Viscount Hanworth (Lab)

My Lords, there are four key stages that have mandatory elements in the maths curriculum. The fourth stage concerns pupils aged 14 to 16. Here there is an abundant list of topics that the student should be taught and which they might presume to know by the age of 16. The list is both complete and unexceptional. My primary interest is with stage 5, which corresponds to ages 16 to 18 and is the stage at which students prepare for their A-level examinations. Nothing at all is specified in the national curriculum for this stage. Nevertheless, at this level, the topics and methods of teaching and the texts of mathematics have hardly changed over the course of half a century or more. The fact that there has been so little innovation has a simple explanation. Little has changed in the exam papers set by the various boards of examiners, which tend to concur on what is appropriate. The boards are predominantly owned by large publishers that have made considerable investments in producing A-level texts, which they are understandably unwilling to revise. Typically, these texts are lavishly produced with a liberal use of colours, but they are turgid and uninspiring, and unattractive to many students. The number of students pursuing mathematics at this level is by common consent far lower than is needed to service the demands of the nation. There are too few graduates to satisfy the competing demands of education on the one hand, and of industry and commerce on the other. Teachers who are maths graduates are not liable to remain long in the teaching profession: they are lured away by the higher salaries on offer elsewhere. Therefore, a large proportion of those who teach mathematics in schools have derived their knowledge in pursuit of other subjects such as economics, accountancy, the physical sciences, life sciences and even geography. Many do an excellent job, but many teach with a degree of diffidence that is often perceived by the students. Why is the diet so turgid and indigestible? I contend that it is a legacy from the mathematicians working at the end of the 19th century, when the dominant programme was to secure the axiomatic basis of mathematics. This led to an abstract and brutal style that found its way into the textbooks at the higher levels. It gave rise to a didactic style that filtered down to the lower levels. The diet can be rendered palatable by taking care to associate the elements of a mathematics course with the social, historical and scientific context from which they have emerged.