CONCLUSIONS

This report demonstrates that there are many problems concerning education in mathematics in England and Wales to which solutions must be urgently sought. Below we put forward some proposals. Apart from the first two recommendations, these are intended to fuel discussion --- for there are many parties not involved in the writing of this report who must be involved in discussions of such proposals. But the two main recommendations, which would provide appropriate settings for such discussions and decision-taking, are for immediate and urgent action.

MAIN RECOMMENDATIONS FOR IMMEDIATE ACTION

1

We strongly recommend that the DFEE set up a standing committee, including substantial representation from higher education, to provide an overview of education in mathematics from primary school through to university, and to ensure that sound advice and adequate support are provided to those involved in its organisation and delivery.

The questions of what mathematics should be taught, how, when and to whom, are not easy to answer. There are strong, but sometimes subtle, connections within the subject; there are also important links with other disciplines. Some of the connections stretch forward several years in the student's experience and can rely heavily on facility in specific techniques or upon understanding of earlier ideas. Therefore any decisions about change need to be made within an informed context, with a complete overview of the subject and in the light of informed international comparisons. The current system, relying merely upon a small secretariat within SCAA, is not adequate for the task. It cannot achieve the level of trust required nor, indeed, can it be relied upon always to provide sound advice.

It is clear, from the earlier sections of this report and from other recommendations below, that there are many issues requiring serious and sensible debate and mediation. These provide both a justification and a remit for such a committee, which would be expected to establish ad hoc working groups on specific issues, and to receive and act on their reports. In order to develop the required long term overview and to monitor the effects of the changes made, this needs to be a standing committee.

Its membership should include representation from two distinct groups within higher education --- from mathematicians and from other major users of mathematics. Higher education not only contains specialists with the necessary insight in to the internal structure of the discipline, but is now, as we have explained elsewhere, a major `end-user' of the school system. In particular, almost all students achieving A-level in mathematics now go on to higher education and most will make use, in that context, of their previous training.

2

The government should establish, as a matter of urgency, a Committee of Enquiry, on which higher education is strongly represented, with the express task of examining the current curricula in mathematics, both age 5--16 and age 16--19, and making proposals in time to allow carefully considered action at the end of the current moratorium on change in the National Curriculum.

The committee's brief should include the aims and content of the curriculum, the manner in which it should be specified, principles underlying the ways in which the needs of all types of students can be met, and means of assessment. The committee's concerns should also include mathematics and numeracy provision overseen by NCVQ. Data from examination boards and the DFEE, together with the evidence provided from higher education --- both from mathematicians and from engineers and scientists --- make it abundantly clear that a rethink is needed, and that the thinking should begin immediately if we are not to repeat the old cycle of over-hasty and ill-considered change.

PROPOSALS FOR DISCUSSION

3

The National Curriculum 5--16

(a)

The current system, which aims to cater for different abilities by varying the speed of progress through the same material, must be reconsidered. It is inappropriate for progression to A-level and higher education. (Its suitability for low-attainers must also be questioned.)

(b)

There needs to be more emphasis in national curriculum mathematics on important basic topics and on the acquisition of those techniques which will form a firm foundation for further study. Nowadays, a third of all students progress to higher education and most of these use some mathematics in their degree courses. It is also essential that the exactness of mathematics and its notion of proof should not be distorted and that close attention should be paid to accuracy and clarity of oral and written mathematical communication, including the setting out of logical arguments in good English.

(c)

Teachers would be greatly assisted if the National Curriculum were more explicit about the basic facts, methods and ideas which are fundamental to subsequent mathematical progress.

(d)

Methods of assessment must be reviewed. Until major changes can be made, the decision to allow Grade B to be obtained on GCSE intermediate mathematics papers, other than in exceptional circumstances, should be reconsidered.

(e)

The recent substantial cut in time spent on mathematics, especially at age 11--16, must be urgently reviewed.

4

On alternatives to A-level

The present A-level system would no longer seem appropriate for many students and militates against their opting for a course in which mathematical and scientific studies form a coherent component. This seriously damages the nation's scientific and technological well-being. The Government should reconsider its support for the status quo and immediately begin to investigate the feasibility, on educational and logistic grounds, of alternative systems which could preserve --- or increase --- academic values while offering students more broadly-based and coherent educational options. However, this should not prejudice the review of the 5--16 curriculum.

5

On changes to the existing A-level in mathematics

(a)

Methods of dealing with A- and AS-level students with different needs, ability and attainment must be given serious attention. In particular, the desirability of papers differentiated by need (as in the French Baccalauréat), the position of further mathematics, and the need for a Special Paper demand urgent review.

(b)

The size and detail of the `core' should be reconsidered. A larger, more detailed core would ease the transfer from school to university greatly, with negligible loss to teachers and students.

(c)

Modular A-levels have some advantages. However, a single summative examination on core topics (along the lines of that recommended in IMA (1995) [16]) could have considerable merits --- especially for more ambitious students, and for more selective HE institutions.

(d)

We recommend that the government should establish a bursary scheme for students who go to university to study mathematics, physics, physical chemistry or engineering, based on the results of some such examination as that in (c). (To encourage the study of mathematics in maintained schools, we would propose that the proportion of such awards available to students from non-maintained schools should be strictly circumscribed.)

(e)

The comparative difficulty of mathematics A-level should be kept under review. Moreover, simplistic measures of success based on league tables which, for example, fail to distinguish between modular and non-modular syllabuses or mathematics and further mathematics, should be re-examined as a matter of urgency.

(f)

Consideration should be given to the obvious merits of cutting the number of different A-level syllabuses. This would simplify the transition from school to university and would make it possible to insist on improvements in question-setting and in moderation.

6

On GNVQ

We have recommended (Recommendation 2) that the form GNVQ should take in the medium-term should be considered along with the future of academic 16--19 qualifications. Since GNVQ can lead to higher education, it is important that mathematicians in higher education at all types of university should be included in discussions at NCVQ.

7

On teacher training

The government and universities must co-operate to improve the supply of highly qualified mathematics teachers at all levels. The government should provide extra support, in the way of subject-based mathematics in-service training, to existing teachers of the subject. There needs to be a greater effort to increase the fund of mathematical expertise in primary, as well as in secondary schools. The minimum mathematical preparation required by those wishing to become teachers of mathematics at different levels should be reviewed (see Section 13). In view of the complexity and the extreme importance of this matter, it may well be appropriate to establish a committee to investigate and report on these issues.

8

On universities

(a)

All mathematics departments in universities should provide, or collaborate in providing, appropriate courses or modules to attract and stimulate potential school teachers of mathematics.

(b)

All those involved in higher education need to consider further their provision for incoming students --- particularly in the short term, before changes can be made at secondary level. The effect of wider access, and the resulting widening in the ability range, must be considered further. The moves to four-year courses leading to MPhys and MMath are one response, but there remains a need to consider whether the current honours degree structure is suited to all, or even the majority, of incoming students.

9

On market forces

Steps must be taken to counter the unfortunate effects of `market forces'. In particular, we note the competition between examination boards which has driven down standards, the incentives to schools to shop around for short-term gains, and the pressures on those in higher education both to reduce the mathematical content of their courses in order to attract applicants and also to lower standards in order to retain and reward students.

10

On the provision of data

It is clear from earlier sections that there is a general problem regarding the availability of sensible and reliable statistics about mathematics students, teachers, etc. In particular, at university level, statistics for mathematics and for computing should no longer be aggregated as `Mathematical Sciences'. It is important to know the separate figures and trends for these disciplines which are quite distinct, although with an important interface.

11

On attracting students to mathematics, science and engineering

Government, learned societies, professional bodies, university mathematics departments, etc. should collaborate to increase publicity for mathematics and for mathematics related careers with a view to increasing the supply of young mathematicians. In particular, government attempts to publicise Science and Technology should be renamed --- e.g. from SET to STEM (Science, Technology, Engineering and Mathematics) --- making explicit the underlying importance of mathematics.