4.3 Evidence

Some data relating to the first two criticisms 4A and 4B in Section 4.1 were publicised in the press during 1995. While symptomatic of our concerns, none of this information is as robust as one would like it to be, either in the range of mathematics tested or in its use of strictly comparable groups of students .

Various universities have offered us data supporting the case we are putting forward. We have chosen not to reproduce, or even to try to summarise, all these, largely because of difficulty in ensuring that the groups of students involved are strictly comparable. However, in Appendix A, we give some results (from a test given in October 1994 to students entering the honours school of mathematics at one university) which illustrate the problems now faced by universities. We also present, in the same spirit, some evidence from large-scale national mathematics competitions aimed at the top third of the relevant age groups in secondary schools. We suggest that these should be studied bearing in mind the question `Are these standards appropriate?' rather than `Were students better in the past?'

The third area of criticism, 4C, depends crucially upon what experienced university lecturers infer about the perceptions of their students from their spoken or written work. It is therefore more difficult to substantiate this criticism in quantitative terms. However, the criticism as stated would appear to reflect the considered judgement of almost everyone we have consulted (including many scientists and engineers (see Engineering Council (1995) [9]). There is some research evidence which supports these widely held concerns: for example, the study of Coe and Ruthven (1994) [4] showed that, of sixty mathematics students engaged in a piece of coursework to complete an A-level module ``directly concerned with proof'', only two students appeared to understand what was required in order to prove a hypothesis. Evidence over the last 5--6 years from national mathematics `olympiads' , each aimed at one thousand or so of the very best students in School Years 7--8, 10--11, and 12--13 reinforces this concern.

No evidence was presented to the working group which would contradict any of the criticisms 4A, 4B, 4C.

We were unanimous in our judgement that:

(a)

such criticisms are justified;

(b)

most of the observed weaknesses stem from current content, emphases, aims and assessment procedures; they will not be removed as a result of recent changes to the National Curriculum; and they will only be remedied by a far-reaching review and by much improved guidance for teachers;

(c)

urgent attention must be paid to ensure that students bound for higher education in future leave school better prepared to continue their studies;

(d)

while higher education has adjusted, and will continue to adjust, to changes in the preparation of its entrants, the nature and scope of the current shortfall cannot be addressed satisfactorily at 18+ or, indeed, at 16+.