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Real mathematics: One aspect of the future of A-level

Published online by Cambridge University Press:  01 August 2016

John Monaghan
John Monaghan*
Affiliation:
18 Portland Street, Lancaster LA1 ISZ
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Extract

The “real” in the title refers to real numbers rather than real life. I expect, and hope, that many articles on the future of A-level will expound the cognitive and mathematical necessity of making A-level more practical. While I applaud and try to practise this, classroom teaching and research have convinced me that the notion of the real number line has subtle conflicts that will not go away by simply not mentioning them; they need to be addressed. Moreover teacher-led explorations of the real number line are essential if we are to lead students to an understanding of higher mathematics.

Type
Research Article
Information
The Mathematical Gazette , Volume 72 , Issue 462 , December 1988 , pp. 276 - 281
Copyright
Copyright © The Mathematical Association 1988

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References

1. DES, Mathematics in the sixth form, HMSO (1982).Google Scholar
2. Monaghan, J., Adolescents’ understanding of limits and infinity, unpublished PhD thesis, University of Warwick (1986).Google Scholar
3. Tall, D. and Schwarzenberger, R., Conflicts in the learning of real numbers and limits, Mathematics Teaching 82 (1978).Google Scholar
4. Orton, A., When should we teach calculus?, Mathematics in School 14 (1985).Google Scholar