Acceleration or enrichment: Report of a seminar held at the Royal Society
on 22 May 2000, The De Morgan Journal, 2 no. 2 (2012), 97-125.

Full title of the paper:

Acceleration or Enrichment?
Serving the needs of the top 10% in school mathematics.
Exploring the relative strengths and weaknesses of “acceleration” and “enrichment”.
Report of a seminar held at the Royal Society on 22 May 2000.

The report includes contributions from Tim Gowers, Gerry Leversha, Ian Porteous, John Smith, and Hugh Taylor.

Abstract:

This report was originally published in 2000 by the UK Mathematics Foundation (ISBN 0 7044 21828). It was widely red, and was surprising influential. However, it appeared only in printed form. Various moves made by the present administration have drawn attention once more to this early synthesis— which remains surprisingly fresh and relevant. Many of the issues raised tentatively at that time can now be seen to be more central. Hence it seems timely to make the report available electronically so that its lessons are accessible to those who come to the debate afresh.

While the thrust of the report’s argument remains relevant today, its peculiar context needs to be understood in order to make sense of its apparent preoccupations. These were determined by the gifted and talented policy’ adopted by the incoming administration in 1997, and certain details need to be interpreted in this context. There are indications throughout that many of those involved would probably have preferred the underlying principles to be applied more generally than simply to “the top 10%”, and to address the wider question of how best to nurture those aged 5–16 so as to generate larger numbers of able young mathematicians at age 16–18 and beyond. The focus in the report’s title and subtitle on “acceleration” and on “the top 10%” stemmed from the fact that those schools and Local Authorities who opted at that time to take part in the Gifted and Talented strand of the Excellence in Cities programme were obliged to make lists of their top 10% of pupils; and the only provision made for these pupils day-to-day was to encourage schools to “accelerate” them on to standard work designed for ordinary older pupils. The wider mathematics community was remarkably united in insisting that this was a bad move. This point was repeatedly and strongly put to Ministers and civil servants. But the advice was stubbornly resisted; (indeed, some of those responsible at that time are still busy pushing the same linez.

The present administration seems determined once more to make special efforts to nurture larger numbers of able young mathematicians, and faces the same problem of understanding the underlying issues. Since this report played a significant role in crystallising the views of many of our best mathematics teachers and educationists, it may be helpful to make it freely available—both as a historical document and as a contribution to current debate.

Read the whole paper. 

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.