Tony Gardiner: Mathematics GCSE (England). Proposed subject content: Suggested revisions. I.

A. D. Gardiner, Mathematics GCSE (England). Proposed subject content: Suggested revisions. I.  The De Morgan Journal 3 (2013) 7–15.

From the Introduction:

The draft for consultation was published on 11 June 2013 for comment by 20 August. This is the document that will determine the nature of assessment at age 16 for the next 10 years or so; and one suspects that even those who contributed to the drafting process might agree that, despite all the work that has been done, the current version still needs serious attention. Yet the timing of the consultation leaves the mathematical community insufficient time to analyse, to debate, and to reach a consensus on the changes that are needed. Moreover, July/August is scarcely the ideal time of year for hammering out a response – let alone acoordinated response.

There is no obvious ‘right way’ to respond to this situation. The art of drafting such national specifications is not something most of us find easy: we may discern curious omissions, or distortions, in the proposed version, yet not know how best to correct them. I hope I might therefore be excused for publishing suggested revisions as a contribution to discussion and debate.

To emphasise that the intention is constructive, I have accepted the constraint of working within the structure adopted in the draft listing of subject content, and suggest minimal changes and additions designed to improve the current version (rather than proposing what one might have preferred to see), in order to transform the draft into something more consistent with its own declared goal of adopting a curriculum

  • that builds upon the foundations that have been (partially) laid at earlier stages,
  • that ensures progression to A level, and
  • that is consistent with that of high-attaining education systems internationally.

Compiling and cross-checking such “minimal changes and additions” is itself a major task, which should ideally take many months – time we do not have. In the hope of generating some communal debate and a degree of consensus it has proved necessary to publish this commentary in two or three parts, addressing the listed sections in groups. I appreciate that this is far from ideal (since each section impinges on other sections). But as Chesterton reminded us, in an emergency

the best is often the enemy of the good’.

The goals of the consultation draft are quite different from those of the much more detailed “mathematics curriculum for all written from a humane mathematical perspective” (; so the suggestions proposed here were initially drafted without consulting that much more detailed list, but were then modified slightly by checking against it.


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