*(Mathematicians and mathematics educators around the world are
discussing "Tackling the Mathematics Problem," a British report on
problems relating to the mathematical preparation of entrants to
university courses commissioned jointly by the London Mathematical
Society, the Institute of Mathematics and its Applications, and the Royal
Statistical Society. At the invitation of EXTEND, Geoffrey Howson of the
University of Southampton and chair of the commission that prepared the
report, wrote a brief preface for our readers. Excerpts from the report
iself follow this preface. The
full text of the
report is available on-line, or in TeX by anonymous ftp.)*

It would be easy to dismiss "Tackling the Mathematics Problem" as a ritual moan by a group of aging mathematics faculty members looking back nostalgically to the golden days of their youth, particularly since they come from a country altogether too inclined to wallow in its former glories. To do so would be dangerous.

Of course, some of the issues raised are peculiarly English: the problems of an over-specialized Senior High School Curriculum; an obsession with external examinations and with the attachment of grades, labels, and classes to students; and the after-effects of the over-hasty imposition of an ill-conceived National Curriculum. But such local issues mask wider issues affecting the majority of developed countries.

Many countries have experienced a marked drift away from the study of mathematics, science, and engineering once these subjects become optional. Paradoxically, as Eric Hobsbawn remarks in "Age of Extremes," the "Golden Age" (l947-1973) "whose only claim to have benefited humanity rested on the enormous triumphs of a material progress based on science and technology, ended in a rejection of these by substantial bodies of public opinion and people claiming to be thinkers in the West." This trend has now operated for so long that its effects are observable within the teaching forces of many countries and, as a result of a consequent shortage of subject-able, confident and enthusiastic teachers, the problem of attracting students to these subjects becomes progressively harder.

To some extent this problem has been concealed by the vast expansion of educational opportunities that has, at least, helped to maintain numbers in higher education. But almost universally the question is being asked: "Has quality been sacrificed in the quest for quantity?". In many ways this is not a sensible question. A balance must always be struck so as to optimize the greater "public good." It is perfectly reasonable to relax the standards previously achieved by only a small elite if by doing so one can significantly raise those of a much greater proportion of the population.

But important questions still remain unanswered such as: Does this mean that the previous high standards are now only set for an even more selective population, selected more than ever by social class?" and "Have attempts to increase access to a subject led to its misrepresentation and has 'attractiveness' been increased at the expense of long-term 'usefulness'?"

These questions must be asked of several subjects in many countries. But no subject is universally given so much emphasis as mathematics. Moreover, its teaching has always presented great difficulties. There was no golden age when everybody understood everything they were taught. Yet its vital importance within education has always made mathematics the focus of special attention and this has resulted in numerous attempts to find solutions to the problems of its teaching both in terms of pedagogy and syllabus content.

Much has been attempted, but with frequent lack of success. This has not been because the theoretical objectives of innovations, or even the teaching methods suggested, were in themselves misguided--given ideal conditions--but rather because the many constraints prevented them from being implemented successfully throughout school systems. Often innovations have lacked that degree of practicability which is essential for successful implementation. Moreover, ideas and innovations have spread across national boundaries before essential experience has been gained in the classroom. In particular, the dogma of "market forces" has not been subject to critical examination in the light of its observable consequences.

These are the points then which must be borne in mind by the non-UK reader of our report.

- Are your schools and universities preparing a sufficient number of students suitably qualified in mathematics?
- Is mathematics teaching in schools preparing students effectively to use or to study further mathematics, science, and engineering?
- Has increased popularity been gained without obscuring the essence of the subject?
- Are proposed innovations capable of implementation in other than a few favoured institutions?
- Can sufficient help and support be provided for less-favored teachers?
- Are we attracting sufficient professionally able teachers to our school systems?
- Are institutions of higher education making serious efforts to ensure
that their mathematics graduates are better equipped to become teachers
(because of their increased knowledge about and interest in mathematics in
all its aspects, and increased confidence in their abilities as
professional mathematicians) than they were when they graduated from high
school?

It was pleasing to learn of the interest which our report has created in other countries. I am certain that the underlying problems which we in England face are by no means unique to us, and I very much hope that different countries will not only use their experience and knowledge better to identify and comprehend these problems but will also work collaboratively and profitably towards their solution.

*Geoffrey Howson is Professor Emeritus of Mathematics at the
University of Southampton, where formerly he served as Chair of Mathematical
Studies and as Dean. Previously he served as Secretary of the
International Commission on Mathematical Instruction (ICMI).*