Level 2 Functional Skills Mathematics: An MEI discussion document
What would a suitable alternative to retaking GCSE for post-16 students look like?
Summary




Following the Wolf report, government policy is that post-16 students who have not
achieved grade A*-C in GCSE Mathematics must continue studying mathematics.
Initial results suggest that re-sitting GCSE Mathematics does not lead to success for
around two thirds of these students, but there are no current plans to permit a post16 GCSE specifically designed for this cohort. MEI believes there should be.
Following a report by the Education and Training Foundation (ETF), BiS wishes to
improve the quality of Functional Skills qualifications for post-16 students to prepare
them for employment. If these qualifications are seen to be credible, it is conceivable
that they could eventually be seen as alternatives to GCSE re-sit for some post-16
students and be more appropriate to their needs.
Some initial thoughts are offered on what a level 2 Functional Skills qualification in
mathematics could be.
Background
The Wolf report1 recognised the importance of GCSE Mathematics and English for young
people.
English and Maths GCSE (at grades A*-C) are fundamental to young people’s
employment and education prospects. Yet less than 50% of students have both at
the end of Key Stage 4 (age 15/16); and at age 18 the figure is still below 50%. Only
4% of the cohort achieve this key credential during their 16-18 education.2
This has led to changes to conditions of funding for post-16 students. Students with grade D
in GCSE Mathematics are required to be enrolled in a course leading to retaking GCSE
Mathematics. Students who do not have a grade D can work towards GCSE Mathematics by
taking a stepping stone qualification3.
New GCSEs in Mathematics are being taught from September 2015 with resits of the old
GCSEs planned for November 2016 and summer 2017.
The new GCSEs are graded on a 9 to 1 scale, with 9 as the top grade. For academic years
2017-18 and 2018-19, a pass at grade 4 will exempt students from retaking GCSE post-16;
the intention is to revise this to grade 5 in future (this is roughly equivalent to a high grade C
on the old scale).
Many of the students re-sitting GCSE Mathematics or taking Functional Skills Mathematics
may have a closed mindset about their mathematical ability. To be effective, any new
Functional Skills Mathematics must engage students and build their confidence. Working
with contexts which learners perceive as relevant can improve both motivation and learning.
Review of Vocational Education – The Wolf Report, March 2011
The figures are for the cohort ending KS4 in 2005/6. In 2013/14 54.8% of pupils ending KS4 in
England had achieved A*-C in GCSE Mathematics and English (Table 4a
https://www.gov.uk/government/statistics/provisional-gcse-and-equivalent-results-in-england-2013-to2014 )
3 https://www.gov.uk/government/publications/approved-list-of-new-stepping-stone-qualifications
1
2
1
Extensive research has been conducted on challenging maladaptive beliefs about
maths. This includes work on changing mindsets and improving ‘mathematical
resilience’. Learners’ mindsets must be changed, according to one maths specialist,
from ‘I can’t do maths’ to ‘I can’t do maths yet’. A college representative noted the
positive results achieved by tackling ‘negative psychology with a few minutes each
session looking at attitudes to maths, growth mindsets, value of belief, [and] relating
effort to success’ One maths specialist commented that ‘in the early stages [of
teaching] it’s 90% psychology and only 10% maths’ as many students’ perception of
maths stems from negative association pre-GCSE. 4
Contextualised learning of maths has been found to improve both the understanding
of learners and the extent to which they retain the information they have learned.
Learner motivation is also affected by the perception of relevance; engagement and
motivation amongst learners is improved by the use of real-life contexts and
examples.
Research found that vocational contexts must be authentic and relevant to the
subject being studied, and should build upon the interests and experiences of the
learners being taught. Learners also need to be able to move from working with
familiar contexts, such as those related to their vocation, to unfamiliar contexts in
order to prepare to take functional skills and GCSE assessments.5
Stepping stone qualifications and functional skills reform
Students with grade D in GCSE Mathematics are required to be enrolled in a course leading
to retaking GCSE Mathematics. This can range from basic entry level qualifications to
Functional Skills Mathematics at level 2.
The March 2015 ETF Report Making Maths and English Work for All6 reached the following
conclusions.
The review highlights the view that the main non-GCSE employability qualification,
Functional Skills, should be viewed as an alternative route rather than a “steppingstone”. It should continue to be seen as a qualification in its own right with the key
purpose of satisfying employer requirements. This clarity of purpose will give it
greater currency with employers. It will also lead to a greater debate about what is
expected from Functional Skills and whether standards, assessment and rigour are
meeting the needs of the labour market.
However, there is awareness that an alternative route will only have validity and
currency if two criteria are met. Firstly, the standards have to be aligned to
employability and the content has to be based on what employers need for their
workforce. Secondly, Functional Skills have to have flexible but more standardised
and rigorous assessment to give employers confidence in them.
4
Effective Practices in Post-16 Vocational Maths, ETF, December 2014
Effective Practices in Post-16 Vocational Maths, ETF, December 2014
6
http://www.et-foundation.co.uk/wp-content/uploads/2015/03/Making-maths-and-English-work-for-all25_03_2015001.pdf
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A letter from the Minister for Skills on 21 July 20157 includes the following information.
In my previous letter, I mentioned that I had commissioned the Education and
Training Foundation to carry out a review of the best way to achieve and accredit
Maths and English in post-16 education outside of GCSEs. The Foundation’s
recommendations, published in March 2015, provide valuable new evidence for
improving the quality and recognition of Functional Skills qualifications to ensure they
meet the needs of employers and learners. I believe that Functional Skills should
continue to be the main alternative English and Maths qualifications to GCSEs.
However, to be well-respected and credible, it is critical they suit employers’ needs
and are properly taught and assessed. I have, therefore, asked the Foundation to set
out what a programme of reform to update English and Maths Functional Skills
qualifications would involve, working closely with BIS, DfE and Ofqual.
It is highly regrettable that, even after Functional Skills Mathematics has been reformed, it is
still the intention, enforced by Post-16 funding regulations, that all students who achieve a D
in GCSE Mathematics at age 16 must pursue the GCSE re-sit route, regardless of their
future aspirations. This seems to send out a clear message that Functional Skills
Mathematics is a second-rate qualification compared to GCSE Mathematics. This is likely to
undermine students’ motivation and significantly reduce its currency with employers.
Success rates for GCSE retake
GCSE Mathematics for UK candidates aged 17 and over8,9
Year
2012
2013
2014
2015
Number
sat
69494
77501
100587
130979
A*
1.5
1.4
1.1
1.0
A
4.5
4.5
3.8
3.1
Cumulative percentages by grade
B
C
D
E
F
11.0
43.1
75.1
89.1
95.4
11.8
41.1
72.2
87.5
94.5
10.0
38.9
69.1
85.4
92.6
8.1
35.8
69.2
85.6
92.1
G
98.2
97.8
96.3
95.6
U
100
100
100
100
Since 2013 there has been a requirement for post-16 learners to continue working towards
Mathematics GCSE. The table shows that the numbers taking this qualification have almost
doubled from 69494 in 2012 to 130979 in 2015. However, during this time the pass rate
(grade C or above) has fallen, with only just over a third succeeding in the 2015 cohort. This
suggests that alternative provision would be more appropriate for the majority of these
candidates.
7
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/447179/Minister_s_Ter
mly_Letter_-_July_2015_Final__2__to_FE_Colleges.pdf
8 http://www.jcq.org.uk/examination-results/gcses/2015/gcse-full-course-results-by-age-group-2015
9
http://www.jcq.org.uk/examination-results/gcses/2013
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Level 2 mathematics qualifications for post-16
GCSE Mathematics serves two essential purposes: it is a preparation for further study in
mathematics and it is also a grounding in the mathematics needed in life and work.
GCSE Mathematics is used by many employers as a filter when choosing candidates for
employment and is a general requirement for university degrees and other courses. A post16 GCSE Mathematics, not constrained by the national curriculum, or the possible future
requirements of further mathematical study, would allow students who have not achieved a
grade C or above in GCSE Mathematics to have a fresh start with a qualification which is
more in line with their needs and ambitions.
Professor Alison Wolf (author of the Wolf report, Review of Vocational Education10), quoted
in the Vorderman11 Report, said the following.
If we want everyone to study maths successfully, both in the years after GCSE and
as adults, then we need to develop an interesting and varied curriculum. This is
especially, though by no means only, true for people who have found maths difficult
or who were badly taught at school and so may well have failed GCSE. That is one
reason why, several years ago, I was involved in developing freestanding maths
qualifications which cover important parts of the maths syllabus in a different way
from the standard GCSE. Qualifications of this sort can be very effective in helping
people to progress towards GCSE, and well beyond, and I hope they will be used
more in the future. Unfortunately, in the period since they were first developed, we
have actually gone backwards in terms of what is available for post-16 students.
GCSE Mathematics for adults has vanished, even though it was highly successful,
and recognised that a single approach cannot work for all age groups. I would be
delighted to see it re-established.
MEI strongly endorses these views and further believes that such a qualification would have
the advantage of currency, with its content being focused on the mathematics candidates
need for work and life. The limited content of such a GCSE could be recognised by limiting
the maximum grade to, say, grade 5 equivalent to a good pass in the pre-16 GCSE.
Unfortunately, there is no current intention to develop such a qualification. MEI regards this
situation as extremely discouraging and unsupportive for those candidates who do not
achieve a grade C or above in GCSE Mathematics by the end of Key Stage 4.
Skills appropriate to level 2 Functional Skills in Mathematics
Ofqual’s 2015 review of Functional Skills at level 2 found that 70% of employers said that the
qualifications assessed the skills needed in the workplace.
Analysis of the responses shows that support for functional skills qualifications was
due to the value attributed to the real-life focus of assessments. Practical skills were
seen as useful, relevant and motivating for students. Skills such as writing coherent
letters and emails or taking accurate measurements were seen as relevant for
10
11
Review of Vocational Education – the Wolf report, March 2011
A world-class mathematics education for all our young people, August 2011
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employment. Skills such as budgeting, understanding a utility bill or interest rates
were seen as useful for daily life. In this context respondents often drew favourable
comparisons with academic qualifications, or with the key and basic skills
qualifications that functional skills qualifications replaced.12
Where a need for improvement was identified, it was in making contexts used in questions
more realistic and in making standards more consistent between different awarding
organisations.
Appropriate assessment for level 2 Functional Skills in Mathematics
The current skills standards for level 2 Functional Skills in Mathematics are drawn from the
following processes, which are to be assessed by functional skills qualifications in
mathematics.13
Representing and selecting
the mathematics and
information to model a
situation

Learners recognise
that a situation has
aspects that can be
represented using
mathematics
Analysing
processing and using
mathematics

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Learners make an
initial model of a
situation using suitable
forms of representation
Learners decide on the
methods, operations
and tools, including
information and
communication
technology (ICT), to
use in a situation


Learners use
appropriate
mathematical
procedures
Learners examine
patterns and
relationships
Learners change
values and
assumptions or adjust
relationships to see the
effects on answers in
models
Learners find results
and solutions.
Interpreting and
communicating the results of
the analysis

Learners interpret
results and solutions

Learners draw
conclusions in light of
situations

Learners consider the
appropriateness and
accuracy of results and
conclusions

Learners choose
appropriate language
and forms of
presentation to
communicate results
and solutions.
Learners select the
mathematical
information to use.
The assessment of Functional Skills Mathematics at level 2 must currently be 100% by
external examination. This makes it virtually impossible for learners to choose to use
appropriate ICT.
12
13
Improving Functional Skills Qualifications, Ofqual 2015
Functional Skills Criteria for Mathematics, Ofqual, September 2011
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The standards for level 2 Functional Skills in Mathematics (Appendix 1) relegate ICT to
statistical work; this is an impoverished preparation for working and adult life. For example,
the use of spreadsheets should be incorporated into Functional Skills; if coursework is not
permitted, spreadsheet use could easily be assessed online and awarding organisations
should be required to do this.
It is natural to consider the accuracy of results and conclusions when solving an extended
problem in a context which the solver understands well. It is not possible to achieve this in a
timed examination where the contexts are unfamiliar to students. Artificial, contrived
questions are sometimes used in an attempt to meet the requirement to assess these skills.
Such questions undermine the credibility of the qualification.
It is important that artificial contexts and contrived questions are not used in timed
examinations in an attempt to meet the requirement that certain skills are assessed.
Questions not only need to be referring to real-life problems but also need to be in realistic
contexts. Jo Boaler in “What’s Math got to do with it?”14 describes how students who use
their real world knowledge to help solve these pseudo context questions may fail.
Functional Skills needs some of its assessment to be non-examination, to allow the
appropriate use of ICT applied to an unfamiliar realistic context with appropriate
communication of and reflection on the results obtained. This would also allow students to
work on a problem related to their other studies and be entirely appropriate for adult students
who are preparing for work.
Fluency and accuracy in mental arithmetic, proportional reasoning and estimation could be
tested on line, perhaps through an ‘on-demand’ assessment. Fluency in these areas is
highly valued by employers and should be properly assessed. Online testing is efficient to
administer and, if students have the opportunity to practice and test themselves online when
preparing for the assessment, it can also be motivational.
Regulation and Functional Mathematics
The purpose of developing qualifications in functional mathematics was to provide a clear
opportunity for leaners to demonstrate that they could use and apply their mathematical
skills, knowledge and understanding to solve problems. Thus candidates would be asked to
demonstrate that they could apply their mathematics to quite complex contexts, rather than
just showing a basic grasp of a range of mathematical skills.
Inevitably, the great challenge for this kind of learning is in its assessment. The questions
that need to be asked must embrace contextual complexity rather than shying away from it.
This means that examination papers need to be developed with great care, so that, whilst
requiring sufficiently complex thinking from candidates, the wording of the questions is
simple and clear. Moreover, questions need to be set that permit almost all candidates to
make some progress towards finding a reasonable answer. It is not satisfactory to pose
problems that depend on candidates having a flash of inspiration that suddenly cuts through
the difficulties. Equally, however, questions should rarely be so basic that every candidate
knows at once how to proceed. Nor should questions be inauthentic; such questions
encourage the view that maths is only relevant in examinations and is not useful ‘in the real
world’.
Finally, functional mathematics qualifications from all awarding organisations should be
broadly comparable, and should appear so to teachers and users of the awards.
14
Boaler J. Penguin 2015 ISBN 978-0143128298
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In short, the assessment of functional skills mathematics is challenging. A corollary of this is
that the work of awarding organisations needs to be carefully regulated to ensure that the
most obvious pitfalls are avoided. Regulatory authorities should also work to ensure that a
gradual consensus on the most promising ways to assess the qualification is developed
amongst examiners through a programme of CPD for key members of examining staff.
Functional mathematics is vital for many learners. It needs to develop a clear separate
identity that enables users to value it alongside GCSE qualifications. Effective regulation of
functional skills qualifications is the most important component of the work needed to
achieve this outcome.
How large a qualification should level 2 Functional Skills Mathematics be?
Currently, Functional Skills Mathematics at level 2 has 45 guided learning hours. GCSE
qualifications are regarded as having 120 to 140 guided learning hours. For Functional
Skills to become an alternative qualification to GCSE Mathematics, it must be of comparable
size. At least 100 guided learning hours would be appropriate. This increase in time would
allow for the inclusion of non-examination assessment.
Suitable content for a level 2 post-16 Mathematics qualification
It is important in designing a level 2 post-16 qualification that it should be seen to be useful
to both the candidates and future employers. The starting point should be consideration of
the mathematical knowledge and skills they need to be able to perform effectively in the
workplace and in their lives as competent citizens.
Hodgen and Marks reported the following key findings from their 2013 review of the
mathematics used in employment15.
Mathematical
content
“Complex
settings”
Technology
rich
environments
Collaborative
working
environments
15
The mathematical content used within, and appropriate to, the
workplaces of today includes: Number, Statistics and Probability,
Algebra and Geometry and Measures. Of particular importance
are mental proportional reasoning, approximation and estimation,
the interpretation of graphs, and the use of spreadsheets and
calculators.
Although the mathematical content may be at GCSE level, it is
embedded within complex settings. These settings require the
sophisticated use of mathematics particularly when people in the
workplace are faced with modelling scenarios.
Evidence across the literature base suggests that workplaces are
technology rich environments with much of the mathematics
people in the workplace are engaged in embedded within ICT,
particularly in the use of spreadsheets and graphical outputs. This
has implications for how mathematics in taught in schools.
Increasingly, and particularly in combination with the use of
technology such as Computer Aided Design and modelling
software, employees work in collaboration reaching joint
understandings. This should be reflected in approaches to post16 mathematics provision.
The Employment Equation, July 2013
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Based on this report and other relevant reports16, MEI has outlined a list of the mathematical
tasks which students who are ready for employment and adult life should be able to do; this
is found in Appendix 2; it is intended to stimulate and inform further discussion.
Currently, the mathematical content of level 2 Functional Skills Mathematics is aligned to
levels 1 to 6 of the old national curriculum. This is no longer appropriate; there are no levels
in the current national curriculum. In order to be able to use mathematics confidently in a
variety of contexts, students need to understand some suitable mathematical content; this
should be defined once the mathematical tasks that students need to be able to do have
been decided; it is likely that much of the suitable mathematical content will be found in
current GCSE Mathematics at Foundation tier and the associated assumed learning, which
forms a subset of that content.
However, the key difference between GCSE and a Functional Skills qualification is that the
latter should concentrate on the assessment of the ability to use mathematics. It is crucial
that a level 2 Functional Skills qualification in mathematics should enable learners to be
confident in using the mathematics they know in a wide variety of contexts, making
appropriate use of technology to do so. Consequently, it would be inappropriate for students
aiming at level 2 Functional Skills to focus on first learning all the content of the current
Foundation tier in Mathematics and then learning to apply it.
Progression from level 2 Functional Skills
There is a national ambition in England to increase the number of students studying
mathematics until age 18. For students who have not achieved a good GCSE pass in
Mathematics, their focus is currently on retaking GCSE. An alternative qualification, more in
line with the needs of the students could increase their confidence and enthusiasm for
mathematics as well as improving their chances of succeeding.
Many 16 and 17 year old students are not ready to make final decisions about their future
working lives. Although it is reasonable to design a level 2 Functional Skills qualification in
Mathematics with the mathematical needs of life and work to the fore, students who succeed
in such a qualification and wish to take their mathematical learning further could still go on to
take GCSE Mathematics and so progress to further study of mathematics.
16
Building for growth: business priorities for education and skills, CBI, 2011
Impact of Poor Basic Literacy and Numeracy on Employers, BIS RESEARCH PAPER NUMBER 266,
Feb 2016
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Appendix 1: Current level 2 Mathematics Functional Skills standards
Skill standards
Coverage and range
Representing
1. Understand routine and
non-routine problems in
familiar and unfamiliar
contexts and situations.
2. Identify the situation or
problems and identify the
mathematical methods
needed to solve them.
3. Choose from a range of
mathematics to find
solutions.
Assessment
weighting
30–40%
a) Understand and use positive and
negative numbers of any size in
practical contexts;
b) Carry out calculations with numbers of
any size in practical contexts, to a
given number of decimal places;
c) Understand, use and calculate ratio
and proportion, including problems
involving scale;
d) Understand and use equivalences
between fractions, decimals and
percentages;
e) Understand and use simple formulae
and equations involving one- or twostep operations;
Analysing
f)
4. Apply a range of
mathematics to find
solutions.
g) Find area, perimeter and volume of
common shapes;
5. Use appropriate
checking procedures
and evaluate their
effectiveness at each
stage.
7. Draw conclusions and
provide mathematical
justifications.
30–40%
h) Use, convert and calculate using
metric and, where appropriate, imperial
measures;
i)
Collect and represent discrete and
continuous data, using ICT where
appropriate;
j)
Use and interpret statistical measures,
tables and diagrams, for discrete and
continuous data, using ICT where
appropriate;
Interpreting
6. Interpret and
communicate solutions to
multi-stage practical
problems in familiar and
unfamiliar contexts and
situations.
Recognise and use 2D representations
of 3D objects;
30–40%
k) Use statistical methods to investigate
situations;
l)
Use probability to assess the likelihood
of an outcome.
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Appendix 2: What should students who have completed level 2 Functional Skills in
Mathematics be able to do?
The following list is intended to provoke discussion and to be added to. It lists MEI’s initial
suggestions for what students who successfully complete level 2 Functional Skills in
Mathematics should be expected to be able to do. A variety of appropriate realistic contexts
should be used in the assessment of Functional Skills.
This list should be read in conjunction with the current functional skills standards, which sets
out the dimensions of mathematical problem solving in context and could be appropriately
updated once the list of things that students should be able to do has been agreed.
In addition to this, once there is an agreed list of what students should be able to do, a list of
supporting mathematical content should also be constructed. This is likely to be mainly a
subset of Foundation tier GCSE mathematics and its associated prerequisite knowledge.
The list is not intended to be in order of importance.
Students should be able to

Recognise when mathematics is useful to address a problem.

Identify what information is required to solve a problem.

Structure a solution to a problem involving mathematics.

Recognise when a problem is related to one which has been encountered before.

Adapt a solution to a problem to solve a related problem.

Make a rough estimate and recognise when a calculation is likely to be incorrect.
Recognise the importance of checking procedures in order to avoid waste in contexts
such as manufacturing and ordering. Work to an appropriate level of accuracy.

Use a spreadsheet to draw graphs from data and judge which graphs are suitable
when interpreting data.

Interpret graphs representing real situations, including statistical graphs.

Read information from a table and recognise when data are clearly not realistic.

Use diagrams to represent information and extract information from diagrams
including scale drawings and 2-D representations of 3-D objects.

Work with time to perform calculations in context.

Use a spreadsheet to perform calculations using simple spreadsheet functions such
as SUM and AVERAGE.

Justify a decision made on the basis of calculations in context such as whether an
object will fit into a space, whether a budget is adequate to cover costs, how much of
a product to order.

Know that likelihood and impact are important when assessing risk and be able to
perform and interpret a risk assessment using a given method.

Use percentage increase and decrease in a variety of contexts, including discounts
and VAT.
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
Recognise and use proportional relationships in context, including those resulting
from percentage increase and decrease. Know that some relationships are not
proportional e.g. flat rate increases.

Understand and use compound interest calculations, using a spreadsheet or
calculator, in contexts such as savings and loans.

Use and interpret given models for appreciation and depreciation such as those
found online for cars. Understand that a model can give useful information about the
real world but depends on simplification.

Construct and interpret a simple budget.

Measure accurately and know which measurements need to be taken for a given
purpose. Understand that measurements sometimes need to be between particular
limits.

Convert between units of measurement, including appropriate metric and imperial
units. Be able to visualise the approximate size of common units of measurement.

Carry out foreign currency exchange calculations and related approximations.

Be able to work with a formula expressed in words or symbols. Construct simple
formulae on a spreadsheet.

Understand how averages can summarise data and use them in context.

Use systematic strategies such as listing.

Use mental arithmetic in contexts typical of those encountered in the workplace and
everyday life, including checking for errors in calculations.

Use the links between fractions, decimals and percentages, when tackling
calculations and dealing with proportions.

Demonstrate an understanding of place value in context and when expressing
answers to a required level of accuracy.
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