The origins and degree of contextualization in A level mathematics. (English)

Math. Sch. (Leicester) 40, No. 2, 28-31 (2011).

From the text: In [the authors, ibid. 40, No. 1, 13‒15 (2011; ME 2016b.00304)], I outlined two approaches to A/AS level pure mathematics which are exemplified by ‘traditional’ and ‘modern’ syllabuses. In the ‘pure’ approach, the emphasis is on teaching pure mathematics in its own right, by developing skills of algebraic manipulation, analytical methods in, for example, calculus, teaching the language of proof and mathematical notation, and so on. In the ‘modelling’ approach, pure mathematical ideas are taught through their applications to the real world, and problems are presented using real-world contextual framing. I am not suggesting that these two approaches are in any way mutually exclusive: it would be futile to attempt to teach pure mathematics entirely through its applications, and, indeed, there would appear to be only certain topics which are amenable to this sort of approach (try setting the binomial theorem in the real world). However, take two current A/AS specifications, such as OCR A and B (MEI), and a little simple analysis of the pure mathematics papers reveals that questions set in real-world context are much more common in the latter than the former, which focuses on mathematical technique to a greater degree than application. Where do these differences in approach originate, and why?