Tackling the Mathematics Problem

An Abridged Summary

Excerpts from "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. A special Preface to the report was prepared for EXTEND readers by Geoffrey Howson, Chairman of the committee that wrote the report. The full text of the report is available on-line, or in TeX by anonymous ftp.)

There is unprecedented concern among academics about the decline in the mathematical preparedness of those entering undergraduate courses in science and engineering. ... 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.

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

• Students enrolling in 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.

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

• 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.

1. In recent years less emphasis has been placed on the acquisition of skills involving arithmetic, fractions, ratios, algebraic technique, and the basic geometry of triangles, lines and circles;
2. All of these neglected topics are vital for further study in mathematics, science and engineering.

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.

Proposals for Discussion:

• The current [National Curriculum], which aims to cater for different abilities by varying the speed of progress through the same material, must be reconsidered. It is inappropriate for progression to A-level and higher education. (Its suitability for low-attainers must also be questioned.)

• There needs to be more emphasis in national curriculum mathematics on important basic topics and on the acquisition of those techniques which will form a firm foundation for further study. Nowadays, a third of all students progress to higher education and most of these use some mathematics in their degree courses.

• It is also essential that the exactness of mathematics and its notion of proof should not be distorted and that close attention should be paid to accuracy and clarity of oral and written mathematical communication, including the setting out of logical arguments in good English.

• Steps must be taken to counter the unfortunate effects of `market forces'. In particular, we note the competition between examination boards which has driven down standards, the incentives to schools to shop around for short-term gains, and the pressures on those in higher education both to reduce the mathematical content of their courses in order to attract applicants and also to lower standards in order to retain and reward students.

• The lack of sufficient well-qualified mathematics teachers has been a major problem facing English education for over 30 years. Moreover, changes to the educational system have served to exacerbate existing problems. ... In particular, the concentration of well-qualified teachers in 16-19 colleges means that younger secondary pupils are less likely to be taught their mathematics by teachers who are both enthusiastic about the subject and have a clear grasp of its internal structure.

• The exclusion of [mathematicians in higher educaton] from real involvement in decision making has led to school curricula which are, in important ways, inconsistent with mathematics as specialists understand it-- in short, which misrepresent what to many is "the essence of the discipline." This has caused severe problems for those teaching or using mathematics in higher education and has had the regrettable consequence that many in higher educaiton have lost confidence in the manner in which school mathematics is organized and decisions regarding it are taken.