*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.

- 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;
- 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.

- 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.