A level reform
Position statement
16 May 2013
1
Introduction
ACME is keen to ensure that any newly-introduced qualifications, or changes to existing
qualifications, do not lead to a decline in the numbers taking mathematical subjects at AS and A
level. The last major reform of A level mathematics in 2000 had a significant negative impact on
the engagement of young people with mathematics post 16. Urgent revisions were required in
2002 in order to address these issues. 1
This position statement has been produced as a response to the Secretary of State for
Education’s announcement of 22 January 2013 on the reform of A levels 2 and subsequent
correspondence with Ofqual. 3 The paper focuses on the impact these reforms on the Secretary
of State’s goal that within a decade, ‘the vast majority of pupils are studying maths right through
to the age of 18’. 4
The current proposals set out that:
(1)
(2)
(3)
(4)
AS levels would be standalone qualifications and not contribute to A level grades
A levels would be linear, with all examinations taken in the same assessment window
there would be increased synoptic assessment
the first tranche new qualifications would be ready for first teaching in 2015.
In this position statement we identify the extent that the A level reforms may impact negatively
on the take-up of AS and A level qualifications in Mathematics and Further Mathematics and
propose ways of minimising these risks.
1
Hodgson, A. & Spours, K. Beyond A-levels: Curriculum 2000 and the Reform of 14-19 Qualifications,
Routledge.
2
http://media.education.gov.uk/assets/files/pdf/l/ofqual%20letter%20alevels%20v2.pdf
3
http://www.education.gov.uk/childrenandyoungpeople/youngpeople/qandlearning/alevels;
http://www.ofqual.gov.uk/files/2013-03-22-letter-to-secretary-of-state-for-education-alevel-reform.pdf
4
http://www.acme-uk.org/news/news-items-repository/2011/6/speech-from-the-education-secretarymichael-gove-on-mathematics-and-science-education
1
2
Background
2.1 The impact of Curriculum 2000
Curriculum 2000 involved modest changes to the core content of A level Mathematics,
alongside a reduction in the level of challenge of other subjects. Coupled with the general
expectation that students would study four rather than three subjects in their first year, AS level
Mathematics pass rates fell significantly. 5 This had the effect of encouraging the belief among
young people and centres alike that A level Mathematics was a high risk and inaccessible
subject for all but a ‘clever core’ of students. 6 Uptake of mathematics courses decreased
greatly, 7 with a downstream impact on university mathematics departments. A level Further
Mathematics also suffered a decline in numbers opting for the subject. This impact was in part
an unintended consequence of the regulatory framework at the time.
2.2 Developments since Curriculum 2000
Mathematics A levels have developed through a number of incremental changes since the
introduction of Curriculum 2000. A series of small changes from 2002, most significantly the
conversion of the three Pure Mathematics units (P1, P2 and P3) into four Core units (C1-4),
served to increase the numbers choosing to study Mathematics A level. An AS in Further
Mathematics was also introduced by some awarding bodies which could readily be taught
alongside A level Mathematics in either a student’s first or subsequent year of advanced level
study. 8 In 2004 (2008 in Edexcel’s case) specifications were designed to facilitate parallel
teaching (as well as other modes of delivery) of Mathematics and Further Mathematics. 9
Mathematics A level also benefitted from the establishment of the Further Mathematics Network
(later FMSP 10 ) in 2004. This initiative took advantage of the modular structure of AS and A2 to
attempt to make AS and A2 Further Mathematics available to a much wider cohort of students,
including those not readily identifiable as high achieving students. Essential to this project is the
possibility that students can take extra units flexibly during the course of their AS and A2 Maths
study, sometimes by distance learning or in twilight and weekend sessions, and decide at a later
stage whether to aggregate for the additional qualification(s). The Joint Council for
5
http://www.acme-uk.org/media/3896/rises%20in%20a-level%20mathematics%20%20some%20preliminary%20thoughts%20by%20acme.pdf;
6
Matthews, A. & Pepper, D. (2007) Evaluation of Participation in A level Mathematics: Final Report,
London: Qualifications and Curriculum Authority.
7
http://www.acme-uk.org/media/3896/rises%20in%20a-level%20mathematics%20%20some%20preliminary%20thoughts%20by%20acme.pdf ;
http://mathstore.ac.uk/headocs/7430_porkess_r_moremathcompgrads.pdf
8
The Advanced Subsidiary Level in Further Mathematics had been around since the beginning of
Curriculum 2000 (and the Advanced Supplementary Level in Further Mathematics went back further still.
9
There was also a reduction in the content in A level Mathematics, making the subject more comparable
to other A levels.
10
http://www.fmnetwork.org.uk/
2
Qualification’s (JCQ) aggregation rules 11 ensure that students are not disadvantaged by taking
additional units that may lead to a qualification in Further Mathematics. Indeed, the rules ensure
that students optimise the grades available to them in Mathematics, and in Further
Mathematics. Optimisation means that candidates do not have to decide in advance how to
allocate units between the qualifications, so that grades are awarded on mathematical ability
alone.
2.3 International comparisons and A levels in Mathematics and Further Mathematics
Ofqual’s international comparison study of post-16 mathematics qualifications found that A
Level Mathematics compares favourably with qualifications in other countries and that ‘A-level
Further Mathematics was the broadest and deepest qualification reviewed’. 12 There is
widespread agreement that the content of the A levels is broadly appropriate, although
adjustments might be made to the ways in which they are assessed. 13
2.4 Participation in A level Mathematics and Further Mathematics
Mathematics and Further Mathematics are both growth subjects at AS and A level and this
growth contributes to the overall increase in post-16 participation. In England the numbers of
students taking A level Mathematics has risen by 72% since 2003, 14 and the numbers taking A
level Further Mathematics has increased by 152%. The growth of AS Further Mathematics is
also particularly significant.
There are also increased numbers reading for mathematics degrees, and those that are using
mathematics, such as those in physics, psychology and biological sciences, and a range of
courses require young people to be confident in using mathematics. 15 ACME understands that
many Higher Education departments note the need for mathematical knowledge and skills for a
range of courses.
11
www.jcq.org.uk/...maths.../gce-maths-rules---guidance-for-centres
http://www.ofqual.gov.uk/news-and-announcements/83-news-and-announcements-news/899comparison-of-international-qualifications
13
ACME meeting with stakeholders and awarding organisations, August 2012.
14
In 2012, about 9.95% of all A level entries were for mathematics (85,741 candidates), only English had
a higher proportion of entries 10.4%).AS Mathematics had the largest entry (11%, 148,550 candidates),
http://www.jcq.org.uk/media-centre/news-releases/entry-trends-2012-a-as-aea-tables
15
http://www.publications.parliament.uk/pa/ld201213/ldselect/ldsctech/37/37.pdf; http://www.acmeuk.org/media/7624/acme_theme_a_final%20(2).pdf
3
12
3
ACME recommendations regarding the current proposals for A level reform
3.1 Timescale
It has been proposed that mathematics A levels will be reformed for 2015. ACME has argued
that mathematics should be reviewed over a longer timescale and maintains that this timescale,
although one year later than the original proposal, could potentially affect quality and take-up of
A level Mathematics and Further Mathematics.
There are several interdependencies that ACME recommends are taken into account when
considering the timescale for reform of mathematical subjects:
•
•
•
•
•
The Key Stage 4 programme of study for mathematics and GCSE Mathematics are also
being revised. The content and level of demand of the GCSE need to be taken into
consideration when developing A level Mathematics
Core Mathematics qualifications will be introduced in 2015 at the earliest. These
qualifications need to be embedded and provide a viable alternative mathematics
qualification beyond GCSE. Otherwise there is a potential that the total numbers taking
mathematics post-16 will fall rather than increase.
Mathematics and Further Mathematics at AS and A level involve a wide range of course
options. There is a need to reflect on how reform will affect the choices open to students.
Students will have a heavy assessment load at end of Year 13, which might change
behaviour in applied modules, which, for example, might make offering two modules in
the same discipline more likely than at present.
Mathematics provides the population with general numeracy skills. Also, within the
school and Higher Education systems, many other subjects depend upon skills gained in
mathematics. Any revisions to the content criteria for A level Mathematics need to draw
on the needs of other disciplines.
Even with limited changes to content, as proposed below and in ACME’s briefing paper,
there would still need to be some changes to resources and textbooks. These have a
lead time, making effective introduction of new qualifications in 2015 challenging.
Recommendation:
Revised A level Mathematics and Further Mathematics, and AS
Mathematics and Further Mathematics, with minimal changes are
introduced in 2016.
4
ACME believes that relatively little reform of the A level content is required, but that there should
be improved quality of assessment with changes made incrementally over time. 16 This is hard to
achieve with the current regulatory structure and when there are competing awarding
organisations.
Even implementing limited revisions for first teaching in 2016 seems optimistic – it will not allow
for an assessment of the successes of the current model, why participation levels are rising, and
what the risks of change might be, as well as identifying positive means of reform.
Recommendation:
A level Mathematics and Further Mathematics (and the associated
AS levels) are fully reviewed over a longer time period (for example
5 years).
3.2 Subject criteria
ACME is particularly concerned to ensure that new qualifications are developed in relation to
appropriate subject criteria.
A common core of mathematics within the qualifications supports users of the qualifications by
enabling them to work on the basis that all students with the qualification have studied the
common material. The common material also supports students who move from one school to
another where a different awarding body’s qualification may be taught.
Recommendation:
New criteria for A level Mathematics must ensure that qualifications
incorporate a large core of common material. The extent of the
common material in A level Mathematics should be no smaller than
the current two-thirds core.
There is also a strong case for introducing some core material into Further Mathematics
qualifications.
Recommendation:
Criteria for A level Mathematics should provide common
assessment structures that ensure the demands of the various
16
http://www.acmeuk.org/media/10163/acme%20response%20to%20ofqual%20consultation%20on%20a-level%20%20final%20submitted.pdf
5
qualifications are highly comparable. These assessment structures
should permit co-teaching of material that may ultimately be
aggregated either within A level Mathematics or within AS or A level
Further Mathematics.
3.3 AS Mathematics as a standalone qualification
In correspondence between Ofqual and the Secretary of State, Glenys Stacey (Ofqual) has
noted the Secretary of State’s request that the AS qualification be ‘decoupled’
‘so that the marks do not contribute to an A level grade, though the standard of the new AS will
remain broadly as it is now. The purpose of this new AS qualification will be to encourage
curriculum breadth’. 17
ACME’s view is that decoupling AS Mathematics from A level Mathematics is likely to affect
participation in mathematics post-16:
•
Students may have started an AS level in Year 12 with the intention of dropping the
subject, but have enjoyed it and taken it to a full A level. These students may no longer
commence AS, or may no longer transfer onto the A level.
•
Many or even most centres will continue to use AS assessment at the end of Year 12 if it
is one half of an A level, not least because learners very frequently use their AS level
results to directly inform their choice of three subjects for their second year, and indeed
their higher education choices. The outcome could be increased assessment burden
and raised assessment costs.
HEIs have also noted the importance of AS level results for determining entry to competitive
courses. 18
Recommendation:
The AS in mathematics continues to provide material that may be
regarded as the first half of the A level, even if the qualification no
longer contribute to a student’s A level grade.
3.4 Perceptions of challenge
The relative challenge of any new qualifications also requires close observation and
assessment so that mathematics is not perceived as being unreasonably difficult, both by
17
18
http://www.ofqual.gov.uk/files/2013-03-22-letter-to-secretary-of-state-for-education-alevel-reform.pdf
http://www.russellgroup.ac.uk/russell-group-latest-news/154-2013/5450-aslevel-reform/
6
students and centres. 19 Where students are taking courses with terminal assessment, the
relative difficulty of subjects is also likely to have a higher profile in determining choices. 20 There
is also an issue of the volume of assessment that students would encounter in the summer of
Year 13. The impact of this on mathematics participation should be monitored.
Currently, A level Mathematics can be perceived by many 16 year olds as a relatively
demanding subject, and students can be discouraged from attempting it unless they have
achieved high GCSE grades or are part of the ‘clever core’. 21 This is frequently done with the
help of Value Added charts from organisations such as the Advanced Level Information System
(ALIS) 22 or Advanced Level Performance System (ALPS) 23 to which most institutions subscribe.
However, ACME notes that C, D and E grades in AS and A level Mathematics and Further
Mathematics can be useful for HEIs and employers given the mathematical skills that have been
acquired to gain those grades.
Within centres teaching Mathematics A level, senior managers will be mindful of the
comparative ‘success rates’ of different subjects for accountability and inspection purposes. At
present, some senior managers will discourage recruitment to subjects whose success rates is
lower than for other subjects: this is a direct threat to participation in Mathematics and Further
Mathematics at A level, and needs to be counterbalanced by clear statements by HEI about the
non-mathematics subjects, such as economics, chemistry and biology, about the value of A
level Mathematics and Further Mathematics.
Mathematics, alongside a number of other subjects, is designated a facilitating subject – these
can be defined as subjects that are particularly valued by more selective institutions as
providing greater rigour and transferable academic skills.
Recommendation:
A range of Higher Education (HE) departments should be
encouraged to mirror their claimed valuing of these subjects with
greater use of ‘preferred qualifications’ and differential entry offers.
19
http://www.cem.org/attachments/SCORE2008report.pdf
Brown, M., Brown, P. & Bibby, T. (2008) ‘I would rather die’: reasons given by 16-year-olds for not
continuing their study of mathematics. Research in mathematics education, 10 (1), 2-18
21
Matthews, A. & Pepper, D. (2007) Evaluation of Participation in A level Mathematics: Final Report,
London: QCDA;
http://www.conservatives.com/news/news_stories/2011/08/~/media/files/downloadable%20files/vorderma
n%20maths%20report.ashx; http://www.cem.org/attachments/SCORE2008report.pdf;
22
ALIS http://www.cem.org/alis/introduction
23
ALPS http://www.alps-va.co.uk/
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20
4
ACME recommendations regarding revisions to A level Mathematics for 2016
4.1 Proposed approach
ACME cannot see how changes can be effectively introduced for teaching in September 2015
as suggested by the Secretary of State. However, ACME proposes some principles which need
to be borne in mind in making minor adjustments to the A level Mathematics suite for 2016.
Additional detailed advice on options to adapt the current qualifications, which could meet the
Government’s objectives, is provided in a briefing paper submitted to the Department for
Education in April 2013. 24
4.2 Synoptic assessment of the pure core mathematics content
In its response to the Ofqual consultation, ACME argued that A levels in Mathematics already
provide synoptic assessment. 25 ACME has also noted that there is scope for core content
currently specified within core mathematics C1, C2, C3 and C4 in A level Mathematics to be
assessed in two papers (C1+C2, and C3+C4), providing increased opportunities for synoptic
assessment. 26
4.3 Choice of subject matter within A level Mathematics
The current model for A level Mathematics and Further Mathematics has a common core of
pure mathematics and a student takes applied modules, depending on the options offered by
their school or college. This means that there are currently many routes to A level Mathematics,
though the ‘Pure Common Core’ accounting for two thirds of the course is quite rightly
constrained.
Some centres have the opportunity to timetable alternative applied mathematics pathways to
support students’ other subjects, for example: mechanics to support physics and design
technology, statistics to support biology and the social sciences or decision mathematics to
support business studies and computing. A loss of flexibility might mean that many existing
courses are no longer offered and that students are forced into taking inappropriate options.
ACME cautions against removing discretion from centres in terms of choices available to A level
Mathematics centres, and the relationships between Further Mathematics and Mathematics
optional content. Consequent participation should be closely monitored and significant threats to
participation addressed.
24
PUT IN LINK to BRIEFING ONCE ON WEBSITE (16 May)
http://www.acmeuk.org/media/10163/acme%20response%20to%20ofqual%20consultation%20on%20a-level%20%20final%20submitted.pdf
26
This approach was piloted by AQA and was evaluated as part of the Evaluating Mathematics Pathways
project, with favourable results across the attainment range; PUT IN LINK to BRIEFING ONCE ON
WEBSITE
8
25
Recommendation:
Centres should retain discretion of choice within the qualification.
Reducing A level Mathematics to a subject where no choice is
possible is very likely to result in decreased uptake in Mathematics
for 16-18 year olds.
4.4 Connections between A level Mathematics and AS and A level Further Mathematics
The interrelationships between the A level qualifications in Mathematics and Further
Mathematics and the AS qualifications in the same subjects have been a key factor in the
growth in participation in these subjects.
Recommendation:
The linkages between A level Mathematics and AS and A level
Further Mathematics should be maintained for the revised A levels
introduced in 2016.
In Further Mathematics, a contributing factor of the recent growth in take-up has been the fact
that students have been able to gradually extend their commitment to the subject. For instance
they can begin by taking the components that make up the AS level qualification, but can then
build upon this foundation and undertake the full A level if they find they are coping well with the
demand of the subject. Students studying A level Mathematics benefit from the fact that they are
taking Further Mathematics as well by getting increased exposure to the subject and improve
their grades in both
ACME recommends that the opportunity is extended to those studying Further Mathematics, as
is the case for those studying A level Mathematics, to undertake additional studies in the subject
leading to AS Further Mathematics and also to choose to extend their study to a larger
qualification when appropriate.
Recommendation:
Some components of AS Further Mathematics must also be
components of A level Further Mathematics.
9
5
The next phase of reform
ACME has a unique role within the mathematics community and has a track record of providing
advice on qualification development. ACME is willing to play an active part in providing advice
during the review of A level Mathematics and Further Mathematics.
ACME is clear that mathematics curricula and qualifications need to be developed coherently,
such that GCSEs, A levels and new post-16 qualifications form a suite of qualifications which
complement each other. ACME is also mindful that curriculum and qualification reform cannot
be undertaken lightly or over short timescales. As Curriculum 2000 has shown, seemingly small
changes to a qualification can have significant implications for participation.
ACME notes that for mathematics there are many interested parties, from within mathematics
and without. It will also be essential for any review group to draw on expertise of:
•
•
•
•
teachers
a wide range of HEIs
those with understanding of the needs of the workplace
those with qualifications expertise.
The learned societies for mathematics, the subject associations and ACME itself will all have an
interest in the review and hold expertise that that can be drawn upon by those involved in the
reform process.
Any reform of A level Mathematics and Further Mathematics should have links with those
reviewing GCSE Mathematics and those involved with developing the new Core Mathematics
qualifications. The awarding organisations and Ofqual should therefore work closely with
bodies, such as ACME, who have in-depth subject expertise.
ACME would also expect any body or organisation leading on A level reform in mathematics for
2016 or beyond to have a long term role and responsibility for ensuring the quality and
effectiveness of these qualifications to ensure continuity and coherence.
10