Tony Gardiner: Nurturing able young mathematicians

A. D. Gardiner, Nurturing able young mathematicians, The De Morgan Journal  2 no. 7 (2012), 87-96.

Abstract:

We summarise the developments of the last 20 years—highlighting the key underlying assumptions, and indicating certain unfortunate consequences. We show how official policy has been based on

  • persistent failure: (i) to develop and to implement a suitably challenging curriculum, and (ii) to provide ordinary teachers with good texts, suitable subject-specific professional development, and appropriate assessment targets;
  • a misconception of the curriculum as a one-dimensional ‘ladder’ (with each topic nominally the same for everyone, with uniform expectations for all pupils at a given ‘level’), up which pupils progress at their personal rate, and
  • associated accountability measures that have unintended consequences.

We then outline the alternative conception of a two-dimensional “*-curriculum”, in which each theme in the standard curriculum sequence is explored (and where necessary, assessed) to different depths, and where those who manage to dig deeper and to lay stronger foundations emerge naturally as the ones who are well-placed to subsequently progress further. In such a model, able pupils in Years 5 and 6 would not be pushed ahead to achieve a premature and superficial mastery of ‘Level 6’ material, but would spend time exploring harder problems at ‘Level 4’ and ‘Level 5’ (so-called 4* and 5* material). Similarly, able students in Years 10 and 11 would not be entered early for an accessible but superficial GCSE, but would instead be expected to master core GCSE material more deeply, so as to make the subsequent transition to A level in Year 12 straightforward.

Read the rest of the paper. 

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