Page 1 of 31 Do GCSE maths results give the same indication of learner’s levels of maths skills as do initial assessment tools? Gail Lydon 19 June 2013
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1 of 31
Do GCSE maths results give the same indication of learner’s levels of maths skills as do initial assessment tools?
Gail Lydon
19 June 2013
Page 2 of 31
Abstract
The purpose of this research study was to investigate whether GCSE results in mathematics give the same
indication of maths skills as do the initial assessment tools used within a particular Further Education (FE)
College in the North of England. Further to this: what patterns can we see in the results and what further
questions need to be asked?
The research question aimed to investigate some of the assumptions made in the Further Education sector:
That learners with a grade C and above in GCSE have level 2 skills and hence don’t need to be initially
assessed. This leads to an assumption that learners will have the skills required to access their chosen
programmes of study.
That learners with a lower than grade C have lower than level 2 skills and hence will need further
maths support. This leads to an assumption that such learners may not be able to access certain
programmes of study and guidance will be given accordingly.
The focus of the work was on the 16 to 18 age range within an FE college. All learners in this age group
commenced programmes of study in September 2012.
The research involved comparing GCSE maths results and initial assessment results. These results were
then formed into bubble diagrams to aid discussion.
For this particular cohort, in this particular FE College it was found that there was a general trend between
GCSE and initial assessment results. However 50% of learners with GCSE grade C and above did not
achieve level 2 in the initial assessment. This raises many issues, for example:
using GCSE to place learners on programmes of study
maths support learners need and
the demotivating effect of informing learners that although they have ‘passed’ GCSE they may not have
level 2 skills.
Page 3 of 31
The research raised a range of issues for further study including:
the impact of feeder schools’ approaches to teaching maths
would other cohorts within this or other colleges produce the same results
whether the initial assessment tool and GCSE results are valid and reliable
Page 4 of 31
Table of Contents
Abstract ............................................................................................... Error! Bookmark not defined.
Introduction ..................................................................................................................................... 5 Aim of the research..................................................................................................................... 5 Rationale ...................................................................................................................................... 5 Why the research is important ................................................................................................... 6 GCSE maths ................................................................................................................................ 8 Initial assessment ....................................................................................................................... 8
The research .................................................................................................................................... 9
Results ........................................................................................................................................... 10 Table 4: Initial assessment results against GCSE results ....................................................... 11
Analysis of the results .............................................................................................................. 11 Further investigation into the figures ..................................................................................... 12
Table 5: Maths comparison ..................................................................................................... 13 Chart 1: Learner maths results GCSE by initial assessment .................................................. 14
Conclusions .................................................................................................................................. 15
Review of the approach ................................................................................................................ 16
Next steps - Further study needed .............................................................................................. 17 Feeder school differences: ...................................................................................................... 17
Table 6: Schools Comparison ................................................................................................. 19
Appendices .................................................................................................................................... 21 Appendix 1 Table 1: Comparison of functional maths and GCSE maths criteria .................... 22 Appendix 2 Table 2: Ofqual requirements of GCSE maths and Functional Skills maths qualifications ........................................................................................................................... 24 Appendix 3 Table 3: QCA Curriculum Lenses ........................................................................ 25
Bibliography .................................................................................................................................. 27
Page 5 of 31
Introduction
Aim of the research
The aim of the research was to investigate whether GCSE results in mathematics give the same indication
of maths skills as do the initial assessment tool used within a particular FE college. Further to this: what
patterns can we see in the results and what further questions need to be asked. The focus of the work is on
the 16 to 18 year olds within the college.
Initial investigation found research looking into adult learners and school learners but the 16-18 year olds
had not been so closely scrutinised. Initially the scope of the research was much wider but following the
reading on research methods it became clear to the researcher that this initial, although small, piece of work
could be the basis of further work and would check some of the assumptions made in the Further Education
sector. This research will only scratch the surface of what needs to be known and is therefore only seen as
a start. But as Pearson (2013b) states “Rather than being able to pronounce the last word, then, education
research is still learning how to promote better outcomes.”
Rationale
The focus was on maths as this subject is one that is coming under greater scrutiny following the 2011 SfL
Survey (BIS, 2012) which showed an increase in literacy/English and a drop on numeracy/maths successes.
The raising of the participation age and the expectation that learners will continue to study maths until they
are 18 years old also raises the profile of maths. This is both in terms of learner numbers and of the
effective teaching of maths. Hence the importance of effectively ascertaining the starting points of these
learners will only increase.
The GCSE results and initial assessment results are used to place learners on appropriate programmes of
study. The crux of this research is to find out if this process is based on a correct assumption i.e. that
GCSE and initial assessment results are an indicator of readiness for a certain type of study and give the
same indication. If they are a valid indicator then one would expect them to give similar results.
It was clear from the outset that this was only the start of the journey. Reading around the subject of
research it became clear to the researcher that in the timescales allowed only the very first stage of the
intended research could be achieved. This involved looking at the quantitative data and comparing the
results of all ‘freshers’ from September 2012. The aim was to look for any patterns across the cohort and to
Page 6 of 31
then do further research into these patterns at a later date. This group of learners was chosen as they were
the first cohort to sit the ‘new’ GCSEs in maths which state that 40% of the marks are related to being
‘functional’ in maths.
Before the comparison of GCSE and initial assessment results was carried out a comparison was made of
the criteria on which the two were based. This was in order to establish whether the outcomes in the GCSE
and initial assessment were comparable.
Why the research is important
This research is important because the College is the major provider of A’ level provision in the region and
aims to support its learners in the most appropriate way. To do this it needs to know the starting point of its
learners so that it can attempt to measure the impact of its inputs. This college is striving to improve the
outcomes for all its learners and, as with all FE colleges, is under funding pressure and so is keen to know
what is effective. However the measurement of this distance travelled is not a simple task, as Pearsons,
2013b purports:
‘a lack of “any relationship between inputs and outputs mirrors the extensive academic literature on this
topic. If you try to go beyond simple correlations, the general result is nearly always the same.” Chester
Finn, President of the Thomas Fordham Institute, an education research organisation, and former United
States Assistant Secretary of Education, agrees. “What works,” he says, “takes place inside a black box that
has inputs coming in and outputs going out; but the inputs do not predict the results and what goes on in the
black box is hard to quantify.” ’ Pearsons, 2013b:1
Although this ‘black box’ is a mystery an FE college is expected to measure the distance travelled by any
learner and, perhaps more importantly, to know where a learner is in their understanding in order to plan
their programmes of study.
Retention is a particular concern for the college as this is a key measure of its success and hence has an
impact on funding. Learners need to be on suitable programmes of study as soon as possible in order to
maintain motivation, achievement and hence retention. If GCSE results are not an indicator of basic
underpinning skills (as required within post 16 programmes of study whatever their level) then it is difficult to
ensure that learners are on programmes (made up of courses) that the learner will be able to access and be
Page 7 of 31
successful within. For instance, if a learner wishes to study physics or chemistry then it is important to know
that they have maths skills at a level appropriate for that course. This is also true of courses that have
traditionally been seen as less academic, for example health and social care courses which require a
proficiency in mathematics both within the course and in the workplace. Many colleges stipulate entry
requirements for courses e.g. 5 GCSE’s C and above including English and maths. But if these
qualifications are not actually an indicator of skill level then this process is flawed.
Learner readiness to commence their level 3 studies also has a significant impact on retention and
achievement. The early diagnosis of support needs in English and maths are seen as having an impact on
retention and achievement (Martinez, 2001), and it is a requirement of the funding agents and Ofsted
(2012).
‘Inspectors will make a judgement on the quality of teaching, learning and assessment by evaluating the
extent to which staff initially assess learners’ starting points and monitor their progress, set challenging
tasks, and build on and extend learning for all learners.’ Ofsted (2012, p6)
So an organisation such as this College needs to consider that:
‘Education remains very much a black box in which inputs are turned into outputs in ways that are difficult to
predict or quantify consistently. Experts point out that simply pouring resources into a system is not enough:
far more important are the processes which use these resources.’ (Pearson, 2013a).
Looking at learners’ GCSE and initial assessment results may cast some light on the ‘black box’ by giving a
more reliable starting point, allowing distance travelled to be measured and allow planning of resources to
support learners.
There is also an issue for learners progressing to university: ACME (2011a) found that of the 330,000
students studying university courses that require mathematical knowledge beyond GCSE level, 210,000 of
them (64%) did not have the required skills, causing problems for both students and universities. It seems
reasonable to assume that this lack of skill would also have an impact on learners on some level 3 courses
(many of which require mathematical skills above level 2) for example science A’ levels and engineering. If
learners are accepted on these courses because they have a C, B or A in GCSE mathematics an
assumption is being made that this is an indicator of a certain level of proficiency. If these learners do not
Page 8 of 31
have these skills then they will be disadvantaged and may not be able to access aspects of their chosen
course because of a lack of maths skill. On the other hand if learners are being denied a place on these
courses because they do not have a C or B or A but actually have the skills then they too are being
disadvantaged.
GCSE maths
There is much debate about what a grade C in GCSE might tell us. For example, Mansel (2009) contends
that a C grade in GCSE maths can be obtained by answering questions aimed at G, F and E levels of
difficulty. The issues he raises in the article were supposed to be tackled by the introduction of functional
skills maths test as a requirement for gaining a grade C or above GCSE (QCA, 2006). This requirement
was shelved in 2009. The awarding organisations also highlight issues with the GCSE, for example,
Andrew Taylor, Head of Mathematics at AQA, (AQA, 2013) states that:
‘Those key examinations have got to test and assess what is important about mathematics and at the
moment I think there is a question about how valid some of those assessments are and that is something
that we must work towards to change.”
The GCSE qualifications are based on the criteria established by Ofqual (2011a). Although there are some
differences in the summative assessments for GCSE between the awarding organisations all the English
qualifications are based on the Ofqual criteria and have to be approved by Ofqual.
Initial assessment
The initial assessment tool has been used within the college for many years and is presented to learners by
a trained, experienced and expert staff. For example the purpose and importance of the assessment is
clearly explained to learners and there is regular standardisation of the process and the conditions in which
it is sat.
It should be noted that the funding for most UK educational establishments offering post 16 provision is
predicated on a requirement to initially assess their learners.
“Colleges need to identify and provide support to students with poor numeracy and literacy skills, including
students for whom English is not their first language. ” (National Audit Office, 2001:5).
Page 9 of 31
Some feel that because of this initial assessment has become a tick box process – something that needs to
be done for funding rather than in support of their learners and that the findings of the initial assessment are
not used to support learners by informing the content of individual learning plans
‘‘An individual learning plan cannot be prepared, with any hope of its being pertinent, without the most
careful interview and, probably, well-chosen testing”. AlI, 2002
or used by tutors across a learner’s programme of study. For example is the planning within e.g. Business
Studies or Physics A’ level courses informed by the initial assessment results of the learners on those
courses? In the case of a college such as this where this information is communicated to all staff is the
information valid? If not then the programmes of study and the individual learning plans (and SMART
targets within them) are based on incorrect information. The issue of SMART targets is in itself now coming
under question (CIPD, 2012).
It has been widely believed that such pre-course assessments could improve retention (Estyn, 2006). But it
is not clear whether the tools being used by colleges are actually effective. It should be noted that some FE
colleges do not initially assess learners who have grade C and above and use the GCSE grade as the
indicator of skill level.
It was recognised even at the very earliest stage of the research that neither the initial assessment tool nor
GCSE examinations may be effective tools to measure a learner’s maths expertise and that this research is
the very first stage in establishing the validity of either of the tools.
The research
In order to compare the initial assessment and GCSE it was decided to first compare the criteria for GCSE
grade C and the Functional Skills level 2 requirements. This is because the initial assessment tool used by
this College is based on the Functional Skills requirements. The aim of this comparison was to see if the
qualification and the initial assessment tool were even covering the same content or level of difficulty. A
Page 10 of 31
comparison was done (see Appendix 1) of the GCSE1 and Functional Skills Criteria. The comparison of
GCSE and FS criteria is not a simple process as they are written in very different formats. To aid this
process the curriculum lenses produced by QCA in order to support centres during the pilot of the
Functional Skills (QCA, 2007) were used to supplement (see Appendix 3) the comparison.
The Functional Skills maths criteria states that:
“Specifications at each level must be consistent with the National Curriculum Mathematics and Adult
Numeracy standards at the corresponding levels” at Level 2 ‘ “National Curriculum Mathematics levels 1–6;”
and “Adult Numeracy standards at level 2.”
Problem solving is mentioned as central to both GCSE and Functional Skills qualifications (see Appendix 2).
Further, the technical competencies required for GCSE are broader than that seen in the Functional Skills
criteria and hence it seems reasonable to expect that a learner who achieves C and above in GCSE would
be also be successful in the level 2 functional skills summative assessments – and so be initially assessed
at level 2 or above. The Criteria for Functional Skills Qualifications2 (Ofqual, 2012) applies to all three
functional skills (maths, English and ICT) but is similar in emphasis to the GCSE maths specification –
concentrating on real-world situations (realistic contexts), plus selection and application. Although written in
different formats the two qualifications are very similar (at least as stated in their Ofqual source documents).
As the stated requirements appear to be similar it seems within reason to assume that the demand of the
GCSE and initial assessment should be similar.
Results
Initially a database was set up and the learner data gathered – this proved time consuming but was then
overtaken by a new internal process which gathered much of the data. This allowed the researcher to
highlight learners who had left the college – or had moved from AS onto other courses and it was felt that
1 In September 2011 the GCSE criteria was changed to include functionality and it was therefore expected that the
criteria for the levels within GCSE would change. The 2009 and 2011 level criteria was compared by the researcher
and they were found to be are exactly the same apart from a change in use of the word ‘candidate’ to ‘learner’. The
2009 criteria was used as the 2007 version was not available (all the websites from this time have been archived due
to the closure of QCA/QCDA).
2 The Functional Skills maths qualification is informed by the core curriculum (DfES, 2001), the Criteria for Functional Skills Qualifications (Ofqual, 2012) and the Functional Skills Criteria for Mathematics (Ofqual, 2011b).
Page 11 of 31
this in itself would be useful information for further research. A spreadsheet was developed of all new
learners (‘freshers’) entering college in September 2012 – their school, GCSE maths results, initial
assessment results. Any learner for whom there was not a full set of data (these learners could be
investigated later) was removed. Table 4 below shows the findings - GCSE maths results with FS maths
initial assessment results
Table 4: Initial assessment results against GCSE results
Learners with
maths Grade
IA RESULTS TOTAL NU
OF LEARN
E1 E2 E3 L1 L2 L3
A* 0 0 0 0 1 16 17
A 0 0 1 11 30 18 60
B 0 0 1 19 53 8 81
C 0 3 29 138 64 0 234
D 0 1 31 33 7 0 72
E 0 5 12 8 0 0 25
F 0 5 15 3 1 0 24
G 3 4 4 0 0 0 11
U 1 0 0 0 0 0 1
4 18 93 212 156 42 525
Analysis of the results
Table 4 discussion:
All learners who achieved A* achieved L2 or above
Page 12 of 31
12 learners who achieved A did not achieve L2 or above. 20%
20 learners who achieved B did not achieve L2 or above. 24.7%
170 learners who achieved C did not achieve L2 or above. 72.6%
If the initial assessment and GCSE gave us similar results then we would expect learners with A*, A, B
or C to get level 2 or above. The table above shows 202 learners not achieving level 2 or above. 51.5% i.e.
over half of the learners who have achieved GCSE grade C or above did not achieve what is seen as its
equivalent initial assessment score.
Another interesting finding is that three learners who achieved grade C only achieved entry 2. At the
other end of the spectrum one learner who had achieved a grade F GCSE was initially assessed at level 2.
A total of 239 (45.5%) of the learners achieved less in the initial assessment than would have been
expected by looking at their GCSE grades.
42 learners (0.08%) achieved a higher initial assessment score than would have been expected.
Further investigation into the figures
It is interesting to consider whether achieving grade B or above is more in line with the initial assessment
result: could this be a better indicator than grade C or above? See table 5. 158 learners achieved a grade B
or above, of these 32 did not achieve L2 or above i.e. 20%. If we are looking at simply whether learners
are expected to be working at level 2 or above then these figures may be useful. As would be expected
Grade A*-B is a better predictor than A*-C of whether a learner will achieve an initial assessment score of
level 2 or above but the prediction is wrong in one out of every 5 learners. Grade C does not predict
whether a learner will gain level 2 and above.
Page 13 of 31
Table 5: Maths comparison
GCSE A*-C E1 E2 E3 L1 L2+ total
0 3 31 168 190 392
GCSE A*-B 2 30 126 158
GCSE C 3 29 138 64 234
GCSE D and 4 15 62 44 8 133
Total 4 28 93 212 198 525
It was decided that an image might show the findings more clearly and hence Chart 1 was developed.
Page 14 of 31
Chart 1: Learner maths results GCSE by initial assessment
Chart 1 is a graphical representation of the data in Table 4 (NB the chart was formulated using discrete data
i.e. grades and levels rather than scores and so only general statements can be made). The balloon option
was chosen so that the 3 dimensions of the data could be visualised i.e. initial assessment result, GCSE
result and the numbers of learners achieving each. The graph shows a clear trend between GCSE and
initial assessment results however the spread of results is worth investigating. The spread is in both
directions i.e. a learner achieving any grade other than A* could achieve almost any initial assessment
result. For example:
The gradient of the line of best-fit y=0.4062x + 0.8838 implies that the higher the level a learner achieves
in GCSE the greater their initial assessment result – which one would expect.
The purpose of using the initial assessment at the college is in particular to be able to plan the support
for learners who are working below level 2. The figures show more consistency at the top end (where it is
less crucial). Looking at the figures for lower achievers the spread of their results, if the initial assessment is
accurate, then the GCSE results do not indicate a learner’s skills level. It should be noted that some
Page 15 of 31
colleges do not initially assess any learners who achieve a GCSE C or above and hence would not be
aware of the 72.6% of learners who are working below level 2 (as indicated by the initial assessment).
Learners achieving Grade F GCSE shows a staggering 4 grades from Entry 2 to level 2. Learners gaining
grade D in GCSE ranged from Entry 2 to Level 2.
Conclusions
Looking at the criteria for the Functional Skills (on which the initial assessment is based) and the GCSE it
would appear that their requirements are similar in terms of level and some of the content. Further study
into the summative assessments of the two qualifications is required in order to see if the differences are
within the assessment (rather than the criteria) and hence the preparation for that assessment rather than in
the content.
The findings imply that for a significant number of learners within this FE college their GCSE results and
initial assessment results do not tell the same story. An important consideration of these findings is the
confusion that this may engender among the learners represented by these findings. Learners are routinely
informed that grade C and above is a success in GCSE, but then on initial assessment they may be told that
they need further support within their studies (or in discrete maths classes) to develop the skills they need
for further study. If testing is only a motivator for those who are successful (ARG, 2002) then the initial
assessment may be demotivating for some learners and may increase the gap between achievers and non-
achievers. As a college of further education this College could be a fresh start for learners who have not
performed as well as they could in school. However by starting their FE career with an initial assessment
the college may be cementing the learner’s view of their likelihood of success (or failure). The ARG, 2002
research found that learners who believed they would be successful in tests were more persistent in the
tests – there might be a message in this research for how post 16 providers administer the test (this might
be an area of further study). What the ARG, 2006 research also highlights is the importance of teachers
and tutors using the GCSE (which is summative in nature) and initial assessment results as tools for
formative assessment i.e. assessment for learning. The research goes on to suggest that management
should:
“resist pressure for ‘hard’ data from tests and encourage use of a range of types of evidence of pupil’s
learning.”
ARG, 2006 pp13
The figures suggest that for most learners their GCSE results are not a good predictor of their skills levels.
Many practitioners in further education have been stating this (based on their anecdotal evidence). It seems
Page 16 of 31
appropriate therefore to continue to initially assess all learners rather than to use their GCSE results as
indicators of their maths skills. But it will be essential to present the case for this, and the actions following,
clearly and appropriately to learners.
As was expected this research is only the starting point in looking at initial assessment of maths skills of
learners in order to prepare them for further study.
Review of the approach
A relatively small sample from one college may mean that this could not be replicated for another college.
This small sample may mean that the findings are a result of ‘noise’? There are techniques to look at noise
e.g. student’s t-test and perhaps the data could have been more effectively triangulated.
The findings can only be supported by a larger data set. This could be either by looking at other cohorts
across college in other years and/or looking at other colleges or providers. The researcher has already
begun to look at the figures for this same cohort for English to see if the findings are the same.
The findings may be specific to a ‘time culture and situation’ Robson (2002). The findings may be incorrect
because it can only be based on what is known and so much is unknown. But this is not a reason to not
make statements. Does the data and hypothesis match? Well yes, the findings are what were expected.
Scott and Usher (2002) state that for the findings to be valid they must come from being located outside of
any context. There is a range of contexts which may influence the findings, e.g. feeder schools, social
background of learners, learner’s approach to GCSE and indeed their approach (and understanding) of
initial assessment. The researcher has knowledge and understanding of how the mechanism works
(Robson, 2002) but is aware that the impact of variables cannot be removed. Neither can just one variable
be manipulated it might from a positivist perspectives, causes are not ‘simple & single’ Byrne in Robson
(2002). The researcher was aware of these weaknesses and saw this as simply a first step in investigating
assumptions, often stated anecdotally, by FE practitioners.
An area which does need further scrutiny is the initial assessment tool itself. It may be worth investigating
whether different initial assessment tools give comparable results – this was a recommendation of Estyn,
2006. There is some evidence (see paragraph 48 of the Estyn report) that “Results showed a significant
Page 17 of 31
percentage of learners assessed as needing basic skills support with the BSA assessment were not
identified with a basic skills need on the BKSB assessment.“ So there are already highlighted differences
between the initial assessment tools which could be chosen.
Next steps - Further study needed
There is a whole range of further research to be done, for example:
specific learners outside the range (outliers may highlight useful factors);
learner attributes, for example family circumstances and income. Schools can use free school meals as
an indicator of the social class of their learners – this is not available to FE colleges. The relative
deprivation of the catchment area of the College may have an impact, however Martinez (2001) did not view
this as a good indicator of achievement;
feeder school differences.
Feeder school differences:
GCSEs are used not only as an indicator of learner performance but also as an indicator of ‘the
performance of teachers, schools and the education system” (ARG, 2002). This may skew the results.
There has been a concern for some time that learners are not prepared for A’ level study by our feeder
schools. 11-16 schools are seen by some to focus on maximising their C and above GCSE results:
“There are concerns that the current high stakes assessment system in the form of 'league tables', creates a
situation where institutions are more accountable for results than for the mathematical understanding of their
pupils.” (ACME, 2011b pp3)
this is supported by Ofsted, 2012 pp2 who state:
“GCSE and A-level results continue to rise, as a consequence of the high priority accorded to them by
teachers and leaders in secondary schools, but without corresponding evidence of pupils’ better
understanding of mathematics to equip them for the next stages of their education and future lives. “
Any school must ensure that 30% of its pupils gain five GCSEs (including English and maths) or it faces a
closure threat (TLRP, 2009). This means that the GCSE outcomes are being used for more than one
purpose i.e. for measuring both school and learner performance. But which takes priority? This may result
Page 18 of 31
in some learners having qualifications but not the skills and could disadvantage more able learners,
particularly if they take the GCSE before year 11. In January 2013 Sir Michael Wilshaw, Chief Inspector at
Ofsted ordered a report into how more able learners are taught. He noted in particular the issue of learners
taking summative assessments too early (Henry, 2013). It may well also disadvantage less able learners by
giving an indication of higher skills than they actually possess.
Some further areas to investigate:
Which school did learners go to? This could include looking at the aspects of the school e.g. GCSE
results, league table results (have they been under some pressure to improve their pass rates?) or changes
in staffing. If possible the qualifications of those teaching maths in the feeder schools for example, whether
they are specialist teachers may be available. Gardiner (2012) has highlighted the importance of qualified
staff and the number of schools using staff who are not fully competent leading to non specialists teaching
to the GCSE test. This may result in learners achieving higher GCSE results than their skills would suggest.
Did learners sit higher or lower tier GCSE and did this make a difference?
Did some of the learners sit their GCSE exam year 11 or earlier and did they have any teaching
afterwards?
Ofsted, 2012 has stated that the responsibility for supporting learners in schools to develop the
mathematical skills they need is not being met for all learners with 36% of learners nationally not gaining
grade C GCSE. The main feeder schools to the College are A High, B High, C High, and C High Schools.
What extra support did learners have at school might be a useful question.
Page 19 of 31
Table 6: Schools Comparison
School % of good GCSEs or
equivalents (including En
and maths)
Value Added
A statistical measure of h
well pupils are helped to
progress from their starti
point. A score above 1,0
better than the national a
Five good GCSEs only
(including English and m
A 57 995.5 53
B 44 959.6 41
C 56 979.6 56
D 52 981.8 46
Source: BBC, 2012
There is much to investigate in these figures for example comparing the schools, which are all performing
below the national average for value added, but higher than the national average of schools in relation to
learners gaining grade C GCSE.
The Ofsted, 2012 research notes that learners who are eligible for free school meals do not do as well as
those who are not eligible. It would be an interesting next step to find out how many of the learners whose
GCSE and initial assessment results are not in line with each other were in receipt of free school meals. It
is particularly concerning that learners are not achieving across both measures (GCSE and initial
assessment) when ‘considerable resources’ have been deployed via National Strategies (Ofsted, 2012).
This thinking leads on to looking at the Ofsted results of the feeder schools to see if there are any patterns
within. Ofsted, 2012 saw links between the performance of ‘satisfactory’ teaching of mathematics which
enabled learners to pass GCSEs but did not equip them with an understanding and fluency in maths. It
would be interesting if possible to look at whether the feeder schools got a mathematically rich curriculum or
whether discrete maths classes are the main source of skills development.
Page 20 of 31
One very interesting point in the Ofsted, 2012 report was that:
“Schools were more aware than at the time of the previous survey of the need to improve pupils’ problem-
solving and investigative skills, but such activities were rarely integral to learning except in the best schools
where they were at the heart of learning mathematics. Many teachers continued to struggle to develop skills
of using and applying mathematics systematically. “
These are the very skills that learners need to be successful in functional maths and hence the initial
assessment of functional maths. Perhaps what is needed is for school staff teaching maths (and other
subjects where maths can be embedded) the importance of maths skills and application.
The researcher plans to follow these particular learners through to the end of their programmes (mainly over
two years) and by doing this longitudinal study of this group of learners to assess their distance travelled.
There may be differences between learners on non A’ level courses e.g. apprenticeships, BTEC in terms of
the predictability of their GCSEs. This further work will involve investigating retention and achievement for
the whole cohort and exit interviews for early leavers.
Page 21 of 31
Appendices
Page 22 of 31
Appendix 1 Table 1: Comparison of functional maths and GCSE maths criteria
Functional Maths at Level 2
(Ofqual, 2011b)
Functional skills requirements are inform
GCSE, core curriculum and key skills
standards and guidance. The criteria at
level assumes that the levels below are
understood/secure.
GCSE maths requirement at grade C
(Ofqual, 2001a)
1. Understand routine and non-rou
problems in familiar and unfamil
contexts and situations.
2. Identify the situation or problems
identify the mathematical metho
needed to solve them.
3. Choose from a range of mathem
find solutions.
They identify strategies to solve problems involving a limited
of variables.
Learners identify relevant information, select appropriate
representations and apply appropriate methods and knowled
They are able to move from one representation to another, in
to make sense of a situation
Analysing
4. Apply a range of mathematics to
solutions.
5. Use appropriate checking proce
and evaluate their effectiveness
stage.
Learners tackle problems that bring aspects of mathematics
together.
Learners use a range of mathematical techniques, terminolo
diagrams and symbols consistently, appropriately and accura
Learners are able to use different representations effectively
they
recognise some equivalent representations; for example num
graphical and algebraic representations of linear functions;
percentages, fractions and decimals.
Page 23 of 31
Their numerical skills are sound
and they use a calculator accurately.
They apply ideas of
proportionality to numerical problems and use geometric pro
of angles, lines and shapes.
They communicate their chosen strategy, making changes a
necessary.
6. Interpret and communicate solutions
multi-stage practical
problems in familiar and unfamiliar cont
and situations.
7. Draw conclusions and provide mathe
justifications.
Learners use different methods of mathematical communicat
They understand the limitations of evidence and sampling, a
difference between a mathematical argument and conclusion
based on experimental evidence.
They identify evidence that supports or refutes conjectures a
hypotheses.
They construct a mathematical argument and identify
inconsistencies in a given argument or exceptions to a
generalisation.
Page 24 of 31
Appendix 2 Table 2: Ofqual requirements of GCSE maths and Functional Skills m
qualifications
These documents are written for awarding organisations to write assessments.
GCSE specifications in Mathematics must enable learners to:
develop knowledge, skills and understanding of mathematical methods and concep
acquire and use problem-solving strategies;
select and apply mathematical techniques and methods in mathematical, everyday
real-world situations;
reason mathematically, make deductions and inferences and draw conclusions;
interpret and communicate mathematical information in a variety of forms appropriate
information and context.
Ofqual, 2011a pp3
Criteria for Functional Skills Qualifications
Assessment must be consistent with the levels set out in the skills standards and with t
associated coverage and range specified within the functional skills subject criteria. In
addition, it must:
5.1 provide realistic contexts, scenarios and problems;
5.2 specify tasks that are relevant to the context;
5.3 require application of knowledge, skills and understanding for a purpose;
5.4 require problem solving;
Ofqual, 2012, pp2
Page 25 of 31
Appendix 3 Table 3: QCA Curriculum Lenses
GCSE (KS4) Functional skill level 2
Representing Representing - making sense of situations and
representing them
Identify the mathematical aspects of the situatio
problem
Recognise that a situation has aspects that can
represented using mathematics
Simplify the situation or problem in order to rep
mathematically, using appropriate variables, symbo
diagrams and models
Make an initial model of a situation using suitab
of representation
Compare and evaluate representations of a situ
before making a choice
Select mathematical information, methods and
use
Decide on the methods, operations and tools, in
ICT, to use in a situation
Select mathematical information, methods and
use
Select the mathematical information to use
Analysing Analysing - processing and using the mathema
Use appropriate mathematical procedures Use appropriate mathematical procedures
Look for and examine patterns and classify
Make and justify conjectures and generalisation
considering special cases and counter examples
Examine patterns and relationships
Explore the effects of varying values and look f
invariance
Change values and assumptions or adjust relat
to see the effects on answers in the model
Work logically towards results and solutions Find results and solutions
Page 26 of 31
recognising the impact of constraints and assumpt
Interpreting and evaluating Interpreting - interpreting and communicating t
results of the analysis
Form convincing arguments to justify findings a
general statements
Interpret results and solutions
Relate their findings to original question or conj
and indicate reliability
Draw conclusions in the light of the situation
Consider the assumptions made and the
appropriateness and accuracy of results and concl
Consider the appropriateness and accuracy of t
results and conclusions
Communicating and reflecting Interpreting - interpreting and communicating t
results of the analysis
Use a range of forms to communicate findings t
different audiences
Engage in mathematical discussion of results
Use appropriate language and forms of present
communicate results and conclusions
Bibliography
ACME, 2011a. Mathematical Needs Summary. [online] Available at:
http://www.nuffieldfoundation.org/sites/default/files/files/ACME_4pp_overarching_ report_summary.pdf
[Accessed 21 January 2013].
ARG, 2002. Testing, Motivation and Learning. [online] Available at:
http://assessmentreformgroup.files.wordpress.com/2012/01/tml.pdf Accessed 6 February 2013.
ARG, 2006. The role of teachers in the assessment of learning. [online] Available at:
http://assessmentreformgroup.files.wordpress.com/2012/01/asf_english.pdf [Accessed 6 February 2013].
ACME, 2011b. ACME Mathematical Needs Project. [online] Available at: http://www.acme-
uk.org/news/news-items-repository/2011/6/launch-of-the-acme-mathematical-needs-project [Accessed 22
January 2013].
ALI, 2002. Initial Assessment Survey Report [online] Available at:
http://dera.ioe.ac.uk/10379/1/finalinitialassessment.pdf Accessed 6 February 2013.
AQA, 2013. How do you measure a student’s progress? [online] Available at: http://youtu.be/AwJYb-Bmd8A
[Accessed 30 January 2013].
BBC, 2012. Secondary school league tables in North Yorkshire. [online] Available at:
http://www.bbc.co.uk/news/special/education/school_tables/secondary/11/html/five_gcses_815.stm?compar
e=8154232+8154225+8154216+8154224 [Accessed 22 February 2013].
BIS, 2012 The 2011 Skills for Life Survey: A Survey iof Literacy, Numeracy and ICT Levels in England.
[online] Available at:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/36000/12-p168-2011-skills-
for-life-survey.pdf [Accessed 27 February 2013].
CIPD, 2012. Your objective for 2013? Not to have SMART objectives. [online] Available at:
<http://blog.peoplemanagement.co.uk/2013/01/your-objectives-for-2013-not-to-have-smart-
objectives/?utm_medium=email&utm_source=cipd&utm_campaign=pmdaily&utm_content=030113_comme
nt_1> [Accessed 6 February 2013].
Estyn, 2006. Post 16 Basic Skills Provision: Basic skills initial assessment, support and monitoring systems
– 2006. [online] Available at: <http://www.estyn.gov.uk/english/docViewer/172071.9/post-16-basic-skills-
provision-basic-skills-initial-assessment-support-and-monitoring-systems-2006/?navmap=30,163,>
[Accessed 3 January 2013].
DfES, 2001. Adult Numeray core curriculum. [online] Available at:
http://www.counton.org/resources/adultcc/pdfs/resource_130.pdf. [Accessed 6 February 2013].
Gardiner, T., (2012) Tony Gardiner: A mathematician’s view of the current education scene in the UK.
[online] Available at: http://education.lms.ac.uk/2012/10/tony-gardiner-on-education-policy-2/ [Accessed 22
February 2013].
Henry J., (2013) Brightest pupils failed by state schools, chief inspector warns The Telegraph, [online]
Available at: http://www.telegraph.co.uk/news/9828734/Brightest-pupils-failed-by-state-schools-chief-
inspector-warns.html [Accessed 22 February 2013].
Ofqual, 2011a. GCSE criteria for English and maths. [online] Available at:
http://www2.ofqual.gov.uk/downloads/category/192-gcse-subject-criteria [Accessed 30 January 2013].
Ofqual, 2011b. Functional Skills regulatory criteria. [online] Available at:
http://www2.ofqual.gov.uk/downloads/category/68-functional-skills-subject-criteria [Accessed 6 February
2013].
Ofqual, 2012. Criteria for Functional Skills Qualifications. [online] Available at:
http://www2.ofqual.gov.uk/downloads/category/68-functional-skills-subject-criteria [Accessed 6 February
2013].
Ofsted, 2013. Mathematics: made to measure. [online] Available at:
http://www.ofsted.gov.uk/resources/mathematics-made-measure [Accessed 14 February 2013].
Pearson, 2013a. Learning Curve. [online] Available at: http://thelearningcurve.pearson.com/the-
report/executive-summary Accessed 29 January 2013 [Accessed 6 February 2013].
Pearson, 2013b. Learning Curve. [online] Available at: http://thelearningcurve.pearson.com/the-
report/education-inputs-and-outputs [Accessed 29 January 2013].
QCA, 2006 Report of consultation on draft functional skills standards January to May 2006 [online] Available
at: http://dera.ioe.ac.uk/8895/1/spb_12-4_standards_consultation_report2.pdf [Accessed 22 February 2013].
QCAa, 2007. Functional skills in the revised programme of study for mathematics. [online] Available at:
http://archive.naaidt.org.uk/news/docs/conf2007/docs/secondarycurriculumreviewcdrom/qca/lenses/skills/fu
nctional-skills/maths-ks4/index [Accessed 6 February 2013].
QCAb, 2007. The importance of mathematics. [online] Available at:
http://archive.naaidt.org.uk/news/docs/conf2007/docs/secondarycurriculumreviewcdrom/qca/subject/ks4/mat
hematics/index.htm [Accessed 6 February 2013].
QCAc, 2007. Curriculum aims. [online] Available at:
http://archive.naaidt.org.uk/news/docs/conf2007/docs/secondarycurriculumreviewcdrom/qca/subject/ks4/mat
hematics/index.htm [Accessed 6 February 2013].
Martinez P., 2001. Improving student retention and achievement: what do we know and what do we need to
find out? LSDA Report. Available at: http://core.kmi.open.ac.uk/display/4153982 [Accessed 3 January
2013].
NCSALL, 2005. Helping adults persist. [online] Available at:
http://www.ncsall.net/fileadmin/resources/teach/persistence_role.pdf [Accessed 3 January 2013].
Ofsted, 2012. Common inspection framework. [online] Available at:
<http://www.ofsted.gov.uk/resources/handbook-for-inspection-of-further-education-and-skills-september-
2012> [Accessed 22 January 2013].
Robson C. (2002). Real world research. Oxford: Blackwell
Scott, D., and Usher R., (2002) Understanding educational research London: Routledge.
TLRP, 2009. Assessment in schools: Fit for purpose? [online] Available at:
http://www.tlrp.org/pub/documents/assessment.pdf [Accessed 6 February 2013].
Warwick, M. 2006 Maths ‘dumbed down’ at GCSE. TES Available at:
http://www.tes.co.uk/article.aspx?storycode=2199505 [Accessed 3 January 2013].
About the author – Gail Lydon
After graduating Gail worked for a number of bIue chip companies including PWC, IBM and British Gas
before she moved into teaching – she describes this as the best career decision she has ever made. Gail
has a passion for lifelong learning for all – and has worked in teaching, training and staff development for
over 25 years. Initially working as a Business and Economics teacher Gail became convinced of the
importance of secure literacy, numeracy and ICT skills for her learners – this led her to move into SfL and
key skills support and the pioneering of embedding skills within the programmes she was teaching in FE.
She was the Y&H Regional Facilitator for the Functional Skills Support Programme and Key Skills Support
Programmes. Here she supported centres to develop good practice in functional skills teaching and
learning and management. She is also an associate lecturer for Hull University and has a number of
freelance projects writing and delivering CPD around the country.
Presently she teaches both Functional English and maths in an FE college and is planning to continue her
practitioner research into issues around literacy and numeracy.
Related Documents
