A BRIEF OUTLINE OF THE PROBLEM AND THE REQUIRED RESPONSE

This section presents a brief summary of our position; the background discussion and the supporting justification for assertions in this section will be presented in later sections. Our first concern has been to document as clearly as we can the nature of the problems as seen from the viewpoint of those in higher education. Moreover, though the working group included only one practising schoolteacher and one teacher trainer, we have consulted widely with teachers and teacher's organisations to try to ensure that, insofar as possible, our findings are presented in a way which takes account of their concerns. We stress at the very outset that, in our view, the main responsibility for the weaknesses we identify cannot be laid at the door of classroom teachers.

The report DfE (1994) [8] highlighted inadequacies in the flow of qualified young people into science and technology. We welcome this official recognition of some of the problems and support much that is to be found therein. However, the picture presented by it, and by the subsequent report OFSTED (1994) [22], is too often obscured by a general air of complacency. For example, both reports take comfort in the fact that graduate numbers in mathematics and computer science combined have expanded steadily, even though the picture for mathematics alone is more worrying. All our evidence suggests (see Sections 5--10) that such statements as ``The picture, therefore, can be said to be relatively reassuring'' (OFTSED, 1994 [22], p.1) are dangerously misleading.

An equally serious concern of higher education is its observation of a qualitative change in the mathematical preparation of incoming undergraduates (see Section 4). This is in no way restricted to those `new undergraduates' who ten years ago would not have proceeded to higher education. The problem is more serious; it is not just the case that some students are less well-prepared, but that many `high-attaining' students are seriously lacking in fundamental notions of the subject. This trend is new, and is a significant indicator that something has gone wrong.

The working group's primary finding, recognised in Dearing (1995) [7] p.39, is that the United Kingdom faces extremely serious problems relating to the supply and the mathematical preparation of entrants to university courses in mathematics, science, engineering and technology.

We need to improve the mathematical foundations laid at school level for all our students, whether or not they are likely to proceed to higher education. There is no painless or short-term way of achieving this; in particular, it is clear to us that recently implemented and currently envisaged initiatives will not have the required effect. This report puts forward in its conclusions (Section 16) the need for amendments to National Curriculum and A-level mathematics, while stressing that any changes instituted must be extremely carefully thought through. At the same time, it makes proposals concerning assessment, teacher recruitment and training, vocational courses, the effect of `market forces', and other matters --- for the impact of mere curriculum change on the problems noted above will be limited if these other aspects of the educational system are not also subjected to serious scrutiny. On all these matters, higher education has a distinctive perspective and authority --- but so too have others. Therefore our conclusions in such matters are presented as a contribution to serious discussion leading to action.

Our two main recommendations concern the manner in which discussion and decision making should be conducted. Discussion and review of the kind we recommend must begin quickly and be carried out thoroughly in a way that, much more than at present, commands the confidence of all concerned, including mathematicians throughout higher education. This national problem can be overcome only by much more carefully considered long-term planning than hitherto, and by determined, co-operative implementation.