SUMMARY

1. There is unprecedented concern amongst mathematicians, scientists and engineers in higher education about the mathematical preparedness of new undergraduates. There is also a very long-standing worry about the numbers of prospective students in these disciplines. This report, on behalf of the London Mathematical Society, the Institute of Mathematics and its Applications, and the Royal Statistical Society, explains these concerns and suggests some actions.
2. While we believe that our analysis is factually correct, we recognise that `facts' and `trends' in education are open to different interpretations. Any such analysis is based on judgement, and is not susceptible of absolute `proof'. Some may dispute details of our analysis but they cannot ignore the fact that the underlying concerns shared, with increasing conviction, by almost all those who have experience of teaching mathematically-based courses in higher education.
3. It is economically important to this country that it produces both numerate citizens and top class mathematicians, scientists and engineers. This is almost impossible if the mathematical foundations for all these disciplines are not laid at the appropriate time.
4. Recent changes in school mathematics may well have had advantages for some pupils, but they have not laid the necessary foundations to maintain the quantity and quality of mathematically competent school leavers and have greatly disadvantaged those who need to continue their mathematical training beyond school level.
5. The serious problems perceived by those in higher education are:

   (i)

   a serious lack of essential technical facility --- the ability to undertake numerical and algebraic calculation with fluency and accuracy;

   (ii)

   a marked decline in analytical powers when faced with simple problems requiring more than one step;

   (iii)

   a changed perception of what mathematics is --- in particular of the essential place within it of precision and proof.

6. International comparisons confirm many of these perceptions and also indicate what other countries have achieved. Insufficient attention has been paid to such findings.
7. A major cause of these problems has been the flawed method of planning change in the past decade. There is no representative, authoritative, continuing forum for mathematics, bringing together mathematicians, scientists, engineers, employers, teachers etc. Rather, there is a one-sided dialogue between SCAA and individual bodies, with agenda-setting and decision-making controlled by a small and necessarily unrepresentative group within SCAA.
8. Most of the suggestions and proposals contained in this document are tentative and need to be tested both by open debate and by discussion within such a representative forum. Hence, our two major proposals are organisational.
9. 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. Such a group should ensure that the many issues raised in this report are debated openly and fully by all parties concerned. The process of identifying suitable representation from higher education should include consultation with professional and learned societies.
10. Given the concern about the current mathematics curriculum in schools, we recommend that, as a matter of urgency, a Committee of Enquiry be established by the DFEE with the express task of examining the current situation and making proposals in time to allow carefully considered action at the end of the current moratorium on change.