QCDA’s latest proposal for A Level Mathematics & Further Mathematics
March 2010
Introduction
After four previous unsuccessful attempts to reform A Level Mathematics, QCDA have now come up with a further proposal.
This model is not completely new since it is similar to one of the options considered in the consultation in the summer of 2010, model B1, which received just 13% support, much less than that for options that involved no or little change. However, the latest proposal has some additional features.
Given the very considerable expense and inconvenience involved in replacing an existing syllabus, there must be a reasonable expectation that the new proposal will result in an improvement in both the uptake and the quality of the mathematics learnt.
However, this is not the case. While it avoids some of the worst problems of QCDA‟s earlier proposals, others still remain.
What is the latest proposal ?
In the current syllabus:
AS Mathematics consists of two compulsory pure units, C1 and C2, and one applied unit to be chosen from Mechanics 1, Statistics 1 and Decision
Mathematics 1; for the full A Level two more compulsory pure units, C3 and C4, are required together with another applied unit.
In the proposed syllabus, the two pairs of pure units would be combined into single units of double weight, “C1+C2” and “C3+C4”.
This is the only structural alteration. However, there would be three other changes.
The AEA in mathematics would be discontinued and the paper on the C3+C4 unit would be made harder. QCDA‟s overarching issues questionnaire from the summer 2009 consultation implies that the amount of “stretch and challenge” would be equivalent to that in the AEA:
“
Given that the revised A levels in mathematics and further mathematics will have more 'stretch and challenge' questions in the A2 assessments, there will no longer be a need for an AEA-style examination in mathematics.
” 1
The content of many units would be prescribed.
Mathematics would become subject to new general regulations. It is expected that mathematics would be allowed only one mode of assessment per unit, in line with the proposals for Use of Mathematics from 2012.
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The implications of this model
In looking at the implications of the model it is important to realise that A Level
Mathematics is offered by a wide variety of institutions, some of them with very different types of student, including schools with high academic standards throughout and FE colleges taking students from local 11-16 schools and allowing entry to A
Level Mathematics to students who have grade C at GCSE.
A great strength of the present system is that it is flexible enough to meet their diverse needs; there are features which some schools and colleges do not use but which are very important to others.
Change of unit structure
The proposed change of unit structure would have different effects on AS and A2 students.
AS students
Combining C1 and C2 into a single unit would make a January entry in the first year impossible for nearly all students. Some schools do not use January entries anyway and so this would have little effect on them. However, such schools are in a minority; there is a very large January candidature for C1 and even students who currently take both units in the summer are likely to find a paper testing the whole of C1 and C2 more challenging than separate papers.
Many schools use the January C1 to provide students with early information about how they are getting on. A poor result often tells them, and their parents, that they are not working hard enough. At that stage, there is time to do something about it; they are able to retrieve the situation by the summer when they re-sit C1 alongside C2, and then go on to complete the full A Level the next year. A consequence of removing the
January C1 would be that such students do not get their wake-up call until the end of the first year. By then it is too late; they have a mountain to climb and may choose to give up mathematics altogether.
This aspect of the proposal would close opportunities for many average students.
Some students who, under the present arrangements, would have completed A Level successfully would give up after one year.
A higher drop-out rate after the first year would send the message along the grapevine that “Maths is hard”.
Consequently fewer average students would opt for mathematics and the overall uptake would be likely to fall.
Many of the students involved would be those who go on to university to read subjects in which some mathematics or statistics is embedded. They would be doing so from a disadvantaged starting point.
The impact would also be felt at a national level. Having more students playing catchup with mathematics and statistics would make it harder for universities to meet international standards.
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March 2010

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A2 students
Similarly, the effect of making C3 and C4 into a single unit would be that taking C3 in January would no longer be an option for most students. For many this would not be a particularly serious loss. However, there is quite a large candidature for C3 in
January and many of these are also taking Further Mathematics; the change would increase the demands of the final summer examination session for them.
The really serious effect, however, would come from the increase in difficulty. The present papers for C3 and C4 are certainly not too easy. If they were, their mark distributions would show excessive proportions of high marks and that is not the case, indeed many students who achieve an overall grade „A‟ in A level mathematics do not get grade „a‟s in C3 and C4.
In order to differentiate reliably between the best candidates, there would need to be some questions which many candidates were unable to attempt. This would result in unduly low grade thresholds, with candidates who are likely to pass A Level with grade D or E gaining very few marks. We are keen to attract more students with
GCSE grades B and C into A level Mathematics. Making already difficult papers even more demanding is not the way to achieve this.
Relatively small changes were made to the difficulty of A Level Mathematics for
Curriculum 2000 but the effects were catastrophic. The number of students completing the course fell by 20%, resulting in serious knock-on effects on the mathematical preparation of students starting STEM degrees in higher education.
However, Curriculum 2000 seems quite mild when compared with the “stretch and challenge” requirements of the proposed changes, and so it is hard to see its effects being any less severe.
The mathematics community is united in its view that making A Level Mathematics harder is not the right way to do provide strong students with additional stretch and challenge. There are other ways that it can be achieved and these should be promoted.
Further Mathematics is now available to all suitable students and is taken by many of them. Its uptake has doubled over the last five years.
The AEA is available to test the high-level mathematical problem solving skills of the most mathematically-able students. Mathematical problemsolving at this level goes beyond the understanding of syllabus topics and fluency in applying techniques to standard problems. It cannot be adequately assessed as an „add-on‟ to a standard A level examination. The development of online tuition in mathematics at this level means that appropriate support for such a qualification can be available to all. With universal support available, and encouragement from universities for students to take an AEA-type qualification in mathematics, uptake can rise significantly, as it has for Further Mathematics.
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Prescription of content
For the first time ever, the content of the pure part of Further Mathematics and that of
Mechanics 1, Statistics 1 and Decision Mathematics 1 would be prescribed.
This would end a long tradition of curriculum development in A Level Mathematics in this country. It would no longer be possible for groups of mathematicians from schools and universities to come together to develop syllabuses at this level that are up to date, mathematically sound and foster good teaching. Instead, there would be one syllabus, determined by government officials and awarding bodies. There would be no room for innovation.
It is entirely predictable that the resulting syllabuses would be dull, with a focus on what is most easily assessed. The rich learning experience that MEI and, until recently, SMP have brought to students would no longer be possible.
General regulations
The introduction of the new specifications would mean that mathematics would need to conform to new general regulations. The general regulations for GCE state that there should normally be only one mode of assessment
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; there can be exceptions to this and we feel that there is a strong case for mathematics being an exception.
The implication of a single mode of assessment is that the assessment of each unit has to be either 100% examination or 100% coursework. In practice, a unit with 100% coursework is just not viable in A Level Mathematics and so all the assessment would be by examinations, whereas at present it is possible to have small pieces of coursework attached to particular units.
The consequence of this is that important mathematics within the syllabus could not be assessed appropriately and so would not be taught properly; examples are numerical methods (requiring the use of computers) and mathematical modelling in applied mathematics units.
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March 2010

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What problem is QCDA’s latest proposal trying to solve?
It is unclear what problem the latest proposed model for A Level Mathematics is trying to solve. What improvement would be achieved by combining C1 and C2 into a single unit? In what way will applied units with prescribed content be better than the current applied units? QCDA has put forward a number of arguments for change.
These are given in the appendix. They have been demolished one by one. The only remaining justification for any change seems to be the need to introduce more stretch and challenge.
If this means including questions of comparable difficulty to AEA, then this will not work and is likely to have disastrous consequences, as argued earlier. However,
QCDA‟s guidance regarding stretch and challenge 3
is very similar to the general criteria for GCE which state that A2 assessments should
“provide appropriate demand through the use of a variety of stems in questions ensuring connectivity between sections of questions requiring extended writing in all subjects, except where agreed with the regulatory authorities as inappropriate using a wide range of question type to address different skills including synoptic assessment” 4
Before making expensive, and potentially damaging, changes, it is important to realise that these requirements are already being met in many C3 and C4 assessments.
In conclusion
There is a danger of thinking that, after all the angst over QCDA‟s earlier proposals, perhaps this might be a time for compromise.
The earlier proposals included ideas that very obviously would not work. Now that they have been removed, it is tempting to think that what remains is not all that bad.
That would be case of taking one‟s eye off the ball. The crucial question is whether this proposal will be an improvement on the present successful syllabus and the answer is “No”.
The new proposal would be an expensive way of doing the job less well.
Notes
1. Level 3 mathematics overarching issues questionnaire, QCDA, April 2009, http://www.qcda.gov.uk/22158.aspx
2, 4. GCE AS and A level qualification criteria, February 2007, QCA/06/2866.
3. Guidance on preparing students for 'stretch and challenge' in the revised A2
Assessments, June 2009, QCA/09/4299.
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March 2010

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Appendix Reasons given by QCDA for changing A Level Mathematics
Reason given Commentary
The present aggregation procedures are too complicated for the awarding bodies.
The awarding bodies are handling them without undue difficulty and have told QCDA so.
In contrast to other subjects, A Level
Mathematics may be awarded on 4
AS and 2 A2 units.
This occurs when a student does two different strands of applied mathematics. A recent Ofqual report stated that the extra demand of studying two different areas was sufficient compensation for the lack of depth.
A Level in other subjects is based on
4 units so the same should be true of mathematics.
Several other subjects have retained 6 units and in
QCDA‟s own proposals Further Mathematics, Use of
Mathematics and Use of Statistics would all be based on 6 units. A Level Mathematics would thus be the odd one out. As explained above, there are also strong educational reasons for retaining 6 units.
In contrast to other subjects including (Further Mathematics), the
A* for Mathematics would be awarded on performance on less than 50% of the content.
The plan is for it to be awarded on the units C3 and
C4 which are the A2 part of the compulsory subject core (all pure mathematics). No one outside QCDA expects this to cause the slightest problem, and many see it is an advantage since it is the same for all candidates.
There is not enough scope for stretch and challenge.
Ample scope for stretch and challenge already exists.
Typical mark distributions for C3 and C4 do not show excessive bunching in the high mark ranges.
Most candidates find these units challenging.
Deliberately to make them more so would have the effect that very many candidates would find that there are questions on which they are simply unable to make any realistic attempt. For the most talented, both Further Mathematics and the AEA papers are available, and it would be better to direct them towards those.
Change is needed to line up with the changes in GCSE.
Ofqual will not allow the present arrangements.
The first students taking the new GCSE will enter sixth form in 2012. Only then will it be possible to see what, if any, changes are needed to AS and A
Levels to bring them into line with the attributes of the new entrants from GCSE. So the timing is completely wrong.
The proper function of QCDA and Ofqual is to ensure that any regulation applied to a particular subject serves it well, rather than that subjects are bound by the same regulations.
QCDA‟s latest proposal for A Level Mathematics
March 2010