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This will make you reflect

THINKING MATHS By Mundher Adhami, David Johnson and Michael Shayer. Heinemann. #163;69.95.

Thinking Maths is a new resource for Years 7 and 8. It provides 30 activities from the Cognitive Acceleration in Mathematics Education project (CAME), based on principles developed in science, which have led to significant improvements in pupil achievement.

The introduction sets out the pack's rationale and explains the presentation of the activities. This provides an important discussion of the ideas and research underpinning Thinking Maths. The development of formal operation thinking is seen as important for effective learning at GCSE, and yet research suggests that only "28 per cent of Year 10 pupils demonstrate some ability to think formally": a "disturbingly low" proportion. The CAME project has developed intervention strategies through which pupils collaboratively construct reasoning patterns for themselves to solve new problems. The activities in Thinking Maths exemplify this teaching technique.

Following a teacher introduction and a pupil discussion to ensure that pupils acquire a common understanding of the task, each activity is presented for pupils on photocopiable notesheets. These give a clearly structured sequence of questions, initially closed, but becoming progressively more open, inviting explanation and general reasoning. Notesheets are intended to be used for rough working and to support communication between pupils in small groups.

Extensive teachers' notes for each activity give a summary plan with suggested timings for the stages of the lesson, illustrating the pace and challenge required. The mathematical content underlying each activity is described, as are the aspects of concrete and formal operations that pupils might work through.

The activities are rich and the teaching approach is designed to encourage pupils to exploit the richness for themselves. Whether or not you agree with the approach, this pack will provoke you to reflect on your practice as a teacher. I thoroughly recommend it.

Peter Johnston-Wilder is senior lecturer in mathematics education at De Montfort University, Bedford

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