Educators for Reform opposes the introduction of the Use of Mathematics A-level. There are strong and encouraging trends in mathematics, with increasing demand from business and the development of a culture where maths is valued. Use of Maths threatens to undermine these developments.
- The content of the qualification is not of A-level standard and does not provide sufficient preparation for studying at university. In particular, algebra and calculus are weak.
- Mathematics teachers are already in short supply (only 76 per cent of those teaching maths have a maths qualification). The introduction of Use of Maths will stretch this resource further. It should instead be focused on A-level Mathematics.
- The qualification may cannibalise A-level Mathematics as schools and students seek the "easier" option. Case studies show other subjects have suffered from "easier" alternatives being introduced; for example Economics A-level entries fell by 62 per cent between 1992 and 2004, while Business Studies entries rose by 70 per cent.
- Poorly-informed students - in particular those at the weaker schools - will either be frustrated as they find that universities continue to insist on A-level Mathematics, or may be accepted for courses with mathematical content only to discover that Use of Mathematics is inadequate as preparation for university.
The QCA is wrong to encourage the introduction of Use of Mathematics as a solution to widening participation. Mathematics in Education and Industry (MEI) has already objected to its introduction.
Educators for Reform suggests that existing Free Standing Mathematics Qualifications (FSMQs) are better suited to provide the additional post-16 maths that may be needed by, for example, social scientists. A significant expansion of participation in post-16 maths will only be achieved by improving the GCSE and making A-level more interesting, challenging and attractive.
Problems with Use of Mathematics
Content is not A-level standard
Consultees have been asked to comment on Use of Maths when A-level pilot papers have been not been publicised. However the content can be examined on the basis of the existing AS level and the pilot A2 papers, obtained by Educators for Reform.
Based on the existing AS-level Use of Mathematics and the pilot papers for the A2, the core content does not provide an adequate foundation for higher education:
- The compulsory algebra and calculus units are considerably less demanding and cover less content than A-level.
- The optional units are a "hotchpotch" which will not give a solid base of preparation.
- The draft criteria[3] suggest that students will be required to sketch graphs. In fact graphical calculators will be permitted in all papers, so students will be able to copy the screen.
- The draft criteria stress practical application. The specimen papers suggest unrealistic scenarios that are a bogus version of real life, for example presenting a polynomial equation to model temperatures.
- The course focuses on working from data sheets to answers, presenting a "sat-nav" approach rather than asking students to think through answers for themselves.
AS-level Use of Maths contains compulsory algebra, plus a choice of two optional units. Algebra in particular is not covered in sufficient depth, with the content focused mostly on finding graphical solutions to algebraic problems. The proposed A2 Use of Maths will contain compulsory calculus and a "controlled assessment", plus a choice of one optional unit. From the pilot paper the calculus component is not of the standard or breadth of A-level.
Curriculum time is taken up with practical activities - such as using "technology as an exploratory tool for developing mathematical understanding" - rather than developing the advanced mathematical understanding that is required for higher education.
The course contents could be useful to students wishing to continue their maths at sub-A-level standard, if taught well. However it does amount to an A-level, which as Reform has previously argued, should be explicitly for preparing students for higher education.
Teaching quality may be diluted
There is an urgent shortage of mathematics teachers. Research conducted by the Campaign for Science and Engineering found that just 76 per cent of Mathematics teachers in state schools are subject specialists.
The introduction of the Use of Mathematics A-level will exacerbate this problem. Although in theory much of the qualification will be taught by non-subject specialists, the advanced content in the Use of Mathematics A-level - in particular the calculus component - will require the expertise of a subject specialist to be taught effectively. The Evaluating Mathematics Pathways project has already warned that the proposed reforms will place "increased demands on mathematics teacher and departments".
Increased demand for already stretched resources will inevitably detract from Mathematics A-level. The impact will be particularly severe in small schools that lack the resources to timetable both Mathematics and Use of Mathematics A-level. Extra funding was provided to schools in the pilot phase that helped minimise this issue but similar funding will not be provided when the qualification rolls out.
Use of Mathematics may cannibalise A-level Mathematics
Schools and sixth form colleges are under pressure to ensure that students achieve good grades at A-level. There is a risk that weaker schools, motivated by this pressure, will encourage students to study the Use of Maths A-level rather than risk poor results in A-level Mathematics.
The MEI position paper on this consultation observes that over half of schools offering A-level Maths do so with cohorts of fewer than 15 students, and such schools are unlikely to be able to offer both Maths and Use of Maths.
The Use of Mathematics A-level, in its pilot phase, has so far succeeded in targeting students who would not otherwise have studied Mathematics A-level. But as the case studies below show, there is strong evidence to suggest that perverse incentives created by forces - such as league tables - mean that more students will end up studying for poorer qualifications.
Case study: Economics and Business Studies A-level
The number of students studying A-level Economics in England dropped by 62 per cent between 1992 and 2004. In the same period the number entered for Business Studies A-level increased by 70 per cent.[8] Research evidence suggests that Business Studies benefited from being seen as interchangeable with Economics but a less challenging qualification. One academic study suggested that nearly 40 per cent of students who obtained a Grade C in Business Studies A-level would not have done so in Economics A-level.
Case study: Mathematics GCSE
Interviews conducted with admissions tutors suggest that some schools are encouraging students to study for Intermediate Tier GCSE, where a B Grade is easier to obtain, than the Higher Tier paper on which a Grade B is perceived to be harder. Although the student achieves the same result - a Grade B GCSE - they have missed out on covering more challenging material.
Case study: Information and Communication Technology GCSE
In March 2009 Ofsted suggested that schools had "moved away" from GCSE Information and Communication Technology over the last decade because it was "perceived to be more difficult". It asked the Government to review the qualification to "evaluate the degree of challenge" in vocational courses that have replaced it.
Students will be misled
The Use of Mathematics A-level is sold as a qualification that is separate but equal to A-level mathematics. The QCA emphasises its equivalence to other Level 3 Mathematics qualifications. This is misleading. Some universities have already specified that the existing AS-level Use of Maths qualification is not acceptable preparation for further study and should only be offered in combination with traditional, academic A-levels.
Most universities will continue to demand A-level Mathematics for Physics, Economics, Chemistry, Computer Science and Engineering. Students attending schools - usually in the poorest areas - that do not have a detailed knowledge of university admission policies will be unaware of this. Some university admissions tutors have already had to turn away bright students whose teachers (wrongly) believed that a Grade A in AS-level Use of Mathematics was appropriate preparation for subjects requiring a high degree of mathematical literacy.
The way forward for Mathematics
FSMQs for those who want to study aspects of Mathematics
There is undoubtedly a need for a post-16 Mathematics option for social scientists or those who wish to continue to do some maths but would rather not take an A or AS-level. The existing FSMQs that will make up much of the new Use of Maths A-level already serve this purpose. FSMQs should be better promoted so that students who just wish to take one or two specialist options are encouraged to do so.
Reform the GCSE
Poor attainment at GCSE, in particular among students from lower socio-economic groups, is the main reason that more students do not go on to study Mathematics post-16. The Use of Mathematics is designed to offer a route into Mathematics for these students. But this is addressing the symptom, not the cause. A better solution would be to provide more rigorous preparation for students at GCSE level. Reform has previously proposed that an end to modularisation would reintroduce rigour. Freeing up teachers to use their initiative would help enthuse pupils. Research interviews conducted by Reform suggests that many students would be capable of meeting this challenge. Admissions tutors at lower-ranked universities interviewed by Reform believe that their undergraduate students were capable of covering more challenging material at GCSE.
Make A-level more interesting
Mathematics A-level suffers from being perceived by pupils as a boring subject. Some of this is down to poor marketing of the subject. Reform has previously argued that popular mathematicians such as Marcus du Sautoy should lead this.[10] Initiatives such as the UK Maths Challenge are a positive step forward and should be extended. But the current A-level itself should also share some of the blame. Pressure to mechanise the marking and examination process means that questions have become dull. R. A. Bailey, Professor of Statistics at Queen Mary, University of London, has described the questions on one 2008 paper as "mind-numbingly boring". The current bureaucratic examination process should be replaced with a new system that allows examiners to set more interesting, open-ended questions.
1- Details of the consultation are at http://www.qca.org.uk/qca_21230.aspx
2 - Mathematics in Education and Industry (2009), QCA consultation on level 3 mathematics: MEI position paper, available at http://www.mei.org.uk/files/pdf/MEI_A-level_position_statement_Final.pdf
3 - Available at http://www.qca.org.uk/libraryAssets/media/QCA-09-4177_A_level_use_of_mathematics_criteria_consultation_draft.pdf
4 - Bassett, D. et al. (2009), A new level, Reform.
5 - Campaign for Science and Engineering in the UK (2007), Opinion Forum, May.
6 - Evaluating Mathematics Pathways (2009), Interim report: executive summary.
7 - Mathematics in Education and Industry (2009), QCA consultation on level 3 mathematics: MEI position paper.
8 - Bachan, R. (2004), Curriculum choice at A-level: why is Business Studies more popular than Economics?
9 - Bachan, R. (2005), A comparison of A-level performance in economics and business studies: How much more difficult is economics?
10 - Kounine, L. et al. (2008), The value of mathematics, Reform.
