This report provides a timely call to deal with a real crisis in the teaching and learning of mathematics. The stress in the report on the importance of mathematics as an intellectual discipline and for society at large is important. Particularly welcome is the stress laid on the special place and importance of statistics, as a mathematically based discipline, both for learning in schools and for employment (paragraph 1.7). There is a welcome recognition that there is a severe decline in young people with mathematical skills and understandings at all levels and that urgent action is needed.
The remit of the enquiry, chaired by Professor Adrian Smith, was to make recommendations on the 14-19 Mathematics curriculum. The committee has chosen as its starting point a particular approach to the problem that provides little analysis of the underlying reasons of why Mathematics seems to be so unpopular, and the following comments are intended to raise some of these. I also offer some comments on the position of statistics and statistical literacy, and the Royal Statistical Society (RSS) too responded with concerns in this area. The RSS is also preparing a detailed report on the position of statistics within the school curriculum, and this is due to be published in January 2005.
Throughout the report there is very little evidence about, or analysis of, the societal context of mathematics in England. There is a mention of Scotland as not having the same problems of take-up, but no real attempt at explanation. There are statements about the rest of Europe but no analysis of why mathematics education appears to be more successful there. Undoubtedly, answers to such questions are very difficult and complex, but given that the report's intention is to recommend solutions, a failure to attempt to provide an explanatory model seems curious. Certain specific factors such as the changes to the 16-19 curriculum in 2000 have undoubtedly had an effect, but are hardly a complete explanation for what is a long term problem. In particular, the kinds of solutions proposed reflect a particular, implicit, explanatory model: recruitment of more and better teachers, more time for learning manipulative skills (remove statistics and data handling), more rewards for students (a double award GCSE), more rewards for teachers (salary), and more bureaucratic coordination. These solutions are essentially 'managerial' ones based on a causal model that views the decline in the study of mathematics as resulting entirely from a lack of resources and concomitant poor curriculum and assessment organisation. A drive towards recruiting and retaining more and better-trained teachers is desirable and it is difficult to argue against better co-ordination. It is certainly possible, however, that 'hostility' towards mathematics partly, or even largely, arises from more general cultural attitudes, reflected similarly in attitudes towards science and scientists. Thus, the lack of teachers may reflect not merely poor material rewards or competition from other employers, but also a deep-seated unwillingness by adults to take up mathematical careers in teaching and elsewhere: this view would seem to be supported by the quoted responses from employers. If this is so, then the solutions suggested by the report may be relatively ineffective and, worse, divert attention from tackling the issue at a more fundamental level. For example, many would argue, with some evidential support, that there is a crisis in teaching and teacher morale that results from the application of past and present governmental policies on pay, curriculum, assessment, league tables and target setting. Tackling mathematics provision without attention to such wider issues may not be very productive.
I also have concerns at the somewhat narrow intellectual scope of the enquiry. For example, the assumption that removing statistics and data handling from mathematics at key stage 4 will enhance the learning of mathematics as such by allowing more time for 'core mathematical concepts'. I can find no sound evidence provided in the report that a (properly taught) statistics component is less motivating for students than the provision of more algebra or geometry. Nor is it clear, given the importance that the Report attaches to statistics, why the substitution of more 'core' mathematics for statistics and data handling is more useful to learners.
Some specific concerns are as follows:
Finally, while there is much to applaud in this Report, there are concerns about its implicit assumptions and there are potentially serious problems with some of the detailed recommendations. The Qualifications and Curriculum Authority has been asked to review and take further many of the recommendations. This should provide an opportunity both for a debate on the wider issues surrounding societal attitudes to Mathematics, and an opportunity for the likely consequences of the recommendations to be explored in more depth.
Harvey Goldstein, 24/2/04