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Forty Problems for the Classroom
Challenge curiosity: give a taste for, and a means of, independent thinking
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For anyone who enjoys thinking about non-routine problems.
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 Forty Problems for the Classroom
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Forty Problems for the Classroom
Teachers of mathematics have a great opportunity... If they challenge the curiosity of students by setting them problems proportionate to their knowledge, and help them to solve their problems with stimulating questions, they may give them a taste for, and some means of, independent thinking.
The words of Polya are as pertinent now as they were sixty years ago.
What mathematicians do is solve mathematical problems and what pupils in schools need to do if they are to be mathematicians is to solve problems. Solving the problems in this book will help learners of all ages to develop strategies for doing this. This collection is based on problems offered by Nick Eyres, a retired school teacher in Keswick (see Foreword). Nick suggests using the problems as breaks from the current topic or on a Friday afternoon. I would want the problems to be used as an integral part of pupil learning on any day of the week!
The hints and prompts, and suggestions for further activities on pages 23 to 36 outline in general terms what pupils need to know to be able to solve each problem and sometimes indicate possible problem-solving strategies. An important aspect of solving problems is to be able to pose your own problems, and the suggestions include prompts for how pupils might ask and answer more questions around the problems with which they have been presented.
None of the problems require mathematical knowledge outside the National Curriculum for KS2, KS3 and KS4 (except that it would be possible to use calculus to solve the last problem, instead of trial and improvement). However, a high level of skill in solving problems is needed to solve some of these problems. Problems are organised so that the ones near the beginning tend to involve less mathematical knowledge.These judgements are always difficult to make, however.
The publication has been designed so that you can photocopy activities to give out to your class.
