Two months ago a report on the teaching of mathematics in schools caused a big stir in the British Media. Here Dr. K.E. Hirst of the University of Southampton, gives a brief account of this important document.

Tackling the Mathematics Problem

A Report from the London Mathematical Society, the IMA and the RSS

UK mathematicians in Higher Education are not alone in Europe in expressing concern at the present time about the mathematical preparation of undergraduates entering courses in mathematics and related subjects (particularly science and engineering).

The situation has recently been changing again in England & Wales (the Scottish pre- university curriculum is different in structure), and this prompted the London Mathematical Society, together with the Institute of Mathematics and its Applications and the Royal Statistical Society, to set up a committee of enquiry to consider the issues involved, under the Chairmanship of Professor Geoffrey Howson of Southampton University. Its conclusions were published in October 1995 as a report Tackling the Mathematics Problem.

The enquiry, together with other studies recently undertaken, found an unprecedented degree of concern in higher education, summarised as

“(i) a serious lack of essential technical fluency - 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.”

The report makes the point that these perceptions are confirmed by international comparisons which have been undertaken in recent years.

The report has been widely circulated and so it was appropriate that the continuing reasons for the importance of mathematics as an intellectual, cultural, technological and economic tool should be stressed: they paraphrase the title of the 1982 Cockcroft report^{1} as “Why Mathematics Still Counts”.

Early on the report states “We stress at the very outset that, in our view, the main responsibility for the weaknesses we identify cannot be laid at the door of classroom teachers.”

The report identifies a number of factors which are felt to be important in giving rise to the perceived problems. Among the most important is “English school mathematics has seen a marked shift of emphasis, introducing a number of time-consuming activities (investigations, problem-solving, data surveys, etc.) at the expense of ‘core’ technique. In practice, many of these activities are poorly focused;... Such approaches, if well-directed, have value, but priorities must be agreed.” It is

1 Mathematics Counts Report of the Committee of Inquiry into the Teaching of Mathematics in Schools. HMSO 1982 pointed out that there has been an effective reduction of around 20% in the time available in school for mathematics. It is felt that the recent changes to the National Curriculum, and the impending changes to the GCE Advanced level^{2} examinations in mathematics, will not address the problem, and could exacerbate it. There are also concerns about student numbers. There has been a period of demographic decline since 1965, while the total number of A-level entries has doubled. Over that period the number of male students taking A-level mathematics has remained stationary at around 36,500, and the number of female entries has increased from 6,400 to 20,400. However, mathematics entries as a proportion of all A-level entries has declined from 15.9% in 1965 to 8.7% in 1994. Much more worrying is the position of Further Mathematics ^{3}. The number of entries has dropped from 15,600 in 1965 to only 5,400 in 1994. The reasons for this are various, including a shortage of well-qualified mathematics teachers and other pressures on resources. This has had a major effect on university mathematics departments. To take the University of Southampton Mathematics Department as an example, in 1965 around 95% of the undergraduates entered with two mathematics A-levels. In 1994 that figure had dropped to less than 30%. Another factor highlighted in the report arises from the peculiar structure of the A-level examining boards. Historically these arose from universities setting entrance examinations, but now they are autonomous bodies (although some still retain university affiliation), and more importantly are selffinancing. The presence of competitive market forces as a factor within the examinations system is seen as having possible consequences in terms of standards of syllabuses and grading. Unlike some other countries, the examination boards are not government agencies. Their activities are monitored and syllabuses approved by a government Schools Curriculum and Assessment Authority (SCAA), and one of the criticisms in the report is the lack of effective mathematical presence in the work of SCAA. So to summarise, the main conclusions of the report are that:

(i) the lack of a proper input from professional mathematicians into discussion of the school curriculum and examinations needs to be addressed, at government level;

(ii) changes in emphasis in the National Curriculum for mathematics are needed; (iii) the reduction in content in the core A-level mathematics syllabus should be seriously questioned

and a larger core agreed; (iv) consideration should be given to cutting the number of A-level syllabuses (the report draws

particular attention to the present diversity);

(v) steps should be taken to counter the unfortunate effects of ‘market forces’ within the examination system

(vi) efforts must be made to increase the supply of well-qualified mathematics teachers; (vii) efforts must be made to attract more able students into mathematics, science and engineering.

A final quotation from the report: “We are facing serious challenges. Only if all parts of the education system work together will true progress be made.”

2 GCE Advanced level (A-level) is the examination taken at around age 18 by pupils in England, Wales and Northern Ireland (and some overseas countries), and it is the primary subjectbased entrance qualification for university undergraudate study. 3 Mathematics is almost unique in having two A-level subjects. Further Mathematics has the single subject Mathematics A-level as prerequisite. Sometimes the two A-level subjects are organised as Pure Mathematics and Applied Mathematics (mechanics and/or statistics).