Some reactions to the mathematics 14-19 report
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:
- Supply of specialist teachers: Given the importance of statistics, emphasised in the report, it is disappointing that there appears to be little data on the distribution of adequate qualifications to teach statistics, either among mathematics teachers or non-mathematics teachers (e.g. in Geography or biology). This is especially important when considering the proposal to move the teaching of statistics out of mathematics at key stage 4. The report's call for more and better data in the area of supply is therefore welcome.
- The report is concerned about the quality of ITT in mathematics. Of particular concern is the ability of ITT provision to provide suitable training in the teaching of statistics. At present, mathematics students entering teaching may have neither a proper understanding of statistical techniques because these have not been encountered at undergraduate level, nor be provided with adequate ITT. As a result such trainees cannot be expected to cope adequately with statistics and data handling in the curriculum. Urgent attention should be paid to the compulsory inclusion of suitable statistical training for all potential teachers of mathematics, as long as mathematics teachers have responsibility for this aspect of the curriculum. To the extent that statistics is taught outside of mathematics, then suitable provision for this in ITT should also be made.
- The structure of the curriculum, as examined in Chapter 4 of the report is clearly important, and there are a number of issues about the position of statistics. First, recent years have seen, in the UK and abroad, an expansion of high quality statistics teaching materials, within a flourishing international community of statistics educators and a high priority given to the teaching of statistics within many educational systems. In the UK, the Royal Statistical Society Centre for Statistical Education is a world leader, collaborating with industry and the public sector such as the Office for National Statistics, to produce materials that are motivating and increasingly being used in schools and colleges.
- There are good foundations for the continuation and development of statistics teaching 14-16 as a compulsory part of the curriculum devoted to mathematics and mathematically based subjects. The report (4.17) itself stresses the importance of statistics and data handling for all students. Yet in recommendation 4.4 the report suggests that statistics and data handling be taken out of maths for GCSE. The report does indicate that it may be given its own curriculum 'slot' and integrated with other subjects which already teach statistics. While perhaps this is superficially attractive there are serious concerns about how this might be implemented in practice. I have already alluded to the quality of the teaching of statistics, whether within mathematics or other school subjects. As a result, it seems sensible that there should be no move to remove statistics and data handling from the mathematics 14-16 curriculum until proper arrangements are in place to ensure that all students in the relevant subjects receive an adequate training in statistics and data handling and that there is adequate provision in terms of teacher training. Mathematics is surely one of these relevant subjects and others include those such as biology and geography that already have statistical components and new parts of the curriculum such as citizenship for which statistics is an important tool. Yet it is possible to interpret the Report's recommendation in such a way that it would in future be possible for a student to reach the age of 16 and encounter little or no statistics or data handling. It is difficult to believe that such an outcome is intended by the Report, but care is needed to see that it does not occur. There is, moreover, a strong case for the role of a specialist statistical co-ordinator in schools to take responsibility for teaching across the curriculum, and this should be a full time appointment with appropriate CDP support coordinated nationally. Likewise, a statistical co-ordinator for ITT should be implemented.
- I certainly support the call for more and better CPD. Statistics should be included within the review of this area and the review should recognise the use of statistics and statistical reasoning across the curriculum. In particular, teachers of all relevant subjects, including mathematics, should be exposed to statistical CPD. In the context of CPD (paragraph 5.43) there is the statement that statistics and data handling are seen as 'an area of mathematics'. If statistics and data handling are to be a part of mathematics CPD this seems inconsistent with the proposal to separate these from mathematics 14-16.
- If a national system of Centres delivering CPD is established these should include a strong focus on statistics and that statistics should be a component of a national co-ordinating Centre.
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