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The pigeonhole principle: “Three into two won’t go”

Published online by Cambridge University Press:  22 September 2016

Richard Walker
Richard Walker*
Affiliation:
Chells School, Stevenage, Herts
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Extract

When I began teaching secondary mathematics after several years in industry, I hadn’t been trained as a teacher. Having been away from school mathematics for so long, I was sometimes nonplussed by pupils’ questions.

One day I was showing a mixed-ability first-year class how to obtain the decimal expansion of a vulgar fraction. After explaining the how and, I hoped, the why of the method I did several examples on the blackboard and concluded by telling them that the expansion would either terminate or recur (or words to that effect). At once a small boy demanded to be told how I knew this. This floored me: I hadn’t got a ready answer and I had to promise to think about it.

Type
Research Article
Information
The Mathematical Gazette , Volume 61 , Issue 415 , March 1977 , pp. 25 - 31
Copyright
Copyright © Mathematical Association 1977

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References

1. Percus, J. K., Combinatorial methods. Springer-Verlag (1971).CrossRefGoogle Scholar
2. Stein, S. K., Mathematics the man-made universe. Freeman (1963).Google Scholar