13 41 5
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Practical
papers
onlyas a0 proportion
12 45
9
25and 032 for26
35 participants
1
20 from
47
for chemistry;
physics).
this was
measured
of the0total 10 1438 0
industry
were
also
consulted
more
generally
but
as
most
number of question parts containing mathematics.
science-related industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
Table 4c: Percentage of single, multiple and extended
step calculations
in directly
physics
A-level,
at graduate
level rather than
referring
to a-level.
suite of 2010 examinations papers of aQa, ccea,
weighted to take account of the theory component (80%) and practical component (20%)
edexcel, ocr and WJec for their respective subjects
of the A-level assessments
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
A
B
C
D
E
experimental and practical papers (Units 3 and 6).
Number ofwere
steps
E assumption
M S that
E theory
M S
E
M S
E
M S
E
M S
calculations
based on the
papers
make
up
80%
of
the
complete
a-level
and
the
Theory papers only
11 22 13 2
27 14 6
30 18 2
15 18 10 33 4
2
experimental
and
practical
papers
the
remaining
20%
.
(80%)
Practical papers only
(20%)
0
2
9
0
2
3
0
2
5
0
5
7
0
A-level
total organisations use11
24 22 requirements
2
29
17by ofqual
6 in developing
32 23their specifications
2
20 for25
10
the five awarding
the mathematical
defined
biology,
chemistry and physics. the mathematical requirements are available in the full report.
(weighted)
1
2
3
4
9
37
13
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
17
question parts identified as containing single,
Percentage of question parts
in a complete A level
mathematics enables students to understand and
multiple and extended step calculations in a
describe many scientific phenomena yet there is concern
complete physics A-level for each of the five
that science assessments at a-level are not reflecting the
awarding organisations
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty
of mathematical questions within
TOTAL
science a-levels.Extended
the findings
show that
Singlea large number of
Multiple
mathematical
requirements listed in the biology, chemistry
70
and physics
specifications
are not assessed. those that
60
are assessed
are
covered
repeatedly
and often at a lower
50
level than required.
this
is
likely
to
have
an impact on
40
the way that
30 the subjects are taught and therefore on
students’ ability
to have the necessary skills to progress
20
10 stem higher education and employment.
effectively to
in addition, 0the findings
show
a CdisparityD in the way
A
B
E
mathematics is assessed
across the different awarding
Awarding Organisations
organisations. score recommends that there is a review
of the mathematical requirements for each of the sciences
at a-level and that a framework is developed to regulate
Figure
5b: Percentage
of mathematical
the
way mathematics
is assessed
within the sciences to
question
parts
identified
ensure parity across the system.as containing single,
multiple and extended step calculations in
theory examination papers for physics A-level
Background
Percentage of question parts
in a complete A level
there has been growing concern across the science
THEORY
community about the mathematical
demand of science
Extended
Multiple
qualifications, specifically
that
GcseSingle
and a-level science
70 are not meeting the needs of students in
qualifications
60 assess the analytical nature of science.
the way they
50
in 2009 score
published evidence on Gcse science
40
examination
30 papers which reported a wide variation in
the amount20of mathematics assessed across awarding
10 and confirmed that the use of mathematics
organisations
0
within the context
of science
was
examined
inEa very
A
B
C
D
limited way. score organisations
felt
that
this
was
Awarding Organisations
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
18
SCORE Maths
report
score
mathsininscience
science
report
Figure 5c: Percentage of mathematical
question parts identified as containing single,
multiple and extended step calculations in
practical examination papers for physics
A-level
PRACTICAL
Extended
Percentage of question parts
in a complete A level
ExEcutivE
summary of mathematical
Figure 5a: Percentage
aims
Multiple
Single
70
60
50
40
30
20
10
0
A
B
C
D
E
score’s overall objective
for this project was to
Awarding Organisations
gather evidence on the type, extent and difficulty of
mathematics required to access the sciences in current
a-level specifications and to establish whether this
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
COMPLEXITY
OF TASK
mEthodology
Question
parts
that
contained
the project was designed
in threemathematics
phases. the within
afirst
fullwas
suite
A-levelthe
examinations
measured
to of
establish
nature of thewere
mathematics
against
four
levels
of
complexity,
with
Level
4 being
assessed within the biology, chemistry and physics
considered
the
most
difficult.
These
levels
included
a-level examinations in 2010. the full suite of
Level
1 (straight
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Level
2 (requires
examinations
papers
from aQa, ccea,
edexcel,
understanding
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ocr and WJecand
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within
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and application of mathematics across domains)
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the type
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theand
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and
4 (requires
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application
assessed were
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against
the stated
of mathematics
across
a number
of domains).
mathematical
requirements
for
biology,
Appendix 5b shows an example of each chemistry
level of
and physics respectively1.
complexity.
2. the extent of the mathematics. the proportion
Tableof5athe
shows
theparts
percentage
of mathematical
question
within a paper
that
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parts
classified
as
Level
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included mathematics was measured
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A-levela-level
unit and
as an
complexity
the groups 12
comprised
practising
teachers,
average
for theory
only in
and
practicalresearch
only papers.
teachers with
experience
curriculum
and
These
figuresand
areindividuals
calculated
as a percentage
development
working
for awarding
of
the question
parts identified
containing
organisations
as markers,
questionaswriters
or examiners.
mathematics.
5b shows
these percentages
standardisationTable
exercises
were employed
throughout the
of
the total
number
of question
parts andwithin
Tableand
5c
analysis
to verify
the reliability
of judgements
takes
accountexpert
the weighting
acrossinto
the subject
groups. of theory papers
(80%) and practical papers (20%) to calculate the
the second phase aimed to measure the coherence
average percentage of Level 1, 2 and 3 complexity
between the teaching and learning of mathematics
in a complete A-level. Figure 6a illustrates the
and the sciences. there is an assumption that the
percentage of Level 1, 2 and 3 complexity type
mathematical concepts used to access the sciences
calculations in a complete A-level for each of the
are first taught within a mathematical context, i.e. within
five awarding organisations. Figures 6b and 6c
the mathematics curriculum. the project compared the
illustrate these percentages for theory only and
mathematical requirements for the sciences at a-level
practical only papers respectively.
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
that required mathematics.
was carried out by a researcher and by a mathematics
Table 5a: Percentage of Level 1, 2 and 3 complexityteacher.
type calculations in physics A-level,
3. the difficulty of mathematics. this was measured
calculated as a percentage of question parts identified as containing mathematics
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
A
B
the complexity of the question.
each category
had varying levels of difficulty
Complexity
3
2and each
1 was
3
2
measured as a proportion of the total number of
AS units 1 and 2
12 61 28 5
67
question parts containing mathematics. it was not
AS unit
3
2
16
82 0
0
measured
against the number
of marks.
A2
4 and 5
63 21We2
4. units
the appropriateness
of 17
mathematics.
63
looked
required
A2 unit
6 at whether the answer
0
20
80 scientific
0
58
comprehension in addition to mathematical skill.
15 62 25 4
65
this was measured as a proportion of the total
Practical
papers
only parts
1 containing
18 81mathematics.
0
29
number
of question
Theory papers only
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
C
D
E
in a-level science assessments. this was achieved
1 through
3 an2 online
1 survey
3 for2stakeholders
1
3 in the
2 science
1
29 community.
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14 0 on their
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87 4 participants
85 12
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100 0
75 25 0
20 80 0
5
95
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0
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22survey
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19 78 8
86 8
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0 were
50 also
50 consulted
0
21
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28as most
73
more79
generally
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their comments tended to focus more on the outcomes
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a subject expert group was established for each
of the three sciences. each group analysed the full
Table
Percentage
Levelof1,aQa,
2 and
3 complexity type calculations in physics A-level,
suite of5b:
2010
examinationsofpapers
ccea,
calculated
asand
a percentage
the total
number of question parts in a complete A-level
edexcel, ocr
WJec for theirof
respective
subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1,A2, 4 and 5) and the
B
C
D
E
experimental and practical papers (Units 3 and 6).
Complexity
3
2
1
3
2
1
3
2
1
3
2
1
3
2
calculations were based on the assumption that theory
AS units
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6
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0
8
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11
39
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11
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0
8
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29
Theory
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only use9the mathematical
the five awarding
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defined
biology,
35 14 requirements
2
34
17by ofqual
8 in developing
37 21their specifications
2
9 for34
5
49
5
1
chemistry and physics. the mathematical requirements are available in the full report.
2Practical
papers
only
46 marks
0 from 9the theory
14papers
0 (Unit 17
17 5) make
0 up 13
0
17
a complete science
a-level
is made1up of 611
units. the
1, 2, 4 and
80% of 47
the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
revised4 mathematics
12theLevel
was omittedGcses.
from the findings as very few examination papers included questions of this complexity.
SCORE
Mathsininscience
science report
report
score
maths
51
3
19
ExEcutivE
summary of Level 1, 2 and 3 complexity type calculations in physics A-level, weighted
Table 5c: Percentage
70
Background
60
50
been
there has
growing concern across the science
community40about the mathematical demand of science
30 specifically that Gcse and a-level science
qualifications,
20
qualifications
are not meeting the needs of students in
10
the way they assess the analytical nature of science.
0
A
B
C
D
E
Percentage of question parts
in a complete A level
in 2009 score published evidence on Gcse science
Awarding Organisations
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
Figure 6b: Percentage
mathematical
organisations
and confirmedof
that
the use of mathematics
question
parts of
identified
as examined
contanining
within
the context
science was
in a very
Level way.
1, Level
2 and
Level 3 complexity-type
limited
score
organisations
felt that this was
calculationsmathematics
in theory examination
unacceptable.
is integral to thepapers
teachingfor
physics
A-level
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately
THEORY represented in the
Level 2 curricula
Level 1 and their
Level
3 physics
biology, chemistry
and
assessments.
70
60
to provide 50further evidence to support these
concerns, 40
score set up this project to investigate the
mathematics
30 found in the 2010 science assessments
at a-level across
the unitary awarding organisations in
20
england, Wales
and northern ireland.
10
0
A
B
C
D
Awarding Organisations
2
20
SCORE Maths
report
score
mathsininscience
science
report
E
and practical component (20%) of the A-level
C
D
E
1
3
2
1
3
2
1
3
2
1
14
6
30
17
2
7
27
4
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4
3
0
3
3
0
3
9
0
3
10
17
6
33
20
2
10
36
4
42
14
Figure 6c: Percentage of mathematical
question parts identified as contanining
score’s
for this3 project
was to
Level 1, overall
Level objective
2 and Level
complexity-type
gather
evidencein
onpractical
the type, extent
and difficulty
of
calculations
examination
papers
mathematics
required
to
access
the
sciences
in
current
for physics A-level
aims
a-level specifications and to establish whether this
was being appropriately
met by the assessments. the
PRACTICAL
work did not compare
the
mathematical
Level
2
Level 1 requirements
Level 3
between physics,
chemistry
and
biology
as it is accepted
70
these will differ
between the disciplines.
60
Percentage of question parts
in a complete A level
Percentage of question parts
in a complete A level
to take account
the theory
component
mathematics
enablesofstudents
to understand
and (80%)
assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level
are not reflecting
A
B the
subject’s analytical nature. to explore whether there was
Complexity
3
2
1
3
2
any evidence for this concern, score investigated the
Theory
papers
only of mathematical
7
28 questions
11 2 within
27
type,
extent
and difficulty
(80%)a-levels. the findings show that a large number of
science
mathematical
requirements
chemistry
Practical papers
only listed
0 in the
2 biology,
9
0
2
and
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specifications
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assessed.
those
that
(20%)
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A-level
total this is likely7 to have
30 an20
level
than required.
impact2 on 29
(weighted)
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively
to stem
higher education
and employment.
Figure 6a:
Percentage
of mathematical
in
addition,
the
findings
show
a
disparity
in the way
question parts identified as containing
mathematics
is assessed
across 3
thecomplexity-type
different awarding
Level 1, Level
2 and Level
organisations.
recommends
that there
is a review
calculationsscore
in a complete
A-level
for each
of
of
the
mathematical
requirements
for
each
of
the
sciences
the five awarding organisations
at a-level and that a framework is developed to regulate
the way mathematics isTOTAL
assessed within the sciences to
ensure parity across
the
system.
Level 2
Level 1
Level 3
50
the findings aim to provide score with evidence to
40
inform the 30
development of policy on the type, extent
and difficulty
of the mathematics in the criteria and
20
assessments
for a-levels in biology, chemistry and
10
physics. the
project
also supports score’s work on
0
A
B
C
D
E
how the examinations system should operate to ensure
Awarding Organisations
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
CONTEXT
mEthodology
The
parts
that contained
mathematics
the question
project was
designed
in three phases.
the
within
a full
suite of the
A-level
examinations
were
first was
to establish
nature
of the mathematics
classified
as
Level
1,
Level
2
or
Level
3,
with
Level
assessed within the biology, chemistry and physics
1a-level
the most
familiar
context.
Level
1
is
a
context
examinations in 2010. the full suite of
typically
met papers
throughfrom
theaQa,
learning
programme,
examinations
ccea,
edexcel,
Level
2 is WJec
a context
contains
novel
ocr and
werethat
analysed
usingsome
the four
aspects
and
Level
3
is
an
unfamiliar
context
unlikely
measures that follow:
to have been met before. Appendix 5c shows an
1. the type
of mathematics.
the mathematical areas
example
of levels
of familiarity.
theory
only comprised
and practical
only papers.
These figures
the groups
practising
a-level teachers,
are
calculated
as a percentage
of the
question
teachers
with experience
in curriculum
research
and
parts
identified
containing
mathematics.
Table
development
andas
individuals
working
for awarding
6b
shows these
percentages
of the
total
organisations
as markers,
question
writers
or number
examiners.
of
question parts
and Table
takes into
accountthe
standardisation
exercises
were6c
employed
throughout
the
weighting
theory
papers
(80%) andwithin
practical
analysis
to verifyofthe
reliability
of judgements
and
papers
(20%)
to calculate
the average percentage
across the
subject
expert groups.
of Level 1, 2 and 3 context in a complete A-level.
the second phase aimed to measure the coherence
Figure 7a illustrates the percentage of Level 1, 2
between the teaching and learning of mathematics
and 3 context calculations in a complete A-level for
and the sciences. there is an assumption that the
each of the five awarding organisations. Figures 7b
mathematical concepts used to access the sciences
and 7c illustrate these percentages for theory only
are first taught within a mathematical context, i.e. within
and practical only papers respectively.
assessed were categorised against the stated
requirements
forofbiology,
chemistry
Tablemathematical
6a shows the
percentage
mathematical
1
and
physics
respectively
.
question parts classified as Level 1, 2 or 3 context
within
each
A-level
unit
and as an the
average
for
2. the
extent
of the
mathematics.
proportion
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
of the question parts within a paper that
with the mathematics curriculum prior to Key stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
mathematics.
Tablethat
6a:required
Percentage
of Level 1, 2 and 3 context-type
physics A-level,
calculated
wascalculations
carried out by in
a researcher
and by a mathematics
as a percentage of question parts identified as containing
mathematics
teacher.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
A of the context and
B
calculation, the familiarity
the complexity of the question.
Context
3
2 each
1 category
3
2
had varying levels of difficulty and each was
AS units 1 and 2
0
27 69 0
61
measured as a proportion of the total number of
AS unit
3 parts containing
0 mathematics.
21 79 it0was not
100
question
measured
against
of marks.
A2 units
4 and
5 the number
7
40
54 0
46
the aim of the third phase was to determine the nature
C
D
E
of mathematics that the community would like to see
1 in a-level
3
2science
1 assessments.
3
2
1
3 achieved
2
1
this was
40 through
14 an
26online
61 survey
0 for
12stakeholders
89
0 in the
0 science
100
community. Depending on their expertise, participants
0
0
6
94 0
60 40
0
0
100
answered the survey for biology, chemistry or physics
54 a-level
4 assessment.
30 66 2
11 87 were
0 chosen
0
100
the participants
in
three
groups;
teaching
profession;
higher
education;
4. unit
the appropriateness
of 6mathematics.
A2
6
21 74We0
75
25 33 13 53 0
0
100 0
44 56and
professional bodies. an online survey was completed by
looked at whether the answer required scientific
Theory papers only
4
34 62 0
54
47 9
28 64 1
12 88
0
0
100
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Practical
papers
only as a3 proportion
21 77
1338 17
10 74and032 for
30physics).
70 participants
0
22 from
78
for chemistry;
this was
measured
of the0total 88
industry
were
also
consulted
more
generally
but
as
most
number of question parts containing mathematics.
science-related industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
at graduate
level rather
than directly
referring
to a-level.
Table 6b: Percentage of Level 1, 2 and 3 context-type
calculations
in physics
A-level,
calculated
suite of 2010 examinations papers of aQa, ccea,
as a percentage of the total number of question parts in a complete A-level
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
B
C
D
E
all the theory papers (Units 1,A2, 4 and 5) and the
experimental
(Units 1
3 and 36). 2
Context and practical papers
3
2
1
3
2
1
3
2
1
3
2
1
calculations were based on the assumption that theory
AS units 1 and 2
0
13 34 0
35 23 10 18 41 0
5
37 0
0
51
papers make up 80% of the complete a-level and the
2
AS unit 3 and practical papers
0
12
44 0 20%15
0
0
2
31 0
23 15 0
0
76
experimental
the remaining
.
A2 units 4 and 5
4
25
33
0
22
26
3
19
42
1
5
40
0
0
63
A2 unit 6
3
12
43
0
23
8
11
4
17
0
0
82
0
26
32
Theory
papers only
2
19 34 0
29 25 7
19 42 1
5
39 0
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
0
57
chemistry andpapers
physics. the
mathematical
requirements
Practical
only
2
12 44 are0available
19in the4full report.
6
13
54
1
2
3
3
24
0
12
49
0
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
21
ExEcutivE
summary of Level 1, 2 and 3 context-type calculations in physics A-level, weighted
Table 6c: Percentage
70
Background
60
50
been
there has
growing concern across the science
community40about the mathematical demand of science
30 specifically that Gcse and a-level science
qualifications,
20
qualifications
are not meeting the needs of students in
10
the way they assess the analytical nature of science.
0
A
B
C
D
E
Percentage of question parts
in a complete A level
in 2009 score published evidence on Gcse science
Awarding Organisations
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
Figure 7b: Percentage
ofthat
mathematical
question
organisations
and confirmed
the use of mathematics
partsthe
identified
asscience
containing
calculations
set
within
context of
was examined
in a very
in a Familiar,
withorganisations
Some NovelfeltAspects,
and
limited
way. score
that this was
Unfamiliar context
in theory
examination
papers
unacceptable.
mathematics
is integral
to the teaching
for
physics
A-level
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately
THEORY represented in the
Unfamiliar
Some curricula
Novel
Familiar
biology, chemistry
and physics
and
their
assessments.
70
60
to provide 50
further evidence to support these
concerns, 40
score set up this project to investigate the
mathematics
30 found in the 2010 science assessments
at a-level across
the unitary awarding organisations in
20
england, Wales
and northern ireland.
10
0
A
B
C
D
Awarding Organisations
2
22
SCORE Maths
report
score
mathsininscience
science
report
E
and practical component (20%) of the A-level
C
D
E
1
3
2
1
3
2
1
3
2
1
20
6
15
34
0
4
31
0
0
46
1
1
1
5
0
2
10
0
3
11
21
7
16
39
0
6
41
0
3
57
Figure 7c: Percentage of mathematical question
parts identified as containing calculations set
score’s
overallwith
objective
forNovel
this project
was toand
in a Familiar,
Some
Aspects,
gather
evidence
on theintype,
extent and
difficulty of
Unfamiliar
context
practical
examination
mathematics
required to
access the sciences in current
papers for physics
A-level
aims
a-level specifications and to establish whether this
was being appropriately
met by the assessments. the
PRACTICAL
work did not compare
the
mathematical
requirements
Unfamiliar
Some Novel
Familiar
between physics,
chemistry
and
biology
as it is accepted
70
these will differ
between the disciplines.
60
Percentage of question parts
in a complete A level
Percentage of question parts
in a complete A level
to take account
the theory
component
mathematics
enablesofstudents
to understand
and (80%)
assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level
are not reflecting
A
B the
subject’s analytical nature. to explore whether there was
Context
3
2
1
3
2
any evidence for this concern, score investigated the
Theory
papers
only of mathematical
2
15 questions
27 0 within
23
type,
extent
and difficulty
(80%)a-levels. the findings show that a large number of
science
mathematical
requirements
chemistry
Practical papers
only listed
0 in the
2 biology,
9
0
4
and
physics
specifications
are
not
assessed.
those
that
(20%)
are assessed are covered repeatedly and often at a lower
A-level
total this is likely2 to have
17 an36
level
than required.
impact0 on 27
(weighted)
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively
to Percentage
stem higher education
and employment.
Figure 7a:
of mathematical
question
in
addition,
the
findings
show
a
disparity
in the way set
parts identified as containing calculations
mathematics
is assessed
across
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awarding
in a Familiar,
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Aspects,
and
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scorein
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Unfamiliar context
a complete
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of
the
mathematical
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each of the five awarding organisations
at a-level and that a framework is developed to regulate
the way mathematics isTOTAL
assessed within the sciences to
ensure parity across
the
system.
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Some Novel
Familiar
50
the findings aim to provide score with evidence to
40
inform the 30
development of policy on the type, extent
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assessments
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10
physics. the
project
also supports score’s work on
0
A
B
C
D
E
how the examinations system should operate to ensure
Awarding Organisations
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
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in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
3.1.1.4
APPROPRIATENESS
mEthodology
addition
to comprised
mathematical
skill ita-level
was classified
the groups
practising
teachers, as
some
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andresearch
questionand
parts
teachers
with experience
in curriculum
where
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comprehension
development
and required
individualsscientific
working for
awarding
were
classified
scientific
comprehension.
organisations
as as
markers,
question
writers or examiners.
Appendix
5d shows
an example
of each
category.
standardisation
exercises
were employed
throughout
the
the project was designed in three phases. the
APPLICATION
first was to establish
the nature
the mathematics
Judgements
were made
as toofwhether
the content
assessed
within part
the biology,
chemistry
and physics is
of
the question
reflected
how mathematics
a-level
in in
2010.
full suite
of
used
inexaminations
the real world
the the
scientific
context.
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examinations
papers
from
aQa,
ccea,
edexcel,
the question parts with mathematics were judged to
ocr and
were analysed
using the
the four
reflect
an WJec
appropriate
way in which
mathematics
measures
that follow:
could
be used
in a real scientific context.
analysis to verify the reliability of judgements within and
Table
percentage
across7a
theshows
subjectthe
expert
groups. of mathematical
question parts classified as all marks (S), some
the second phase aimed to measure the coherence
marks (B) or no marks (M) requiring scientific
between the teaching and learning of mathematics
comprehension within each A-level unit and as an
and the sciences. there is an assumption that the
average for theory only and practical only papers.
mathematical concepts used to access the sciences
These figures are calculated as a percentage
are first taught within a mathematical context, i.e. within
of the question parts identified as containing
the mathematics curriculum. the project compared the
mathematics. Table 7b shows these percentages
mathematical requirements for the sciences at a-level
of the total number of question parts and Table 7c
with the mathematics curriculum prior to Key stage 5
takes into account the weighting of theory papers
using the current national curriculum level descriptions
(80%) and practical papers (20%) to calculate
the
and a 2012 mathematics Gcse specification3. this work
average percentage of mathematical question parts
was carried out by a researcher and by a mathematics
where all marks, some marks or no marks require
teacher.
scientific comprehension in a complete A-level.
Figure
the percentage
of mathematical
the aim8a
of illustrates
the third phase
was to determine
the nature
question
parts that
where
some and
no like
marks
of mathematics
the all,
community
would
to see
require
comprehension
a complete
in a-levelscientific
science assessments.
thisinwas
achieved
A-level
each of
the five
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through for
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survey
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in the science
Figures
8b Depending
and 8c illustrate
percentages
for
community.
on theirthese
expertise,
participants
theory
only
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only chemistry
papers respectively.
answered
theand
survey
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1. the type of mathematics. the mathematical areas
STRUCTURAL
OR TAGGED ON
assessed were categorised against the stated
One of
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mathematical requirements for biology, chemistry
the mathematics
was a structural part of the
and physics respectively1.
question or whether the mathematics was tagged
of theInmathematics.
the proportion
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the extent
question.
all of the question
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of
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question
parts
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paper
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mathematics
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measured as was the
to beincluded
a structural
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proportion of the marks within these questions
that required mathematics.
MATHEMATICS
SKILLS OR SCIENTIFIC
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against 3 criteria: the number of steps in a
A-level
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extentthetocomplexity
which scientific
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required
to
achieve
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full
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required
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measured as a proportion of the total number of
the full
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question parts containing mathematics. it was not
comprehension
(mathematical skill only), if part
measured against the number of marks.
of the marks required scientific comprehension in
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
professional bodies. an online survey was completed by
looked at whether the answer required scientific
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Table 7a: Percentage of mathematical question parts
asand
all32
mark
(S), some
marks from
38 classified
for chemistry;
for physics).
participants
this was measured as a proportion of the total
(B) and no marks (M) requiring scientific comprehension
in
physics
A-level,
calculated
industry were also consulted more generallyas
butaas most
number of question parts containing mathematics.
percentage of question parts identified as containing
mathematics
science-related
industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
A
B
D than directly referring
E
at C
graduate level rather
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suite of 2010 examinations papers of aQa, ccea,
Scientific
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S
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M S
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M S
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edexcel,
ocr and WJec forStheir B
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49
calculations were based on the assumption that theory
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the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
23
Table 7b: Percentage
ExEcutivE
summary of mathematical type question parts where all marks (S), some marks (B) or
no marks (M) require scientific comprehension in physics A-level, calculated as a percentage of
mathematics enables students to understand and
the total number of question parts in a complete A-level
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B was
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E
subject’s analytical nature. to explore
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M S theB
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type,
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AS units 1 and 2
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0
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mathematical requirements listed in the biology, chemistry
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in addition, the findings show a disparity in the way
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score’s overall objective for this project was to
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gather evidence on the type, extent and difficulty of
Table 7c: Percentage of mathematical type question parts where all marks (S), some marks (B)
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
and no marks (M) require scientific comprehension in physics A-level, weighted to take account
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
of the theory component (80%) and practical component (20%) of the A-level assessments
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
A
B
Background
Scientific
S
B
M S
B
there
has been growing concern across the science
comprehension
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41 2
2
41 0
qualifications, specifically that Gcse and a-level science
(80%)
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only
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0
9
4
0
the
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(20%)
in 2009 score published evidence on Gcse science
A-level total
44 2
11 45 0
examination papers which reported a wide variation in
(weighted)
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
24
SCORE Maths
report
score
mathsininscience
science
report
C
D
between
physics, chemistry
and biologyEas it is accepted
differ between
M these
S will B
M S theBdisciplines.
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B
M
the findings aim to provide score with evidence to
2 inform
46 the2development
6
30of policy
0
5 the 45
0
1
on
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biology,
1 assessments
6
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10 in 0
2 chemistry
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0and 4
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how the examinations system should operate to ensure
3 science
52 qualifications
2
7
40
0
7
54 0
5
are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
ocr and WJec were analysed using the four
measures that follow:TOTAL
Scientific
Some Scientific
No Scientific
type Comprehension
of mathematics.
the mathematical
areas
Comprehension
Comprehension
70
Percentage of question parts
in a complete A level
1. the
assessed were categorised against the stated
60
mathematical requirements for biology, chemistry
50
and physics respectively1.
40
2. the extent
of the mathematics. the proportion
30
20 question parts within a paper that
of the
10
included
mathematics was measured as was the
0
proportion
of the marks
within
these
questions
A
B
C
D
E
that required mathematics.
Awarding Organisations
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation,
the familiarity
of the context and
Figure
8b: Percentage
of mathematical
the
complexity
of
the
question.
each category
question parts requiring scientific
had
varying
levels
of
difficulty
and
each was
comprehension in addition to mathematical
measured
as all
a proportion
of the total
number
of
skill to
achieve
marks, some
of the
marks
containing
mathematics.
it was for
not
or noquestion
marksparts
in theory
examination
papers
measured
against
the
number
of
marks.
physics A-level
Percentage of question parts
in a complete A level
4. the appropriateness of mathematics. We
THEORY
looked at whether
the answer required scientific
Scientific in addition
Some Scientific
No Scientific
comprehension
to mathematical
skill.
Comprehension
Comprehension
Comprehension
this 70
was measured as a proportion of the total
60 of question parts containing mathematics.
number
50
a subject expert group was established for each
40
of the three sciences. each group analysed the full
30
suite of 2010
examinations papers of aQa, ccea,
20
edexcel, ocr
and WJec for their respective subjects
10
at a two-day
workshop.
examination papers included
0
A
B
C
D
E
all the theory papers (Units 1, 2, 4 and 5) and the
Awarding Organisations
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
Figure
8c: comprised
Percentage
of mathematical
the groups
practising
a-level teachers,
question
parts
requiring
scientific
teachers with
experience
in curriculum
research and
comprehension
in addition
to mathematical
development and individuals
working
for awarding
skill
to achieve
all marks,
some
of the
marks
organisations
as markers,
question
writers
or examiners.
or
no marks inexercises
practical
examination
papersthe
standardisation
were
employed throughout
for
physics
A-level
analysis
to verify
the reliability of judgements within and
across the subject expert groups.
PRACTICAL
the second phase aimed
to measure the coherence
Scientific
Some Scientific
No Scientific
between the teaching and learning
of mathematics
Comprehension
Comprehension
Comprehension
70
and the sciences.
there is an assumption that the
60
mathematical
concepts used to access the sciences
50
are first taught
within a mathematical context, i.e. within
40
the mathematics curriculum. the project compared the
30
mathematical
requirements for the sciences at a-level
20
with the mathematics curriculum prior to Key stage 5
10
using the current national curriculum level descriptions
0
3E
A
B Gcse
C specification
D
and a 2012 mathematics
. this work
Awarding
Organisations
was carried out by a researcher and by a mathematics
teacher.
Percentage of question parts
in a complete A level
Figure
8a: Percentage of mathematical
mEthodology
question
requiring
scientific
the projectparts
was designed
in three
phases. the
comprehension
addition
mathematical
first was to establishinthe
nature ofto
the
mathematics
skill
to
achieve
all
marks,
some
marks
assessed within the biology, chemistry of
andthe
physics
or
no
marks
in
a
complete
physics
A-level
for
a-level examinations in 2010. the full suite of
each
of
the
five
awarding
organisations
examinations papers from aQa, ccea, edexcel,
the aim of the third phase was to determine the nature
3.1.2
PHASE 2that
– PHYSICS
A-LEVEL
IN to see
of mathematics
the community
would like
COMPARISON
WITH GCSEthis
MATHEMATICS
in a-level science assessments.
was achieved
AND
NATIONAL
CURRICULUM
LEVEL
through
an online survey
for stakeholders
in the science
DESCRIPTORS
community. Depending on their expertise, participants
answered
the surveywere
for biology,
chemistry
or the
physics
Two
comparisons
used to
establish
a-level
assessment.
the
participants
were
chosen
in
coherence of physics A-levels and the mathematics
three
groups;
teaching
profession;
higher
education;
and
accessed up to Key Stage 4: comparison
professional
bodies.
an online
survey
was completed
with
National
Curriculum
level
descriptors
and by
97
participants
across
the
three
groups
(27
for
biology;
comparison with the 2012 mathematics GCSE
38
for
chemistry;
and
32
for
physics).
participants
from
specification. These comparisons are displayed
in
industry
were
also
consulted
more
generally
but
as
most
Table 8.
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
25
ExEcutivE
summary of mathematical requirements for physics A-level with mathematics found
Table 8: Comparison
in the National
Curriculum
Descriptors
and GCSE mathematics specification
mathematics
enables
students to Level
understand
and
describe many scientific phenomena yet there is concern
Found in the
Mathematical
requirements
Corresponding
Comment
that
science assessments
at a-level are not reflecting
the
Edexcel
GCSE
as
listed
in
the
physics
A-level
NC
level(s)
for
subject’s analytical nature. to explore whether there was
specification
specification
mathematics
any
evidence for this concern, score investigated
the
Foundation (F)
type, extent and difficulty of mathematical questions within
and Higher (H)
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
1. Arithmetic
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F
H
and
physics specifications
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are
are covered
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ü
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use a calculator
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unacceptable. mathematics is integral to the teaching
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mass of humans
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26
n
number of significant
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Table
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Table 8: continued
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describe
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equations as mathematical models
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type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
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community
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science
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levels
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evidence
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england, Wales and northern ireland.
2
28
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report
score
mathsininscience
science
report
This is only found in the
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specification as it
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Table
8: continued
mEthodology
the project was designed in three phases. the
5. Graphs
NC levels
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assessed
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EP
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SCORE
Mathsininscience
science report
report
score
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3
29
Table 8: continued
ExEcutivE
summary
mathematics enables students to understand and
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qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
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organisations and confirmed that the use of mathematics
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limited way. score organisations felt that this was
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as such it should be appropriately represented in the
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assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
30
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report
score
mathsininscience
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3.1.3
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AT A-LEVEL PHYSICS
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In
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consider
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Figure
10:
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survey respondents
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35
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calculations were based on the assumption that theory
25
papers make up 80% of the complete a-level and the
20
experimental
and practical papers the remaining 20%2.
1
2
3
15
10
5
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
0 physics. the mathematical requirements are available in the full report.
chemistry and
1a 1b 1c 1d 1e 1f 1g 1h 2a 2b 2c 2d 2e 3a 3b 3c 3d 3e 3f 4a 4b 4c 4d 4e 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n 5o
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical
and experimental
papers (Unitfor
3 and
6) make
up the remaining 20%. in the analysis,
Mathematical
Requirements
Physics
A-Level
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
31
In Part B, after
receiving the findings from the
ExEcutivE
summary
analysis, more than 75% of respondents felt it
mathematics enables students to understand and
was unacceptable that mathematical content
describe many scientific phenomena yet there is concern
areas they considered essential were hardly or
that science assessments at a-level are not reflecting the
not at all assessed. When comparing Figure 4 and
subject’s analytical nature. to explore whether there was
Figure 10 it is clear there is a mismatch between
any evidence for this concern, score investigated the
mathematical content areas that are assessed
type, extent and difficulty of mathematical questions within
and those that the science community would like
science a-levels. the findings show that a large number of
to be assessed (for example selecting appropriate
mathematical requirements listed in the biology, chemistry
variables for graph plotting; understand that y = mx
and physics specifications are not assessed. those that
+ c represents a linear relationship and rearrange
are assessed are covered repeatedly and often at a lower
relationships into this form where appropriate; and
level than required. this is likely to have an impact on
determining the slope / gradient and intercept of a
the way that the subjects are taught and therefore on
linear graph in the appropriate physical units).
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
Furthermore nearly three quarters felt it was
in addition, the findings show a disparity in the way
inappropriate that a few mathematical requirements
mathematics is assessed across the different awarding
were assessed repeatedly, both throughout the
organisations. score recommends that there is a review
question papers within a qualification and across
of the mathematical requirements for each of the sciences
awarding organisations, rather than a spread
at a-level and that a framework is developed to regulate
of skills being assessed. Many acknowledged
the way mathematics is assessed within the sciences to
the importance of testing some of the key
ensure parity across the system.
mathematical skills more frequently, for example,
graphs and using formulae, in order to improve
Background
mathematical fluency. However, a broader spread
there
hastobeen
growing concern
across
the science
was felt
be important
in order
to understand
community
the mathematical
of science
the breadthabout
of physics
that woulddemand
be required
qualifications,
specifically
that Gcse
a-level science
for progression
and to test
deeperand
thinking,
as
qualifications
are
not
meeting
the
needs
of
students
opposed to substitution in formulae. The same in
the
way they
analytical
of were
science.
concern
wasassess
raisedthe
again
that ifnature
topics
not
assessed they would not be taught.
in 2009 score published evidence on Gcse science
examination
papers
which reported a wide variation in
EXTENT OF
MATHEMATICS
the
amount
of
mathematics
assessed
across
In Part A, 59% of respondents
felt that
theawarding
amount
organisations
andinconfirmed
that
thenot
useenough
of mathematics
of mathematics
the paper
was
within
the context
of science
was examined
a very
to adequately
prepare
for progression
to in
higher
limited
way.
score
organisations
felt
that
this
was
education in a physics or related subject. After
unacceptable.
mathematics
is
integral
to
the
teaching
viewing the findings of Phase 1, the majority thought
and
of the sciences,
and offers
valuable aid
that learning
the percentage
of question
partsacontaining
in
understanding
and
describing
scientific
phenomena;
mathematics was appropriate. However,
40% of
as
such
it
should
be
appropriately
represented
respondents thought the lower limit of 47%inofthe
marks
biology,
chemistry
and
physics
curricula
and
their
requiring mathematics was too low.
assessments.
No consensus was reached in Part A or B on
to provide further evidence to support these
whether the mathematics in the theory papers and
concerns, score set up this project to investigate the
the mathematics in the practical papers should be
mathematics found in the 2010 science assessments
different. Those who felt that it should be the same
at a-level across the unitary awarding organisations in
felt the A-level examination papers should be seen
england, Wales and northern ireland.
as a unified subject, the two being inter-dependent.
Those who felt it should be different explained that in
the practical units there would be more interpretation
of graphs, data handling, and calculation of errors,
derivations, and ‘show’ questions. Some explained
that the theory papers should test rigour and the
understanding of concepts whereas the practical
units should be testing experimental planning,
data collection, statistics and analysis so the
mathematical element would naturally be different.
DIFFICULTY OF MATHEMATICS
Part A of the survey showed that 100% of the
representatives from higher education and
professional bodies were not concerned if the
level of difficulty was perceived to go up due to the
A-levels containing more mathematics. However,
aims
only 62% of teachers agreed, largely because
score’s
overall
objectivethe
for level
this project
was toof the
they felt that
increasing
of demand
gather
evidence
on
the
type,
extent
and
difficulty
mathematics in physics A-level would result inofthe
mathematics
required
to access the
in current
overall A-level
being perceived
as sciences
more demanding.
a-level specifications and to establish whether this
was
being
appropriately
by difficulty
the assessments.
In Part
A, when
asked met
about
in terms the
work
did
not
compare
the
mathematical
requirements
of the number of steps in the calculations on the
between
physics,
chemistry and
as it should
is accepted
paper, 44%
of respondents
feltbiology
that there
these
will multiple-step
differ between calculations,
the disciplines.with a further
be more
15% wishing to see more extended questions. In
the findings aim to provide score with evidence to
Part B, nearly two-thirds of the respondents felt that
inform the development of policy on the type, extent
there should be an even spread of all three types of
and difficulty of the mathematics in the criteria and
calculation and nearly half of the respondents felt
assessments for a-levels in biology, chemistry and
that there should be more multiple-step calculations
physics. the project also supports 13
score’s work on
and more extended calculations .
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
When considering context as a measure of difficulty
work on improving the coherence between the sciences
in Part A of the survey, two thirds of the respondents
and mathematics.
felt that the number of mathematical questions set
within
a familiar
was appropriate.
In Part
in
the project,
wecontext
looked across
all assessments
at B
respondents
were
informed
that
the
analysis
had
a-level for a given year, including both experimental and
found that
the two awarding
practical
examination
papers. organisations had over
70% of the mathematical calculations set in a familiar
context. Results were evenly split between whether
this was appropriate, with half of the respondents
expressing the view that there should be less
mathematics set in familiar contexts so that students
have more experience at applying mathematics in
unfamiliar situations. However, overall 65% of the
respondents felt that the high level of mathematical
assessment set within a familiar context impacted
adversely on students’ ability to apply mathematics
in a novel situation.
13 Some respondents supported both statements so these percentages do not necessarily represent two different findings.
2
32
SCORE Maths
report
score
mathsininscience
science
report
Respondents
were asked to make a judgement
mEthodology
on
the
mathematical
difficulty
in phases.
the paper
the project was designed
in three
thein terms
of
complexity.
In Part
no respondents
thought
first
was to establish
theAnature
of the mathematics
that
the
complexity
was
too
difficult
and
there
assessed within the biology, chemistry and physics
was
an
even
split
between
those
who
thought
it
a-level examinations in 2010. the full suite of
was
too
easy
and
those
who
thought
that
it
was
examinations papers from aQa, ccea, edexcel,
appropriate.
In Part
when respondents
ocr and WJec
wereB,
analysed
using the four were
told
that
the
vast
majority
of
questions
across
measures that follow:
awarding organisations required Level 1 and Level
1. the type (i.e.
of mathematics.
the mathematical
areas
2 complexity
use of straightforward
and familiar
assessed
were categorised
against
thedomain
stated
concepts
or required
application
of one
mathematical
requirements
for
biology,
chemistry
of mathematics), 88% of respondents felt that the
1
physics respectively
.
recalland
of common
mathematical
procedures should
be2.assessed
alongside
procedures
that
involve
the extent of the mathematics. the
proportion
application
in one orparts
more
content
areas,
of the question
within
a paper
that that is,
that the
difficulty
should be
increased.
included
mathematics
was
measured as was the
proportion of the marks within these questions
COMPARABILITY
ACROSS AWARDING
that required mathematics.
ORGANISATIONS
3. the
mathematics.
this was
measured
In Part
A difficulty
88% of of
respondents
agreed
that
it was
against
3
criteria:
the
number
of
steps
in
a
important that the A-levels from all of the awarding
calculation,
thethe
familiarity
the of
context
andin
organisations
had
same of
level
difficulty
the
complexity
of
the
question.
each
category
terms of the mathematical content. Only 59% of
had varying
levelsthat
of difficulty
and each was
respondents
agreed
it was important
that
measured
as
a
proportion
of
the
total
number
all of the awarding organisations assessed the of
parts containing
mathematics.
it was not
samequestion
mathematical
content areas.
The remainder
measured
against
the
number
of
marks.
considered it only important for the same key
areas
to be
assessed byofallmathematics.
of the awarding
4. the
appropriateness
We
organisations.
The vast
also
thought
looked at whether
themajority
answer (91%)
required
scientific
that the
proportion of
questions
with mathematical
comprehension
in addition
to mathematical
skill.
content
should
be
similar
across
the
awarding
this was measured as a proportion of the total
organisations.
of respondents
feltmathematics.
that
number of 63%
question
parts containing
awarding organisations should use a framework
a subject expert group was established for each
to ensure a broad spread of mathematical
of the three sciences. each group analysed the full
requirements is assessed.
suite of 2010 examinations papers of aQa, ccea,
edexcel,
WJec for their
respective
In
Part Bocr
mostand
respondents
(59%)
felt thatsubjects
at
a
two-day
workshop.
examination
papers
differences across awarding organisationsincluded
in
all the
theory papers
1, 2,
and
5) andwith
the
the
proportion
of the(Units
marks
in 4an
A-level
experimental and
practical
papers
3 and 6).
mathematical
content
were
not (Units
acceptable.
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
COHERENCE
BETWEEN
MATHEMATICS
the groups comprised
practising
a-level teachers,
AND
THE
SCIENCES
teachers
with
experience in curriculum research and
The
appropriateness
of theworking
mathematics
was
development
and individuals
for awarding
deemed
by 97%
of the respondents
to be
most
organisations
as markers,
question writers
or the
examiners.
important
aspect
of mathematical
assessment
overthe
standardisation
exercises
were employed
throughout
demand
extent
of mathematics.
analysis toand
verify
the reliability
of judgements within and
across the subject expert groups.
All respondents felt that physics A-levels should
the second phase aimed to measure the coherence
contain mathematics beyond that found in the
between the teaching and learning of mathematics
current mathematics GCSE. There were mixed
and the sciences. there is an assumption that the
views on whether the mathematics GCSE should
mathematical concepts used to access the sciences
include these extra requirements to ensure GCSE
are first taught within a mathematical context, i.e. within
is adequate preparation for the mathematics in a
the mathematics curriculum. the project compared the
science A-level, with some agreeing that a new
mathematical requirements for the sciences at a-level
mathematics qualification for use alongside physics
with the mathematics curriculum prior to Key stage 5
A-levels would support the students.
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
3.2
CHEMISTRY
teacher.
3.2.1
PHASE
1: A-LEVEL
the aim
of the third
phase wasPAPERS
to determine the nature
of mathematics
that the community would like to see
3.2.1.1
EXTENT
in a-level science assessments. this was achieved
This measure seeks to capture how much of the
through an online survey for stakeholders in the science
A-level chemistry assessment is mathematical
community. Depending on their expertise, participants
(independent of the type, appropriateness or
answered the survey for biology, chemistry or physics
difficulty). It is quantified by the proportion of
a-level assessment. the participants were chosen in
questions or question parts within a complete
three groups; teaching profession; higher education; and
A-level that require mathematics and the proportion
professional bodies. an online survey was completed by
of marks requiring mathematics. Table 9a shows
97 participants across the three groups (27 for biology;
the percentage of question parts containing
38 for chemistry; and 32 for physics). participants from
mathematics within each unit and the percentage
industry were also consulted more generally but as most
of question parts containing mathematics for
science-related industries employ at a graduate level
theory only and practical only papers. Table 9b
their comments tended to focus more on the outcomes
takes into account the weighting of theory papers
at graduate level rather than directly referring to a-level.
(80%) and practical papers (20%) to calculate the
average percentage of question parts containing
mathematics in a complete A-level. Figure 11
illustrates the percentage of question parts in a
complete A-level containing mathematics for the
five awarding organisations.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
33
Table 9a: Percentage
ExEcutivE
summary of question parts containing mathematics within each unit and within the
set of theory and practical papers across the five awarding organisations
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
science assessments at a-level are notAreflecting the B
C
D
E
that
subject’s
analytical
to explore whether
AS units
1 and nature.
2
41 there was 60
41
35
50
any evidence for this concern, score investigated the
AS unit 3
49
27
35
40
53
type, extent and difficulty of mathematical questions within
A2 units
4 and
5 findings show that a large
51 number of 55
66
42
55
science
a-levels.
the
mathematical
A2 unit 6 requirements listed in the biology,
51 chemistry 34
21
55
41
and physics specifications are not assessed. those that
Theory papers only
46
58
54
39
53
are assessed are covered repeatedly and often at a lower
Practical
papers
only
31
28
48
47
level
than required.
this
is likely to have an 50
impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in
addition,
findings show
disparity in the
wayweighted to
Table
9b: the
Percentage
of aquestions
parts
take account of the theory component
mathematics
is assessedcomponent
across the different
awarding
overall objective for this project was to
(80%) and practical
(20%)
of the A-levelscore’s
assessments
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
the sciences in current
A
B mathematics
C required to access
D
E
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
Theory
contribution
(80%) within the37sciences to 46 was being appropriately
43
31by the assessments.
42
the
way mathematics
is assessed
met
the
ensure
paritycontribution
across the system.
requirements
Practical
(20%)
10
6 work did not
6 compare the mathematical
10
9
Total A-level
47
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications,
specifically that
and a-level
Figure 11: Percentage
ofGcse
question
partsscience
qualifications
are
not
meeting
the
needs
of
students in
containing mathematics in a complete
the
way they A-level
assess the
of science.
chemistry
foranalytical
the fivenature
awarding
organisations
Percentage of question parts
in a complete A level
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics
assessed
across awarding
Theory
Practical
Contribution
(80%)
Contribution
(20%)
organisations and confirmed that the use of mathematics
60
within the context
of science was examined in a very
limited way.50score organisations felt that this was
unacceptable.
mathematics is integral to the teaching
40
and learning
of the sciences, and offers a valuable aid
30
in understanding
and describing scientific phenomena;
20
as such it should be appropriately represented in the
10
biology, chemistry and physics curricula and their
0
B
C
D
E
assessments. A
Awarding Organisations
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
34
SCORE Maths
report
score
mathsininscience
science
report
52
between physics, chemistry and biology as it is accepted
49
41
51
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
Table
10a shows the percentage of marks requiring
mEthodology
mathematics
fordesigned
each unit
and for
theory
only and
the project was
in three
phases.
the
practical
only
papers.
takes
into account
first was to
establish
theTable
nature10b
of the
mathematics
the
weighting
of
theory
papers
(80%)
and
practical
assessed within the biology, chemistry and physics
papers
(20%)
to calculate
the average
percentage
the groups
comprised
practising
a-level teachers,
of
markswith
requiring
mathematics
in aresearch
complete
teachers
experience
in curriculum
and
A-level.
Figure
12individuals
illustratesworking
this asfor
a graph.
development
and
awarding
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
analysis to verify the reliability of judgements within and
across the subject expert groups.
a-level examinations in 2010. the full suite of
examinations papers from aQa, ccea, edexcel,
ocr and WJec were analysed using the four
Table
10a:
Percentage
of marks14 that require mathematics
within
and within
the set of
measures
that
follow:
the second
phaseeach
aimedunit
to measure
the coherence
theory and practical papers across the five awarding
organisations
between the teaching and learning of mathematics
1. the type of mathematics. the mathematical areas
and the sciences. there is an assumption that the
assessed were categorised against the stated
mathematical requirements for biology,
A chemistry B mathematical
C concepts used
D to access theEsciences
1
are
first
taught
within
a
mathematical
context, i.e. within
and physics
.
AS units
1 andrespectively
2
38
46
33
23
38
the mathematics curriculum. the project compared the
2. unit
the extent
of the mathematics. the 49
proportion
AS
3
10 mathematical
44 requirements36
22at a-level
for the sciences
of the question parts within a paper that
curriculum
A2 units 4 and 5
44
45 with the mathematics
49
20 prior to Key
42 stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
A2 unit
6
29
32
26
22
proportion
of the marks within these46
questions
and a 2012 mathematics Gcse specification3. this work
that papers
required mathematics.
Theory
only
41
46 was carried41
22 and by a mathematics
40
out by a researcher
3. the difficulty
of mathematics. this was
Practical
papers
48 measured 20 teacher. 38
31
22
1
Percentage of question parts
in a complete A level
against 3 criteria: the number of steps in a
the aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics that the community would like to see
the complexity of the question. each category
in a-level
science
assessments.
this was achieved
Tablehad
10b:
Percentage of marks requiring mathematics
within
a total
A-level, weighted
to
varying levels of difficulty and each was
through
an
online
survey
for
stakeholders
in the science
take measured
account as
ofathe
theory
component
(80%)
and
practical
component
(20%)
of
the
A-level
proportion of the total number of
community. Depending on their expertise, participants
assessments
question parts containing mathematics. it was not
answered the survey for biology, chemistry or physics
measured against the number of marks.
A
B
C
D
E
a-level assessment. the participants were chosen in
Theory
33We
37 three groups;
33 teaching profession;
18
32
higher education;
and
4. the contribution
appropriateness(80%)
of mathematics.
completed by
lookedcontribution
at whether the(20%)
answer required
Practical
10 scientific
4 professional8 bodies. an online
6 survey was 4
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Total A-level
43
41 38 for chemistry;
41
24
36
and 32 for physics). participants from
this was measured as a proportion of the total
industry were also consulted more generally but as most
number of question parts containing mathematics.
science-related industries employ at a graduate level
a subject expert group was established for each
Figure 12: Percentage of marks requiring
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
mathematics in a complete A-level for the five
at graduate level rather than directly referring to a-level.
suite of 2010 examinations papers of aQa, ccea,
awarding organisations
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers
5) and the
Theory (Units 1, 2, 4 and
Practical
Contribution (80%)
Contribution (20%)
experimental and practical papers (Units 3 and 6).
50
calculations were based on the assumption that theory
papers make
40 up 80% of the complete a-level and the
experimental
and practical papers the remaining 20%2.
30
20
10
0
the five awarding
organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
A
B
C
D
E
chemistry and physics. the mathematical requirements are available in the full report.
2 a complete science a-level
Awarding
is madeOrganisations
up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
14theArevised
mark mathematics
was judgedGcses.
to require mathematics if part or all of the mark could not be achieved without mathematics.
SCORE
Mathsininscience
science report
report
score
maths
3
35
ExEcutivE
summary
3.2.1.2 TYPE
mathematics
students toofunderstand
and
The numberenables
of occurrences
each mathematical
requirement listed in Chemistry A-level was measured
describe
many
scientific
phenomena
yet
there
is
concern
to identify the type of mathematics assessed and the frequency of each type of mathematics assessed.
that
at a-level
are13.
not reflecting the
Thescience
results assessments
are displayed
in Figure
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
Mathematical requirements listed in x-axis on Figure 13
type,
extent and difficulty of mathematical questions within
science
a-levels.
the
findingscomputation:
show that a large number of
1 Arithmetic
and
numerical
(d) solve simple algebraic equations;
(a)
recognise
and
use
expressions
in
decimal
and
(e)use logarithms in relation to quantities which range
mathematical requirements listed in the biology, chemistry
standard
form;
over several orders of magnitude.
and physics specifications are not assessed. those that
(b) use ratios, fractions and percentages;
are assessed are covered repeatedly and often at a lower
(c)make estimates of the results of calculations
4 Graphs:
level than
required.
is likely to have an impact on
(without
using this
a calculator);
(a)translate and interpret information between graphical,
the(d)
way
that
the subjects
and therefore
on
use
calculators
to findare
andtaught
use power,
exponential
numerical and algebraic forms;
and ability
logarithmic
functions
(xn, 1/x, √x,skills
logl0xto, progress
e x, log ex);
(b) plot two variables from experimental or other data;
students’
to have
the necessary
(e) +, -, to
x, ÷.
(c)understand that y = mx + c represents a linear
effectively
stem higher education and employment.
relationship;
aims
in addition, the findings show a disparity in the way
2 Handling data:
(d) determine the slope and intercept of a linear graph;
mathematics is assessed across the different awarding
score’s
objective
fora this
project
was
to
(a) use an appropriate number of significant figures;
(e)
calculateoverall
rate of change
from
graph
showing
a linear
organisations.
score
recommends that there is a review
gather
evidence on the type, extent and difficulty of
(b) find arithmetic
means;
relationship;
of the
mathematical
requirements
for tables
each of
the
sciences
(c)construct
and interpret
frequency
and
diagrams,
(f)
draw and userequired
the slopetoofaccess
a tangent
a curve asina current
mathematics
thetosciences
bar and
charts
anda histograms;
measure
of
rate
of
change;
at a-level
that
framework is developed to regulate
a-level specifications and to establish whether this
use
an appropriate
of decimal
places.
(g) interpret a spectrum.
the(d)
way
mathematics
is number
assessed
within the
sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
3 Algebra:
(a)understand and use the symbols: =, <, <<, >>, >, ,
Background
~, μ;
(b) change the subject of an equation;
there has been growing concern across the science
(c)substitute numerical values into algebraic equations
community about the mathematical demand of science
using appropriate units for physical quantities;
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
5 Geometry and trigonometry:
between
physics,
biology
it is3-D
accepted
a)
appreciate
angles chemistry
and shapesand
in regular
2-Das
and
these
will differ between the disciplines.
structures;
b)visualise and represent 2-D and 3-D forms including
the
findings aim to
provide score
with
evidence to
two-dimensional
representations
of 3-D
objects;
c)inform
understand
the symmetryofofpolicy
2-D and
the development
on3-D
theshapes.
type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project
also supports
score’s
Figure 13: The number of occurrences for each mathematical
requirement
in a full
suitework
of on
how
the
examinations
system
should
operate
to ensure
examination
a complete
chemistry
in
2009 score papers
publishedfor
evidence
on Gcse
science A-level in each of the awarding organisations.
science qualifications are fit for purpose and also its
examination
papers
reported
wide variation
It has no relation
to thewhich
number
of marksaawarded
for eachinmathematical requirement.
work on improving the coherence between the sciences
the amount of mathematics assessed across awarding
and mathematics.
organisations and confirmed that the use of mathematics
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
Number of Occurrences
Awarding
Organisations
within the context
of science
was examined in a very
A
B
C
D
E
limited way. score organisations
felt that
this was
80
unacceptable. mathematics is integral to the teaching
70
and learning
of the sciences, and offers a valuable aid
60
in understanding and describing scientific phenomena;
50
as such it should
be appropriately represented in the
biology, chemistry
and physics curricula and their
40
assessments.
30
to provide 20
further evidence to support these
10
concerns, score
set up this project to investigate the
mathematics0 found in the 2010 science assessments
1a 1b 1c 1d 1e 2a 2b 2c 2d 3a 3b 3c 3d
at a-level across the unitary awarding organisations in
Arithmetic and
Algebra
Handling
england, Wales andNumerical
northern ireland. Data
Computation
2
36
SCORE Maths
report
score
mathsininscience
science
report
3e
4a
4b
4c
4d
4e
Graphs
Mathematical Requirements for Chemistry A-Level
4f
4g
4h
5a
5b
5c
5d
Geometry and
Trigonometry
mEthodology
3.2.1.3
DIFFICULTY
the project was designed in three phases. the
For each of the following measures, percentages
first was to establish the nature of the mathematics
are stated as the number of question parts
assessed within the biology, chemistry and physics
containing mathematics. The percentages do not
a-level examinations in 2010. the full suite of
relate in any way to the number of marks awarded
examinations papers from aQa, ccea, edexcel,
for mathematical understanding.
ocr and WJec were analysed using the four
measures that
NUMBER
OFfollow:
STEPS
The
involvedthe
in a
calculation areas
was
1. number
the typeof
of steps
mathematics.
mathematical
used assessed
as one measure
of
difficulty
based
on
the
were categorised against the stated
assumption
that questions
containing
mathematics
mathematical
requirements
for biology,
chemistry
1
that required
multiple
step or. extended calculation
and physics
respectively
(e.g. value x had to be found and used in a
2. the extent of the mathematics. the proportion
subsequent calculation in order to find the solution
of the question parts within a paper that
to the problem, y) were more difficult than single
included mathematics was measured as was the
step calculations, as they require students to
proportion of the marks within these questions
use higher order skills and extended reasoning.
that required mathematics.
Appendix 5a shows an example of each type of
calculation.
3. the difficulty of mathematics. this was measured
the groups
comprised
a-level
teachers,
Table
11a shows
the practising
percentage
of mathematical
teachers
with
experience
in
curriculum
research
question parts classified as containing singleand
development
and individuals
working
for awarding
step
(S), multiple
step (M) or
extended
step (E)
organisations
as
markers,
question
writers
examiners.
calculations within each A-level unit andoras
an
standardisation
exercises
were
employed
throughout
average for theory only and practical only papers.the
analysisfigures
to verifyare
thecalculated
reliability ofas
judgements
within and
These
a percentage
across
the subject
expert
groups. as containing
of
the question
parts
identified
mathematics.
Table
11btoshows
these
percentages
the second phase
aimed
measure
the coherence
of
the
total
number
of
question
parts
and
Table 11c
between the teaching and learning of mathematics
takes
into
account
the
weighting
of
theory
papers
and the sciences. there is an assumption that the
(80%)
and
practical
papers
(20%)
to
calculate
the
mathematical concepts used to access the sciences
average
percentage
single step,context,
multiplei.e.step
are first taught
within aof
mathematical
within
and
extended
step
calculations
in
a
complete
the mathematics curriculum. the project compared the
A-level.
Figure
14a illustrates
thesciences
percentage
of
mathematical
requirements
for the
at a-level
single,
multiple
and
extended
step
calculations
with the mathematics curriculum prior to Key stage 5in
ausing
complete
A-level
for each
of the level
five awarding
the current
national
curriculum
descriptions
organisations.
Figures
14b
and
14c
illustrate
these
and a 2012 mathematics Gcse specification3. this
work
percentages
for
theory
only
and
practical
only
was carried out by a researcher and by a mathematics
papers
teacher. respectively.
against 3 criteria: the number of steps in a
the aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics that the community would like to see
Tablethe
11a:
Percentage
of single,
multiple
complexity
of the question.
each
categoryand extended step calculations in chemistry A-level,
in a-level science assessments. this was achieved
calculated
as alevels
percentage
question
had varying
of difficultyof
and
each wasparts identified as containing mathematics
through an online survey for stakeholders in the science
measured as a proportion of the total number of
community. Depending on their expertise, participants
A mathematics. it B
C
D
E
question parts containing
was not
answered the survey for biology, chemistry or physics
measured against the number of marks.
Number of steps
E
M S
E
M S a-level
E assessment.
M S the
E participants
M S were
E chosen
M inS
three
groups;
teaching
profession;
higher
education;
and
4. units
the appropriateness
of 33
mathematics.
AS
1 and 2
30 39We 19 2
80 16 13 72 15 58 28 28 7
66
professional bodies. an online survey was completed by
looked at whether the answer required scientific
AS unit
3
19 3
78 0
33 67 97 0
15 85
0 groups
48 0(27 for56
44
participants
across53
the three
biology;
comprehension in addition to mathematical skill.
for chemistry;
physics).
A2 units
4 and
5
this was
measured
as a14
proportion
of the32
total 0
12 75
69 38 18
4
79and 832 for12
81 participants
42 2 from
57
industry
were
also
consulted
more
generally
but as most
number of question parts containing mathematics.
A2 unit 6
14 7
79 31 6
64 17 17 67 83 0
17 0
33 67
science-related industries employ at a graduate level
aTheory
subject papers
expert group
was
established
for
each
only
24 21 57 26 1
75their17comments
9
76
12to focus
35 more
55 on
35the outcomes
5
62
tended
of the three sciences. each group analysed the full
to
Practical papers only 17 5
79 16 20 66at graduate
9
16level76rather
68than0directly
33referring
0
45a-level.
56
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
Table
11b: Percentage
of2,single,
multiple
all the theory
papers (Units 1,
4 and 5)
and the and extended step calculations in chemistry A-level,
calculated
as
a
percentage
of
the
total
number of question parts in a complete A-level
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
B the
C
D
E
papers make up 80% of the A
complete a-level and
2
experimental
practical papers
the remaining
Number ofand
steps
E
M
S
E 20%M.
S
E
M S
E
M S
E
M S
AS units 1 and 2
14
12
16
11
1
48
7
5
30
5
20
10
14
4
33
AS unit 3
9
1
38
0
9
18
0
5
30
21
0
19
0
30
23
1
31
the units
five awarding
organisations
use7the mathematical
biology,
A2
4 and
5
6
38 requirements
18 0defined38by ofqual
12 in developing
3
52their specifications
3
5 for34
23
1
chemistry and physics. the mathematical requirements are available in the full report.
2A2
unit 6science a-level is made7up of 64units. the
40 marks
11from 2the theory
22papers
4 (Unit 41, 2, 4 and
14 5) make
46 up 080% of 9the complete
0
14
a complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
Theory
papers
only
10 used9in the 27
15but we
1 maintained
43 the
9 80:204weighting.
41 4
13 22 19 2
question parts
rather than
marks were
calculation
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
Practical
papers only 8
3
39 5
5
20 2
4
22 33 0
14 0
22
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
27
32
25
3
37
ExEcutivE
summary of single, multiple and extended step calculations in chemistry A-level,
Table 11c: Percentage
weighted to
take students
accounttoof
the theory
mathematics
enables
understand
andcomponent (80%) and practical component (20%) of the
A-level
assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B
C
D
E
subject’s analytical nature. to explore whether there was
Number
M investigated
S
E theM S
E
M S
E
M S
E
M S
any
evidenceofforsteps
this concern,Escore
type,
extent
and
difficulty
of
mathematical
questions
within
Theory papers only
8
7
22 12 1
34 7
3
33 3
10 18 15 2
26
science
(80%)a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
Practical papers only
1
8 those
1 that1
4
0
1
4
7
0
3
0
4
5
and physics specifications are2not assessed.
(20%)
are assessed are covered repeatedly and often at a lower
level
than required.
impact13on 2
A-level
total this is likely10to have
8 an30
38 7
4
37 10 10 21 15 6
31
the
way that the subjects are taught and therefore on
(weighted)
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
Figure 14c: Percentage of mathematical
Figure
14a:
mathematical
in
addition,
thePercentage
findings show aofdisparity
in the way
questionoverall
partsobjective
identified
as project
containing
question
parts
identified
as
containing
single,
mathematics is assessed across the different awarding
score’s
for this
was tosingle,
multiple
and
extended
step
calculations
in
multiple
and
extended
step
calculations
in
a
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
practical examination
papers
for chemistry
complete
A-levelrequirements
for each of
awarding
of
the mathematical
forthe
eachfive
of the
sciences
mathematics
required to access
the sciences
in current
A-level
organisations
at
a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
TOTAL
PRACTICAL
ensure parity across the
system.
work did not compare
the mathematical requirements
Multiple
Single
Single
Extended
Multiple
between physics,
chemistry
and biology
as it is accepted
60
these will differ between the disciplines.
Percentage of question parts
in a complete A level
Background
60
50
there has been
growing concern across the science
community40about the mathematical demand of science
30 specifically that Gcse and a-level science
qualifications,
20 are not meeting the needs of students in
qualifications
the way they
10 assess the analytical nature of science.
0
Percentage of question parts
in a complete A level
B
C
in 2009 score Apublished
evidence
onD GcseEscience
Awarding
Organisations
examination papers which
reported
a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
Figure
Percentage
of mathematical
within
the14b:
context
of science was
examined in a very
question
identified
as containing
single,
limited
way.parts
score
organisations
felt that this was
multiple andmathematics
extended step
calculations
in
unacceptable.
is integral
to the teaching
theory
examination
papers
for
Chemistry
A-level
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
THEORY
as such it should be appropriately
represented in the
Singleand their
Extended
Multiple
biology, chemistry
and physics
curricula
60
assessments.
50
to provide further evidence to support these
40
concerns, score set up this project to investigate the
30
mathematics found in the 2010 science assessments
20
at a-level across
the unitary awarding organisations in
10
england, Wales
and northern ireland.
0
A
B
C
D
Awarding Organisations
2
38
SCORE Maths
report
score
mathsininscience
science
report
E
Percentage of question parts
in a complete A level
Extended
50
the findings
aim to provide score with evidence to
40
inform the development of policy on the type, extent
30
and difficulty of the mathematics in the criteria and
20
assessments for a-levels in biology, chemistry and
10
physics. the project also supports score’s work on
0
how the examinations
system
should
operate
A
B
C
D
Eto ensure
science qualificationsAwarding
are fit forOrganisations
purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
COMPLEXITY
OF TASK
mEthodology
Question
parts
that
contained
the project was designed
in threemathematics
phases. the within
afirst
fullwas
suite
A-levelthe
examinations
measured
to of
establish
nature of thewere
mathematics
against
four
levels
of
complexity,
with
Level
4 being
assessed within the biology, chemistry and physics
considered
the
most
difficult.
These
levels
included
a-level examinations in 2010. the full suite of
Level
1 (straight
forward/routine),
Level
2 (requires
examinations
papers
from aQa, ccea,
edexcel,
understanding
of mathematics
ocr and WJecand
wereapplication
analysed using
the four
within
one
domain),
Level
3
(requires
understanding
measures that follow:
and application of mathematics across domains)
1. Level
the type
of mathematics.
theand
mathematical
areas
and
4 (requires
synthesis
application
assessed were
categorised
against
the stated
of mathematics
across
a number
of domains).
mathematical
requirements
for
biology,
Appendix 5b shows an example of each chemistry
level of
and physics respectively1.
complexity.
2. the extent of the mathematics. the proportion
Tableof12a
the
percentage
of mathematical
the shows
question
parts
within a paper
that
question
parts
classified
as
Level
1, 2 oras3was the
included mathematics was measured
within each
A-levela-level
unit and
as an
complexity
the groups 15
comprised
practising
teachers,
average
for theory
only in
and
practicalresearch
only papers.
teachers with
experience
curriculum
and
These
figuresand
areindividuals
calculated
as a percentage
development
working
for awarding
of
the question
parts identified
containing
organisations
as markers,
questionaswriters
or examiners.
mathematics.
12bwere
shows
these percentages
standardisationTable
exercises
employed
throughout the
of
the total
number
of question
parts andwithin
Tableand
12c
analysis
to verify
the reliability
of judgements
takes
accountexpert
the weighting
acrossinto
the subject
groups. of theory papers
(80%) and practical papers (20%) to calculate the
the second phase aimed to measure the coherence
average percentage of Level 1, 2 and 3 complexity
between the teaching and learning of mathematics
in a complete A-level. Figure 15a illustrates the
and the sciences. there is an assumption that the
percentage of Level 1, 2 and 3 complexity type
mathematical concepts used to access the sciences
calculations in a complete A-level for each of the
are first taught within a mathematical context, i.e. within
five awarding organisations. Figures 15b and 15c
the mathematics curriculum. the project compared the
illustrate these percentages for theory only and
mathematical requirements for the sciences at a-level
practical only papers respectively.
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
that required mathematics.
was carried out by a researcher and by a mathematics
Table
12a:
Percentage
of Level
1,was
2 and
3 complexity
type calculations in chemistry A-level,
teacher.
3. the
difficulty
of mathematics.
this
measured
calculated
a percentage
against as
3 criteria:
the numberofofquestion
steps in a parts identified as containing mathematics
calculation, the familiarity of the context and
A
B
the complexity of the question.
each category
had varying levels of difficulty
Complexity
3
2and each
1 was
3
2
measured as a proportion of the total number of
AS units 1 and 2
0
48 53 0
12
question parts containing mathematics. it was not
AS unit
3
19 43
38 0
0
measured
against the number
of marks.
A2
4 and 5
23 78We 2
4. units
the appropriateness
of 0mathematics.
24
looked
required
A2 unit
6 at whether the answer
11 76
14 scientific
0
38
comprehension in addition to mathematical skill.
0
36 66 1
18
this was measured as a proportion of the total
Practical
onlyparts
15containing
60 26
0
19
numberpapers
of question
mathematics.
Theory papers only
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
C
D
E
in a-level science assessments. this was achieved
1 through
3 an2 online
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3 for 2stakeholders
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1
89 community.
17 46Depending
38 0 on their
35 expertise,
66 0 participants
25 75
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100 0
42 58 0
60 40 0
59 41
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75 three
11groups;
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76 7profession;
72 22
50 0and
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62 professional
0
38 bodies.
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71survey
29 was
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74 26by
97 participants across the three groups (27 for biology;
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14chemistry;
29 57and 432 for54
44 25 38 38
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0 were
40 also
60 consulted
0
66
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67as most
34
more35
generally
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
a subject expert group was established for each
of the three sciences. each group analysed the full
Table
Level
1, 2 and
3 complexity type calculations in chemistry A-level,
suite of12b:
2010Percentage
examinations of
papers
of aQa,
ccea,
calculated
asand
a percentage
the total
number of question parts in a complete A-level
edexcel, ocr
WJec for theirof
respective
subjects
at a two-day workshop. examination papers included
B
C
D
E
all the theory papers (Units 1,A2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
Complexity
3
2
1
3
2
1
3
2
1
3
2
1
3
2
calculations were based on the assumption that theory
AS units
1 and
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20 a-level
22 and
0 the7
53 7
19 16 0
12 23 0
13
papers
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2
experimental
the remaining
AS unit 3 and practical papers
9
21
19 0 20%0.
27 0
15 20 0
24 16 0
31
1
38
22
A2 units 4 and 5
0
12
40
1
13
41
7
8
50
3
30
9
28
28
0
A2 unit 6
6
39
7
0
13
21
0
8
13
0
39
16
0
30
11
20
19
Theory
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only use0the mathematical
16 31 requirements
1
10
47by ofqual
7 in developing
13 33their specifications
1
21 for16
14
the five awarding
organisations
defined
biology,
1
chemistry and physics. the mathematical requirements are available in the full report.
papers
only
13 marks
0 from 6the theory
24papers
0 (Unit 11
17 5) make
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0
31
2Practical
a complete science
a-level
is made7up of 630
units. the
1, 2, 4 and
80% of 16
the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
revised4 mathematics
15theLevel
was omittedGcses.
from the findings as very few examination papers included questions of this complexity.
SCORE
Mathsininscience
science report
report
score
maths
16
3
39
Table 12c: Percentage
ExEcutivE
summary of Level 1, 2 and 3 complexity type calculations in chemistry A-level,
weighted to take account of the theory component (80%) and practical component (20%) of the
60
Background
50
there has 40
been growing concern across the science
community30about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
20
qualifications are not meeting the needs of students in
10
the way they assess the analytical nature of science.
0
A
B
C
D
E
Percentage of question parts
in a complete A level
in 2009 score published
evidence on Gcse science
Awarding Organisations
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
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confirmed that
the use of mathematics
Figure 15b: and
Percentage
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within
the context
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in a very
question
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identified
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containing
limited
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Level way.
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mathematics
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THEORY
as such it should be appropriately
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Level 1 and their
Level
3 physics
biology, chemistry
and
60
assessments.
50
to provide further evidence to support these
40
concerns, score set up this project to investigate the
30
mathematics found in the 2010 science assessments
20
at a-level across
the unitary awarding organisations in
10
england, Wales
and northern ireland.
0
A
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SCORE Maths
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Figure 15c: Percentage of mathematical
aims
question parts identified as containing
score’s
for this3 project
was to type
Level 1, overall
Level objective
2 and Level
complexity
gather
evidence
on
the
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mathematics
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between physics,
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60
these will differ
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50
Percentage of question parts
in a complete A level
Percentage of question parts
in a complete A level
mathematics enables students to understand and
A-level assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B
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8
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0
1
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impact0 on 9
(weighted)
the way that the subjects are taught and therefore on
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higher education
and employment.
Figure 15a:
Percentage
of mathematical
in addition, the findings show a disparity in the way
question parts identified as containing
mathematics is assessed across the different awarding
Level 1, Level 2 and Level 3 complexity type
organisations. score recommends that there is a review
calculations in a complete A-level for each of
of the mathematical requirements for each of the sciences
the five awarding organisations
at a-level and that a framework is developed to regulate
the way mathematics isTOTAL
assessed within the sciences to
ensure parity across
Level 2
Level 1
Level 3the system.
40
the findings
aim to provide score with evidence to
inform the 30
development of policy on the type, extent
20 of the mathematics in the criteria and
and difficulty
assessments
10 for a-levels in biology, chemistry and
physics. the
0 project also supports score’s work on
A
B
C
D
E
how the examinations system should operate to ensure
Awarding Organisations
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
CONTEXT
mEthodology
The
parts
that contained
mathematics
the question
project was
designed
in three phases.
the
within
a full
suite of the
A-level
examinations
were
first was
to establish
nature
of the mathematics
classified
as
Level
1,
Level
2
or
Level
3,
with
Level
assessed within the biology, chemistry and physics
1a-level
the most
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Level
1
is
a
context
examinations in 2010. the full suite of
typically
met papers
throughfrom
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ccea,
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a context
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ocr and
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analysed
usingsome
the four
aspects
and
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an
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unlikely
measures that follow:
to have been met before. Appendix 5c shows an
1. the type
of mathematics.
the mathematical areas
example
of levels
of familiarity.
assessed were categorised against the stated
requirements
for biology,
chemistry
Tablemathematical
13a shows the
percentage
of mathematical
1
and
physics
respectively
.
question parts classified as Level 1, 2 or 3
context
unit and
an
2. thewithin
extenteach
of theA-level
mathematics.
theasproportion
average
forcomprised
theory only
and practical
papers.
the groups
practising
a-level only
teachers,
These
figures
are calculated
as a percentage
teachers
with experience
in curriculum
research and
of
the question
identified
as containing
development
andparts
individuals
working
for awarding
mathematics.
13bquestion
shows these
organisations asTable
markers,
writerspercentages
or examiners.
of
the total number
of question
parts and
Table 13c
standardisation
exercises
were employed
throughout
the
takes
into
account
the weighting
of theory
papers
analysis
to verify
the reliability
of judgements
within
and
(80%)
practical
papers
(20%) to calculate the
across and
the subject
expert
groups.
average percentage of Level 1, 2 and 3 context
the second phase aimed to measure the coherence
in a complete A-level. Figure 16a illustrates the
between the teaching and learning of mathematics
percentage of Level 1, 2 and 3 context calculations
and the sciences. there is an assumption that the
in a complete A-level for each of the five awarding
mathematical concepts used to access the sciences
organisations. Figures 16b and 16c illustrate these
are first taught within a mathematical context, i.e. within
percentages for theory only and practical only
the mathematics curriculum. the project compared the
papers respectively.
mathematical requirements for the sciences at a-level
of the question parts within a paper that
with the mathematics curriculum prior to Key stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
proportion of the marks within these questions
3
and acalculations
2012 mathematics
Gcse specification
Tablethat
13a:
Percentage
of Level 1, 2 and 3 context-type
in chemistry
A-level, . this work
required
mathematics.
was carried
out by a researcher
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calculated as a percentage of question parts identified
as containing
mathematics
teacher.
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A
B
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2
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0and each
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E the nature
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in a-level science assessments. this was achieved
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95
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this was measured as a proportion of the total
industry were also consulted more generally but as most
number of question parts containing mathematics.
science-related industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
Table
13b: sciences.
Percentage
Level
1, 2 and
3 context-type calculations in chemistry A-level,
of the three
each of
group
analysed
the full
at graduate level rather than directly referring to a-level.
calculated
a percentage
total
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suite of 2010as
examinations
papersofofthe
aQa,
ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination
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A
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E
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50
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experimental and practical papers the remaining 20%2.
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the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
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0
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0
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3
chemistry and physics. the mathematical requirements are available in the full report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
44
1
SCORE
Mathsininscience
science report
report
score
maths
3
41
Table 13c: Percentage
ExEcutivE
summary of Level 1, 2 and 3 context-type calculations in chemistry A-level,
weighted to take account of the theory component (80%) and practical component (20%) of the
60
Background
50
there has 40
been growing concern across the science
community30about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
20
qualifications are not meeting the needs of students in
10
the way they assess the analytical nature of science.
0
A
B
C
D
E
Percentage of question parts
in a complete A level
in 2009 score published
evidence on Gcse science
Awarding Organisations
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations
and confirmedofthat
the use of mathematics
Figure 16b: Percentage
mathematical
question
within
context ofas
science
was examined
in a very
partsthe
identified
containing
calculations
limited
score organisations
that Aspects,
this was
set in way.
a Familiar,
with Some felt
Novel
unacceptable.
mathematics
is
integral
to
the
teaching
and Unfamiliar context in theory examination
and
learning
the sciences,
and offers a valuable aid
papers
forofchemistry
A-level
in understanding and describing scientific phenomena;
THEORY
as such it should be appropriately
represented in the
Unfamiliar
Some curricula
Novel
Familiar
biology, chemistry
and physics
and
their
60
assessments.
50
to provide further evidence to support these
40
concerns, score set up this project to investigate the
30
mathematics found in the 2010 science assessments
20
at a-level across
the unitary awarding organisations in
10
england, Wales
and northern ireland.
0
A
B
C
D
Awarding Organisations
2
42
SCORE Maths
report
score
mathsininscience
science
report
E
C
D
E
1
3
2
1
3
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1
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46
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0
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0
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Figure 16c: Percentage of mathematical question
aims
parts identified as containing calculations set
score’s
overallwith
objective
for this
project
was to and
in a Familiar,
Some
Novel
Aspects,
gather
evidence
on
the
type,
extent
and
difficulty
of
Unfamiliar context in practical examination
mathematics
required
to
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the
sciences
in
current
papers for chemistry A-level
a-level specifications and to establish whether this
was being appropriately
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PRACTICAL
work did not compare
requirements
Unfamiliar the mathematical
Some Novel
Familiar
between physics,
chemistry
and
biology
as it is accepted
60
these will differ
between the disciplines.
50
Percentage of question parts
in a complete A level
Percentage of question parts
in a complete A level
mathematics enables students to understand and
A-level assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B
subject’s analytical nature. to explore whether there was
Context
2 investigated
1
3 the2
any
evidence for this concern,3score
type,
extent
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questions
Theory
papers
only of mathematical
0
1
36 0 within
0
science
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the
findings
show
that
a
large
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of
(80%))
mathematical requirements listed in the biology, chemistry
Practical papers only 0
0
10 0
1
and physics specifications are not assessed. those that
(20%)
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A-level
total this is likely0 to have
1 an46
level
than required.
impact0 on 1
(weighted)
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively
to stem
higher education
and employment.
Figure 16a:
Percentage
of mathematical
question
in addition, the findings show a disparity in the way
parts identified as containing calculations set
mathematics is assessed across the different awarding
in a Familiar, with Some Novel Aspects, and
organisations. score recommends that there is a review
Unfamiliar context in a complete A-level for
of the mathematical requirements for each of the sciences
each of the five awarding organisations
at a-level and that a framework is developed to regulate
the way mathematics isTOTAL
assessed within the sciences to
ensure parity across
the system.
Unfamiliar
Some Novel
Familiar
40
the findings
aim to provide score with evidence to
inform the 30
development of policy on the type, extent
20 of the mathematics in the criteria and
and difficulty
assessments
10 for a-levels in biology, chemistry and
physics. the
0 project also supports score’s work on
A
B
C
D
E
how the examinations system should operate to ensure
Awarding Organisations
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
3.2.1.4
APPROPRIATENESS
mEthodology
addition
to comprised
mathematical
skill ita-level
was classified
the groups
practising
teachers, as
some
scientific
comprehension
andresearch
questionand
parts
teachers
with experience
in curriculum
where
all marks
comprehension
development
and required
individualsscientific
working for
awarding
were
classified
scientific
comprehension.
organisations
as as
markers,
question
writers or examiners.
Appendix
5d shows
an example
of each
category.
standardisation
exercises
were employed
throughout
the
the project was designed in three phases. the
APPLICATION
first was to establish
the nature
the mathematics
Judgements
were made
as toofwhether
the content
assessed
within the
chemistry
and physics
of
the question
partbiology,
reflected
how mathematics
in 2010.
thescientific
full suite of
isa-level
usedexaminations
in the real world
in the
context.
examinations
papers
from
aQa,
ccea,
edexcel,
All of the question parts with mathematics
were
ocr and
analysed using
theinfour
judged
toWJec
reflectwere
an appropriate
way
which the
measures that could
follow:be used in a real scientific
mathematics
context.
1. the type of mathematics. the mathematical areas
analysis to verify the reliability of judgements within and
Table
shows expert
the percentage
across14a
the subject
groups. of mathematical
question parts classified as all marks (S), some
the second phase aimed to measure the coherence
marks (B) or no marks (M) requiring scientific
between the teaching and learning of mathematics
comprehension within each A-level unit and as an
and the sciences. there is an assumption that the
average for theory only and practical only papers.
mathematical concepts used to access the sciences
These figures are calculated as a percentage
are first taught within a mathematical context, i.e. within
of the question parts identified as containing
the mathematics curriculum. the project compared the
mathematics. Table 14b shows these percentages
mathematical requirements for the sciences at a-level
of the total number of question parts and Table 14c
with the mathematics curriculum prior to Key stage 5
takes into account the weighting of theory papers
using the current national curriculum level descriptions
(80%) and practical papers (20%) to calculate
the
and a 2012 mathematics Gcse specification3. this work
average percentage of mathematical question
was carried out by a researcher and by a mathematics
parts where all marks, some marks or no marks
teacher.
require scientific comprehension in a complete
A-level.
17aphase
illustrates
the
percentage
of
the aim Figure
of the third
was to
determine
the nature
mathematical
parts where
all, like
some
and
of mathematicsquestion
that the community
would
to see
no
marksscience
requireassessments.
scientific comprehension
in a
in a-level
this was achieved
complete
for each
of the five awarding
through anA-level
online survey
for stakeholders
in the science
organisations.
Figureson
17b
and
17c illustrate
these
community. Depending
their
expertise,
participants
percentages
for theory
only and
practical
only
answered the survey
for biology,
chemistry
or physics
papers
respectively.the participants were chosen in
a-level assessment.
assessed were categorised against the stated
STRUCTURAL
OR TAGGED ON
mathematical requirements for biology, chemistry
One of
the
measures
was to ascertain whether the
and physics respectively1.
mathematics was a structural part of the question
the extent
of the mathematics.
the proportion
or 2.
whether
the mathematics
was purely
tagged
of
the
question
parts
within
a
paper
that
on to the question. In all of the question parts with
included mathematics
measured as
was
the
mathematical
content thewas
mathematics
was
judged
proportion
of
the
marks
within
these
questions
to be a structural part of the question.
that required mathematics.
MATHEMATICS
SKILLS OR SCIENTIFIC
3. the difficulty of mathematics. this was measured
COMPREHENSION
against 3 criteria: the number of steps in a
Mathematical
question parts within a full suite of
calculation, the familiarity of the context and
A-level
examinations
were measured against the
the complexity of the question. each category
extenthad
to varying
which scientific
comprehension was
levels of difficulty and each was
required
to
achieve
the
full
marks. If a question part
measured as a proportion of the total number of
required
no scientific comprehension to acquire
question parts containing mathematics. it was not
the full
marks
it was classified as no scientific
measured against the number of marks.
comprehension (mathematical skill only), if some
appropriateness
of mathematics.
We
of 4.
thethe
marks
required scientific
comprehension
in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
looked at whether the answer required scientific
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
38 for chemistry; and 32 for physics). participants from
this was measured as a proportion of the total
industry
were alsoas
consulted
more
generally
as most
of question parts
containing mathematics.
Tablenumber
14a: Percentage
of mathematical
question parts
classified
all marks
(S),
some but
marks
science-related industries employ at a graduate level
(B)
and no
marks
(M)
requiring
scientific
a subject
expert
group
was
established
for each comprehension in chemistry A-level, calculated as a
theirmathematics
comments tended to focus more on the outcomes
percentage
of question
partsanalysed
identified
as containing
of the three sciences.
each group
the full
at graduate level rather than directly referring to a-level.
suite of 2010 examinations papers of aQa, ccea,
B
C
D
E
edexcel, ocr and WJec forAtheir respective subjects
at
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examination
papers
included
Context
S
B
M S
B
M S
B
M S
B
M S
B
M
all the theory papers (Units 1, 2, 4 and 5) and the
AS units 1 and 2
97 3
0
100 0
0
100 0
0
74 19 7
100 0
0
experimental and practical papers (Units 3 and 6).
AS unit 3 were based on 0the assumption
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0 theory
67 33 0
90 10 0
88 13 0
67 33
papers make up 80% of the complete a-level and the
A2 units 4 and 5
100 0
0
99 2
0
100 0
0
100 0
0
100 0
0
experimental and practical papers the remaining 20%2.
A2 unit 6
0
69
31
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99
2
0
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1
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3
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0
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0
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0
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4
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0
0
14
0
94
7
0
39
87
66
67
44
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
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3-D shapes
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
48
SCORE Maths
report
score
mathsininscience
science
report
and mathematics.
ü
ü
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
ü
ü
practical examination papers.
ü
ü
3.2.3
PHASE 3 – SURVEY FINDINGS
mEthodology
the project
wasOF
designed
in three phases.
the
3.2.3.1
TYPE
MATHEMATICS
ASSESSED
first
was
to
establish
the
nature
of
the
mathematics
AT A-LEVEL CHEMISTRY
assessed within the biology, chemistry and physics
In
Part A respondents were asked to consider the
a-level examinations in 2010. the full suite of
spread
of mathematical content areas assessed
examinations papers from aQa, ccea, edexcel,
within
chemistry
A-level. Figure 18 illustrates the
ocr and WJec were analysed using the four
percentages
of
respondents
that considered the
measures that follow:
spread to be good, acceptable (key mathematical
1. the
type
of mathematics.
the(limited
mathematical
areas
areas
were
assessed),
average
variation
in
assessed
were categorised
the stated
type of
mathematics)
and pooragainst
(restricted
amount
mathematical
requirements
fortimes).
biology, chemistry
of mathematics
assessed
many
and physics respectively .
1
2. the extent of the mathematics. the proportion
Figure 18: Opinions from the chemistry
of the question parts within a paper that
online survey respondents on the spread
included mathematics was measured as was the
of mathematical content areas within a
proportion of the marks within these questions
chemistry A-level
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
The Key mathematical
calculation, the familiarity of the
context
and
content
areas were
assessed
the complexity of the question. each category
A restricted amount of
had varying levels of difficultymathematical
and eachcontent
was areas
seemed to be assessed
measured as a proportion ofmany
the times
total number of
question parts containing mathematics.
was of
not
There was a gooditspread
different mathematical content
measured against the number
of
marks.
areas being assessed
4. the appropriateness of mathematics.
There was notWe
enough variation
the type of mathematical
looked at whether the answerin
required
scientific
content being assessed
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
Overall,
participants
concerned
about
the groups
comprisedwere
practising
a-level teachers,
the
levelswith
of mathematical
content inresearch
chemistry
teachers
experience in curriculum
and
A-levels,
withand
many
feelingworking
that students
were
development
individuals
for awarding
being
misled as
about
the mathematical
organisations
markers,
question writersrequirements
or examiners.
of
chemistry asexercises
a subject.
Concern
was
also
standardisation
were
employed
throughout
the
expressed
that the
downgrading
the mathematical
analysis to verify
reliability of judgements
within and
requirements
would
alsogroups.
lead to a restriction in the
across the subject
expert
chemistry content that could be assessed. Algebra,
the second phase aimed to measure the coherence
problem solving, calculus, data manipulation and
between the teaching and learning of mathematics
units were all mentioned as areas with which many
and the sciences. there is an assumption that the
chemistry students struggled.
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
63% of repondents felt that awarding organisations
the mathematics curriculum. the project compared the
should use a framework to ensure a broad spread
mathematical requirements for the sciences at a-level
of mathematical requirements are assessed and
with the mathematics curriculum prior to Key stage 5
58% felt that all requirements should be assessed
using the current national curriculum level descriptions
over a two- or three-year cycle of the A-levels
to
and a 2012 mathematics Gcse specification3. this work
ensure they are taught. 63% also felt that if areas
was carried out by a researcher and by a mathematics
were not assessed then it would mean they would
teacher.
not be taught. Very few (16%) felt that only key
requirements
be assessed
as opposed
the aim of the should
third phase
was to determine
the nature
to
all requirements.
of mathematics
that the community would like to see
in a-level science assessments. this was achieved
In
Part B,
receiving
the
findings from
thescience
through
anafter
online
survey for
stakeholders
in the
analysis,
three-quarters
of
respondents
felt
it was
community. Depending on their expertise, participants
unacceptable
that essential
mathematical
answered the survey
for biology,
chemistry or content
physics
areas
hardly orthe
notparticipants
at all assessed.
The quarter
a-levelwere
assessment.
were chosen
in
that
it acceptable
was almost
threefound
groups;
teaching profession;
higherexclusively
education; and
made
up of bodies.
teachers.
Whensurvey
comparing
Figure 13by
professional
an online
was completed
and
Figure 19 itacross
is clear
a mismatch
97 participants
thethere
threeisgroups
(27 forbetween
biology;
mathematical
content
that are
assessedfrom
38 for chemistry;
and 32areas
for physics).
participants
and
those
that
theconsulted
science more
community
would
like
industry
were
also
generally
but as
most
to
be
assessed
(for
example,
recognise
and
use
science-related industries employ at a graduate level
expressions
in tended
decimaltoand
standard
More
their comments
focus
more on form).
the outcomes
positively,
areas that
the to
science
at graduatethere
level were
rathersome
than directly
referring
a-level.
community thought should feature highly and did in
fact feature highly across all awarding organisations
(for example, substituting numerical vales into
algebraic equations using appropriate physical
quantities). Most of the comments related to this
section of the survey indicated that the missing
topics from the assessment were central
to chemistry.
Participants were also asked to comment on the
a subject
expert group was
areas
of mathematics
theyestablished
would likefor
toeach
feature
of the three
sciences. each
group
analysed
full
highly
in assessment,
a little
or not
at all.the
These
suite
of
2010
examinations
papers
of
aQa,
ccea,
results are displayed in Figure 19. Participants
edexcel,
ocrif and
their
respective
subjects
were
asked
thereWJec
werefor
any
other
areas of
at
a
two-day
workshop.
examination
papers
included
mathematics, not listed in the requirements that
all thefelt
theory
papers
(Units 1, 2,
andassessments.
5) and the
they
should
be included
in4the
experimental
and
practical
papers
(Units
3 and
Content areas suggested by more than
one6).
calculations
were
based
on
the
assumption
that theory
respondent were:
papers
make
up
80%
of
the
complete
a-level
and the
•calculus (mentioned by 20% of respondents)
experimental and practical papers the remaining 20%2.
•logarithms
•statistics
•first order, second order equations
•quadratic equations and
1 the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
•powers
/ manipulation of indices and probability.
2
3
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
49
ExEcutivE
summary
Figure 19: Mathematical
requirement areas that chemistry survey respondents would like to
Number of Respondents
feature highly
in assessment,
a little and
in assessment or not at all
mathematics
enables
students to understand
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
Feature
Highlyto explore
Featurewhether
a Little
subject’s analytical
nature.
thereFeature
was Not At All
40 for this concern, score investigated the
any evidence
type, extent35and difficulty of mathematical questions within
science a-levels.
the findings show that a large number of
30
mathematical
requirements listed in the biology, chemistry
25
and physics specifications are not assessed. those that
20
are assessed are covered repeatedly and often at a lower
15
level than required. this is likely to have an impact on
10the subjects are taught and therefore on
the way that
5
students’ ability
to have the necessary skills to progress
effectively to0stem higher education and employment.
1a
1b
1c
1d
1e
2a
2b
2c
2d
3a
3b
3caims
3d
3e 4a
4b
4c
4d
4e
4f
4g
5a
5b
5c
in addition, the findings show a disparity in the way
Mathematical Requirements for Chemistry A-Level
mathematics is assessed across the different
awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
Furthermore,
over
two-thirdsisfelt
it was to regulate
Respondents
were told
that
in the analysis
was
at
a-level and that
a framework
developed
a-level
specifications
and to
establish
whether itthis
inappropriate
that aisfew
mathematical
found
thatappropriately
the percentage
that required
the
way mathematics
assessed
within therequirements
sciences to
was
being
met of
by marks
the assessments.
the
were assessed
repeatedly,
rather than a spread
mathematics
varied across
awarding organisations
ensure
parity across
the system.
work
did not compare
the mathematical
requirements
of skills being assessed. While there was broad
Background
agreement that many key skills would and should
be assessed
as they
are linked
to
there
has beenrepeatedly
growing concern
across
the science
different
content
areas
of
chemistry,
they
felt
that
community about the mathematical demand of science
there
was
an
absence
of
some
other
important
qualifications, specifically that Gcse and a-level science
skills and there
wasmeeting
a danger
theofrepetition
qualifications
are not
the that
needs
students in
encourages
more
rote
learning
rather
than
a deeper
the way they assess the analytical nature of science.
understanding of the material. It was felt that a
in
2009 score
published
evidenceskills
on Gcse
science
broader
range of
mathematical
needed
to be
examination
a wide
variation in
assessed topapers
checkwhich
morereported
in-depth
understanding,
the
amount
of mathematics
across
to give
a more
meaningfulassessed
assessment
ofawarding
students’
organisations
and confirmed
of mathematics
skills and to show
the skillsthat
of the
the use
more
able
within
the context
of science
was examined
in a very
students.
Many felt
that a chemistry
examination
limited
organisations
that this content
was
shouldway.
onlyscore
be concerned
with felt
chemistry
unacceptable.
mathematics
is
integral
to
the
teaching
and that the mathematics should be assessed in
and
learning of
sciences, and offers a valuable aid
the context
ofthe
chemistry.
in understanding and describing scientific phenomena;
as
such it should
be appropriately represented in the
EXTENT
OF MATHEMATICS
biology,
chemistry
physics curricula
In Part A 56% of and
respondents
felt thatand
thetheir
amount
assessments.
of mathematics in the paper was not enough
to adequately prepare for progression to higher
to provide further evidence to support these
education in chemistry or a related subject. However,
concerns, score set up this project to investigate the
after viewing the findings of the analysis, the majority
mathematics found in the 2010 science assessments
(88%) thought that the percentage of question parts
at a-level across the unitary awarding organisations in
containing mathematics was appropriate.
england, Wales and northern ireland.
2
50
SCORE Maths
report
score
mathsininscience
science
report
betweenphysics,
24% and
43%. 60%
of the respondents
between
chemistry
and biology
as it is accepted
thought
the
lower
limit
of
marks
was
too
low and
these will differ between the disciplines.
there was no consensus reached on the higher limit.
the findings aim to provide score with evidence to
inform
the development
of policy
on the type,
No consensus
was found
on whether
the extent
and
difficulty ofin
the
mathematics
in theand
criteria
mathematics
the
theory papers
theand
assessments
for
a-levels
in
biology,
chemistry
and
mathematics in the practical papers should
be
physics.
the
project
also
supports
score’s
work
on
different. However, there was some consensus
how
the
examinations
system
should
operate
to
ensure
when asked their reasons for their opinions. It was
science
qualifications
are fit types
for purpose
and also its
widely agreed
that some
of mathematics
work
on
improving
the
coherence
between
the sciences
were more suitable for use in the practical
and
mathematics.
papers, for example, data handling, processing
experimental results, measurement and in-depth
in the project, we looked across all assessments at
analysis and that the assessments should draw on
a-level for a given year, including both experimental and
appropriate mathematics to support the chemistry
practical examination papers.
content. It was thought to be important across
the whole course to use and apply appropriate
mathematics skills to appreciate the chemistry. It
was felt that mathematical content should not be
stipulated for inclusion in either theory or practical
papers as that would lead to convoluted questions.
Others felt that linking certain mathematical
concepts to only one type of paper could lead
to compartmentalisation of the mathematics and
others felt the mathematics should be found in both
types of paper so that students could apply their
knowledge in a variety of settings.
DIFFICULTY
OF MATHEMATICS
mEthodology
In
Part
A
100%
of the representatives
the project was designed
in three phases.from
the higher
education
that itthe
didnature
not matter
if the level of
first was to felt
establish
of the mathematics
difficulty
was
perceived
to
go
up
due
to physics
the A-levels
assessed within the biology, chemistry and
containing
more
mathematics,
while
only
a-level examinations in 2010. the full suite of 71% of
respondents
overall from
agreed
with
this.edexcel,
examinations papers
aQa,
ccea,
ocr and WJec were analysed using the four
In
Part A, when asked about difficulty in terms
measures that follow:
of the number of steps in the calculations on the
1. the
typerespondents
of mathematics.
paper,
most
feltthe
thatmathematical
the balanceareas
assessed
categorised
against the stated
on the
samplewere
paper
seemed appropriate,
with
biology,from
chemistry
quite mathematical
a number of requirements
respondentsfor(mostly
HE)
1
and
physics
respectively
.
feeling that it was not an important issue. In Part B
the2.participants
told that the the
analysis
found
the extent ofwere
the mathematics.
proportion
that the
majority
of
calculations
were
single
of the question parts within a paper that step.
42% included
felt that mathematics
there shouldwas
be an
even spread
measured
as wasof
the
all three
types of
and these
nearlyquestions
half of the
proportion
of calculation
the marks within
respondents
felt that
there should be more multiple
that required
mathematics.
step calculations (42%) and more extended
3. the difficulty
of16mathematics.
this was measured
.
calculations
(34%)
against 3 criteria: the number of steps in a
thecontext
familiarityasofathe
context of
and
Whencalculation,
considering
measure
the
complexity
of
the
question.
each
category
difficulty, three-quarters of the respondents in
levels
of difficulty
and eachwith
was
Part Ahad
feltvarying
that the
number
of questions
measuredcontent
as a proportion
the totalcontext
numberwas
of
mathematical
set in aoffamiliar
question
parts
containing
mathematics.
it
was
not
appropriate. In Part B respondents were told that
measured
against
the
number
of
marks.
the vast majority of the mathematics in the A-levels
was
contexts typically
met through
4. set
theinappropriateness
of mathematics.
Wethe
learning
programme,
that
is,
it
was
set
in
a familiar
looked at whether the answer required scientific
context
(92%-100%).
Two-thirds
of respondents
comprehension
in addition
to mathematical
skill.
felt that
there
should
be
less
mathematics
set
this was measured as a proportion of the total
in familiar
contexts
so that
students
would
have
number
of question
parts
containing
mathematics.
more experience of applying mathematics in
a subject expert
groupthus
was established
each
unfamiliar
situations;
the majorityforwanted
of the
three sciences.
each
group analysed
the full
an
increase
in difficulty
in terms
of familiarity
of
suite
of
2010
examinations
papers
of
aQa,
ccea,
context. Respondents were asked whether or
edexcel,
ocr and of
WJec
for their respective
subjects
not
the familiarity
the context
in the majority
at
a
two-day
workshop.
examination
papers
included
of the assessments was creating a problem with
all the theory to
papers
(Units
1, 2, 4 and
5) and theand
progression
higher
education
or industry
experimental
and
practical
papers
(Units
6).
students’ ability to apply mathematics3inand
a novel
calculations
were
based
on
the
assumption
that
theory
situation. Two-thirds did feel that this was causing
papers
make
up
80%
of
the
complete
a-level
and
the
a problem.
appropriate.
When considering
a set of
questions,
the groups comprised
practising a-level
teachers,
two
thirds
feltexperience
that the questions
were
appropriate
teachers
with
in curriculum
research
and
in
terms of complexity
while
the remaining
third
development
and individuals
working
for awarding
felt
it was tooaseasy.
In Part
B, when
respondents
organisations
markers,
question
writers
or examiners.
were
told that the
vast majority
of questions
across
standardisation
exercises
were employed
throughout
the
awarding
required
Level 1 and
analysis to organisations
verify the reliability
of judgements
withinLevel
and
2across
complexity
(i.e. expert
use ofgroups.
straightforward and familiar
the subject
concepts or required application of one domain of
the second phase aimed to measure the coherence
mathematics), 72% of the participants felt that the
between the teaching and learning of mathematics
recall of common mathematical procedures should
and the sciences. there is an assumption that the
be assessed alongside procedures that involve
mathematical concepts used to access the sciences
application in one or more content areas, that is
are first taught within a mathematical context, i.e. within
that the difficulty should be increased in terms of
the mathematics curriculum. the project compared the
complexity.
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
COMPARABILITY ACROSS AWARDING
using the current national curriculum level descriptions
ORGANISATIONS
and a 2012 mathematics Gcse specification3. this work
In Part A 100% of respondents agreed that it was
was carried out by a researcher and by a mathematics
important that the A-levels from all of the awarding
teacher.
organisations had the same level of difficulty
in
terms
ofthe
thethird
mathematical
37%
ofnature
the
aim of
phase was content.
to determine
the
respondents
also
that it was
important
that
of mathematics
thatagreed
the community
would
like to see
all
of the awarding
organisations
the same
in a-level
science assessments.
thisassessed
was achieved
mathematical
content
with 61% inthinking
only
through an online
surveyareas,
for stakeholders
the science
that
it was important
the same
key participants
areas were
community.
Dependingthat
on their
expertise,
assessed
by all
of the
organisations.
The
answered the
survey
forawarding
biology, chemistry
or physics
vast
majority
(97%) the
thought
that thewere
proportion
of
a-level
assessment.
participants
chosen in
questions
with
mathematical
content
be and
three groups;
teaching
profession;
highershould
education;
similar
across
the awarding
63% ofby
professional
bodies.
an onlineorganisations.
survey was completed
respondents
that awarding
organisations
should
97 participantsfelt
across
the three groups
(27 for biology;
use
a framework
to ensure
that a broad
spreadfrom
of
38 for
chemistry; and
32 for physics).
participants
mathematical
requirements
is assessed.
there
industry were also
consulted more
generally Lastly,
but as most
were
requests that
the mathematical
requirements
science-related
industries
employ at a graduate
level
across
all of thetended
awarding
organisations
should
be
their comments
to focus
more on the
outcomes
the
same. level rather than directly referring to a-level.
at graduate
In Part B most respondents (89%) felt that the
differences across awarding organisations in the
proportion of the marks at A-level that are for
mathematical content were not acceptable.
COHERENCE BETWEEN MATHEMATICS
AND THE SCIENCES
Respondents were asked which was the most
Respondents were asked to make a judgement on
important feature of the mathematics in chemistry
the mathematical difficulty in terms of complexity
A-levels: proportion, appropriateness or difficulty
in the paper. In Part A no respondents thought
1 the the
mathematical
content.
83%forofbiology,
the respondents
that
complexity
was use
toothe
difficult
and requirements
there
five awarding
organisations
mathematical
defined byofofqual
in developing their
specifications
chemistry
and
physics.
the
mathematical
requirements
are
available
in
the
full
report.
felt that the appropriateness of the mathematical
was
an even split between those who thought it
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
theupmost
significant,
with
14%
was
too
easy
and
those
who
thought
that
it
was
a-level assessment and the marks from the practical and experimental paperscontent
(Unit 3 andwas
6) make
the remaining
20%. in the
analysis,
experimental and practical papers the remaining 20%2.
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
revisedrespondents
mathematics Gcses.
16theSome
supported both statements so these percentages do not necessarily represent two different findings.
3
SCORE
Mathsininscience
science report
report
score
maths
3
51
of respondents
feeling that the difficulty of the
ExEcutivE
summary
3.3 BIOLOGY
mathematics was the most important aspect.
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
All respondents felt that chemistry A-levels should
that science assessments at a-level are not reflecting the
contain mathematics that is not found in current
subject’s analytical nature. to explore whether there was
mathematics GCSE. A third of respondents agreed
any evidence for this concern, score investigated the
that mathematics GCSE should be adequate
type, extent and difficulty of mathematical questions within
preparation for the mathematics in a science A-level
science a-levels. the findings show that a large number of
and two-thirds agreed that the introduction of a
mathematical requirements listed in the biology, chemistry
new mathematics qualification for use alongside
and physics specifications are not assessed. those that
chemistry A-levels would support the students.
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
organisations. score recommends that there is a review
of the mathematical requirements for each of the sciences
at a-level and that a framework is developed to regulate
the way mathematics is assessed within the sciences to
ensure parity across the system.
This measure seeks to capture ‘how much’
mathematics is in the biology A-level assessments
(independent of the type, appropriateness or
difficulty). It is quantified by the number of questions
and question parts within a complete A-level that
require mathematics and the number of marks
within those questions requiring mathematics.
Table 16a shows the percentage of question
parts containing mathematics within each unit
and the percentage of question parts containing
mathematics for theory only and practical only
aims
papers. Table 16b takes into account the weighting
of theory overall
papersobjective
(80%) and
practical
score’s
for this
project papers
was to (20%)
to calculate
theon
average
percentage
of question
gather
evidence
the type,
extent and difficulty
of
parts containing
mathematics
in asciences
complete
A-level.
mathematics
required
to access the
in current
Figure
20
illustrates
the
percentage
of
question
a-level specifications and to establish whether this
partsbeing
in a appropriately
complete A-level
mathematics
was
met bycontaining
the assessments.
the
for the
organisations.
work
didfive
notawarding
compare the
mathematical requirements
Background
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
3.3.1 PHASE 1: A-LEVEL PAPERS
3.3.1.1 EXTENT
there
been
growing concern
across the
science
Tablehas
16a:
Percentage
of question
parts
containingthe
mathematics
unitwith
and
withintothe
findings aim towithin
provideeach
score
evidence
community
aboutand
the practical
mathematical
demand
of science
set of theory
papers
across
the five awarding
organisations
inform the development of policy on the type, extent
qualifications, specifically that Gcse and a-level science
and difficulty of the mathematics in the criteria and
qualifications are not meeting the needs of students in
A
B assessments
C for a-levels inDbiology, chemistry
E and
the way they assess the analytical nature of science.
physics.
the
project
also
supports
score’s
AS units 1 and 2
19
23
11
18
4 work on
how
the
examinations
system
should
operate
to ensure
in 2009 score published evidence on Gcse science
AS unit 3
59
0 science qualifications
55
100
53
are fit for purpose and also its
examination papers which reported a wide variation in
the coherence
between3the sciences
A2amount
units 4ofand
5
27 awarding 7 work on improving
3
22
the
mathematics
assessed across
and
mathematics.
organisations and confirmed that the use of mathematics
A2 unit 6
58
50
50
88
71
B
C
D
E
12
6
16
3
5
11
19
12
17
17
35
15
within the context of science was examined in a very
at
Theory papers only
23
15 in the project,
7 we looked across
20 all assessments
4
limited way. score organisations felt that this was
a-level for a given year, including both experimental and
Practical papers
only is integral to the
59 teaching
25
53
94
62
unacceptable.
mathematics
practical examination papers.
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
Table 16b: Percentage of question parts weighted to take account of the theory component
biology, chemistry and physics curricula and their
(80%) and practical component (20%) of the A-level assessments
assessments.
to provide further evidence to support these
A
concerns, score set up this project to investigate the
Theory contribution (80%)
18
mathematics found in the 2010 science assessments
contribution
12
atPractical
a-level across
the unitary(20%)
awarding organisations
in
england,
Wales
and
northern
ireland.
Total A-level
30
2
52
SCORE Maths
report
score
mathsininscience
science
report
mEthodology
Table
17a shows the percentage of marks requiring
mathematics
fordesigned
each unit
and for
theory
only and
the project was
in three
phases.
the
practical
only
papers.
takes
into account
first was to
establish
theTable
nature17b
of the
mathematics
the
weighting
theory
papers
(80%)
and
practical
assessed
withinofthe
biology,
chemistry
and
physics
the groups
comprised
practising
a-level teachers,
papers
(20%)
to calculate
the average
percentage
teachers
with
experience
in
curriculum
and
of marks requiring mathematics in aresearch
complete
development
and
awarding
A-level.
Figure
21individuals
illustratesworking
this asfor
a graph.
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
analysis to verify the reliability of judgements within and
across the subject expert groups.
a-level examinations in 2010. the full suite of
examinations papers from aQa, ccea, edexcel,
ocr and
WJec
were analysed
using the parts
four in a
Figure
20:
Percentage
of question
measures that
follow:containing mathematics for
complete
A-level
Figure 21: Percentage of marks requiring
the second phase
to measure
the coherence
mathematics
in aimed
a complete
A-level
for the five
between theorganisations
teaching and learning of mathematics
awarding
the1.five
organisations
the awarding
type of mathematics.
the mathematical areas
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
Theory
Practical
are first taught within
a mathematical
context, i.e. within
Contribution (80%)
Contribution (20%)
the mathematics
curriculum. the project compared the
30
mathematical requirements for the sciences at a-level
25
with the mathematics curriculum prior to Key stage 5
20
using the current national curriculum level descriptions
15
and a 2012 mathematics Gcse specification3. this work
10
was carried
out by a researcher and by a mathematics
teacher. 5
Percentage of question parts
in a complete A level
Percentage of question parts
in a complete A level
assessed were categorised against the stated
mathematical requirements for biology, chemistry
Theory
Practical
1
and physics
respectively
Contribution
(80%) .
Contribution (20%)
40
2. the extent
of the mathematics. the proportion
35
of the30question parts within a paper that
included
mathematics was measured as was the
25
20
proportion
of the marks within these questions
15
that required mathematics.
10
5
3. the difficulty
of mathematics. this was measured
0
0
against 3 criteria:
the number
of steps
inEa
A
B
C
D
A
B
D
E nature
the aim of the third
phase
wasCto determine
the
calculation, theAwarding
familiarityOrganisations
of the context and
Awarding
Organisations
of mathematics that the community would like to see
the complexity of the question. each category
in a-level science assessments. this was achieved
had varying levels of difficulty and each was
through an online survey for stakeholders in the science
measured as a proportion of the total number of
community. Depending on their expertise, participants
parts containing mathematics.
was not
answered the
survey
for biology,
chemistry
physics
Tablequestion
17a: Percentage
of marks17 thatitrequire
mathematics
within
each
unit and
withinorthe
set
measured against the number of marks.
a-levelorganisations
assessment. the participants were chosen in
of theory
and practical papers across the five awarding
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
completed by
looked at whether the answer required
A scientific
B professionalCbodies. an online
D survey was E
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
AS units 1 and 2
16
22 38 for chemistry;
10
15
3
and 32 for physics). participants from
this was measured as a proportion of the total
AS unit
3 of question parts containing46
industry were
38 also consulted
56more generally
41but as most
number
mathematics. 0
at a graduate level
unitsexpert
4 andgroup
5 was established for
21each
5 science-related
4 industries employ
12
3
aA2
subject
their comments tended to focus more on the outcomes
of
three
A2the
unit
6 sciences. each group analysed
48the full
48 at graduate40
45directly referring
68 to a-level.
level rather than
suite of 2010 examinations papers of aQa, ccea,
Theory papers only
19
14
7
14
3
edexcel, ocr and WJec for their respective subjects
Practical
onlyexamination papers
47 included 24
39
51
55
at
a two-daypapers
workshop.
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
Table 17b: Percentage of marks requiring mathematics within a total A-level, weighted to take
papers make up 80% of the complete a-level and the
account of the theory component (80%) and practical
component (20%) of the A-level assessments
experimental and practical papers the remaining 20%2.
A
B
C
D
E
Theory contribution (80%)
15
11
6
11
2
the five awarding
organisations use
the mathematical
their specifications
Practical
contribution
(20%)
9 requirements defined
5 by ofqual in developing
8
10 for biology, 11
chemistry and physics. the mathematical requirements are available in the full report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
Total A-level
24
16
14
21
13
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
17theArevised
mark mathematics
was judgedGcses.
to require mathematics if part or all of the mark could not be achieved without mathematics.
1
SCORE
Mathsininscience
science report
report
score
maths
3
53
ExEcutivE
summary
3.3.1.2 TYPE
mathematics
students toofunderstand
and
The numberenables
of occurrences
each mathematical
requirement listed in Biology A-level was measured
describe
many
scientific
phenomena
yet
there
is
concern
to identify the type of mathematics assessed and the frequency of each type of mathematics assessed.
that
at a-level
are22.
not reflecting the
Thescience
results assessments
are displayed
in Figure
subject’s analytical nature. to explore whether there was
requirements
listed in investigated
x-axis on Figure
anyMathematical
evidence for this
concern, score
the 22
type,
extent
and
difficulty
of
mathematical
questions
within
1 Arithmetic and numerical computation:
(k)understand probability in order to understand how
(arecognise
use
expressions
decimal
andnumber of
science
a-levels.and
the
findings
showinthat
a large
genetic ratios arise;
standard
form;
(l)
frame null hypothesis.
mathematical requirements listed in the biology, chemistry
(b) calculate or use ratios, fractions and percentages;
and physics specifications are not assessed. those that
3 Algebra:
(c)make estimates of the results of calculations (without
are assessed are covered repeatedly and often at a lower
(a) change the subject of an equation;
using a calculator);
(b)substitute numerical values into algebraic equations
level
than
required.
this
is
likely
to
have
an
impact
on
(d)use calculators to find and use mean, standard
using appropriate units for physical quantities;
the way
that the power,
subjects
are taught
and
thereforefunctions;
on
deviations,
exponential
and
logarithmic
(c)
understand the use of logarithms in relation to quantities
(e)use ability
calculations
involving
simple arithmetic
algebraic
students’
to have
the necessary
skills toand
progress
that range over several orders of magnitude;
transformations:
effectively to stem higher education and employment.
(d)derive an equation;
(f)understand and use correlations;
aims
in addition, the findings show a disparity in the way
(e) =, <, >.
(g) +, -, x, ÷.
mathematics is assessed across the different awarding
score’s overall objective for this project was to
4 Graphs:
2 Handling data:
organisations.
score recommends that there is a review
gather
evidence
on the
type, graphical,
extent and
difficulty
of
(a)
translate
information
between
numerical
and
(a) use
an appropriate
number of significant
figures;
of the
mathematical
requirements
for each of
the sciences
mathematics
required
to
access
the
sciences
in
current
algebraic forms;
(b) find arithmetic means;
at a-level and that a framework is developed to regulate
(b)
plot two
variables fromand
experimental
or other
data;this
a-level
specifications
to establish
whether
(c)construct or interpret tables, frequency tables and
(c)
calculate
of change from
graph
showing a linearthe
the way
mathematics
is assessed
within the sciences to
was
being rate
appropriately
met aby
the assessments.
diagrams,
bar charts
and histograms;
relationship;
ensure
parity across
theprobability;
system.
(d) understand
simple
work
did not compare the mathematical requirements
(e)understand the principles of sampling as applied to
scientific data;
Background
(f)understand the terms mean, median and mode and
there standard
has beendeviation;
growing concern across the science
community
about the
mathematical
demand
science
(g)use a scatter
diagram
to identify positive
andofnegative
correlation
between two
variables;
qualifications,
specifically
that
Gcse and a-level science
(h) select and
simple statistical
test; of students in
qualifications
areuse
nota meeting
the needs
(i) make order of magnitude calculations;
the way they assess the analytical nature of science.
(j)determine and interpret population variance, standard
deviation and standard deviation (error) of the mean;
(d)draw and use the slope of a tangent to a curve as a
between physics, chemistry and biology as it is accepted
measure of rate of change;
will differ
the
disciplines.
(e)these
construct
and /between
or interpret
line
graphs.
5 the
Geometry:
findings aim to provide score with evidence to
(a)
visualise
dimensional
dimensional
inform
thethree
development
offorms
policyfrom
on two
the type,
extent
representations of three dimensional objects;
and difficulty of the mathematics in the criteria and
(b)calculate circumferences and areas of circles, surface
assessments
for a-levels in biology, chemistry and
areas and volumes of regular blocks and cylinders when
physics.
the
project
also formulae.
supports score’s work on
provided with appropriate
Number of Occurrences
how the examinations system should operate to ensure
in 2009 score published evidence on Gcse science
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
Figure 22: The number of occurrences for each mathematical requirement in a full suite of
work on improving the coherence between the sciences
the amount of mathematics assessed across awarding
examination papers for a complete biology A-level in each of the awarding organisations.
and mathematics.
organisations and confirmed that the use of mathematics
It has no relation to the number of marks awarded for each mathematical requirement.
within the context of science was examined in a very
in the project, we looked across all assessments at
limited way. score organisations felt that this was
Awarding Organisations
a-level for a given year, including both experimental and
unacceptable. mathematics
is integral
toEthe teaching
A
B
C
D
practical examination papers.
and learning
40 of the sciences, and offers a valuable aid
in understanding
and describing scientific phenomena;
35
as such it should be appropriately represented in the
30
biology, chemistry and physics curricula and their
25
assessments.
20
to provide further
evidence to support these
15
concerns, score set up this project to investigate the
10
mathematics found in the 2010 science assessments
5
at a-level across the unitary awarding organisations in
0
england, Wales
1aand
1b northern
1c 1d 1e ireland.
1f 1g 2a 2b 2c 2d 2e 2f
Arithmetic and
Computation
2g 2h
Handling Data
2i
2j
2k
2l
3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 5a 5b
Algebra
Mathematical Requirements for Biology A-Level
2
54
SCORE Maths
report
score
mathsininscience
science
report
Graphs
Geometry and
Trigonometry
3.3.1.3
DIFFICULTY
mEthodology
Table
18a shows
the practising
percentage
of mathematical
the groups
comprised
a-level
teachers,
question
parts
classifiedinas
containing
singleand
teachers with
experience
curriculum
research
step
(S), multiple
step (M) or
extended
step (E)
development
and individuals
working
for awarding
calculations
each question
A-level unit
andoras
an
organisations within
as markers,
writers
examiners.
average
for theory
only and
papers.the
standardisation
exercises
werepractical
employedonly
throughout
These
a percentage
analysisfigures
to verifyare
thecalculated
reliability ofas
judgements
within and
of
the question
parts
identified
across
the subject
expert
groups. as containing
mathematics. Table 18b shows these percentages
the second phase aimed to measure the coherence
of the total number of question parts and Table 18c
between the teaching and learning of mathematics
takes into account the weighting of theory papers
and the sciences. there is an assumption that the
(80%) and practical papers (20%) to calculate the
mathematical concepts used to access the sciences
average percentage of single step, multiple step
are first taught within a mathematical context, i.e. within
and extended step calculations in a complete
the mathematics curriculum. the project compared the
A-level. Figure 23a illustrates the percentage of
mathematical requirements for the sciences at a-level
single, multiple and extended step calculations in
with the mathematics curriculum prior to Key stage 5
a complete A-level for each of the five awarding
using the current national curriculum level descriptions
organisations. Figures 23b and 23c illustrate
these
and a 2012 mathematics Gcse specification3. this work
percentages for theory only and practical only
was carried out by a researcher and by a mathematics
papers respectively.
theeach
project
three phases.
the
For
ofwas
the designed
followinginmeasures,
percentages
first
was
to
establish
the
nature
of
the
mathematics
are stated as a proportion of the number of
assessed parts
within containing
the biology, mathematics.
chemistry and physics
question
The
a-level
examinations
in
2010.
the
full
suite
of
percentages do not relate in any way to the number
examinations
papers
aQa, ccea,
edexcel,
of
marks awarded
forfrom
mathematical
understanding.
ocr and WJec were analysed using the four
measures that
NUMBER
OFfollow:
STEPS
The
number of steps involved in a calculation was
1. the type of mathematics. the mathematical areas
used assessed
as one measure
of difficulty, based on the
were categorised against the stated
assumption
that questions containing mathematics
mathematical requirements for biology, chemistry
that required
multiple step or extended calculation
and physics respectively1.
(e.g. value x had to be found and used in a
2. the extent
of the mathematics.
subsequent
calculation
in order tothe
findproportion
the solution
of
the
question
parts
within
a
paper
that
to the problem, y) were more difficult than single
included mathematics
measured
as was
step calculations,
as they was
require
students
to the
proportion
of
the
marks
within
these
questions
use higher order skills and extended reasoning.
that required
mathematics.
Appendix
5a shows
an example of each type of
calculation.
3. the difficulty of mathematics. this was measured
teacher.
against 3 criteria: the number of steps in a
the aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics
that the community
would
like to see
Tablethe
18a:
Percentage of single, multiple and extended
step calculations
in biology
A-level,
complexity of the question. each category
in
a-level
science
assessments.
this
was
achieved
calculated
as a percentage of question parts identified as containing mathematics
had varying levels of difficulty and each was
through an online survey for stakeholders in the science
measured as a proportion of the total number of
community. Depending on their expertise, participants
A mathematics. itBwas not
C
D
E
question parts containing
answered the survey for biology, chemistry or physics
measured
against the number
Number
of steps
E
Mof marks.
S
E
M S a-level
E assessment.
M S
E participants
M S were
E chosen
M inS
the
higher
and
4. units
the appropriateness
of0mathematics.
AS
1 and 2
13 88We0
31 69 three
17groups;
29 teaching
54 6 profession;
35 60
0 education;
0
100
professional bodies. an online survey was completed by
looked at whether the answer required scientific
AS unit
3
2
12 86 0
0
0
17 17 67 0
40 60 0
18 82
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
A2 units
4 and
5
9
92
50 50and732 for62
32 participants
50 50 from
0
physics).
this was
measured
as 0
a proportion
of the0total 88 13 38 0for chemistry;
industry
were
also
consulted
more
generally
but
as
most
number
A2 unit
6 of question parts
21containing
12 67mathematics.
20 53 28 8
46 46 13 43 43 7
15 78
science-related industries employ at a graduate level
aTheory
subject papers
expert group
established
onlywas 0
11 for
90 each
0
60 41 9
40 52 7
49 46 25 25 50
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
Practical papers only 12 12 77 10 27 14 at graduate
13 32 level
57rather
7 than42
52 referring
4
17a-level.
80
directly
to
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
Table
18b: Percentage
of2,single,
multiple
all the theory
papers (Units 1,
4 and 5)
and the and extended step calculations in biology A-level,
calculated
as
a
percentage
of
the
number of question parts in a complete A-level
experimental and practical papers (Units 3total
and 6).
calculations were based on the assumption that theory
B the
C
D
E
papers make up 80% of the A
complete a-level and
2
experimental
practical papers
the remaining
Number ofand
steps
E
M
S
E 20%M.
S
E
M S
E
M S
E
M S
AS units 1 and 2
0
2
17
0
7
16
2
3
6
1
6
11
0
0
4
AS unit 3
1
7
51
0
0
0
9
9
37
0
40
60
0
10
43
2
0
the units
five awarding
organisations
use0the mathematical
A2
4 and
5
2
25 requirements
0
6defined1 by ofqual
0 in developing
2
2 their specifications
2
14 for7biology,2
1
chemistry and physics. the mathematical requirements are available in the full report.
2A2
a complete
up of 67units. the
the theory
1, 2, 4 and
80% of 38
the complete
unit 6science a-level is made12
39 marks
10from 27
14papers
4 (Unit 23
23 5) make
11 up 38
5
11
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
Theory
papers
only
0 used2in the 21
0 but we
7 maintained
8
1 80:202weighting.
4
1
10 9
1
1
question parts
rather than
marks were
calculation
the
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
Practical
papers only
7
45 5
13 7
7
16 30 6
39 49 2
10
the revised mathematics
Gcses. 7
SCORE
Mathsininscience
science report
report
score
maths
55
2
49
3
55
Table 18c: Percentage
ExEcutivE
summary of single, multiple and extended step calculations in biology A-level,
weighted to take account of the theory component (80%) and practical component (20%)
Extended
Multiple
Single
Percentage of question parts
in a complete A level
Background
40
35
there has been
growing concern across the science
30
community25about the mathematical demand of science
20 specifically that Gcse and a-level science
qualifications,
15
qualifications
are not meeting the needs of students in
10
the way they assess the analytical nature of science.
5
0
Percentage of question parts
in a complete A level
B
C
in 2009 score Apublished
evidence
onD GcseEscience
Awarding
Organisations
examination papers which
reported
a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
Figure
Percentage
of mathematical
within
the23b:
context
of science was
examined in a very
question
identified
as containing
single,
limited
way.parts
score
organisations
felt that this was
multiple andmathematics
extended step
calculations
in
unacceptable.
is integral
to the teaching
theory
examination
papers
for
biology
A-level
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
THEORY represented in the
as such it should be appropriately
Singleand their
Extended
Multiplecurricula
biology, chemistry
and physics
25
assessments.
20
to provide further evidence to support these
concerns, 15
score set up this project to investigate the
mathematics
10 found in the 2010 science assessments
at a-level across the unitary awarding organisations in
5
england, Wales and northern ireland.
0
A
B
C
D
Awarding Organisations
2
56
SCORE Maths
report
score
mathsininscience
science
report
E
C
D
E
S
E
M
S
E
M
S
E
M
S
7
1
2
3
1
8
7
1
1
2
1
1
3
6
1
8
10
0
2
10
8
2
5
9
2
16
17
1
3
12
aims
Figure 23c: Percentage of mathematical
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average percentage of Level 1, 2 and 3 complexity
the second phase aimed to measure the coherence
in a complete A-level. Figure 24a illustrates the
between the teaching and learning of mathematics
percentage of Level 1, 2 and 3 complexity type
and the sciences. there is an assumption that the
calculations in a complete A-level for each of the
mathematical concepts used to access the sciences
five awarding organisations. Figures 24b and 24c
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illustrate these percentages for theory only and
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ocr and WJecand
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assessedacross
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mathematical
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proportion of the marks within these questions
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Table
19a:
Percentage
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2010Percentage
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of aQa,
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Table
Level
1, 2 and
3 complexity type calculations in biology A-level,
edexcel,
ocr
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calculated as a percentage of the total
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B
C
D
E
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revised4 mathematics
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SCORE
Mathsininscience
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Table 19c: Percentage
ExEcutivE
summary of Level 1, 2 and 3 complexity type calculations in biology A-level,
weighted to take account of the theory component (80%) and practical component (20%)
Level 2
Level 3
Level 1
Percentage of question parts
in a complete A level
Background
40
35
there has 30
been growing concern across the science
community25about the mathematical demand of science
20 specifically that Gcse and a-level science
qualifications,
15
qualifications
are not meeting the needs of students in
10
the way they assess the analytical nature of science.
5
0
Percentage of question parts
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B
C
in 2009 score Apublished
evidence
onD GcseEscience
Awarding
Organisations
examination papers which
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Figure
Percentage
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within
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context
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identified
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was 1,
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calculations
unacceptable.
mathematics
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to the
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examination
papers
for biology
A-level
and
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and offers
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THEORY represented in the
as such it should be appropriately
Level 2 curricula
Level 1 and their
Level
3 physics
biology, chemistry
and
25
assessments.
20
to provide further evidence to support these
concerns, 15
score set up this project to investigate the
mathematics
10 found in the 2010 science assessments
at a-level across the unitary awarding organisations in
5
england, Wales and northern ireland.
0
A
B
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D
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aims 24c: Percentage of mathematical
Figure
question
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as project
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and
Level
3
complexity
gather evidence on the type, extent and difficultytype
of
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in practical
examination
mathematics required
to access
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in current
for
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a-level
specifications
was being appropriately met by the assessments. the
PRACTICAL
work did not compare
the mathematical requirements
Level 2
Level 1
Level 3
between physics,
chemistry
and biology
as it is accepted
100
these will differ between the disciplines.
Percentage of question parts
in a complete A level
mathematics enables students to understand and
of the A-level assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B
subject’s analytical nature. to explore whether there was
Number
2 investigated
1
3 the2
any
evidenceofforsteps
this concern,3score
type,
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Theory papers only
0
1
18 0 within
0
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(80%)
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0
12those
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are assessed are covered repeatedly and often at a lower
level
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impact
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0 to have
1 an30
0 on 1
the
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(weighted)
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Figure
24a:
mathematical
in
addition,
thePercentage
findings show aofdisparity
in the way
question
parts
identified
as
containing
mathematics is assessed across the different awarding
Level 1, Level
2 andrecommends
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organisations.
score
that there is type
a review
calculations
in arequirements
complete A-level
for
of
of
the mathematical
for each of
theeach
sciences
the
five and
awarding
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at
a-level
that a framework
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TOTAL
ensure parity across the
system.
90
80
the findings
70 aim to provide score with evidence to
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50
and difficulty
40 of the mathematics in the criteria and
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0
how the examinations
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should
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A
B
C
D
Eto ensure
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purpose and also its
work on improving the coherence between the sciences
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in the project, we looked across all assessments at
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practical examination papers.
CONTEXT
mEthodology
The
parts
that contained
mathematics
the question
project was
designed
in three phases.
the
within
a full
suite of the
A-level
examinations
were
first was
to establish
nature
of the mathematics
classified
as
Level
1,
Level
2
or
Level
3,
with
Level
assessed within the biology, chemistry and physics
1a-level
the most
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Level
1
is
a
context
examinations in 2010. the full suite of
typically
met papers
throughfrom
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learning
programme,
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ccea,
edexcel,
Level
2 is WJec
a context
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ocr and
werethat
analysed
usingsome
the four
aspects
and
Level
3
is
an
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context
unlikely
measures that follow:
to have been met before. Appendix 5c shows an
1. the type
of mathematics.
the mathematical areas
example
of levels
of familiarity.
These
figures
are calculated
asa-level
a percentage
the groups
comprised
practising
teachers,
of
the question
parts identified
as containing
teachers
with experience
in curriculum
research and
mathematics.
Table
20b shows
these
percentages
development and
individuals
working
for awarding
of
the total number
of question
Table 20c
organisations
as markers,
questionparts
writersand
or examiners.
takes
into account
the weighting
of theory
papersthe
standardisation
exercises
were employed
throughout
(80%)
practical
papersof(20%)
to calculate
analysisand
to verify
the reliability
judgements
within the
and
average
of Level
1, 2 and 3 context
across thepercentage
subject expert
groups.
in a complete A-level. Figure 25a illustrates the
the second phase aimed to measure the coherence
percentage of Level 1, 2 and 3 context calculations
between the teaching and learning of mathematics
in a complete A-level for each of the five awarding
and the sciences. there is an assumption that the
organisations. Figures 25b and 25c illustrate these
mathematical concepts used to access the sciences
percentages for theory only and practical only
are first taught within a mathematical context, i.e. within
papers respectively.
assessed were categorised against the stated
requirements
for biology,
chemistry
Tablemathematical
20a shows the
percentage
of mathematical
1
and
physics
respectively
.
question parts classified as Level 1, 2 or 3
context
unit and
an
2. thewithin
extenteach
of theA-level
mathematics.
theasproportion
average
for
theory
only
and
practical
only
of the question parts within a paper that papers.
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
included mathematics was measured as was the
using the current national curriculum level descriptions
proportion of the marks within these questions
and a 2012 mathematics Gcse specification3. this work
that required mathematics.
was carried out by a researcher and by a mathematics
Table
20a:
Percentage
of Level
1,was
2 and
3 context type
calculations in biology A-level, calculated
teacher.
3. the
difficulty
of mathematics.
this
measured
as a against
percentage
of
question
parts
identified
as
containing
mathematics
3 criteria: the number of steps in a
the aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics that the community would like to see
A
B
C
D
E
the complexity of the question.
each category
in a-level science assessments. this was achieved
had
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each
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Context
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2
1
3
2
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an
measured as a proportion of the total number of
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0
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suite of20b:
2010Percentage
examinations of
papers
of aQa,
ccea,
Table
Level
1, 2 and
3 context type calculations in biology A-level, calculated
edexcel,
ocr and WJec
their number
respectiveof
subjects
as
a percentage
of thefortotal
question parts in a complete A-level
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
A
B
C
D
E
experimental and practical papers (Units 3 and 6).
Number ofwere
steps
3 assumption
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1 that
3 theory
2
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3
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the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
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0
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0
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0
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0
0
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chemistry and physics. the mathematical requirements are available in the full report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
Practical papers only 40 0
19 20 0
6
46 0
7
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6
41 0
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
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3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
4
24
3
59
ExEcutivE
summary of Level 1, 2 and 3 context type calculations in biology A-level, weighted
Table 20c: Percentage
to take account of the theory component (80%) and practical component (20%) of the A-level
Percentage of question parts
in a complete A level
Unfamiliar
Some Novel
Familiar
40
Background
35
there has 30
been growing concern across the science
community25about the mathematical demand of science
20
qualifications, specifically that Gcse and a-level science
15
qualifications
are not meeting the needs of students in
10
the way they
5 assess the analytical nature of science.
0
Percentage of question parts
in a complete A level
B
C
in 2009 score Apublished
evidence
onD GcseEscience
Awarding Organisations
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations
and confirmedofthat
the use of mathematics
Figure 25b: Percentage
mathematical
question
within
the
context
of
science
was
examined
in
a
very
parts identified as containing calculations
limited
way.
score
organisations
felt
that
this
was
set in a Familiar, with Some Novel Aspects,
unacceptable.
mathematics
integral to the in
teaching
and Unfamiliar
context iscalculations
theory
and
learning of the
sciences,
and offersA-level
a valuable aid
examination
papers
for biology
in understanding and describing scientific phenomena;
as such it should be appropriately
THEORY represented in the
biology, chemistry
and
and
their
Unfamiliar physics
Some curricula
Novel
Familiar
assessments.
25
to provide20further evidence to support these
concerns, 15
score set up this project to investigate the
mathematics found in the 2010 science assessments
10
at a-level across the unitary awarding organisations in
5
england, Wales
and northern ireland.
0
A
B
C
D
Awarding Organisations
2
60
SCORE Maths
report
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Figure
aims 25c: Percentage of mathematical question
parts identified as containing calculations set
score’s overall objective for this project was to
in a Familiar, with Some Novel Aspects, and
gather evidence on the type, extent and difficulty of
Unfamiliar context in practical examination
mathematics required to access the sciences in current
papers for biology A-level
a-level specifications and to establish whether this
was being appropriately met by the assessments. the
PRACTICAL
work did not compare the mathematical requirements
Unfamiliar
Some Novel
Familiar
between physics, chemistry and biology as it is accepted
100
these will differ
between the disciplines.
90
Percentage of question parts
in a complete A level
mathematics enables students to understand and
assessments
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B
subject’s analytical nature. to explore whether there was
any
evidenceofforsteps
this concern,3score
Number
2 investigated
1
3 the2
type, extent and difficulty of mathematical questions within
Theory papers only
0
1
18 0
0
science a-levels. the findings show that a large number of
(80%)
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Practical
papers onlyare8not assessed.
0
4 those
4 that0
and
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(20%)
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level
than required.
impact
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total this is likely
8 to have
1 an22
4 on 0
the
way that the subjects are taught and therefore on
(weighted)
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
Figure 25a: Percentage of mathematical question
in addition, the findings show a disparity in the way
parts identified as containing calculations set
mathematics is assessed across the different awarding
in a Familiar, with Some Novel Aspects, and
organisations. score recommends that there is a review
Unfamiliar context in a complete A-level for
of the mathematical requirements for each of the sciences
each of the five awarding organisations
at a-level and that a framework is developed to regulate
the way mathematics is assessed within the sciences to
TOTAL
ensure parity across the system.
80
70 aim to provide score with evidence to
the findings
60
inform the50development of policy on the type, extent
40 of the mathematics in the criteria and
and difficulty
30
assessments
20 for a-levels in biology, chemistry and
10 project also supports score’s work on
physics. the
0
A
B
C
D
Eto ensure
how the examinations
system
should
operate
Awarding
Organisations
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
3.3.1.4
APPROPRIATENESS
mEthodology
mathematical
skill it was
classified
as some
scientific
the groups comprised
practising
a-level
teachers,
comprehension
and question
parts where
all marks
teachers with experience
in curriculum
research
and
required
scientific
comprehension
classified as
development
and individuals
workingwere
for awarding
scientific
comprehension.
Appendix
5d shows
an
organisations
as markers, question
writers
or examiners.
example
of eachexercises
category.
standardisation
were employed throughout the
the project was designed in three phases. the
APPLICATION
first was to establish
the nature
the mathematics
Judgements
were made
as to of
whether
the content
assessed
withinpart
the biology,
chemistry
and physicsis
of
the question
reflected
how mathematics
a-level
the full suite
of All of
used
in examinations
the real worldinin2010.
the scientific
context.
examinations
papers
from
aQa,
ccea,
edexcel,
the question parts with mathematics were judged to
ocr and
WJec were analysed
usingthe
themathematics
four
reflect
an appropriate
way in which
measures
that follow:
could
be used
in a real scientific context.
analysis to verify the reliability of judgements within and
Table
percentage
across21a
the shows
subjectthe
expert
groups. of mathematical
question parts classified as all marks (S), some marks
the second phase aimed to measure the coherence
(B) or no marks (M) requiring scientific comprehension
between the teaching and learning of mathematics
within each A-level unit and as an average for theory
and the sciences. there is an assumption that the
only and practical only papers. These figures are
mathematical concepts used to access the sciences
calculated as a percentage of the question parts
are first taught within a mathematical context, i.e. within
identified as containing mathematics. Table 21b
the mathematics curriculum. the project compared the
shows these percentages of the total number of
mathematical requirements for the sciences at a-level
question parts and Table 21c takes into account
with the mathematics curriculum prior to Key stage 5
the weighting of theory papers (80%) and practical
using the current national curriculum level descriptions
papers (20%) to calculate the average percentage
of
and a 2012 mathematics Gcse specification3. this work
mathematical question parts where all marks, some
was carried out by a researcher and by a mathematics
marks or no marks require scientific comprehension
teacher.
in a complete A-level. Figure 26a illustrates the
percentage
of third
mathematical
partsthe
where
all,
the aim of the
phase wasquestion
to determine
nature
some
and no marks
require
scientific
comprehension
of mathematics
that the
community
would
like to see
in aa-level
complete
A-level
for each of
thewas
fiveachieved
awarding
science
assessments.
this
organisations.
Figures
and 26c illustrate
through an online
survey26b
for stakeholders
in thethese
science
percentages
for theoryon
only
and
practicalparticipants
only papers
community. Depending
their
expertise,
respectively.
answered the survey for biology, chemistry or physics
1. the type of mathematics. the mathematical areas
STRUCTURAL
OR TAGGED ON
assessed were categorised against the stated
One of
the measures was to ascertain whether the
mathematical requirements for biology, chemistry
mathematics
was a structural part of the question
and physics respectively1.
or whether the mathematics was tagged on to the
2. the extent
of the
mathematics.
themathematical
proportion
question.
All of the
question
parts with
of
the
question
parts
within
a
paper
that
content were judged to be a structural part of the
included mathematics was measured as was the
question.
proportion of the marks within these questions
that required mathematics.
MATHEMATICS
SKILLS OR SCIENTIFIC
COMPREHENSION
3. the difficulty of mathematics. this was measured
Mathematical
question parts within a full suite of
against 3 criteria: the number of steps in a
A-level
examinations were measured against the
calculation, the familiarity of the context and
extentthetocomplexity
which scientific
comprehension was
of the question. each category
required
to
achieve
the
full
marks. If a question part
had varying levels of difficulty and each was
required
no
scientific
comprehension
to acquire
measured as a proportion of the total number of
the full
marks it was classified as no scientific
question parts containing mathematics. it was not
comprehension
(mathematical skill only), if part of the
measured against the number of marks.
marks required scientific comprehension in addition to
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
professional bodies. an online survey was completed by
looked at whether the answer required scientific
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Table 21a: Percentage of mathematical question parts classified as all mark (S), some marks
38 for chemistry; and 32 for physics). participants from
this was measured as a proportion of the total
(B) and no marks (M) requiring scientific comprehension in biology A-level, calculated as a
industry were also consulted more generally but as most
number of question parts containing mathematics.
percentage of question parts identified as containing mathematics
science-related industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
of the three sciences. each group
analysed theBfull
A
D than directly referring
E
at C
graduate level rather
to a-level.
suite of 2010 examinations papers of aQa, ccea,
Scientific
S
B
M S
B
M S
B
M S
B
M S
B
M
edexcel, ocr and WJec for their respective subjects
comprehension
at a two-day workshop. examination papers included
AStheunits
1 and
2 (Units 1,402, 4 7and 5)54
0
25 76 0
75 25 0
53 47 0
75 25
all
theory
papers
and the
experimental
(Units59
3 and06). 0
AS unit 3 and practical papers
0
41
0
0
25 75 0
100 0
6
41 53
calculations were based on the assumption that theory
A2 units 4 and 5
0
71 29 0
13 88 0
100 0
0
76 24 0
0
100
papers make up 80% of the complete a-level and the
2
A2 unit 6 and practical papers
0
43
57 0 20%
81
23 77 0
100 0
52 0
48
experimental
the remaining
. 20 0
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20
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1
2
3
39
42
0
19
82
0
88
13
0
65
36
42
58
0
41
10
0
24
76
0
100 0
0
38
63
29
21
51
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
61
Table 21b: Percentage
ExEcutivE
summary of mathematical type question parts where all marks (S), some marks (B)
or no marks (M) require scientific comprehension in biology A-level, calculated as a percentage
mathematics enables students to understand and
of the total number of question parts in a complete A-level
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
A
B was
C
D
E
subject’s analytical nature. to explore
whether there
any
evidenceofforsteps
this concern,3score
Number
2 investigated
1
3 the2
1
3
2
1
3
2
1
3
2
1
type, extent and difficulty of mathematical questions within
AS units 1 and 2
8
1
10 0
6
17 0
8
3
0
10 8
0
3
1
science a-levels. the findings show that a large number of
AS unit 3 requirements listed
0 in the
24 biology,
35 chemistry
0
0
0
0
14 41 0
100 0
3
22 28
mathematical
and
are0not assessed.
A2physics
units 4specifications
and 5
19 8 those
0 that1
6
0
3
0
0
17 5
0
0
3
are assessed are covered repeatedly and often at a lower
A2 unit 6
0
25 33 0
41 10 0
12 39 0
88 0
37 0
34
level than required. this is likely to have an impact on
Theory
papers
only are taught
4
10
9
0 on 3
12 0
6
1
0
13 7
0
2
2
the
way that
the subjects
and therefore
students’
ability
to have
the necessary
Practical
papers
only
0
25skills34to progress
0
20 5
0
13 40 0
94 0
20 11 31
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
Table 21c: Percentage
of mathematical
question
parts
where
(S), some
marks
organisations.
score recommends
that there is type
a review
gather
evidence
onall
themarks
type, extent
and difficulty
of (B)
and
no
marks
(M)
require
scientific
comprehension
in
biology
A-level,
weighted
to
take
account
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
ofa-level
the theory
component
(80%)
and to
practical
(20%) of the
A-level
assessments
at
and that
a framework is
developed
regulate component
a-level specifications
and
to establish
whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
A
B
C did not compareDthe mathematical Erequirements
work
Number of steps
3
2
1
3
2
physics,
1 between
3
2
1 chemistry
3
2and biology
1
3as it is2accepted
1
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3
8
7
0
3
9
there has been growing concern across the science
Practicalabout
papers
0
5demand
7 of 0
4
community
the only
mathematical
science
qualifications,
specifically that3Gcse13
and a-level
A-level total
14 0science
7
qualifications
are
not
meeting
the
needs
of
students in
(weighted)
the way they assess the analytical nature of science.
Percentage of question parts
in a complete A level
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
Figure
26a:
of mathematical
the
amount
of Percentage
mathematics assessed
across awarding
question
parts
requiring
scientific
organisations and confirmed that the use of mathematics
comprehension
addition
mathematical
within
the context ofin
science
was to
examined
in a very
skill
to
achieve
all
marks,
some
of the
marks
limited way. score organisations felt that
this was
or no marksmathematics
in a complete
A-level
forteaching
each of
unacceptable.
is integral
to the
the
five
awarding
organisations
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
TOTAL
as such it should be appropriately
represented in the
Scientific
Some
Scientific and
No Scientific
biology, chemistry
and physics
curricula
their
Comprehension
Comprehension
Comprehension
assessments.
40
35
to provide 30
further evidence to support these
concerns, 25
score set up this project to investigate the
20
mathematics found in the 2010 science assessments
15
at a-level across
the unitary awarding organisations in
10
england, Wales
and northern ireland.
5
0
A
B
C
D
Awarding Organisations
2
62
SCORE Maths
report
score
mathsininscience
science
report
E
these will differ between the disciplines.
0
5
1
0
11
5
0
1
2
the findings aim to provide score with evidence to
1
0
3
8
0
19 0
4
2
6
inform the development of policy on the type, extent
10and0difficulty
7 of 8
0
30 in5the criteria
4
3and 8
the mathematics
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
Figure
Percentage
of mathematical
work
on 26b:
improving
the coherence
between the sciences
question
parts requiring scientific
and
mathematics.
comprehension in addition to mathematical
in
the to
project,
we looked
acrosssome
all assessments
at
skill
achieve
all marks,
of the marks
a-level
for a given
including
both experimental
or no marks
in year,
theory
examination
papers and
for
practical
examination
papers.
biology A-level
THEORY
Percentage of question parts
in a complete A level
Background
25
Scientific
Comprehension
Some Scientific
Comprehension
No Scientific
Comprehension
20
15
10
5
0
A
B
C
D
Awarding Organisations
E
mEthodology
Figure
26c: Percentage of mathematical
question
requiring
scientific
the projectparts
was designed
in three
phases. the
comprehension
addition
mathematical
first was to establishinthe
nature ofto
the
mathematics
skill
to achieve
allbiology,
marks,
some of
marks
assessed
within the
chemistry
andthe
physics
or
no marks
in practical
a-level
examinations
in 2010. examination
the full suite of papers
for
biology A-level
examinations
papers from aQa, ccea, edexcel,
ocr and WJec were analysed using the four
measures that follow:
PRACTICAL
Percentage of question parts
in a complete A level
Some Scientific
No Scientific
1. the type Scientific
of mathematics.
the mathematical
areas
Comprehension
Comprehension
Comprehension
100
assessed were categorised against the stated
90
mathematical
requirements for biology, chemistry
80
70
and physics
respectively1.
2.
60
50
the extent
of the mathematics. the proportion
40
of the
30 question parts within a paper that
20
included
mathematics was measured as was the
10
0
proportion
of the marks within these questions
A
B
C
D
E
that required mathematics.
Awarding Organisations
3.3.2
PHASE
2 – BIOLOGY
IN
the groups
comprised
practisingA-LEVEL
a-level teachers,
COMPARISON
WITH in
GCSE
MATHEMATICS
teachers with experience
curriculum
research and
AND
NATIONAL
CURRICULUM
LEVEL
development
and individuals
working for
awarding
DESCRIPTORS
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
Two comparisons were used to establish the
analysis to verify the reliability of judgements within and
coherence of biology A-levels and the mathematics
across the subject expert groups.
accessed up to Key Stage 4: comparison
with
National
Curriculum
descriptors
and
the second
phase
aimed tolevel
measure
the coherence
comparison
with theand
2012
mathematics
GCSE
between the teaching
learning
of mathematics
specification.
These
comparisons
are displayed
and the sciences.
there
is an assumption
that the
in
Table 22. concepts used to access the sciences
mathematical
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
the aim of the third phase was to determine the nature
calculation, the familiarity of the context and
of mathematics
the community
would like tofound
see
Table 22: Comparison of mathematical requirements
for biology that
A-level
with mathematics
the complexity of the question. each category
in
a-level
science
assessments.
this
was
achieved
in the National Curriculum Level Descriptors and GCSE mathematics specification
had varying levels of difficulty and each was
through an online survey for stakeholders in the science
measured as a proportion of the total number of
community.
Depending
expertise, participants
Found
in the on their
Mathematical
requirements
Comment
question parts
containing mathematics. it Corresponding
was not
answered
the
survey
for
biology,
chemistry or physics
Edexcel GCSE
as listed
in the
Biology
A-level
measured
against
the number
of marks. NC level(s) for
a-level
assessment.
the
participants
were chosen in
specification
specification
mathematics
three
groups;
teaching
profession;
higher
education; and
4. the appropriateness of mathematics. We
Foundation (F)
professional
bodies. an
looked at whether the answer required scientific
and Higher
(H)online survey was completed by
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
38 for chemistry;
and
this was measured
as a proportion of the total
1 Arithmetic
and numerical
F
H 32 for physics). participants from
industry
were
also
consulted more generally but as most
number of question parts containing mathematics.
computation:
science-related industries employ at a graduate level
ü
ü
a(a)subject
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group
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recognise
usewas
expressions
L4 to L8 (L4
Decimals
their comments tended to focus more on the outcomes
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sciences.
each
group analysed thedecimals
full
decimal
and
Standard
Form;
to L8
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suite of 2010 examinations papers of aQa, ccea,
standard form)
edexcel, ocr and WJec for their respective subjects
û
ü
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at a two-day workshop. examination papers included
be taken off the new
all the theory papers (Units 1, 2, 4 and 5) and the
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specification
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ü
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or 80%
use ratios,
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2
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exclusive to higher level
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1
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
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to 6 in(NB
chemistry
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mathematical
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2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
calculations (without using a calculator); students will
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
always have a
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
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calculator)
of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
63
Table 22: continued
ExEcutivE
summary
mathematics enables students to understand and
ü
ü
(d) use calculators to find and use
L4 to EP (L4
Mean
describe many scientific phenomena yet there is concern
mean,
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subject’s analytical nature. to explore whether there was
Exponential
any evidence for this concern, score investigated the
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found in biology)
mathematical requirements listed in the biology, chemistry
û
û
Standard deviation:
and physics specifications are not assessed. those that
recently removed from
are assessed are covered repeatedly and often at a lower
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û
ü
Power functions:
aims
in addition, the findings show a disparity in the way
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mathematics is assessed across the different awarding
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graphs
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these
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gather evidence on the type, functions
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of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
û
ü
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at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
students are required to
the way mathematics is assessed within the sciences to
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draw graphs of these
ensure parity across the system.
work did not compare the mathematical requirements
functions
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û differ between
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these will
the disciplines.
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simple arithmetic and algebraic
the
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transformations:
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in 2009 score published evidence on Gcse science
Algebraic
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
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work on improving the coherence between the sciences
the amount of mathematics assessed across awarding
not found in and mathematics.
organisations and confirmed that the use of mathematics
biology.)
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numbers)
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ü
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Table
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Table 22: continued
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sides of the original
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assessments.
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22: continued
mEthodology
the groups comprised practising a-level teachers,
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5 Geometry:
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proportion of the marks within these questions
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3.3.3that
PHASE
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SURVEY FINDINGS
Figure
27: out
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online
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respondents
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3.3.3.1
OFofMATHEMATICS
against 3 BIOLOGY
criteria: the number of steps in a
AT A-LEVEL
calculation, the familiarity of the context and
In Part A respondents were asked to consider the
the complexity of the question. each category
spread of mathematical content areas assessed
had varying levels of difficulty and each was
within biology A-level. Figure 27 illustrates the
measured as a proportion of the total number of
percentages of respondents that considered the
question parts containing mathematics. it was not
spread to be good, acceptable (key mathematical
measured against the number of marks.
areas were assessed), average (limited variation in
4. of
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type
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looked at whether
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of mathematics
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comprehension in addition to mathematical skill.
this waswere
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total
Participants
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the
of questionthey
partswould
containing
mathematics.
areasnumber
of mathematics
like to
feature
highly in assessment, a little or not at all. These
a subject expert group was established for each
results are displayed in Figure 28. Participants
of the three sciences. each group analysed the full
were also asked if there were any other areas of
suite of 2010 examinations papers of aQa, ccea,
mathematics not listed in the requirements that
edexcel, ocr and WJec for their respective subjects
they felt should be included in the assessments.
at a two-day workshop. examination papers included
The only area that was mentioned more than once
all the theory papers (Units 1, 2, 4 and 5) and the
was converting between different units.
mathematical content areas within a
the aim of
the third phase was to determine the nature
biology
A-level
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
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participants
The Key mathematical
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answered the survey for biology, chemistry or physics
A restricted
of in
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wereamount
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three groups; teaching profession;seemed
higher
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professional bodies. an online survey was completed by
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97 participants across the three groups
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industry were also consulted moreThere
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most
was not enough
in the type of mathematical
science-related industries employ content
at a graduate
level
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their comments tended to focus more on the outcomes
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In Part A, prior to the findings of the analysis, 74% of
respondents felt that awarding organisations should
use a framework to ensure that a broad spread of
experimental and practical papers (Units 3 and 6).
mathematical requirements are assessed and 52%
calculations were based on the assumption that theory
felt that all requirements should be assessed over
The main concern voiced by participants was the lack
papers make up 80% of the complete a-level and the
a 2- year or 3- year cycle of the A-levels to ensure
of assessment of statistics, with others expressing 2
experimental and practical papers the remaining 20% .
they are taught. A third of respondents felt that if
concern that mathematics should always be taught
areas are not assessed then it would mean that area
within a biology context. The lack of alignment
would not be taught at all. No respondents felt that
with mathematics courses also worried some
only key requirements should definitely be assessed
respondents, since this would mean some students
1 the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
as opposed to all requirements.
would
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chemistry and physics. the mathematical requirements are available in the full report.
some
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2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
Part
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some of the
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and theabout
marks from
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andshould
experimental papersIn
(Unit
3 and
make up the remaining
20%. in
the analysis,
expressed
as a query
whether
there
question parts rather than marks were used in the calculation but we maintained
the 80:20 weighting.
mathematical
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in
be
a minimum requirement set for biology A-level in
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the
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Figure 28: Mathematical
requirement areas that biology survey respondents would like to feature
ExEcutivE
summary
highly in assessment, a little in assessment or not at all
Number of Respondents
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
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Feature Highly
Feature a Little
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30
any evidence for this concern, score investigated the
type, extent25and difficulty of mathematical questions within
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20
mathematical
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15 specifications are not assessed. those that
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10
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this is likely to have an impact on
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1a 1b 1c 1d 1e 1f 1g 2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 5a 5b
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Mathematical Requirements for Biology A-Level
mathematics is assessed across the different awarding
score’s overall objective for this project was to
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of requirements were relevant so the majority of
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community about the mathematical demand of science
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qualifications, specifically that Gcse and a-level science
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qualifications are not meeting the needs of students in
clear there is a mismatch between mathematical
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limited way. score organisations felt that this was
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in understanding and describing scientific phenomena;
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fewprovide
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2
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were necessary for future study or jobs.
between physics, chemistry and biology as it is accepted
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3.3.3.2 EXTENT OF MATHEMATICS
the
findings
aim
provide
score with
evidence
In Part
A half
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respondents
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inform
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type,
amount of mathematics in the paper was extent
not
and
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theprogression
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how
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its
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appropriate (39-54% of question parts across
and
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in the project, we looked across all assessments at
mathematics varied across awarding organisations
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from 13% to 25%. The most common opinion on
practical examination papers.
these results was that differences like this across
awarding organisations were not acceptable (77%).
48% of respondents felt that 13% was too low and
no census was reached on whether the upper limit
was too low.
In Part A, when asked whether the mathematical
content in the theory papers and in the practical
papers should be different, nearly two-thirds
of respondents felt that it should be different. It
was felt that mathematical requirements were
appropriate to the topic and that the papers lent
themselves to different skills. Many cited examples
of
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mEthodology
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ocr and
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3.3.3.3
DIFFICULTY
OF MATHEMATICS
proportion
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within these questions
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mathematics.
In Part
A required
of the survey
nearly 60% of respondents
felt3.that
did not ofmatter
if the level
difficulty
of
theitdifficulty
mathematics.
thisofwas
measured
biology
A-levels
was
perceived
to
go
up
due
to
against 3 criteria: the number of steps in a
themcalculation,
containingthe
more
mathematics.
There
was a
familiarity
of the context
and
split in
opinions
from
all
three
participant
groups.
the complexity of the question. each category
had varying levels of difficulty and each was
Whenmeasured
asked about
difficulty in terms of the number
as a proportion of the total number of
of steps
in the calculations on the paper, the
question parts containing mathematics. it was not
most measured
popular opinion
(41%) was that the balance
against the number of marks.
on the sample paper was appropriate. In Part
4. the
appropriateness
of mathematics.
We
B the
participants
were told
that the majority
looked
at
whether
the
answer
required
scientific
of calculations across the examinations papers
comprehension
in
addition
to
mathematical
skill.
were single step, followed by multiple step, with
this was
measuredthe
as aleast
proportion
of thetototal
extended
calculations
likely type
number
of question
containing mathematics.
be found.
About
a third parts
of respondents
felt that
there
should
be group
more was
multiple
step and
extended
a subject
expert
established
for each
19
and
in
total
48%
of
respondents
calculations
of the three sciences. each group analysed the full felt
there
should
be an even spread
of aQa,
the three
types
suite of
2010 examinations
papers of
ccea,
of
calculation.
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
In
Part A when considering context as a measure
all the theory papers (Units 1, 2, 4 and 5) and the
of
difficulty, around two-thirds of the teachers felt
experimental and practical papers (Units 3 and 6).
that
the number of questions with mathematical
calculations were based on the assumption that theory
content
set in a familiar context was appropriate.
papers make up 80% of the complete a-level and the
There
was no agreement between the higher
experimental and practical papers the remaining 20%2.
education and professional body representatives.
In Part B respondents were told that in the analysis
of
the
papers
it was found
thata-level
between
53% and
the
groups
comprised
practising
teachers,
20
69%
ofwith
the experience
calculations
were found
to be set
teachers
in curriculum
research
andin
21
adevelopment
familiar context
. Nearly working
half of the
respondents
and individuals
for awarding
thought
that as
thismarkers,
was about
the right
amount
organisations
question
writers
or examiners.
of
mathematicsexercises
to be setwere
in aemployed
familiar context,
standardisation
throughout the
with
thetoother
there should
analysis
verifyhalf
the agreeing
reliability ofthat
judgements
within and
be
lessthe
mathematics
setgroups.
in familiar contexts so
across
subject expert
that students had more experience of applying
the second phase aimed to measure the coherence
mathematics in unfamiliar situations. However,
between the teaching and learning of mathematics
fewer than half of the respondents felt that this
and the sciences. there is an assumption that the
familiarity of context was creating a problem with
mathematical concepts used to access the sciences
progression to higher education or industry and
are first taught within a mathematical context, i.e. within
students’ ability to apply mathematics in novel
the mathematics curriculum. the project compared the
situations.
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
Respondents were asked to make a judgement on
using the current national curriculum level descriptions
the mathematical difficulty in terms of complexity
and a 2012 mathematics Gcse specification3. this work
in the paper. In Part A just over half (59%) thought
was carried out by a researcher and by a mathematics
that the complexity was appropriate, with the
teacher.
remainder considering the complexity to be
insufficient.
In third
Partphase
B, nearly
the aim of the
was three-quarters
to determine theof
nature
participants
thought
the recall
of common
of mathematics
that thethat
community
would
like to see
mathematical
procedures
should
in a-level science
assessments.
this be
wasassessed
achieved
alongside
involved application
in
through an procedures
online surveythat
for stakeholders
in the science
one
or moreDepending
mathematical
content
areas;
however,
community.
on their
expertise,
participants
the
analysis
the assessments
showed
answered
theof
survey
for biology, chemistry
or that
physics
the
vastassessment.
majority ofthe
theparticipants
mathematics
required
a-level
were
chosen in
the
of only
recall profession;
of procedures
and
relativelyand
threeuse
groups;
teaching
higher
education;
straightforward
application.
professional bodies.
an online survey was completed by
97 participants across the three groups (27 for biology;
3.3.3.4
COMPARABILITY
ACROSS
38 for chemistry;
and 32 for physics).
participants from
AWARDING
ORGANISATIONS
industry were also
consulted more generally but as most
science-related
industries
employ at
a graduate
In
Part A all of the
respondents
agreed
that level
it was
their
comments
tended
to
focus
more
on
the
important that the A-levels from all of the outcomes
awarding
at graduate level
rather
directly
to a-level.
organisations
had
thethan
same
level referring
of difficulty
in
terms of the mathematical content. When asked
about awarding organisations assessing the same
mathematical content areas, 63% felt that only
the same key areas needed to be assessed, with
30% thinking that all of the mathematical content
areas should be assessed in the same way. The
vast majority (93%) thought that the proportion of
questions with mathematical content should be
similar across the awarding organisations. 74%
1
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
19
Some respondents
supported
statements
so these
percentages
not1,represent
different
2 a complete
science a-level
is made upboth
of 6 units.
the marks
from the
theory papersdo
(Unit
2, 4 and 5)two
make
up 80%findings.
of the complete
a-level
assessment
andthe
the average
marks from
experimental
(Unit
3 and
6) make
the remaining
20%.
in theand
analysis,
20
These
figures are
of the
AS practical
and A2 and
papers
and do papers
not take
into
account
theupweighting
of the
theory
practical
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
papers.
3 the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
revisedwas
mathematics
Gcses.
21theThere
no comment
on the finding that almost 100% of the theory papers contained mathematics set in familiar contexts.
SCORE
Mathsininscience
science report
report
score
maths
3
69
of respondents
felt that awarding organisations
ExEcutivE
summary
should use a framework to ensure a broad spread
mathematics enables students to understand and
of mathematical requirements are assessed.
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
In Part B, 78% of respondents felt that the
subject’s analytical nature. to explore whether there was
difference across awarding organisations in the
any evidence for this concern, score investigated the
proportion of marks at A-level for mathematical
type, extent and difficulty of mathematical questions within
content was not acceptable.
science a-levels. the findings show that a large number of
mathematical
requirementsBETWEEN
listed in the biology, chemistry
3.3.3.5 COHERENCE
and
physics
specifications
are
notSCIENCES
assessed. those that
MATHEMATICS AND THE
are assessed are covered repeatedly and often at a lower
Respondents
were
asked
was
most
level
than required.
this
is likelywhich
to have
an the
impact
on
important
feature
of
the
mathematics
in
biology
the way that the subjects are taught and therefore on
A-levels: ability
the proportion
the paper
that
contained
students’
to have theof
necessary
skills
to progress
mathematical
content,
the
appropriateness
of the
effectively to stem higher education and employment.
mathematical
content
covered
in
the
assessments
in addition, the findings show a disparity in the way
or the difficulty
of the mathematics
in theawarding
mathematics
is assessed
across the different
assessments.
Out
of
these
choices,
organisations. score recommends that89%
there agreed
is a review
that
the
appropriateness
of
the
mathematical
of the mathematical requirements for each of the sciences
content
the assessments
was
most
at
a-level covered
and that ainframework
is developed
to the
regulate
important.
the
way mathematics is assessed within the sciences to
ensure parity across the system.
Two-thirds of participants agreed that mathematics
GCSE should be adequate preparation for the
Background
mathematics in a science A-level rather than
there
has needing
been growing
concern of
across
the science
students
the support
a separate
community
about
the
mathematical
demand
mathematics qualification. It was felt thatof science
qualifications,
specifically
Gcsebeand
a-level science
the mathematics
GCSEthat
should
adequate
qualifications
are
not
meeting
the
needs
of
students in
preparation to build on, although the mathematics
the
waybiology
they assess
thewould
analytical
of itscience.
in the
A-level
go nature
beyond
in terms
of
the
application
of
the
mathematics
in
novel
in 2009 score published evidence on Gcse science
situations.
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
3.4 VIEWS
FROM
INDUSTRY
within
the context
of science
was examined in a very
limited way. score organisations felt that this was
3.4.1 TYPE OF MATHEMATICS ASSESSED
unacceptable. mathematics is integral to the teaching
WITHIN SCIENCE A-LEVEL
and learning of the sciences, and offers a valuable aid
There
were concerns
that thescientific
mathematical
in
understanding
and describing
phenomena;
elements
did notbeproperly
prepare
studentsin for
as
such it should
appropriately
represented
the
higher education,
including
fact that
the
biology,
chemistry and
physics the
curricula
and their
mathematics needed for engineering was only
assessments.
found within the further mathematics A-level. There
to
provide
evidence
to support
theseinflation
was
also afurther
feeling
that there
was grade
concerns,
score
set
up
this
project
to
investigate
in the current science A-levels, that there
was the
mathematics
in the 2010 science
assessments
low quality infound
the mathematical
content
and that
at
a-level
the unitary
awarding organisations
there
wasacross
a problem
distinguishing
between thein
england,
Wales and
northern
(mathematical)
ability
of an ireland.
A and an A* graded
science student.
2
70
SCORE Maths
report
score
mathsininscience
science
report
The industry representatives were asked which
mathematical content areas from a given list
they felt were important in the A-level science
assessments. All areas listed (and shown below)
were felt to be important, with the subsequent
comments clarifying their opinions:
•Arithmetic and computation – an important
foundation skill
•Handling data – a vital skill for extracting
information from data
•Algebra – a crucial area, in particular rearranging
equations and using generic formulae
•Geometry – less important and only necessary
at a basic level
•Trigonometry – a lot of scientific work cannot
aims
be completed without trigonometry
score’s overall objective for this project was to
•Graphs – important to communicate data and
gather evidence on the type, extent and difficulty of
trends
mathematics required to access the sciences in current
•Application
of mathematics
– very
important,
a-level
specifications
and to establish
whether
this
if
not
vital,
needs
lots
of
practice.
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
Calculus was mentioned repeatedly as an
between physics, chemistry and biology as it is accepted
important aspect of mathematics, as it was needed
these will differ between the disciplines.
in so many careers. It was felt to be important
for students
to be
able toscore
complete
the
findings aim
to provide
withcalculations
evidence to
withoutthea development
calculator soofthat
they
a feel
inform
policy
on developed
the type, extent
for
numbers
and
could
spot
mistakes.
Complex
and difficulty of the mathematics in the criteria and
numbers, vectors,
risk assessment
and probability
assessments
for a-levels
in biology, chemistry
and
were other
of mathematics
not mentioned
physics.
theaspects
project also
supports score’s
work on
above
the industry
representatives
felttowere
how
thethat
examinations
system
should operate
ensure
important
to
A-level
science
students.
Statistics
science qualifications are fit for purpose and also its
was mentioned
half
of the representatives
work
on improvingby
the
coherence
between the sciences
because
it is commonly used in biology, in process,
and
mathematics.
design and manufacturing engineering and in the
in
the project, of
weexperiments.
looked across all assessments at
optimisation
a-level for a given year, including both experimental and
practical
examination
papers.
There was
general agreement
that the mathematics
in the science A-levels needed to go beyond that
found in mathematics GCSE and that this was not
a problem. It was felt that the mathematics only
needed to be there when the science demanded
it, but that it was necessary to go beyond
mathematics GCSE if it was to prepare students for
higher education.
3.4.2
EXTENT OF MATHEMATICS
mEthodology
theofproject
was designed
in three phases.
the
All
the industry
representatives
agreed
that it
first
was
to
establish
the
nature
of
the
mathematics
would not matter if the amount or difficulty of the
assessed within
physics
mathematics
in the
thebiology,
sciencechemistry
A-levelsand
increased,
a-level
examinations
in
2010.
the
full
suite
of
even if this resulted in the A-levels being perceived
examinations
papers from
aQa, given
ccea,included
edexcel,
to
be more difficult.
Reasons
ocr
and
WJec
were
analysed
using
the
four
that A-levels needed to be more competitive
measures that follow:
internationally,
that if the difficulty was not there
that
were ofthe
less
use to higher
1. the
theassessments
type of mathematics.
mathematical
areas
education
and
industry
and
that
if
it
deterred
a
assessed were categorised against the stated
student,
then perhaps
they should
not have
been
mathematical
requirements
for biology,
chemistry
takingand
thephysics
A-levelrespectively
anyway. It1.was recognised that,
if changes were made, that more mathematics
2. the extent
of the
mathematics.
specialist
support
may
be needed.the proportion
of the question parts within a paper that
mathematics
was measured as was the
3.4.3included
DEMAND
OF MATHEMATICS
proportion of the marks within these questions
Industry
representatives’ main concern regarding
that required mathematics.
the mathematical element of the science A-levels
3. the
theperceived
difficulty of lack
mathematics.
was
measured
was
of fluencythis
and
lack
of
criteria:students
the number
of steps
a
abilityagainst
of the 3A-level
to use
andinapply
their
calculation,
the
familiarity
of
the
context
and
mathematical knowledge in a new situation; this
the complexity
the was
question.
was problematic
asofthis
a skilleach
theycategory
would be
had
varying
levels
of
difficulty
and
each was
expected to use in work.
measured as a proportion of the total number of
parts containing
it was not
Therequestion
were concerns
that themathematics.
mathematical
measured
against
the number
marks. for
elements
did not
properly
prepareofstudents
higher
education, including the fact that the
4. the appropriateness of mathematics. We
mathematics
needed for engineering sat only within
looked at whether the answer required scientific
the further
mathematics
A-level. Lastly, there was a
comprehension in addition to mathematical skill.
feeling
that
there
was
grade
inflation in the current
this was measured as a proportion of the total
science
A-levels, that there was low quality in the
number of question parts containing mathematics.
mathematical content and that there was a problem
a subject expertbetween
group was
for each
distinguishing
theestablished
(mathematical)
ability of
of the
three
each
group analysed
full
an
A and
ansciences.
A* graded
science
student.the
Industry
suite
of
2010
examinations
papers
of
aQa,
ccea,
representatives were asked to comment on
edexcel, of
ocr
and WJec for
their respective
aspects
mathematical
difficulty
used in subjects
the Phase
at
a
two-day
workshop.
examination
papers
1 analysis of the A-level papers. Most
feltincluded
that
all the theory
papers
1, 2,mathematics
4 and 5) and in
thefamiliar
students
should
be (Units
tackling
experimental
and
practical
papers
(Units
3
and
6). be
and unfamiliar contexts; work contexts would
calculations
were
based
on
the
assumption
that
theory
unfamiliar and unfamiliar contexts differentiated
the
papers
make
up
80%
of
the
complete
a-level
and
the
difficulty in the assessments. In terms of complexity,
2
experimental
and practical
papers the remaining
most
of the industry
representatives
reported20%
that.
1
2
3
they
would comprised
like to seepractising
a mixturea-level
of calculations
the groups
teachers, that
involved
straightforward
of routine
classroom
teachers with
experience inrecall
curriculum
research
and
procedures,
those
that required
application
of
development and
individuals
working
for awarding
mathematics
within
one question
area of mathematics
and
organisations as
markers,
writers or examiners.
those
that required
application
in morethroughout
than one the
standardisation
exercises
were employed
area
of mathematics.
Whileofcalculations
analysis
to verify the reliability
judgements involving
within and
straightforward
recall
were
felt to underpin some
across the subject
expert
groups.
science, there was a perceived need to differentiate
the second phase aimed to measure the coherence
by including the more complex calculations and to
between the teaching and learning of mathematics
give a greater challenge to keep students engaged.
and the sciences. there is an assumption that the
It was reiterated that the mathematics should be
mathematical concepts used to access the sciences
what was necessary to support the science, but
are first taught within a mathematical context, i.e. within
that the science should not be ‘dumbed down’
the mathematics curriculum. the project compared the
in order to avoid the inclusion of more complex
mathematical requirements for the sciences at a-level
mathematics. All of the industry representatives
with the mathematics curriculum prior to Key stage 5
wanted to see more multiple step and extended
using the current national curriculum level descriptions
calculations than single step calculations.3
and a 2012 mathematics Gcse specification . this work
was carried out by a researcher and by a mathematics
3.4.4 PARITY ACROSS AWARDING
teacher.
ORGANISATIONS
the aim of the third phase was to determine the nature
Most of the industry representatives felt that there
of mathematics that the community would like to see
should not be differences across the awarding
in a-level science assessments. this was achieved
organisations in terms of the difficulty of the
through an online survey for stakeholders in the science
mathematics assessed, the assessed content
community. Depending on their expertise, participants
or the amount of mathematics assessed in the
answered the survey for biology, chemistry or physics
science A-levels. It was felt that variety in the
a-level assessment. the participants were chosen in
landscape of qualifications was not understood
three groups; teaching profession; higher education; and
by industry and that employers did not want to
professional bodies. an online survey was completed by
ask which awarding organisations awarded the
97 participants across the three groups (27 for biology;
qualification when assessing candidates. They
38 for chemistry; and 32 for physics). participants from
felt that aligning the mathematics element would
industry were also consulted more generally but as most
remove the temptation for awarding organisations
science-related industries employ at a graduate level
to lower standards to attract more candidates
their comments tended to focus more on the outcomes
and for schools to opt for an ‘easier’ examination.
at graduate level rather than directly referring to a-level.
One respondent felt that admissions tutors were
aware of the differences across the awarding
organisations and another that, if there were
transparent differences across the awarding
organisations in terms of mathematical content,
that it may lead to more diversity when it came
to recruitment.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
71
APPENDICES
APPENDIX summary
1: SUMMER 2010 A-LEVEL PAPERS ANALYSED
ExEcutivE
mathematics enables students to understand and
Subject
Awarding Organisation
A level
describe many scientific phenomena yet there is concern
that
science assessments at a-level are not
reflecting the
Physics
AQA
Physics A
subject’s analytical nature. to explore whether there was
CCEA the
Physics
any evidence for this concern, score investigated
type, extent and difficulty of mathematical Edexcel
questions within
Physics
science a-levels. the findings show that a large number of
OCR
Physics B
mathematical requirements listed in the biology, chemistry
WJEC
Physics
and physics specifications are not assessed.
those that
are
assessed are covered repeatedly and often
Chemistry
AQA at a lower
Chemistry
level than required. this is likely to have an impact on
CCEA
Chemistry
the way that the subjects are taught and therefore on
Edexcel
Chemistry
students’ ability to have the necessary skills
to progress
effectively to stem higher education and employment.
OCR
Chemistry A
aims
in addition, the findings show a disparity in the way
WJEC
Chemistry
mathematics is assessed across the different awarding
score’s overall objective for this project was to
Biology
organisations.
score recommends that AQA
there is a review
gather evidence onBiology
the type, extent and difficulty of
of the mathematical requirements for eachCCEA
of the sciences
mathematics required
to access the sciences in current
Biology
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
Edexcel
Biology
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
OCR
Biology
(H421)
ensure parity across the system.
work did not compare
the mathematical
requirements
Background
WJEC
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
72
SCORE Maths
report
score
mathsininscience
science
report
between physics, chemistry
Biology and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
22
APPENDIX
2: MATHEMATICAL REQUIREMENTS FOR
A-LEVEL
mEthodology
thePHYSICS
groups comprised
practising
a-level teachers,
the project was designed in three phases. the
1. Arithmetic and Computation
first was to establish the nature of the mathematics
Candidates should be able to:
assessed
within the
physics and
(a)
use a calculator
for biology,
addition, chemistry
subtraction,and
multiplication
a-level
examinations in 2010. the full suite of
division;
(b)
recognise and
use expressions
decimaledexcel,
form; (‘standard
examinations
papers
from aQa,inccea,
from’
thisanalysed
requirement
andthe
recorded
ocr
anddeleted
WJecfrom
were
using
four separately
as 1(h) to illustrate how commonly each occurred.)
measures that follow:
(c)use ratios, fractions and percentages;
n
(d)
calculators
find and use xthe
, 1/x,
x2, √x, logl0x , areas
1.usethe
type of to
mathematics.
mathematical
e x, log ex;
assessed were categorised against the stated
(e)use calculators to handle sinѲ, cosѲ, tanѲ, sin-1Ѳ, cos-1Ѳ,
mathematical requirements for biology, chemistry
tan-1Ѳ when Ѳ is expressed in degrees or radians.
1
and physics
respectively
. -12, 10-9, 10-6, 10-3, 103,
(f)recognise
and use
SI prefixes 10
106 and 109
2. the extent of the mathematics. the proportion
(g)handle calculations so that significant figures are neither lost
the question
parts
within a paper that
or of
carried
beyond what
is justified;
included
mathematics
was measured as was the
(h)standard form.
proportion of the marks within these questions
2. Handling data
thatanrequired
mathematics.
(a)show
awareness
of the order of magnitude of physical
quantities and make order of magnitude calculations;
3. the difficulty of mathematics. this was measured
(b)use an appropriate number of significant figures;
against 3 criteria: the number of steps in a
(c)find arithmetic means and medians;
calculation,
the
of and
the context
and
(d)express
changes
asfamiliarity
percentages
vice versa;
the complexity
the question.
category
(e)understand
and useoflogarithmic
scaleseach
in relation
to
quantities
whichlevels
range of
over
several and
orders
of magnitude.
had varying
difficulty
each
was
measured as a proportion of the total number of
3. Algebra
question
parts containing
mathematics.
it was
not
(a)change
the subject
of an equation
by manipulation
of the
terms,
including
positivethe
and
negative,
measured
against
number
ofinteger
marks.and fractional
indices and square roots
4.substitute
the appropriateness
mathematics.
We using
(b)
numerical valuesofinto
algebraic equations
appropriate
for physical
quantities
looked atunits
whether
the answer
required scientific
(c)check
the dimensional
physical equations
comprehension
in consistency
addition to of
mathematical
skill.
and substitute numerical values into such equations using
this was measured as a proportion of the total
appropriate units for physical quantities;
number of question parts containing mathematics.
(d) solve simple algebraic equations including y=k/x, y=k/x2
(e)
formulate
and use
simple
algebraic
equations
as
a subject
expert
group
was
established
for each
mathematical models of physical situations, and identify the
of the three sciences. each group analysed the full
inadequacy of such models
suite of 2010 examinations papers of aQa, ccea,
(f)understand and use the symbols: <, <<, >>, >, ~, , ∑, ∆x,
edexcel,
ocr and WJec for their respective subjects
x, dx/dt
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
teachers with experience in curriculum research and
4. Geometry and Trigonometry
development and individuals working for awarding
(a)calculate areas of triangles, circumferences and areas of
organisations as markers, question writers or examiners.
circles, surface areas and volumes of rectangular blocks,
standardisation
exercises were employed throughout the
cylinders and spheres;
analysis
to
verify
the
reliability
of judgements
and
(b)use Pythagoras’
theorem,
similarity
of triangleswithin
and the
angle
sum
of
a
triangle;
across the subject expert groups.
(c)use sines, cosines and tangents in physical problems;
theuse
second
measure
coherence
(d)
sinѲ ≈phase
tanѲ ≈aimed
Ѳ andto
cos
Ѳ ≈ 1 forthe
small
Ѳ;
between
the teaching
and learning
mathematics
(e)
understand
the relationship
betweenofdegrees
and radians
from
one to
other.
andand
thetranslate
sciences.
there
is the
an assumption
that the
mathematical
concepts used to access the sciences
5.
Graphs
(a)
information
graphical,
numerical
are translate
first taught
within abetween
mathematical
context,
i.e.and
within
algebraic
forms;
the mathematics curriculum. the project compared the
(b)plot two variables from experimental or other data using
mathematical requirements for the sciences at a-level
appropriate scales for graph plotting;
with the mathematics curriculum prior to Key stage 5
(c)plot data on a log-linear graph and determine whether they
using
the current
national
level
descriptions
change
exponentially
andcurriculum
determine the
exponent;
3
andplot
a 2012
mathematics
Gcse
. this
(d)
data on
a log-log graph
and specification
decide whether
data work
obey
power law
the exponent;
wasacarried
outand
by determine
a researcher
and by a mathematics
(e)
select appropriate variables for graph plotting;
teacher.
(f)understand that y = mx + c represents a linear relationship
theand
aimrearrange
of the third
phase was
determine
nature
relationships
intoto
this
form wherethe
appropriate;
(g)
determine the that
slopethe
/ gradient
and intercept
of a to
linear
of mathematics
community
would like
see
graph in
the appropriate
physicalthis
units;was achieved
in a-level
science
assessments.
(h)determine the gradient of a tangent to a non-linear graph by
through an online survey for stakeholders in the science
drawing and use the slope of the tangent as a measure of
community.
Depending on their expertise, participants
rate of change;
answered
survey fora biology,
chemistry
physics
(i)
choose the
by inspection
straight line
or curvedorline
which will
serveassessment.
as the best straight
line through were
a set of
data points
a-level
the participants
chosen
in
presented
three
groups;graphically;
teaching profession; higher education; and
(j)understand the possible physical significance of the area
professional bodies. an online survey was completed by
between a curve and the x axis and be able to calculate it or
97 participants
across the three groups (27 for biology;
measure it by counting squares as appropriate;
38
for
chemistry;
physics).
participants
(k)understand andand
use 32
the for
slope
of a tangent
to a curvefrom
as
industry
were
also
consulted
more
generally
butuse
asthe
most
a means to obtain the gradient. Understand and
notation d/dt for
a rate of employ
change; at a graduate level
science-related
industries
(l)
understand
and
use
multiplicative
scales
10,outcomes
100...);
their comments tended to focus more
on(1,the
(m)use logarithmic plots to test exponential and power law
at graduate level rather than directly referring to a-level.
variations;
(n)sketch simple functions including y = k/x, y = kx2 y = k/x2, y
= sinѲ, y = cosѲ, y = e-kx.
(o)understand or recognise the physical significance of a
straight line passing or not passing through the origin.
1
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
2 a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
22During the course of the research it was established that the awarding organisations adapted the mathematical requirements
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
set byparts
Ofqual.
represent
an amalgamation
the
used by the awarding organisations, linked
question
ratherThis
thanlist
marks
were used
in the calculationof
but
wemathematical
maintained the requirements
80:20 weighting.
3 theclosely
thataset
by Ofqual.
The
text
red
represents
changes
made
to the list of
during
analysis
in
edexcelto2012
specification
was
used
forinthe
purpose
of the additions
analysis asand
it was
considered
representative
typicalthe
content
foundprocess
in
theorder
revisedtomathematics
Gcses.
more accurately
capture the mathematical content.
SCORE
Mathsininscience
science report
report
score
maths
3
73
APPENDIX summary
3: MATHEMATICAL REQUIREMENTS FOR CHEMISTRY A-LEVEL22
ExEcutivE
mathematics
enables
students
to understand and
1 Arithmetic and
numerical
computation:
describe
many
scientific
phenomena
yet there
(a)recognise
and
use expressions
in decimal
and is concern
thatstandard
science form;
assessments at a-level are not reflecting the
(b) use ratios,
fractions
and percentages;
subject’s
analytical
nature.
to explore whether there was
(c)make estimates of the results of calculations
any evidence for this concern, score investigated the
(without using a calculator);
type,
extent and difficulty of mathematical questions within
(d)use calculators to find and use power, exponential
science
a-levels. the
findings
that
number
and logarithmic
functions
(xn, show
1/x, √x,
loga
xlarge
, e x, log
x); of
l0
e
mathematical
(e) +, -, x, ÷. requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
2 Handling
data:
are
assessed
are covered repeatedly and often at a lower
(a) use an appropriate number of significant figures;
level than required. this is likely to have an impact on
(b) find arithmetic means;
the
that the
are taughttables
and and
therefore
on
(c)way
construct
and subjects
interpret frequency
diagrams,
students’
ability
have the necessary skills to progress
bar charts
andtohistograms;
(d) use an to
appropriate
number
of decimal
places.
effectively
stem higher
education
and
employment.
in addition, the findings show a disparity in the way
3 Algebra:
mathematics is assessed across the different awarding
(a)understand and use the symbols: =, <, <<, >>, >, ,
organisations.
score recommends that there is a review
~, μ;
of
the
mathematical
for each of the sciences
(b) change the subjectrequirements
of an equation;
at
a-level
andnumerical
that a framework
developed
to regulate
(c)
substitute
values intoisalgebraic
equations
using
appropriate
units
for
physical
quantities;
the way mathematics is assessed within the sciences to
(d) solve
simple
algebraic
ensure
parity
across
the equations;
system.
(e)use logarithms in relation to quantities which range
over several orders of magnitude.
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
74
SCORE Maths
report
score
mathsininscience
science
report
4 Graphs:
(a)translate and interpret information between graphical,
numerical and algebraic forms;
(b) plot two variables from experimental or other data;
(c)understand that y = mx + c represents a linear relationship;
(d) determine the slope and intercept of a linear graph;
(e)calculate rate of change from a graph showing a linear
relationship;
(f)draw and use the slope of a tangent to a curve as a
measure of rate of change;
(g) interpret a spectrum.
5 Geometry and trigonometry:
a)appreciate angles and shapes in regular 2-D and 3-D
structures;
b)visualise and represent 2-D and 3-D forms including
aims
two-dimensional representations of 3-D objects;
c) understand the symmetry of 2-D and 3-D shapes.
score’s overall objective for this project was to
gather evidence on the type, extent and difficulty of
mathematics required to access the sciences in current
a-level specifications and to establish whether this
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
22
APPENDIX
4: MATHEMATICAL REQUIREMENTS FOR
A-LEVEL
mEthodology
theBIOLOGY
groups comprised
practising
a-level teachers,
the project was designed in three phases. the
1 Arithmetic and numerical computation:
first was to establish the nature of the mathematics
(arecognise and use expressions in decimal and
assessed
standardwithin
form; the biology, chemistry and physics
a-level
examinations
in 2010.
the
suite of
(b)
calculate
or use ratios,
fractions
andfull
percentages;
(c)
make estimates
of the
results
of calculations
examinations
papers
from
aQa,
ccea, edexcel,
(without
using awere
calculator);
ocr
and WJec
analysed using the four
(d)use calculators to find and use mean, standard
measures that follow:
deviations, power, exponential and logarithmic functions;
(e)
calculations
involving simplethe
arithmetic
and
1.usethe
type of mathematics.
mathematical
areas
algebraic transformations:
assessed were categorised against the stated
(f)understand and use correlations;
mathematical requirements for biology, chemistry
(g) +, -, x, ÷.
and physics respectively1.
2 Handling data:
2. the extent of the mathematics. the proportion
(a) use an appropriate number of significant figures;
ofarithmetic
the question
parts within a paper that
(b) find
means;
included
mathematics
measured
was the
(c)construct or interpret tables,was
frequency
tablesas
and
diagrams,
bar charts
histograms;
proportion
of the and
marks
within these questions
(d) understand
simple
probability;
that required
mathematics.
(e)understand the principles of sampling as applied
3.to the
difficulty
scientific
data;of mathematics. this was measured
(f)understand
terms mean,
medianofand
mode
against 3the
criteria:
the number
steps
in and
a
standard
deviation;
calculation, the familiarity of the context and
(g)use a scatter diagram to identify positive and negative
the complexity of the question. each category
correlation between two variables;
had varying levels of difficulty and each was
(h) select and use a simple statistical test;
measured
a proportion
of the total number of
(i) make
order of as
magnitude
calculations;
questionand
parts
containing
mathematics.
it was not
(j)determine
interpret
population
variance, standard
deviation
and standard
deviation
(error)
the mean;
measured
against the
number
of of
marks.
(k)understand probability in order to understand how
4.genetic
the appropriateness
of mathematics. We
ratios arise;
(l) frame
null hypothesis.
looked
at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
teachers with experience in curriculum research and
3 Algebra:
development and individuals working for awarding
(a) change the subject of an equation;
organisations as markers, question writers or examiners.
(b)substitute numerical values into algebraic equations
standardisation
exercises
employed
throughout the
using appropriate
units forwere
physical
quantities;
analysis
to
verify
the
reliability
of
judgements
within and
(c)understand the use of logarithms in relation to quantities
that
range
over
several
orders
of
magnitude;
across the subject expert groups.
(d)derive an equation;
the=,second
(e)
<, >. phase aimed to measure the coherence
between the teaching and learning of mathematics
4
Graphs:
and
the sciences. there is an assumption that the
(a)
translate information
and
mathematical
conceptsbetween
used tographical,
access numerical
the sciences
algebraic forms;
are first taught within a mathematical context, i.e. within
(b) plot two variables from experimental or other data;
the calculate
mathematics
project
compared
(c)
rate ofcurriculum.
change fromthe
a graph
showing
a linearthe
mathematical
relationship;requirements for the sciences at a-level
(d)
and use the slope
of a tangent
to to
a curve
as a 5
withdraw
the mathematics
curriculum
prior
Key stage
measure
of ratenational
of change;
using
the current
curriculum level descriptions
(e) construct and / or interpret line graphs.
3
and a 2012 mathematics Gcse specification . this work
was
carried out by a researcher and by a mathematics
5 Geometry:
teacher.
(a)visualise three dimensional forms from two dimensional
representations of three dimensional objects;
the aim of the third phase was to determine the nature
(b)calculate circumferences and areas of circles, surface
of mathematics
that of
theregular
community
would
like towhen
see
areas and volumes
blocks and
cylinders
in a-level
science
assessments.
this
was
achieved
provided with appropriate formulae.
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
75
APPENDIX summary
5a: EXAMPLES OF MATHEMATICAL QUESTIONS WITHIN A SCIENCE A-LEVEL OF
ExEcutivE
A SINGLE STEP CALCULATION, A MULTIPLE STEP CALCULATION AND AN EXTENDED STEP
mathematics enables
students to understand and
CALCULATION23
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
SINGLE STEP CALCULATION
any evidence for this concern, score investigated the
type,
extent
andCCEA
difficultyAY111
of mathematical
questions
Taken
from:
(AS/1) 21
Jun 11within
7(b)(iii)
science
a-levels. the
findings
show that ausing
large definition
number of of e.m.f.
Straightforward
one-line
calculation
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
23These examples are for physics only; chemistry and biology will be added at a later date
2
76
SCORE Maths
report
score
mathsininscience
science
report
MULTIPLE
STEP CALCULATION
mEthodology
the groups comprised practising a-level teachers,
teachers with experience in curriculum research and
the project
was
designed
in three
phases.
the 11 5(b)
Taken
from:
CCEA
AY111
(AS/1)
21 Jun
development and individuals working for awarding
first was to because
establish the
nature of the
mathematics
Multi-step
(i) Equation
must
be constructed; (ii) solved algebraically for square root to give speed
organisations as markers, question writers or examiners.
assessed within the biology, chemistry and physics
standardisation exercises were employed throughout the
a-level examinations in 2010. the full suite of
analysis to verify the reliability of judgements within and
examinations papers from aQa, ccea, edexcel,
across the subject expert groups.
ocr and WJec were analysed using the four
measures that follow:
the second phase aimed to measure the coherence
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
77
EXTENDEDsummary
STEP CALCULATION
ExEcutivE
Taken from:
CCEAstudents
AY111to(AS/1)
21 Jun
mathematics
enables
understand
and11 9(b)(iii)
Extended
calculation
theyetvalue
cross-sectional area found in an earlier part of the question
describe
many
scientific because
phenomena
thereof
is concern
has science
to be combined
with
value of
fromthe
the graph to give a value of the resistivity
that
assessments
at a-level
aregradient
not reflecting
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
78
SCORE Maths
report
score
mathsininscience
science
report
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
mEthodology
EXTENDED
STEP CALCULATION continued
the project was designed in three phases. the
first was to establish the nature of the mathematics
assessed within the biology, chemistry and physics
a-level examinations in 2010. the full suite of
examinations papers from aQa, ccea, edexcel,
ocr and WJec were analysed using the four
measures that follow:
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
the groups comprised practising a-level teachers,
teachers with experience in curriculum research and
development and individuals working for awarding
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
analysis to verify the reliability of judgements within and
across the subject expert groups.
the second phase aimed to measure the coherence
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
79
ExEcutivE
EXTENDEDsummary
STEP CALCULATION continued
mathematics enables students to understand and
describe many scientific phenomena yet there is concern
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
organisations. score recommends that there is a review
of the mathematical requirements for each of the sciences
at a-level and that a framework is developed to regulate
the way mathematics is assessed within the sciences to
ensure parity across the system.
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
80
SCORE Maths
report
score
mathsininscience
science
report
aims
score’s overall objective for this project was to
gather evidence on the type, extent and difficulty of
mathematics required to access the sciences in current
a-level specifications and to establish whether this
was being appropriately met by the assessments. the
work did not compare the mathematical requirements
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
APPENDIX
5b: EXAMPLES OF MATHEMATICAL QUESTIONS
WITHIN Apractising
SCIENCE
A-LEVEL
OF A
mEthodology
the groups comprised
a-level
teachers,
LEVEL
1,
LEVEL
2
AND
LEVEL
3
teachers
with
experience
in
curriculum
research
and
the project was designed in three phases. the
development and individuals working for awarding
first was to establish the nature of the mathematics
organisations as markers, question writers or examiners.
assessed within the biology, chemistry and physics
LEVEL 1
standardisation exercises were employed throughout the
a-level examinations in 2010. the full suite of
analysis to verify the reliability of judgements within and
Taken
from:papers
CCEAfrom
AY121
Jun 11 2(a)
examinations
aQa,(AS/1)
ccea,27
edexcel,
This
a straightforward
application
of four
a standard formulaacross the subject expert groups.
ocrisand
WJec were analysed
using the
measures that follow:
the second phase aimed to measure the coherence
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
81
LEVEL 2 summary
ExEcutivE
Taken from:
CCEAstudents
AY211to(A2/1)
24 May
mathematics
enables
understand
and 2011 6(b)
This requires
of algebra
and
careful application to follow through the calculation correctly
describe
many understanding
scientific phenomena
yet there
is concern
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
Background
LEVEL 3
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
there has been growing concern across the science
the findings aim to provide score with evidence to
Taken from:
CCEA
AY221 (A2/2)
6 Junof 2011
6(b)
community
about
the mathematical
demand
science
inform
the development
on the
type,
This requiresspecifically
understanding
of algebra
and trigonometry
and decision
on how of
topolicy
proceed
with
theextent
solution
qualifications,
that Gcse
and a-level
science
and difficulty of the mathematics in the criteria and
qualifications are not meeting the needs of students in
assessments for a-levels in biology, chemistry and
the way they assess the analytical nature of science.
physics. the project also supports score’s work on
how the examinations system should operate to ensure
in 2009 score published evidence on Gcse science
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
work on improving the coherence between the sciences
the amount of mathematics assessed across awarding
and mathematics.
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
82
SCORE Maths
report
score
mathsininscience
science
report
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
APPENDIX
5c: EXAMPLES OF MATHEMATICAL QUESTIONS
WITHIN Apractising
SCIENCE
A-LEVEL
mEthodology
the groups comprised
a-level
teachers,
OF
A
LEVEL
1,
LEVEL
2
AND
LEVEL
3
CONTEXT
teachers
with
experience
in
curriculum
research
and
the project was designed in three phases. the
development and individuals working for awarding
first was to establish the nature of the mathematics
organisations as markers, question writers or examiners.
assessed within the biology, chemistry and physics
LEVEL 1
standardisation exercises were employed throughout the
a-level examinations in 2010. the full suite of
Taken
from:papers
CCEAfrom
AY221
Jun 2011 6(a)(i) analysis to verify the reliability of judgements within and
examinations
aQa,(A2/2)
ccea,6edexcel,
subject
groups.
On
this
specification,
candidates
have calculated across
V/d asthe
part
of theexpert
learning
programme
ocr
and
WJec were analysed
usingshould
the four
measures that follow:
the second phase aimed to measure the coherence
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
83
LEVEL 2 summary
ExEcutivE
Taken from:
CCEAstudents
AY111to(AS/1)
21 Jun
mathematics
enables
understand
and11 5(a)(i)
Efficiency
calculations
and ratios yet
arethere
not that
routine in the context (of bouncing balls)
describe
many
scientific phenomena
is concern
that science assessments at a-level are not reflecting the
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
LEVEL 3
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
Takenparity
from:
WJEC
ensure
across
the 1324/01
system. (PH4) 21 Jun 11 5(b)(ii)(I)work did not compare the mathematical requirements
It is highly unlikely that the graph and the specific analysis
will have
been chemistry
met before
between
physics,
and biology as it is accepted
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
84
SCORE Maths
report
score
mathsininscience
science
report
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
APPENDIX
5d: EXAMPLES OF MATHEMATICAL QUESTIONS
WITHIN Apractising
SCIENCE
A-LEVEL
mEthodology
the groups comprised
a-level
teachers,
WHERE
ALL
MARKS,
SOME
OF
THE
MARKS,
NONE
OF
MARKS
REQUIRE
SCIENTIFIC
teachers
with
experience
in
curriculum
research
and
the project was designed in three phases. the
COMPREHENSION
ADDITION
TO MATHEMATICAL
SKILL and individuals working for awarding
development
first was to establish theIN
nature
of the mathematics
organisations as markers, question writers or examiners.
assessed within the biology, chemistry and physics
a-level examinations in 2010. the full suite of
Taken
from:papers
2010 OCR
Physics
B edexcel,
(G491) Unit 1 2a analysis to verify the reliability of judgements within and
examinations
from aQa,
ccea,
across
subject expert
This
both
recall
of theusing
scientific
definition of stress
and the
calculation
of thegroups.
quotient
ocrrequires
and WJec
were
analysed
the four
measures that follow:
the second phase aimed to measure the coherence
ALL MARKS REQUIRE SCIENTIFIC COMPREHENSION
standardisation exercises were employed throughout the
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
4. the appropriateness of mathematics. We
looked at whether the answer required scientific
comprehension in addition to mathematical skill.
this was measured as a proportion of the total
number of question parts containing mathematics.
a subject expert group was established for each
of the three sciences. each group analysed the full
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
professional bodies. an online survey was completed by
97 participants across the three groups (27 for biology;
38 for chemistry; and 32 for physics). participants from
industry were also consulted more generally but as most
science-related industries employ at a graduate level
their comments tended to focus more on the outcomes
at graduate level rather than directly referring to a-level.
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
85
SOME OF THE
MARKS REQUIRE SCIENTIFIC COMPREHENSION
ExEcutivE
summary
Taken from:
CCEAstudents
AY211to(A2/1)
24 May
mathematics
enables
understand
and 2011 9(a)(i)
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pressing
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describe
scientific
phenomena
yet there
is ‘lg’
concern
understanding
of the physics,
derived
the question
stem, and the unit has got to be checked as correct
that
science assessments
at a-level
are notfrom
reflecting
the
subject’s analytical nature. to explore whether there was
any evidence for this concern, score investigated the
type, extent and difficulty of mathematical questions within
science a-levels. the findings show that a large number of
mathematical requirements listed in the biology, chemistry
and physics specifications are not assessed. those that
are assessed are covered repeatedly and often at a lower
level than required. this is likely to have an impact on
the way that the subjects are taught and therefore on
students’ ability to have the necessary skills to progress
effectively to stem higher education and employment.
aims
in addition, the findings show a disparity in the way
mathematics is assessed across the different awarding
score’s overall objective for this project was to
organisations. score recommends that there is a review
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
a-level specifications and to establish whether this
the way mathematics is assessed within the sciences to
was being appropriately met by the assessments. the
ensure parity across the system.
work did not compare the mathematical requirements
Background
there has been growing concern across the science
community about the mathematical demand of science
qualifications, specifically that Gcse and a-level science
qualifications are not meeting the needs of students in
the way they assess the analytical nature of science.
in 2009 score published evidence on Gcse science
examination papers which reported a wide variation in
the amount of mathematics assessed across awarding
organisations and confirmed that the use of mathematics
within the context of science was examined in a very
limited way. score organisations felt that this was
unacceptable. mathematics is integral to the teaching
and learning of the sciences, and offers a valuable aid
in understanding and describing scientific phenomena;
as such it should be appropriately represented in the
biology, chemistry and physics curricula and their
assessments.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
2
86
SCORE Maths
report
score
mathsininscience
science
report
between physics, chemistry and biology as it is accepted
these will differ between the disciplines.
the findings aim to provide score with evidence to
inform the development of policy on the type, extent
and difficulty of the mathematics in the criteria and
assessments for a-levels in biology, chemistry and
physics. the project also supports score’s work on
how the examinations system should operate to ensure
science qualifications are fit for purpose and also its
work on improving the coherence between the sciences
and mathematics.
in the project, we looked across all assessments at
a-level for a given year, including both experimental and
practical examination papers.
SOME
OF THE MARKS REQUIRE SCIENTIFIC COMPREHENSION
continued
mEthodology
the groups comprised
practising a-level teachers,
the project was designed in three phases. the
first was to establish the nature of the mathematics
assessed within the biology, chemistry and physics
a-level examinations in 2010. the full suite of
examinations papers from aQa, ccea, edexcel,
ocr and WJec were analysed using the four
measures that follow:
1. the type of mathematics. the mathematical areas
assessed were categorised against the stated
mathematical requirements for biology, chemistry
and physics respectively1.
2. the extent of the mathematics. the proportion
of the question parts within a paper that
included mathematics was measured as was the
proportion of the marks within these questions
that required mathematics.
3. the difficulty of mathematics. this was measured
against 3 criteria: the number of steps in a
calculation, the familiarity of the context and
the complexity of the question. each category
had varying levels of difficulty and each was
measured as a proportion of the total number of
question parts containing mathematics. it was not
measured against the number of marks.
teachers with experience in curriculum research and
development and individuals working for awarding
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
analysis to verify the reliability of judgements within and
across the subject expert groups.
the second phase aimed to measure the coherence
between the teaching and learning of mathematics
and the sciences. there is an assumption that the
mathematical concepts used to access the sciences
are first taught within a mathematical context, i.e. within
the mathematics curriculum. the project compared the
mathematical requirements for the sciences at a-level
with the mathematics curriculum prior to Key stage 5
using the current national curriculum level descriptions
and a 2012 mathematics Gcse specification3. this work
was carried out by a researcher and by a mathematics
teacher.
the aim of the third phase was to determine the nature
of mathematics that the community would like to see
in a-level science assessments. this was achieved
through an online survey for stakeholders in the science
community. Depending on their expertise, participants
answered the survey for biology, chemistry or physics
a-level assessment. the participants were chosen in
three groups; teaching profession; higher education; and
4. the
appropriateness
mathematics.
We
NONE
OF
THE MARKSofREQUIRE
SCIENTIFIC
COMPREHENSION
professional bodies. an online survey was completed by
looked at whether the answer required scientific
Taken from: WJEC 1321/01 (PH1) 24 May 2011 5(b)(i)
97 participants across the three groups (27 for biology;
comprehension in addition to mathematical skill.
Calculation of the area of a circle - no physics required
38 for chemistry; and 32 for physics). participants from
this was measured as a proportion of the total
industry were also consulted more generally but as most
number of question parts containing mathematics.
science-related industries employ at a graduate level
a subject expert group was established for each
their comments tended to focus more on the outcomes
of the three sciences. each group analysed the full
at graduate level rather than directly referring to a-level.
suite of 2010 examinations papers of aQa, ccea,
edexcel, ocr and WJec for their respective subjects
at a two-day workshop. examination papers included
all the theory papers (Units 1, 2, 4 and 5) and the
experimental and practical papers (Units 3 and 6).
calculations were based on the assumption that theory
papers make up 80% of the complete a-level and the
experimental and practical papers the remaining 20%2.
1
2
3
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
87
APPENDIX summary
6: FRAMEWORK FOR ANALYSING A-LEVEL THEORY AND PRACTICAL PAPERS
ExEcutivE
mEthodology
the groups comprised practising a-level teachers,
teachers with experience in curriculum research and
development and individuals working for awarding
organisations as markers, question writers or examiners.
standardisation exercises were employed throughout the
analysis to verify the reliability
of judgements
within and
AS or
A2:
across the subject expert groups.
the project was designed in three phases. the
mathematics enables students to understand and
first was to establish the nature of the mathematics
describe
many
scientificFRAMEWORK
phenomena yet there is concern
THEORY
PAPERS
assessed within the biology, chemistry and physics
that science assessments at a-level are not reflecting the
a-level examinations in 2010. the full suite of
subject’s analytical nature. to explore whether there was
examinations papers from aQa, ccea,
edexcel,
Awarding
Body:
Unit:
Specification:
Date:
any evidence for this concern, score investigated the
ocr
and
WJec
were
analysed
using
the
four
type, extent and difficulty of mathematical questions within
measures
that follow:
Question
Appropriateness:
does
it number
Relationship
of the
Number
Type of
Complexity
Number
Are the associated marks
forphase aimedFamiliarity
science
a-levels. the
findings show that
a large
of
thepurely
second
to measure the coherence
number andrequirements
reflect how
mathematics
mathematics to the question
of steps
mathematics of
of marks the mathematical
mathematicsareas
skills or dobetween
they require
of learning
contextof mathematics
mathematical
listed
in the biology,inchemistry
the teaching and
1. task
the type of mathematics.
partphysics specifications
scienceare
is used
in the real
that
require
scientific
comprehension
and
not assessed.
those that
and
the
sciences.
there
is
an
assumption that the
assessed were categorised against the stated
world? repeatedly and often at a lower
mathematics
are assessed are covered
mathematical
concepts
used
to
access the sciences
mathematical requirements for biology, chemistry
1
level than required. this is likely to have an impact on
are
first
taught
within
a
mathematical
context, i.e. within
and physics respectively .
the way that the subjects are taught and therefore on
the mathematics curriculum. the project compared the
Yes
No
Structural part Tagged on
single
multi
Extended
12.tothe
4 extent of the mathematics.Mathematics
both
1
2
3
the proportion Scientific
students’ ability to have the necessary skills to progress
mathematical requirements for the sciences at a-level
calculation
skills that
comp
of the question parts within a paper
effectively to stem higher education and employment.
with the mathematics curriculum prior to Key stage 5
included
mathematics
was
measured
as
was
the
aims
in addition, the findings show a disparity in the way
using the current national curriculum level descriptions
proportion
of
the
marks
within
these
questions
mathematics is assessed across the different awarding
and a 2012 mathematics Gcse specification3. this work
score’s overall objective for this project was to
that
required
mathematics.
organisations. score recommends that there is a review
was carried out by a researcher and by a mathematics
gather evidence on the type, extent and difficulty of
of the mathematical requirements for each of the sciences
teacher.
3. the difficulty of mathematics. this was measured
mathematics required to access the sciences in current
at a-level and that a framework is developed to regulate
against 3 criteria: the number of steps in a
a-level specifications and to establish whether this
the aim of the third phase was to determine the nature
the way mathematics is assessed within the sciences to
calculation, the familiarity of the context and
was being appropriately met by the assessments. the
of mathematics that the community would like to see
ensure parity across the system.
the complexity of the question. each category
work did not compare the mathematical requirements
in a-level science assessments. this was achieved
had varying levels of difficulty and each was
between physics, chemistry and biology as it is accepted
through an online survey for stakeholders in the science
Background
measured as a proportion of the total number of
these will differ between the disciplines.
community. Depending on their expertise, participants
question parts containing mathematics. it was not
there has been growing concern across the science
answered the survey for biology, chemistry or physics
the findings aim to provide score with evidence to
measured against the number of marks.
community about the mathematical demand of science
a-level assessment. the participants were chosen in
inform the development of policy on the type, extent
qualifications, specifically that Gcse and a-level science
three groups; teaching profession; higher education; and
4. the appropriateness of mathematics. We
and difficulty of the mathematics in the criteria and
qualifications
are
not
meeting
the
needs
of
students
in
professional bodies. an online survey was completed by
PRACTICAL PAPERS FRAMEWORK
looked at whether the answer required scientific
assessments for a-levels in biology, chemistry and
the way they assess the analytical nature of science.
97 participants across the three groups (27 for biology;
comprehension
in
addition
to
mathematical
skill.
physics. the project also supports score’s work on
38 for chemistry; and 32 for physics). participants from
this was measured as a proportion of the total
how the examinations system should operate to ensure
inAwarding
2009 score
published evidence on Gcse science
Body:
Unit:
Specification:
Date:
AS
or A2:
industry were also consulted
more
generally but as most
number of question parts containing mathematics.
science qualifications are fit for purpose and also its
examination papers which reported a wide variation in
science-related industries employ at a graduate level
work on improving the coherence between the sciences
the
amount of mathematics
a subject expert
group
wasfor
established
for each Comments
Question
Number assessed across awarding
Type of
Complexity
Number
Familiarity
Associated
marks
purely
mathematics
their comments tended to focus more on the outcomes
and mathematics.
organisations
confirmed
thethey
threerequire
sciences.
each group
analysed the full
number andand of
steps that the use of mathematics mathematics of task
of marks
of context
orofdo
scientific
comprehension
at graduate level rather than directly referring to a-level.
within
context of science was examined in a very
suite of 2010 examinations papers of aQa, ccea,
part /the
section
require
in the project, we looked acrossthat
all assessments
at
limited way. score organisations felt that this was
edexcel, ocr and WJec for their respective subjects
mathematics
a-level for a given year, including
both experimental and
unacceptable. mathematics is integral to the teaching
at a two-day workshop. examination papers included
practical examination papers.
and learning of the sciences, and offers a valuable aid
all the theory papers (Units 1, 2, 4 and 5) and the
single
Extended
1 to 4
1
2
3
Mathematics
Scientific
both
in understanding and
describingmulti
scientific phenomena;
experimental and
practical papers
(Units 3 and 6).
skills
comp
as such it should be appropriately representedcalculation
in the
calculations were
based on the assumption that theory
biology, chemistry and physics curricula and their
papers make up 80% of the complete a-level and the
assessments.
experimental and practical papers the remaining 20%2.
to provide further evidence to support these
concerns, score set up this project to investigate the
mathematics found in the 2010 science assessments
at a-level across the unitary awarding organisations in
england, Wales and northern ireland.
1
2
3
2
88
SCORE Maths
report
score
mathsininscience
science
report
the five awarding organisations use the mathematical requirements defined by ofqual in developing their specifications for biology,
chemistry and physics. the mathematical requirements are available in the full report.
a complete science a-level is made up of 6 units. the marks from the theory papers (Unit 1, 2, 4 and 5) make up 80% of the complete
a-level assessment and the marks from the practical and experimental papers (Unit 3 and 6) make up the remaining 20%. in the analysis,
question parts rather than marks were used in the calculation but we maintained the 80:20 weighting.
the edexcel 2012 a specification was used for the purpose of the analysis as it was considered representative of typical content found in
the revised mathematics Gcses.
SCORE
Mathsininscience
science report
report
score
maths
3
89
APPENDIX 7: ACKNOWLEDGEMENTS
WORKING GROUP
Charles Tracy
Martin Smith
Kay Stephenson
Clare Thomson
Alice Rogers
Rosalind Mist
Rachel Lambert-Forsyth
Michael Reiss
Mario Moustras
John Bentham
Erica Tyson
Ellen Weavers
Mary Ratcliff
David Swinscoe
Niall MacKay
OTHER ACKNOWLEDGEMENTS AND THANKS
Geoffrey Wake
Tandi Clausen May
Jerry McCarthy
Peter Hall
Stu Lloyd
All those involved in analysing the A-level papers, with particular thanks to:
David Peet
Tony Tooth
David James
Laurie Mansfield
Ginny Hales
Stu Billington
All those involved in completing the survey or questionnaire from teachers, HE representatives,
representatives from Professional Bodies and industry representatives
PROJECT TEAM
Clare Green
90
SCORE Maths in science report
Fiona Miller
Tamsin Barton