MEI response to QCA – GCSE Mathematics subject criteria
consultation questionnaire –
June to September 2008
MEI response in black. Questionnaire in blue.
Introduction
GCSEs are governed by both GCSE qualification criteria and GCSE subject specific criteria. Any
GCSE specification must meet the requirements of both. Awarding bodies use this set of
regulations in developing the details of the specifications.
The following questions address the subject criteria for GCSE mathematics.
Please review the relevant sections of the subject criteria before answering the questions. Please
read the subject criteria alongside the GCSE qualification criteria as awarding bodies will need to
meet the requirements of both in developing specifications.
Completing the questionnaire
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Please note that questions marked with a * are compulsory.
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Please submit your questionnaire by Tuesday 30 September 2008
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If you have any queries about the questionnaire please contact gcse2010@qca.org.uk.
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Section 1: About you
*1a) In what capacity are you responding to this questionnaire? (tick all that apply)
Teacher - Secondary
Lecturer - Tertiary college
Awarding body
comprehensive
Lecturer – University
Disability Group
Teacher - Secondary selective
Lecturer – Other
Employer
Teacher - Secondary nonHead of Curriculum9
A sector skills council
selective
A subject association
Student
Teacher – Independent
A teacher association
Other – please state9
Teacher – Other
Local Authority
Curriculum development body
Lecturer - Further education
college
Lecturer - Sixth-form college
1b) What is your subject specialism? Please tick the one that applies.
English
ICT
Mathematics9
*1c) Are you responding to this consultation as an individual or on behalf of a named group?
Individual
On behalf of a named group (please specify)9 MEI
1d) Do you consider yourself to have a disability or a health condition?
Yes
No9
Do not wish to disclose
1e) Are you:
Female9
Male
Section 2: Functional Skills
*2a) Do you think that the criteria allow awarding bodies to develop GCSEs that will support coteaching of GCSEs and functional skills for students who may be taking a functional skill and/or a
GCSE?
Yes9
No
No comment
If not, please explain briefly why.
Section 3: Aims & learning outcomes
The aims and learning outcomes provide statements about the purpose of studying GCSE
mathematics. Learning outcomes describe what a student completing a GCSE course in the subject
should know, understand and be able to do.
*3a) Do you think that the aims and learning outcomes for GCSE mathematics, as currently stated,
are appropriate?
Yes
No9
No comment
If not, please indicate briefly what you think should be changed or added.
In addition to preparing learners to make informed decisions about further learning opportunities
and career choices, the specifications should prepare learners to take part in further learning
opportunities and careers.
*3b) Do the aims and learning outcomes reflect the new key stage 4 programme of study?
Yes
No9
No comment
If not, please indicate briefly what you think should be changed or added.
See answer to 3a above.
Section 4: Content
The content in the subject criteria represents the core material (skills, knowledge and
understanding) that should be present in all specifications and thus studied by all students,
irrespective of the awarding body. Criteria and specifications are required to incorporate the
programmes of study at key stage 4 since they are a statutory requirement.
*4a) Do you think that the content for GCSE mathematics is up to date?
Yes
No9
No comment
If not, please explain briefly why, including examples.
Use of ICT is not mentioned in the content.
*4b) Do you think that the content is an appropriate basis for progression to A level mathematics
and further study in this subject?
Yes
No9
No comment
If not, please explain briefly why.
Standard deviation was, until recently, in GCSE Mathematics and was removed for good reasons.
It is a very sophisticated topic and was often taught incorrectly at this level. The re-introduction of
this topic will produce the same problems and so it will make it harder for students to progress to
A Level as they will need to unlearn what they have been taught at GCSE. Moreover, when this
topic has been taught at GCSE, the focus has often been on the algorithm for calculating standard
deviation rather than on what it means. As a result, students have been left with the impression
that standard deviation is nothing more than a very complicated calculation.
Graphs of trigonometric functions and their properties are not appropriate at Foundation tier. It
does not make sense to study them for students who have never used trigonometry. Including
them in the content without also including trigonometry is likely to lead to students who are
confused by what they have been taught. It would, however, be fine to include periodic graphs
arising from some data from a context.
It is important for students to be able to solve simultaneous equations at A Level. These are not
included in the content.
More generally, it is important for all students to have covered the same essential content in order
to facilitate progress to A level and further study. There is insufficient detail in the criteria and in
the programme of study to ensure that this will happen.
Section 5: Assessment objectives
Assessment objectives specify what students need to demonstrate, i.e. knowledge and
understanding, application of knowledge and understanding, analysis, evaluation, practical skills.
*5a) Do the assessment objectives indicate clearly what is to be assessed?
Yes
No9
No comment
If not, please explain briefly why.
Skills based assessment objectives are fine in themselves but they do not indicate clearly what is
to be assessed because they do not indicate what content students need to be recalling, using and
applying. Moreover, the criteria as they are written would need careful interpretation. It would be
difficult to write a mathematics question which did not address AO1.
*5b) Do the assessment objectives collectively cover all that is essential to the assessment of
mathematics at GCSE?
Yes
No9
No comment
If no, which requirements do you think should be added?
The criteria would need careful interpretation. The words “rigour” and “proof” are missing.
*5c) Are the relative weightings of the assessment objectives appropriate?
Yes
No9
No comment
If not, please explain briefly why.
It would be appropriate to have differing weightings for the two GCSEs.
*5d) Are the assessment objectives sufficiently distinctive?
Yes
No9
No comment
If not, please explain briefly why.
The general sense of direction provided by the assessment objectives is fine but it may be difficult
to assign a particular mark to a particular assessment objective. There is overlap between the
assessment objectives. For example using mathematics in AO1 and applying mathematical
methods in AO2; communicating in AO1 and using appropriate terms in AO2.
*5e) Will timed written papers enable all the assessment objectives to be adequately assessed?
Yes
No9
No comment
If not, please explain briefly why not.
There is a conflict between the status of GCSE Mathematics and its validity in measuring
students’ mathematical skills. Its high status as a qualification means that as many students as
possible must be enabled to cross this hurdle. Timed written papers may have some advantages
but they cannot assess all that we would like students to be able to do.
It will be particularly difficult to assess AO3 without allowing candidates sufficient planning and
thinking time. Pre-released material could go some way towards enabling this.
Section 6: Tiering
Some GCSE subjects have examination papers that have two tiers. For example some students on
the course will sit either a foundation (can achieve grades C and below) or higher (can achieve
grades A*-D) paper. Other subjects have only one tier of entry, with question papers that cover the
full grade range.
*6a) Are the proposed tiering arrangements specified in the criteria appropriate?
Yes
No9
No comment
If not, please explain briefly why.
Early indications are that present tiering arrangements are not working well so it would be
inappropriate to tie new GCSEs to the same system. A range of possibilities should be considered.
It might be appropriate to have a common paper for at least one of the GCSEs. When this was
trialled by OCR, rules disallowed more than one route to any grade and, consequently, the marks
on one of the two papers were ignored. That rule has now been abandoned so there is no longer
any reason why there should not be a common paper across the two tiers.
Section 7: Scheme of assessment
*7a) Is 30-40% non-calculator assessment appropriate?
Yes
No9
No comment
If not, please explain briefly why not.
Many questions on current “non-calculator” papers could not be done using a calculator and so
could be asked on a “calculator” paper without it making any difference. There is only a small
proportion of the GCSE content for which candidates could use a calculator but which they should
also be able to do without a calculator so 40% is far more than is necessary. To insist on 30-40%
imposes an unnecessary constraint on the setting of examination papers and so is restrictive on
possible forms of assessment. It may be better to be less specific at this stage so that some forms
of assessment are not ruled out. For example, a mental test rather than a written paper might be
appropriate to assess non-calculator methods for one of the GCSEs.
*7b) Will these criteria allow awarding bodies to develop high quality, stimulating assessments
which will engage candidates in their subject as well as adequately assessing the curriculum for
which they have been prepared.
Yes
No9
No comment
If not, please briefly explain your response.
The restrictions in the scheme of assessment will make this difficult.
Section 8: Developing a second GCSE in mathematics
As recommended in the Smith Report, Making Mathematics Count (2004), the government is
committed to the development of a second GCSE in mathematics. As the government has made
clear in the DIUS response to recommendation 7.14 of the Sainsbury Review, published in March
2008, 'All pupils who would benefit should have the option to study the second mathematics
GCSE and schools should find ways to make it available to them.'
In 2006, the then DfES asked QCA to develop a GCSE in mathematics that covers the programme
of study, includes functional skills and secures progression to mathematics A level.
The remit also included a request to develop a second GCSE, which has, during piloting, been
called GCSE in additional mathematics. This is aimed particularly at those students who have a
particular interest in and aptitude for mathematics and two awarding bodies have been piloting
GCSE models since September 2006.
The new programme of study for mathematics at key stage 4, which emphasises the holistic nature
of mathematics and the connections made between mathematical elements, was agreed in 2007.
These two events have resulted in challenges in developing distinctive criteria for two GCSEs in
mathematics based on the same programme of study.
QCA and its partner regulators in Wales and Northern Ireland attempted to draft separate sets of
criteria for GCSE mathematics and GCSE additional mathematics; we have concluded that using
the same programme of study means that the criteria cannot be made sufficiently different and
distinctive.
The Advisory Committee on Mathematics Education (ACME) also attempted to draft two sets of
subject criteria based on the same programme of study, which it shared with QCA and Ofqual.
ACME's draft criteria and Ofqual's response can be viewed on the QCA website. These materials
are also available on the ACME website.
The first part of this questionnaire was about the draft criteria for the GCSE that covers the
programme of study. This qualification is based on the new programme of study - and as such will
contain a greater emphasis on connections and mathematical reasoning - and has functional skills
content embedded within it. Functional skills assessment is contained within separate level 1
functional skills and level 2 functional skills level 2 qualifications.
The second GCSE will need to contain a different skill set and/or cover some different content
from the GCSE that covers the programme of study.
The questions in section 8 relate only to the development of a second GCSE.
*8a) Do you think that there is a need for a second GCSE in mathematics?
Yes9
No
No comment
Please briefly explain your response and answer the following questions
The phrase “second GCSE” is potentially misleading. The preamble makes it clear that this refers
to the GCSE which is other than the one which covers the programme of study. It is our view that
this GCSE should be focussed on the assessment of Contextual Mathematics and contain less than
the full content of the KS4 programme of study. If students took the two GCSEs sequentially,
they would be most likely to take Contextual Mathematics first, followed by GCSE Mathematics,
which covers the full programme of study. Further details are provided in the separate document.
8b) Do you think that a second GCSE should enhance and extend the key stage 4 programme of
study by including additional learning outcomes?
Yes
No9
No comment
Please briefly explain what different skill set/content you think should be changed or added
To us, the word “enhance” implies making the programme of study more exciting. This does not
require additional learning outcomes.
8c) Do you think that a second GCSE should have controlled assessment that allows learners to
undertake an extended piece of work in mathematics?
Yes
No
No comment9
Please briefly explain what you think should be assessed by controlled assessment
It would be good to include the assessment of the use of ICT in mathematics – this is very difficult
to do by timed examination. However, the regulations concerning controlled assessment specify
25% controlled assessment as the minimum if there is controlled assessment and this seems a little
too much for the use of ICT in mathematics.
8d) Do you think that a second GCSE should encourage broader use of ICT software applications?
Yes9
No
No comment
Please briefly explain what you think should be changed or added
The use of spreadsheets for algebraic exploration and graph drawing.
8e) Do you think that a second GCSE would present delivery challenges for schools?
Yes
No9
No comment
Please briefly explain your response
Any change from the current GCSE will present some delivery challenges for schools because
teachers will have to get used to a new system. This is independent of the number of GCSEs but
is a feature of the new national curriculum which is statutory.
8f) When should the new GCSEs in mathematics be introduced?
Introduce the GCSE in
Introduce both GCSEs at the
Other
mathematics that covers the
same time in September
programme of study in 2010
20119
and the second GCSE in 2011
Please briefly explain your response
It makes no sense to introduce the two GCSEs at different times. That would give the message
that the one which is introduced second is an optional extra rather than an important part of the
curriculum.
Please note the remainder of the questions are about the GCSE criteria produced by the regulators.
Section 9: Maximising accessibility and equality
These criteria must fully meet the requirements of the Disability Discrimination Act, Equality Act
2006, Race Relations Act 1976 (as amended) and other equalities legislation. We therefore need to
check whether there are any requirements in these criteria that might form an unnecessary barrier
to candidates with disabilities, those from different ethnic groups and both male and female
learners.
When answering the questions please consider the needs of all learners, including those with
Special Educational Needs, disabled learners, gifted and talented, students of different ethnic
groups, both male and female learners and those whom English or Welsh is not their first language
9a) Do you think that the criteria enable awarding bodies to develop specifications that take into
account the needs of all learners?
Yes
No9
No comment
If not, please explain why not and please specify what type of learner you believe may be
excluded by the criteria.
The scheme of assessment does not fully cater for all kinds of learners. Some students find it very
difficult to demonstrate their potential in timed written examinations but the scheme of assessment
specifies 100% external assessment. The scheme of assessment specifies that papers must be
targeted at foundation or higher tier. Students below foundation, above higher or at the borderline
between foundation and higher are not well-served.
9b) Do you think that the criteria enable awarding bodies to develop specifications that promote
cultural understanding, diversity and gender equality appropriately?
Yes
No
No comment9
If not, please explain why not.
9c) Do you see any requirements in these criteria that you believe might restrict any disabled
candidates’ access to the qualification?
Yes
No9
No comment
If yes, please indicate the requirement restricting access, the disability group(s) likely to be
restricted, and whether you believe the requirement to be essential, desirable or not needed in the
assessment of this subject.
Centres may have to make reasonable adjustments for certain candidates during controlled
assessment, for example practical assistants or readers may be allowed to support learners.
9d) Do you think that the criteria will enable awarding bodies to develop specifications that allow
reasonable adjustments?
Yes9
No
No comment
Please briefly explain your response.
All the kinds of adjustments which are made at present for Mathematics GCSE should still be
possible under the new criteria.
Section 10: Curriculum opportunities within the GCSE subject
criteria
The criteria are being developed so that the subsequent revised specifications will incorporate
ideas from the secondary curriculum and on the wider curricular issues.
10a) Do the revised criteria make clear the ways in which the subject complements and reflects the
revisions to the overall objectives of key stage 4 curriculum?
Yes
No9
No comment
If not, please briefly explain your response.
There is a lack of detail in the subject content but it is not clear what opportunities for
development and differences between specifications this allows. There is a delicate balance to be
struck. All learners must be equally enabled to use mathematics in their lives and studies, no
matter which GCSE Mathematics specification they have followed. On the other hand, there does
need to be some freedom to allow curriculum development.
The aims of the curriculum are to enable young people to become:
• successful learners who enjoy learning, make progress and achieve
• confident individuals who are able to live safe, healthy and fulfilling lives
• responsible citizens who make a positive contribution to society
10b) Do you think that the criteria support these aims sufficiently?
Yes
No9
No comment
If not, please briefly explain your response.
Our proposal for two GCSEs, which is in a separate document, is more supportive of these aims.
The GCSEs in Contextual Mathematics and Mathematics would allow many students to be more
confident and successful in their learning and to acquire the skills they need to make a positive
contribution to society.
10c) Do you think that schools could use this subject to develop learning in contexts beyond the
school?
Yes9
No
No comment
If yes, please suggest how; if not, please briefly explain why not.
Mathematics is widely used beyond school. Whether schools do develop learning in contexts
beyond the school will depend in part on whether the assessment encourages them to do so.
10d) Do the criteria support the development of personal, learning and thinking skills?
Yes9
No
No comment
If not, please briefly explain your response.
10e) Does the revised subject criteria give sufficient flexibility for awarding bodies to develop
specifications that reflect subject and curriculum initiatives and developments?
Yes
No9
No comment
If not, please briefly explain your response.
It is not clear how much flexibility the subject criteria allow – see answer to 10a.
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Next steps
Your response will contribute to the development of the new GCSE criteria which are scheduled
to be published in December 2008. Specifications based on these criteria are scheduled to be
available from autumn 2009 for first teaching in September 2010.