4.1 The view of higher education

There is unprecedented concern among academics about the decline in the mathematical preparedness of those entering undergraduate courses in science and engineering. This can be seen, for example, in the reports of the Engineering Council (1995) [9], the Institute of Physics (1994) [17], and the Institute of Mathematics and its Applications (1995) [16]. (There are some signs that students with A-level mathematics who enter courses such as biology, geography, or business studies, cope relatively well; but many such courses have serious problems with the bulk of their students who gave up the study of mathematics at 16.) While we acknowledge that such a change is, in part, due to the greater numbers now entering higher education, and to the increasing number of options available to students with good grades in mathematics, this does not begin to explain the deficiencies that are being observed. As we have already remarked, the same shortcomings are being seen in those universities which select the best of our young mathematicians, scientists and engineers.

Mathematics, science, and engineering departments appear unanimous in their perception of a qualitative change in the mathematical preparedness of incoming students.

Their criticisms of student preparedness concentrate on three main areas.

4A

Students enrolling on courses making heavy mathematical demands are hampered by a serious lack of essential technical facility --- in particular, a lack of fluency and reliability in numerical and algebraic manipulation and simplification.

4B

Compared with students in the early 1980s, there is a marked decline in students' analytical powers when faced with simple two-step or multi-step problems.

4C

Most students entering higher education no longer understand that mathematics is a precise discipline in which exact, reliable calculation, logical exposition and proof play essential roles; yet it is these features which make mathematics important.

These criticisms affect all those undergraduate courses which presuppose a basis of mathematical technique and are well-illustrated by the report of the Engineering Council (1995) [9], and the problems listed in Appendix A. Faced with modest weaknesses of the kind indicated in 4A, mathematics departments can try to adjust the level of their courses to fit the entry standards of their own specialist mathematics students --- though there is a limit to how many basic weaknesses can be (or should need to be) overcome by undergraduates. Any such adjustment is made much more difficult by the diversity of syllabuses indicated in Appendix B.

It is much less clear how higher education can respond effectively to the more disturbing weaknesses of types 4B and 4C. Science and engineering departments are in a more difficult position than mathematics departments, since they can allocate only a limited proportion of their time to mathematics teaching, and frequently need to make use of mathematical knowledge from the very outset in teaching their own disciplines. If standards of preparedness continue to decline, then so too will the standard of degrees. This will place in jeopardy the value of UK degrees, diminishing their status in relation to qualifications from Europe and elsewhere, and making them less attractive to overseas students.