
4.1 
The Post14 Mathematics Inquiry has proceeded in parallel with the work
of the Working Group on 1419 Curriculum and qualifications reform in England,
chaired by Mike Tomlinson. In its Interim Report in February 2004
(DfES/0013/2004), the Working Group outlined broad proposals for the phase
of 1419 learning, including the development of a new diploma framework that
would cover the whole of the 1419 learning programme. The Interim Report
includes proposals to move away from the existing agerelated qualifications
to a system offering more opportunities for students to achieve qualifications
in their own time and at their own ability and aptitude level, while offering
coherent pathways of progression. Such a framework should provide candidates
with opportunities to demonstrate and record specific mastery of skills and
topics rather than recording overall levels of success or failure. A key
feature of the Tomlinson proposals is a single 1419 learning continuum in
place of the current perception of 1416 and 1619 as two distinct phases. 
4.2 
The Working Group proposals will encourage more students to obtain level
3 qualifications. So far as mathematics is concerned, the proposals incorporate
the possibility of more specialist study of mathematics beyond a mandatory
core of foundational mathematics. Although the Mathematics Inquiry has proceeded
independently from the Working Group on 1419 Reform, the Inquiry has found
there to be a strong consensus within the mathematics community in favour
of a diploma type of approach to qualifications. 
4.3 
So far as mathematics is concerned, the Post14 Mathematics Inquiry agrees
with the 1419 Working Group’s conclusion that the present qualifications
framework is in need of a radical overhaul. The first part of this chapter
will discuss in detail the concerns expressed to the Inquiry about the current
framework. This will lead us to make specific short and mediumterm
recommendations regarding the current framework. We see these not only as
important steps towards improving the current structure, but also as contributing
to a longer term direction of travel, compatible with the Tomlinson notion
of progressive pathways, each with its own mathematical components. We see
some version of the latter as the key to providing a structure whereby all
students have access to a relevant mathematics pathway appropriate to their
learning needs, and relevant to end destinations in the workplace, or continuing
education, post19. In the view of the Inquiry, mathematics should be seen
as an integrated whole when designing 1419 pathways. We begin with a review
of concerns with the current structure. 

4.4 
The Inquiry has no doubt that, compared with the previous Olevel/CSE
structure, GCSE Mathematics has been beneficial to many more students and
has provided them with an adequate background for further study in the subject.
However, respondents to the Inquiry have raised a number of serious concerns,
which the Inquiry believes to be well founded. 
4.5 
In GCSE Mathematics, only about 50 per cent of the candidature achieves
the iconic ‘pass’ grades A*C. Many repeat GCSE to try to improve
their grade, having failed to reach at least a C grade first time round at
age 16. There do not appear to be easily accessible data on resit performance,
but respondents to the Inquiry report that a significant number of resit
candidates do not achieve an improved grade. More generally, far too few
young people in England achieve level 2 qualifications in mathematics and
England seriously lags behind its European competitors in this respect. 
4.6 
Whilst accepting that the decision to have a threetier arrangement for
mathematics was made with the best of intentions, respondents to the Inquiry
have overwhelmingly expressed grave concern that GCSE mathematics is now
the only GCSE subject where a grade C is not accessible on all the tiers.
In the light of concern expressed about the threetier structure, the regulatory
bodies have given further consideration to appropriate assessment mechanisms
and is running a pilot of a two tier GCSE examination in mathematics with
OCR. 
4.7 
The pilot scheme has three examination papers and all candidates sit
a combination of two of these. Candidates studying the Foundation PoS are
entered for Paper 1 (targeting grades EG) and for Paper 2 (targeting grades
CD). Those studying the Higher PoS are entered for Paper 2 and for Paper
3 (targeting grades A*B), but could be entered for Papers 1 and 2 if they
are having difficulty with the course. Every student therefore has access
to a grade C and there will be only one route to each grade. The pilot will
run through two complete cycles. The first examinations took place in June
2003 and there will be a second round in June 2004. Ministers will be notified
of outcomes and advised of any proposed changes in December 2004. Any
modification of the current arrangements in England will require Ministerial
approval. 
4.8 
The Inquiry has been informed that the QCA would wish to see this twotier
assessment structure become the standard examination structure for GCSE
Mathematics within a few years. The assessment structure would then mirror
the revised curriculum structure, a correspondence that many respondents
clearly believe to be important. We believe that this was the original intention
at the time of the 1999 revision of the curriculum, but was shelved on the
grounds that such additional change to the system would be have been too
disruptive at that time. The majority of respondents to the Inquiry seem
to believe that most teachers would now welcome the shift to twotier examining
as fitting in more naturally with their curriculum planning and setting into
cohorts for the Key Stage 4 Higher and Foundation Programmes of Study. 
4.9 
The threetier assessment structure does not mirror the twotier structure
of the revised curriculum. Moreover, the existing threetier arrangement
for assessing GCSE Mathematics disbars about one third of candidates from
having access to a grade C. Since grade D is the highest grade achievable
on the Foundation Tier papers, respondents report that many students feel
themselves to have been classed as “failures” by their teachers
before they even start the course. The Inquiry shares this concern. Rightly
or wrongly, public opinion – no doubt much influenced by school league
tables – has come to regard a grade C at GCSE as a minimal acceptable
level of attainment. It therefore seems to the Inquiry totally unacceptable
to be entering some 30 per cent of the age cohort into a tier in which
“externally perceived success” (ie grade C) is unattainable whatever
the level of achievement. 
4.10 
The existing arrangements for assessing GCSE Mathematics allow raise
issues regarding the interpretation of GCSE grade B. This grade can be awarded
both on the Intermediate Tier papers and also on the Higher Tier papers.
However, respondents are clear that the algebraic and geometric content
associated with the Intermediate Tier is significantly less than the algebraic
and geometric content associated with the Higher Tier and that this means
that there cannot be an unambiguous interpretation of GCSE grade B in
mathematics. In particular, there is concern in relation to preparedness
for AS/Alevel mathematics. Many clearly feel that, without some form of
bridging course, candidates obtaining a grade B in mathematics on the
Intermediate tier have an inadequate basis for moving on to AS and A2. They
have had too little fluency in algebra and too little routine practice with
reasoning about geometric properties and relations. 
4.11 
However, it has been put to the Inquiry that the tactical behaviour of
schools and pupils is being influenced by the perception that it is easier
to get a grade B for GCSE mathematics by being entered for the Intermediate
Tier. We have been informed that when grade B was first introduced as a possible
outcome on the Intermediate Tier, entries for the Higher Tier fell from nearly
30 per cent to about 15 per cent of the candidate cohort and have remained
relatively stable since then. The Inquiry finds these consequences of the
current arrangements to be worrying, both in terms of the interpretability
of grades and the perverse incentives it provides for placing pupils on
educationally inappropriate pathways. We suggest that those piloting the
twotier system take on board these concerns. 
4.12 
The GCSE Mathematics examinations in summer 2003 were the first to assess
the revised twotier curriculum. Anecdotal evidence to the Inquiry indicates
that the new coursework regulations have caused some problems to some teachers
and pupils. It may also be the case that teachers may not have fully acquainted
themselves with the content of the Higher PoS. The Inquiry is not in a position
to properly assess the new twotier initiative or the twotier assessment,
but nevertheless believes that serious consideration should be given to moving
to a twotier structure. 

Recommendation 4.1
The Inquiry recommends that, subject to the present pilot being fully and
successfully evaluated, immediate consideration be given by the QCA and its
regulatory partners to moving as soon as is practicable to a twotier system
of overlapping papers for GCSE Mathematics in England, Wales and Northern
Ireland. The Inquiry recommends that the regulatory authorities try to recruit
more schools and colleges to take part in preimplementation piloting after
summer 2004. 
4.13 
Many respondents clearly feel that mathematics is not rewarded sufficiently
at level 2 in comparison to English and science and this is also reflected
in responses given in focus groups organised by QCA on behalf of the Inquiry.
It is widely believed by pupils and teachers that the amount of effort required
to achieve a single GCSE award in Mathematics is similar to the amount of
effort required to gain the two awards in English Language and Literature
or to gain a Double Award in Science. There is a widespread concern that
this is adding yet further to the perception of mathematics as a
disproportionately hard subject and may be adversely affecting pupils’
subsequent choices post 16. The Inquiry believes that this to be a serious
issue and supports the view that serious consideration should be given to
making a double award available for mathematics for the higher tier route
(either in the current structure, or in a revised twotier structure). 
4.14 
We acknowledge that consideration needs to be given as to how to do this
so as to ensure that such a double award is on a par with the double award
for GCSE Science. The Inquiry has not had the time or resources to provide
detailed practical recommendations regarding the necessary curriculum and/or
assessment adjustments required (in either the twotier or threetier
structures). However, we would wish to make the following clear recommendation. 

Recommendation 4.2
The Inquiry recommends that, at the earliest possible opportunity, consideration
should be given by the QCA and its regulatory partners to redesignating
GCSE Mathematics, appropriately modified if necessary, to merit a double
award at level 2. This redesignation should be considered in tandem with
the possible move to a twotier system (see Recommendation 4.1). 
4.15 
Many respondents have expressed serious doubts about the value of GCSE
mathematics coursework, in particular the datahandling component. There
is concern that current requirements lead to a rather artificial approach
to analysing and interpreting data, rather than encouraging substantive
involvement with “real life” problems. There is also concern over
the comparatively large amount of time spent on GCSE coursework in relation
to the amount of timetabled time for the subject itself. We are aware that
the QCA has amended the coursework marking criteria in response to perceived
teething troubles, but the Inquiry still feels that there is sufficient concern
to merit a review of current requirements. This needs to be considered alongside
Recommendation 4.4. 

Recommendation 4.3
The Inquiry recommends that there should be an immediate review by the QCA
and its regulatory partners of the quantity of coursework in GCSE mathematics
and, in particular, the data handling component, with a view to reducing
the amount of time spent on this specific element of the course. (See, also,
Recommendation 4.4) 
4.16 
More generally, there has been considerable disagreement among respondents
regarding the appropriate treatment of the Handling Data strand of the PoS
for Key Stage 4 (Higher). Basic Probability is clearly seen as part of the
mathematics core, but some have argued that Handling Data should be absorbed
into the using and applying mathematics strands in number and algebra and
in shape, space and measures. Others have argued that the roles of Statistics
and Data Handling are so fundamentally important, both in other disciplines
and in the workplace, that, in the long term, these topics need to be found
their own timetable niche – perhaps embedded in the teaching of other
disciplines – rather than taking up a substantial part of the mathematics
timetable that used to be available for practice and reinforcement of fluency
in core mathematics techniques. In addition, the function of GCSE Statistics
is thought by many respondents to be unclear. The majority view is that it
is not sensible for pupils who achieve a good GCSE Mathematics pass in year
10, or earlier, either to discontinue the study of mathematics altogether
in year 11 or to study GCSE Statistics as an additional GCSE replacing formal
study of mathematics in this year. Conversely, it is suspected that some
pupils are entered for GCSE Statistics because it is seen as a softer option
than GCSE Mathematics itself in terms of grade attainment, rather than for
sound educational reasons. 
4.17 
The Inquiry strongly believes that knowledge of Statistics and Data Handling
is fundamentally important for all students and would wish to see these topics
continue to be given due emphasis and timetable allocation. However, we believe
it would be timely – in the context of a radical rethink of future
14 19 mathematics pathways within the general structure that may emerge
following the 1419 Working Group review – to reconsider the current
positioning of Handling Data within the GCSE mathematics timetable, where
it occupies some 25 per cent of the timetable allocation. Many respondents
believe the current mathematics curriculum at Key Stage 4 to be overloaded.
We have no doubt that much of the concern expressed to us about the perceived
decline of fluency with core mathematical operations reflects the pressure
on the mathematics timetable that has resulted from the inclusion of this
significant element of Handling Data. 
4.18 
We have also received a number of responses arguing that the teaching
and learning of Statistics and Data Handling would be greatly enhanced if
they were more closely integrated with the other disciplines that rely heavily
on these topics, such as biology and geography. We support this view and
believe it to be timely to begin to review this issue in the context of the
general philosophy of the approach to 1419 learning programmes emerging
from the Tomlinson review. This prompts our next recommendation, which should
also be considered in the context of our longerterm recommendations about
future pathways set out later in this chapter. 

Recommendation 4.4
The Inquiry recommends that there should be an immediate review by the QCA
and its regulatory partners of the future role and positioning of Statistics
and Data Handling within the overall 14–19 curriculum. This should be
informed by: (i) a recognition of the need to restore more time to the
mathematics curriculum for the reinforcement of core skills, such as fluency
in algebra and reasoning about geometrical properties and (ii) a recognition
of the key importance of Statistics and Data Handling as a topic in its own
right and the desirability of its integration with other subject areas (see,
also, Recommendation 4.11). 
4.19 
In terms of usable skills, although GCSE grade C is the minimum societal
expectation, evidence to the Inquiry suggests that employers are often less
than happy about the mathematical abilities of recruits with GCSE, even when
the grade obtained is at least a C. The perception of the level of mastery
signified by a grade C has been further damaged by the claim in an article
in the Daily Express in the summer of 2003 that some students were achieving
the grade on the basis of 15 per cent raw marks. More generally, evidence
to the Inquiry and the findings of the report Mathematical Skills in the
Workplace suggest that GCSE Mathematics itself now seems to many employers
to be an inadequate preparation for the growing mathematical needs of the
workplace. The perception is that students are learning most of their mathematics
in a vacuum, with little attention given to any sort of mathematical modelling,
or to a range of problems set in real world contexts and using real data.
In addition, the report Mathematical Skills in the Workplace makes
clear that there is serious concern that students have little exposure to
how ICT can be used to enhance each of these aspects of mathematics, even
though employers today increasingly want a combination of mathematical skills
harnessed to ICT skills. In terms of the appeal of the subject to students,
evidence from focus groups run by the QCA for the Inquiry reveals that for
many students, GCSE Mathematics seems irrelevant and boring and does not
encourage them to consider further study of mathematics. At the same time,
many respondents have impressed on us the dangers of also losing the attention
and interest of some of the most able because of the perceived lack of depth
and challenge in the standard curriculum. 
4.20 
The Inquiry is acutely aware of the dangers of diluting the essence of
the discipline of mathematics by inappropriate attempts to make everything
immediately “relevant” and by the use of clearly unrealistic versions
of “real” problems. That said, we believe that the time has come
for a radical relook at longerterm options for 1416 mathematics provision
that do provide sufficient appropriate pathways for those who need motivating
more through perceived practical relevance. We shall later make recommendations
directed at beginning this process. In the meantime, we believe that there
is an immediate action to be taken in relation to the needs of the most
mathematically able. 

4.21 The Inquiry believes that it is vitally important to
provide appropriate challenge for the mathematically more able and motivated.
We also accept the view of the overwhelming majority of respondents to the
Inquiry that current provision is failing in this respect. Some respondents
to the Inquiry have suggested that the more able students should be catered
for by accelerating their exposure to material covered at higher qualification
levels. The overwhelming majority of respondents disagree. The prevailing
view is that what is required is deeper challenge and exposure to more openended
problem solving with material from the student’s current
qualification stage. The Inquiry supports this latter view. We have an open
mind about whether such provision should be statutory and whether it should
lead to a formal qualification. 

Recommendation 4.5
The Inquiry recommends that the QCA and its regulatory partners should be
funded to develop an extension curriculum and assessment framework for more
able pupils at Key Stages 3 and 4. This extension curriculum should be firmly
rooted in the material of the current Programmes of Study, but pupils should
be presented with greater challenges. These should involve harder problem
solving in nonstandard situations, a greater understanding of mathematical
interconnectedness, a greater facility in mathematical reasoning (including
proof) and an ability to engage in multistep reasoning and more openended
problem solving (see, also, Recommendation 4.11). 

4.22 
The Inquiry also believes that the action is vital to provide appropriate
challenge and motivation for those who need and want to continue the study
of mathematics post16, but are primarily motivated by seeing the relevance
of mathematics in the context of a range of realworld applications. In this
connection, many respondents have indicated to the Inquiry that there is
insufficient awareness and use of the FSMQs and AS Use of Mathematics
qualifications. In particular, respondents have indicated that there is scope
for more level 2 FSMQs, to cover a wider spectrum of mathematics. In particular,
it is argued that a level 2 Use of Mathematics should be developed along
lines similar to the existing AS Use of Mathematics. The Inquiry has not
had the time or resources to consider this in depth. However, we do believe
it would be timely to conduct a review of all these issues and we suggest
a way forward in Recommendation 4.7. 
4.23 
Despite the rapidly increasing numbers making use of FSMQs, take up remains
comparatively small. Despite some very positive reports, the Inquiry does
not feel that there is sufficient experience of their use for it to be able
to judge clearly the merits or otherwise of the current portfolio of FSMQs.
However, the Inquiry has become aware of a number of seemingly unnecessary
current obstacles to delivery and further takeup. These include:

the difficulty of promoting FSMQs in institutions with small class numbers
of students; currently, there is better take up in Colleges of Further Education
and Sixth Form Colleges than in secondary schools;

a lack of awareness of FSMQs among some parents, employers and admissions
tutors in higher education institutions;

the possible difficulty of obtaining funding for teaching; in FE colleges,
it is not possible to claim funding for both Application of Number and FSMQs;
the Inquiry is not able to judge whether reported shortages of funding for
tutorials, key skills and enrichment reflect local management decisions,
or result from national LSC funding rules.

4.24 
The Inquiry accepts that prima facie FSMQs have much to offer, particularly
in the context of a redesign of 1419 mathematics pathways. It would therefore
clearly be highly desirable to have greater experience of their use as part
of the process of working towards a richer portfolio of 1419 pathways. However,
we accept that this is unlikely to happen without at the very least a concerted
campaign to raise the profile and acceptance of these qualifications. More
generally, we are concerned that provision of Application of Number has not
been developed within a coherent framework together with FSMQs and AS Use
of Mathematics. We are concerned about this potentially lack of coherence
and believe that it would now be timely to review this whole portfolio of
provision as a prerequisite to the redesign of more practically oriented
pathways within a new 1419 structure. A specific way forward is detailed
in Recommendations 4.6 and 4.7. 
4.25 
The Inquiry has received a significant number of responses raising serious
concerns about the implementation of the key skills agenda and particularly
the AoN component. While there are doubtless instances where successful
implementation is taking place, the messages we have received are overwhelmingly
negative. The Inquiry is aware of the danger of being overinfluenced by
strongly expressed views and is conscious of the fact that it has had neither
the resources nor the expertise to conduct independent studies or surveys
in relation to many of the issues raised. However, the messages have been
consistent enough for us to be convinced that this whole area requires at
the very least a thorough and radical review. 
4.26 
One key issue around the delivery of AoN has been whether delivery should
be separate or integrated with the students’ other courses, particularly
those of a vocational nature. The Inquiry shares the view of many respondents
that for many students at this stage of their education, particularly those
who have made firm vocational choices, integration of the mathematics with
the vocational subject would be highly desirable. In practice, however, evidence
to the Inquiry makes clear that many teachers on nonmathematical courses
have found it very difficult to provide satisfactory delivery of AoN. Many
teachers of vocational subjects who are not mathematics specialists are not
confident in their understanding of how mathematics can be used to enhance
their own areas of work. They typically have even less confidence in teaching
mathematics to their students, who also work from a very low level of
mathematical understanding. This seems to be especially true of students
on Modern Apprenticeships. Many of these students may need to address problems
with their basic numeracy skills before moving on to AoN. The Skills White
Paper in England announced that the services provided by the Key Skills Support
Programme will continue to be available to practitioners in schools, colleges
and workbased training from 200405. The Inquiry acknowledges the efforts
that are being made here, but continues to be concerned that the issue of
the vocational teachers’ actual skills and confidence levels in mathematics
are not being fully addressed. 
4.27 
We understand from respondents to the Inquiry that, in practice, in most
FE Colleges the delivery of AoN is currently the responsibility of specialist
mathematics staff, many of whom would regard themselves better employed teaching
other aspects of mathematics where their specialist skills are more crucial.
Where this is the case, this has clearly resulted in tensions for local managers
in reconciling teacher preferences and learners’ needs and effectively
deploying specialist teaching resources. Such tensions have often been difficult
to resolve, although in many cases local solutions have been found. In some
cases, mathematics specialists have shared the teaching load with vocational
or other subject specialists. In others, specialist teachers have provided
a resource to support and advise other teachers. Overall, however, the Inquiry
is clear that there is a continuing serious shortterm problem with teaching
delivery of AoN. We cannot see an immediate solution. However, longerterm
we believe that effective support for integrated delivery and for enhancing
the mathematical and mathematics teaching skills of specialists in vocational
subjects can and should be provided through the national infrastructure for
the support of teaching of mathematics. (See, Chapters 5 and 6.) 
4.28 
Separate from the issue of teaching delivery, many respondents to the
Inquiry are concerned that the mathematical content of AoN is too narrow;
in particular, there is concern about what is seen as the superficial approach
to the component relating to collecting and interpreting data. The narrowness
of the content doubtless reflects the original conception of limiting the
mathematics to core numeracy in order not to burden students with unnecessary
content. However, the concern has been raised that this may have resulted
in the too rigid exclusion of closely related and relevant mathematics that
in many cases would help individual students with their vocational specialisms
and other studies. This, in turn, is seen as an obstacle to students fully
appreciating the relevance of application of number element of key skills
to their interests and course of study. The Inquiry notes this widespread
concern, but has not had the resource or expertise to make a definitive
judgement. 
4.29 
There has been some concern that some of the requirements of portfolios
have made them difficult to complete. Also, there are concerns that the form
in which evidence is required may often be too structured and inflexible.
This current inflexibility, together with problems of integrated teaching
delivery referred to above, is felt to lead in many cases to poor integration
of key skills and to encourage standalone key skills activities. We note,
also, that concern about the external tests for AoN has been voiced by
representatives of those involved in delivering the the workbased route.
In particular, it has been argued that the tests are too academic. The Inquiry
notes that the Skills White Paper measures represent a response to these
and other concerns about the key skills external tests. The measures offer
support for key skills teaching and learning, more accessible assessment
and more equitable funding. The Inquiry notes that the QCA and its regulatory
partners have taken these views into account in their recent review. As a
result of the review, the key skills assessment arrangements will remain
unchanged in England, with a continuing use of both test and portfolio evidence.
In Wales, assessment from September 2004 will be based on a portfolio only
model. In Northern Ireland, an operational pilot of a portfolio model with
a taskbased external element will be implemented from September 2004. A
further important factor in the appeal and value of key skills qualifications
has been, and will continue to be, the attitude of universities. The current
position is that some 33 per cent of the total of 45,974 courses on offer
in HE for entry in 2003 accepted the key skills tariff points. 
4.30 
Another concern communicated to the Inquiry is that the AoN qualifications
lead to a serious distortion of the way in which qualifications are deemed
to be equivalent to each other. AoN can be taken at levels 14 in schools,
Sixth Form Colleges and in Colleges of Further Education. Level 3 AoN is
only a small subset of the mathematics provision at the level 2 end of
GCSE Mathematics. Similarly, level 2 AoN is only a very small subset of the
entirety of mathematics at the level 1 end of GCSE Mathematics. However,
the impression has been given that level 2 AoN can be thought of as equivalent
to a GCSE ‘pass’ in Mathematics and that a level 3 AoN can be thought
of as mathematical attainment beyond GCSE. Respondents to the Inquiry are
clear that GCSE Mathematics and level 2 AoN are not fully equivalent in
mathematical content and should not be thought of as equivalent on this basis.
From the perspective of having an unambiguous understanding of mathematics
qualifications, we therefore accept that there is a problem in both GCSE
and level 2 AoN being defined as level 2 qualifications. In the same way,
level 2 AoN is not nearly as mathematically demanding as a level 2 FSMQ.
The fact that AoN demands are not appropriate at their stated level of the
NQF is seen by a number of respondents as potentially bringing the framework
into disrepute. They note that the level 3 AoN qualification contains no
mathematics above the equivalent of grade B GCSE, and only one item at that
level; they also note that the mathematics of the AoN level 3 qualification
corresponds to the bottom end of level 2. This leads to considerable confusion
amongst users, who, not unnaturally, assume that all mathematical qualifications
at level 3 include mathematical material at the same level. Respondents also
views with concern the Universities and Colleges Admissions Services (UCAS)
tariff of 20 points for level 3 AoN. This is the same tariff as for grade
A performance on a level 3 FSMQ, which does represent genuine mathematics
achievement at this level. Decisions on the current allocation of qualifications
to levels within the NQF are the statutory responsibility of the regulatory
authorities. This prompts the following recommendation. 

Recommendation 4.6
The Inquiry recommends that QCA and its regulatory partners undertake a
comparative review and make appropriate redesignations as necessary, to
ensure that claimed equivalences of levels of mathematics qualifications
are well founded. 
4.31 
In our increasingly technological and informationrich society, mathematical
skills are becoming more and more important. Rather than decreasing the need
for mathematics, as evidenced in the Mathematical Skills in the
Workplace report, the rise of information technology has increased the
range of mathematics needed to perform competently in the workplace. The
majority of respondents are clear that AoN does not deliver the full range
of mathematical skills and knowledge that this report shows to be essential
in the workplace across many important sectors of the modern economy. The
Inquiry accepts this, but, in fairness to the developers, also recognises
that AoN was not designed to achieve these ends. However, the fact remains
that evidence to the Inquiry from focus groups organised by QCA on behalf
of the Inquiry makes clear that AoN is disliked by many students and by many
provider institutions and that there is a widespread perception – which
the Inquiry reports rather than endorses – that being in possession
of an AoN qualification rarely results in candidates having transferable
mathematics skills of any worth. Some respondents to the Inquiry have been
much more positive about the extent to which FSMQs have the potential to
impart worthwhile, transferable mathematical skills. In view of the limited
take up thus far of FSMQs, we can again only report, rather than endorse,
this perception. 
4.32 
The Inquiry has also been told that present funding regimes for colleges
create greater incentive to provide AoN at the expense of FSMQs. If this
really reflects national LSC funding rules rather than local management
decisions, this would seem to the Inquiry to be a somewhat perverse incentive.
Piecemeal development has led to patchy provision at levels 1 and 2 and we
are persuaded that it is unhelpful to consider numeracy and AoN to be distinct
from mathematics itself. There is a need for a more coherent and comprehensive
approach. Currently, in FE colleges both the provision of AoN and the widespread
use of GCSE resits stand in the way of such an approach. Gaps and overlaps
in mathematics provision and qualifications at levels 13 were reviewed by
the QCA in 2002 and the findings made available to the Inquiry. The Inquiry
believes that it would now be timely to ask the QCA and its regulatory partners
to extend this work into a general review of problems with the delivery,
content and assessment of AoN and the availability to students of FSMQs and
AS Use of Mathematics, with a view to feeding into work on the design of
future 1419 mathematics pathways. This would also provide an opportunity
to explore and promote greater use of ICT in the delivery of future developments
of these courses. 

Recommendation 4.7
The Inquiry recommends that the QCA and its regulatory partners undertake
an immediate review of current problems of delivery, content, assessment
and availability of courses at levels 1– 3 provided by FSMQs, AS Use
of Mathematics, AoN and Adult Numeracy. The aim of the review should be to
identify scope for improvements in and potential rationalisation of this
provision, including opportunities for more systematic integration of ICT
in teaching and learning, as part of the longerterm design of a new 14–19
pathway structure for mathematics (see, also, Recommendation 4.11). 

4.33 
Although GCE has historically been regarded in some quarters as a gold
standard, there have been a number of serious concerns for some time. The
Dearing Reforms tried to give more rigour to Alevel mathematics and tried
to demand prerequisite achievement at the upper end of GCSE Mathematics.
However, respondents to the Inquiry have overwhelmingly reported that some
of the Dearing recommendations, especially those of a more generic nature
reflected in the Curriculum 2000 AS plus A2 model, have had very negative
consequences for mathematics. The Inquiry is convinced that the serious problems
for Mathematics in 2001 and the subsequent two years arose because the curriculum
model imposed for all subjects worked to the detriment of mathematics. The
numbers of students studying Alevel Mathematics decreased within one year
by 20 per cent as a direct result of the implementation of Curriculum 2000
and has stayed at this level the year after. 
4.34 
In the view of the Inquiry, the seriousness of this cannot be underestimated.
The numbers continuing with GCE mathematics post16 provide the supply chains
for mathematicians, statisticians, scientists and engineers in higher education,
research and employment. This supply chain is key to the strategy for tackling
the problems identified in SET for Success, as well as providing an
increased supply of future qualified mathematics teachers. It is vital that
ways be found to restore the numbers not only to the levels of two years
ago, but to increase them significantly. Far too few achieve level 3
qualifications in mathematics in England and Wales. 
4.35 
Respondents have also wished to challenge the current arrangement whereby
GCE mathematics attracts the same UCAS tariff as any other GCE at either
AS or Alevel. This is seen as unhelpful on two counts. First, there is clear
evidence that mathematics does not present a level playing field in terms
of attaining grades and a clear perception that mathematics is hard. It is
argued that an incentive is needed to counteract this. Secondly, mathematics
is unique in providing the key underpinning of so many other disciplines.
It is argued that this needs to be formally recognised in order to encourage
greater involvement with mathematics post16. In particular, it is noted
that the AEA in Mathematics currently attracts no UCAS points at all thus
providing no incentive to enter for the qualification other than for love
of the subject itself. We understand that UCAS are currently reviewing this
issue. 

Recommendation 4.8
The Inquiry recommends that the effects of the introduction of the revised
specifications for GCE be closely monitored by the QCA and its regulatory
partners as a matter of high priority and that funding be made available
to support this. If there is no significant restoration of the numbers entering
AS and A2 mathematics within the next two or three years, the Inquiry believes
the implications for the supply of post–16 qualified mathematics students
in England, Wales and Northern Ireland to be so serious that consideration
should be given by the DfES and the relevant devolved authorities to offering
incentives for students to follow these courses. One possible form of incentive
could take the form of financial incentives to HEIs to include AS or Alevel
mathematics as a prerequisite for certain degree courses. Another possibility
might be to offer financial incentives directly to students following such
course in HEIs, possibly through fee waivers or targeted bursaries. 

4.36 In addition to these considerable concerns about the
organisation of the curriculum and the serious effects of the Curriculum
2000 changes, there are also serious concerns about the frequency of assessment
of material in GCE AS and Alevel Mathematics. This is felt by many respondents
to hinder the development of the learning and understanding of mathematics
at this level. It is the consensus view that far too much time is devoted
to examinations and preparing for examinations – “teaching to the
test” – and that this is at the expense of the understanding of
the subject itself. Many identify the problem as the splitting of the subject
matter of Alevel mathematics into six separately examined modules. This
is seen as having the effect of splintering the unity and connectedness of
the mathematics to be learned at this level. It is felt that this fragmented
presentation makes it virtually impossible to set genuinely thoughtprovoking
examination questions that assess the full range of mathematical skills.
It is also felt that the style of short examination papers results in a race
against the clock that adversely affects weaker candidates. We are aware
that the criteria for GCE mathematics have just been reviewed and changed,
and we appreciate that there is a natural desire for some stability in the
system. However, we have received such strong representations on this issue
that we nevertheless make the following recommendation. 

Recommendation 4.9
The Inquiry recommends that the QCA and its regulatory partners conduct an
immediate review of the frequency and style of current GCE assessment, with
a view to reducing the time spent on external examinations and preparation
for examinations. 
4.37 
In terms of student choices and the general perception of the subject,
AS and Alevel Mathematics are the mainstream qualifications available at
this level, but do not attract enough students to study some level 3 mathematics
in postcompulsory education. Many respondents have commented that the
distribution of grades for Alevel mathematics presented in Chapter 3 suggests
that the more able students entered for Alevel mathematics are insufficiently
challenged and the least able are frequently overstretched. In the majority
of subjects, the distribution of Alevel grades is roughly bellshaped with
relatively few candidates at the extreme grades A or E. However, historically
in Alevel mathematics, grade A is the modal grade and the distribution of
grades is virtually a straight line down to the lower grades. In terms of
students’ and teachers’ perception of the subject, many respondents
believe that, for other than the mathematically clearly very able students,
there is a tendency for schools to see choosing mathematics Alevel as higher
risk in terms of outcome than many other disciplines. To add to this perception,
it is clear that many weak students do not complete the course in GCE Mathematics
and many of those who do complete are not classified on their examination
performance. At the other end of the scale, Alevel Mathematics is felt not
to discriminate sufficiently amongst those awarded the highest grades in
the subject. University mathematics departments have made clear to the Inquiry
that they are often unsure of the real value of a grade A pass at Alevel. 
4.38 
Following the revision of the GCE criteria for Mathematics in response
to the Curriculum 2000 debacle, many respondents are in no doubt that Alevel
Mathematics has been made easier for the very best candidates. In terms of
the potentially most able mathematics students, the Inquiry believes that
far too few able candidates are entered for AS or Alevel Further Mathematics
because their schools or colleges do not have sufficient resources to provide
these courses. The same appears to be the case for the AEA in Mathematics,
although the original intention of AEAs was that they would not require
additional teaching. There are many students who would benefit from studying
Further Mathematics or the AEA in Mathematics, but who are currently denied
the opportunity. Candidates who have studied Further Mathematics or the AEA
in Mathematics are likely to be much more confident with the inner workings
of the subject. University departments in all subjects identified as vulnerable
in the Roberts SET for Success report would benefit greatly if more
candidates were qualified at this level. Further Mathematics and the Advanced
Extension Award in Mathematics (redesigned if necessary) are the courses
that could and should provide the extra stimulation for the top fifteen per
cent or so of the Alevel mathematics cohort of students and the Inquiry
is deeply concerned that the current system is not able to make adequate
provision for this important cohort. 

Recommendation 4.10
The Inquiry recommends that there should be an immediate review by the DfES,
LSC and the relevant devolved authorities of measures that could be taken
to support and encourage current GCE course provision for the most able
mathematics students. In particular, we believe there is a need to ensure
that there are no funding disincentives in schools and colleges for providing
access to Further Mathematics and the Advanced Extension Award in Mathematics
We also believe that consideration should be given employing the same incentives
as suggested in Recommendation 4.8. 
4.39 
The higher education sector and the learned and professional societies
have made clear to the Inquiry their serious concerns about the interface
and transition between Alevel mathematics and university courses heavily
dependent on mathematics, such as degree courses in mathematics and statistics,
or in physics, electronics, engineering and economics. In the shortterm,
the Inquiry believes that Higher Education has little option but to accommodate
to the students emerging from the current GCE process. Many are, of course,
already doing this through, for example, the provision of first year enhancement
courses. Longer term, we would hope that there would be significant changes
resulting from Recommendations 4.5 and 4.10 and the future redesign of 1419
pathways. More generally, we would hope that there would be significant positive
consequences of the greater interaction of HE with schools and colleges proposed
in Chapters 5 and 6. 

4.40 
There is some concern that employers are not yet fully recognising the
new Adult Numeracy qualifications. It has also been impressed on the Inquiry
that adults want to learn mathematics for a variety of reasons, often not
concerned with gaining qualifications. Respondents to the Inquiry have expressed
some concern that, at present, test questions tend to reflect traditional
“school mathematics”, in the sense of testing mathematical procedures
posed as contextualised problems with multiple choice answers. It is felt
that these tests do not necessarily fit well with the idea of individual
adult learner plans and properly exploit adult learners’ contexts. It
is also felt that the present tests at levels 1 and 2 disadvantage ESOL learners
and those with dyslexia or dyscalculia, or low levels of literacy. Many
respondents feel that:

numeracy capabilities have generally been undervalued, underdeveloped and
underresourced;

support and learning programmes have been few in number and poor in quality;

materials and qualifications have been child rather than adult centred;

teachers have been inadequately trained and in many cases specialist numeracy
teachers have been replaced by literacy teachers, often working beyond their
own levels of mathematical competence;

performance and alignment with GSCE Mathematics and National Curriculum levels
is highlighting inadequacies in the appropriateness of these programmes to
prepare young people for adult life in general and the workplace in particular.

4.41 
Respondents to the Inquiry are clear that the adult numeracy strategy
is a challenging and demanding one for teachers and learners alike. Progress
could easily be undermined by:

uncertainties surrounding the teaching and assessment of mathematics in general
and in particular the future of GCSE Mathematics and key skills;

the limited pool of competent and confident teachers of mathematics and numeracy;

the lack of employer engagement in raising the skill base of new employees.
In Chapter 6, we suggest that the national infrastructure for the support
of the teaching of mathematics include specific support for teachers of adult
numeracy. 

4.42 
In conjunction with the Advisory Committee on Mathematics Education (ACME),
the Inquiry ran a series of workshops attended by a wide range of stakeholders
concerned with possible future mathematics 1419 pathways. These workshops
considered the ways in which mathematics is embedded in educational pathways
in other countries and tried to stimulate initial constructive thinking about
an appropriate future structure for 1419 mathematics pathways in England. 
4.43 
As a result of these and other extensive consultations, the Inquiry believes
that the following principles should guide the construction of a future pathways
approach to mathematics provision 1419 in the UK:

all learners should be provided with a positive experience of learning
mathematics and should be encouraged to realise their full potential;

it should be recognised that not all learners learn in the same manner, or
at the same speed, or respond positively to the same styles of assessment;

all pathways should include progression up the qualifications ladder, with
each pathway having clearly defined destinations into training, employment,
further or higher education;

there should be flexibility within the overall structure and maximal opportunity
to make transitions among the pathways; it will be important to avoid regression
to old style Olevel versus CSE, or any other now defunct rigid qualifications
divide;

new approaches to pedagogy and, in particular, the use of ICT should be adopted
to ensure that all students acquire an appreciation of the power and
applicability of mathematics;

the uses and applications of mathematics, including working with ICT, should
be made central to the mathematics curriculum wherever appropriate, but without
compromising appropriate levels of abstraction and generalisation.

4.44 
In addition to requiring adherence to these principles, respondents to
the Inquiry are clear that in developing pathways it will be essential to
be clear about the positioning in the pathways of the following key mathematical
developments:

working with the rules of number in a range of contexts, including use of
measures;

developing multiplicative and proportional reasoning;

developing the geometry of shape and space and geometrical reasoning;

developing and using algebra in a range of contexts, including 2– and
3–dimensional geometry, the use of variables in formulae and in coordinate
geometry;

developing the calculus of functions and the concept of rate of change, and
related applications;

developing ideas of proof and logic;

developing the mathematics of uncertainty.

4.45 
Subsequent discussion will use ‘pathway’ to describe progression
in mathematics, with the understanding that the mathematics is merely a
component, along with other specialist and optional components, of the larger
curriculum pathways envisaged by the 14–19 Working Group. Each pathway
should be clear in what it offers as a core of mathematics and how it is
applied, and it should also be an adequate preparation for the next stage
of progression. Much work will be needed to develop the Tomlinson proposals
into a coherent curriculum and assessment regime. The Inquiry has had neither
the time nor the resource to attempt to begin to do this for the mathematics
component of such a curriculum and assessment regime. 
4.46 
The approach we have adopted is therefore the following. We outline,
on the basis of suggestions made during the consultation process, schematic
versions of some of the different models and approaches put to us for
consideration. These indicate, in broadbrush terms, possible future pathways
that are guided by the principles summarised above and designed to remedy
the perceived defects of the current structure detailed in this chapter.
Each of these models and approaches has its supporters among one or other
significant grouping of the mathematics community. 
4.47 
It would be inappropriate for the Inquiry to express a clear preference
for one model or approach rather than another, although we are inclined to
believe that Figure 4.2 below will provide something close to the desired
pathway structure for mathematics. We believe that intensive curriculum
development, trialling, feedback and modification will be essential to ensure
that the new structure is workable and better than the system it is designed
to replace. The construction of pathways depends on both curriculum and
assessment considerations and future political imperatives. 
4.48 
A system based primarily on equity might seek to opt for a single pathway,
at least to age 16 and possibly to age 19. In such a model, all students
study precisely the same mathematics curriculum, but progress at different
rates. Students are then credited for the mastery of the stage they have
reached by the chosen age at which the pathway ends. Sweden has adopted
essentially this approach. In the Swedish model (see Figure 4.1, which we
present schematically, without discussion of the programme content) the
mathematics curriculum can be thought of as blocks A,B,C,D,E fitting end
to end and forming a continuum up to the standard required for entry to study
mathematics at university (D, or D+E). Students learn at different rates,
and are certified as successfully completing one or more of the fixed number
of partitioned subsets A,B,C and D that make up the continuum. Only relatively
few students master the whole curriculum. The majority leave secondary education
having achieved a number of ‘stepping stone’ credits along the
mathematical pathway. We note that support for this approach runs counter
to the support the Inquiry has received for the extension rather than
acceleration approach discussed earlier (see paragraph 4.21 and Recommendation
4.5). 


4.49 
In contrast to the above schematic, Figure 4.2 presents a more detailed
possible model of 14–19 pathways. This starts from the assumption that
the present Key Stage 3 Programme of Study should form the common basis for
all students, prior to the age of 14. It then maps out a number of possible
routes through 14–19, five potential pathways from age 14, increasing
to seven from age 16. Each pathway varies in content, difficulty and abstraction
and is designed to enable students to follow the one best suited to their
needs. The model emphasises relative speeds of progression and the nature
of the levels of the mathematics components on different pathways. The model
allows for movement between the pathways. 
4.50 
In Key Stages 4 and post–16, all courses shown in the figure have
the title “Mathematics” followed by a code. The names associated
with the codes are descriptive only. The model emphasises relative speeds
of progression and the nature of the levels of the mathematics components
along the different pathways. Mathematics in levels 1 and 2 of this
qualifications framework would be drawn from the Key Stage 4 PoS, but with
not all students expected to make equal progress. The way the intended curriculum
is delivered and assessed might differ from pathway to pathway, with more
emphasis on applications in some parts and more emphasis on abstract reasoning
in others. In this model, students learn to tackle problems appropriate to
their current level of mathematical understanding and motivation. The pathways
are designed so that individual students would be able to maintain interest
in the subject and to make steady and continuous progress as they move to
age 18 or 19. Each student should be on a pathway that is accessible and
provides meaningful challenges to the student at each stage. 


4.51 
At level 3, students would elect to do mathematics as a minor or as a
major subject, and perhaps some additional mathematics beyond that. Mathematical
techniques, applications and mathematical reasoning would be developed through
a continuum which allows some variation in the applications encountered and
the way mathematics is used to model real problems. The aim would be for
an increasing number of students to progress to both levels 2 and 3 by age
19. A small percentage of students might only progress to level 1. 
4.52 
The degree of mathematical content, difficulty and abstraction increases
as one moves down the figure and along each pathway from left to right. All
courses from level 1 upwards would develop calculation in a variety of contexts,
and, as appropriate, would introduce aspects of algebra, geometry and application
of mathematics in a varying mix for different student groups. Entry level
would focus mainly on numbers and measures and simple applications. The Extension
courses would be for those who absorb mathematics easily and seek a greater
understanding of the subject. Students on these courses would study mathematics
at greater depth and at greater levels of abstraction, but based on the same
curriculum content at a given level. Extension courses would concentrate
more on reasoning, proof, chains of logical reasoning, multistep problem
solving and a range of harder and sometimes openended problems. An example
of an extension curriculum at level 2 is set out in Making Better Use
of Mathematical Talent, published by the Mathematical Association, 2003. 
4.53 
Mathematics E at level 3 would be the nearest equivalent to the current
GCE Further Mathematics and the AEA in Mathematics, although it would be
a new hybrid with its own distinctive features. There was a very strong positive
response to the Inquiry in favour of providing mathematics courses at this
level. Mathematical Literacy at levels 2 and 3 would be the nearest equivalent
to the higher tier end of GCSE Mathematics (KS4 Higher) and Alevel Mathematics,
respectively. These would concentrate on the study of a wide range of
mathematical ideas, techniques and application, but not developing rigour
or harder problem solving to the same extent as on the extension pathway.
At level 2, both Mathematics ML and Mathematics E would be worth a double
award in the qualifications framework (in line with Recommendation 4.2).
Quantitative Literacy level 2 would be the nearest equivalent to working
at around the current C grade level of GCSE Mathematics (KS4 Foundation),
but with a greatly different emphasis. The course would also encompass level
1 as a fall back position. 
4.54 
Application of mathematics (involving number and algebra, measures and
geometry) to analyse substantial real world contexts would be stressed, and
appropriate ICT would be used to analyse realistic data and fit models. Students
would also learn about multiplicative and proportional reasoning. They would
also learn to communicate mathematical ideas to others. QL level 3 would
develop this approach further, building on more mathematical content that
goes beyond that currently in the Key Stage 4 Programme of Study. All QL
courses would develop the philosophy and pedagogy pioneered by Free Standing
Mathematics Qualifications and AS Use of Mathematics. It would be important
here to make full use of the power of ICT to analyse real data using appropriate
mathematical models. This is the sort of course designated as
‘TechnoMathematics’ by the authors of the report Mathematical
Skills in the Workplace. 
4.55 
Numerical Literacy courses would only go as far as level 1. They would
aim to provide familiarity with the most basic ideas in number, measures,
algebra and geometry and how these are used in elementary application and
in making geometrical models and patterns. They would play the role of a
steppingstone to mathematical understanding that might begin to unlock doors
in training or employment, and in further and higher education. At level
3, a mathematics course is proposed for all students progressing to level
3 from level 2. This would follow the pattern of the French Baccalaureate,
in which there is mathematics provision on all the designated academic routes
(the sciences, the social sciences and the humanities), and also on the
vocational and technological routes. The possible course in Public Understanding
of Mathematics (possibly to include Science and Technology) could provide
a form of continuing exposure to mathematics for those with academic aspirations
that do not include technical use of mathematics, but for whom society would
wish – given that many will have influential and opinion forming roles
in their future careers – to understand the role of mathematical ideas
in human culture, the development of science and technology and as an instrument
for social and economic change. 
4.56 
The level 3 Statistical Methods course would be akin to current AS Statistics
and would be an appropriate prerequisite for those intending to progress
to courses in HE which are heavily statistical in nature. Many respondents
to the Inquiry have indicated that such a course would fill an existing serious
gap in the qualifications framework. The symbol (T) in figure 4.2 denotes
that some transition material would have to be mastered to make the indicated
transition from one pathway to another. Other transitions might be possible.
Students might wish to make a transition after starting on a particular pathway,
but then would have to realise that there could be a cost to making such
a transition and that extra effort might be required to make the transition
successfully. 
4.57 
We do not believe it would be desirable to indicate rigidly predetermined
destinations for each of the pathways. However, in very broadbrush terms,
with considerable crossover, we would see the following kinds of destinations
as corresponding to the pathways as we move down the figure:

Low skilled employment, parttime FE (Foundation Modern Apprentice);

Moderate to high skilled employment, parttime FE (Advanced Modern Apprentice);

High skilled employment; ITT; FE/HE (including for example: technology,
engineering, science, business studies, economics);

High skilled employment; FE/HE (including for example: biological and social
sciences, business studies);

High skilled employment; FE/HE (including for example: arts, humanities,
law);

High skilled employment; HE (including for example: mathematics, physical
sciences, electronics, computer science, engineering, medicine, economics);

High skilled employment; HE (all highly mathematical subjects and research
and development in these subjects).

4.58 
There are a number of possible variants of the model. One of is shown
in highly simplified schematic form in Figure 4.3, based around two fundamental
courses Mathematics and Use of Mathematics. The key idea is
that there is scope to develop both a level 1 and a level 2 ‘Use of
Mathematics’ course to complement the level 3 AS ‘Use of
Mathematics’ that exists at present. Starting from these, Figure 4.3
then shows the following common pathways: Mathematics L2 to Mathematics L3
(minor, major and beyond) or to Use of Mathematics L3; (Use of Mathematics
L1 to) Use of Mathematics L2 to Use of Mathematics L3. 


4.59 
A fourth possibility is to develop two or three distinct pathways from
a notionally accepted common curriculum up to age 14. A version of this fourth
model is shown below in Figure 4.4. This proposes three distinct programmes
from age 14. These are referred to here descriptively as EntryVocational
(EV), VocationalTechnical (VT) and TechnicalAcademic (TA). The shared letters
indicate the desirability of allowing for subsequent movement; they do not
necessarily indicate identical content. All the courses would progress from
a common core of mathematics at Key Stage 3, which would act as an effective
foundation for all students. However, those students who do not complete
the whole of Key Stage 3 by age 14 would not be obliged to continue repeating
the same material until it is mastered. 


4.60 
None of the models or approaches presented here has any current validity
or preferred status for the Inquiry. They are simply intended to show how
actual mathematical pathways could be constructed in line with the principles
enunciated earlier and with the aim of overcoming the perceived deficiencies
of the current structure. We indicated earlier that a great deal of work
will be needed to develop such ideas into a coherent curriculum and assessment
regime that will provide appropriate mathematics pathways within the general
structure that emerges from the work of the 14–19 Working Group. We
understand that the final 14–19 Working Group proposals will be available
in Autumn 2004. The Inquiry therefore does not believe it would make sense
to try to select a preferred set of mathematics pathways and to work out
every detail of the curriculum and assessment for such pathways ahead of
understanding the Government’s response to the 14–19 Working Group
proposals. 
4.61 
However, whatever emerges as a new 14–19 structure, the Inquiry
is clear that we shall need to develop some or all of the elements and components
of the models discussed above and to begin to address the major deficiencies
identified in the current framework. We believe, therefore, that it is vital
to begin work immediately on detailed further curriculum and assessment
development based around these pathways models. The aim should be to carry
out a cycle of trialling, feedback and modification of two or three variants
of these models in time to inform a future decision on the preferred way
forward for mathematics in the context of the overall 14–19 structure.
We would suggest that this work should be completed by the end of 2007. 
4.62 
We also firmly believe that in this process of development it will be
vitally important to involve as wide a range of the mathematics community
as possible. We have been struck in the course of this Inquiry by the energy
and commitment of the mathematics community in responding to issues raised.
In particular, the outline models we have presented have emerged from significant
groupings of the community. All this informs the following major recommendation. 

Recommendation 4.11
The Inquiry recommends that funding be provided to the QCA and its regulatory
partners to commission, through an open bidding process, up to three curriculum
and assessment development studies of variants of these pathway models and
approaches, including trialling, feedback and modification and an assessment
of the workload implications. These studies should take on board developments
arising from Recommendations 4.4, 4.5 and 4.7. The aim of this exercise will
be to inform the selection of a preferred pathway model to form part of the
reformed 14–19 structure in England and possible parallel developments
in Wales and Northern Ireland. Given the importance of ensuring the widest
possible involvement and commitment of the mathematics community to the outcome,
the Inquiry recommends that the regulatory authorities work in partnership
with ACME and mathematics community representatives from Wales and Northern
Ireland, and that the DfES and relevant devolved authorities provide appropriate
funding to support this. 