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Mathematical operators and ways of reasoning

Published online by Cambridge University Press:  01 August 2016

David Ginat
David Ginat*
Affiliation:
Science Education Department, Sharet Building, Tel-Aviv University, Tel-Aviv 69978, Israel email: [email protected]
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Extract

Given a mathematical operator, how should one reason about the outcome of its repeated invocation? This question is relevant in both mathematics and computer science, where iterative operator invocations are core, algorithmic elements.

An initial approach, which one may naturally follow, is to try the operator in diverse situations, observe the results, and suggest a general outcome. Such an approach embodies operational reasoning, where inference derives from ‘behaviours’ of invocation sequences. This may indeed reveal some behavioural characteristics, but is it sufficient for rigorous argumentation of the general outcome? Not quite.

Type
Articles
Information
The Mathematical Gazette , Volume 89 , Issue 514 , March 2005 , pp. 7 - 14
Copyright
Copyright © The Mathematical Association 2005

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References

1. Dijkstra, E.W. et al, A debate on teaching computing science, Communications of the ACM, 32 (1989) pp. 1397–1414.Google Scholar
2. Dijkstra, E.W., A discipline of programming, Prentice-Hall (1976).Google Scholar
3. Floyd, R., Assigning meaning to programs, Mathematical Aspects of Computer Science, 19 (American Mathematical Society) 1967 pp. 1932.Google Scholar
4. Gries, D., The science of programming, Springer-Verlag (1981).CrossRefGoogle Scholar
5. Polya, G., How to solve it (2nd edn), Princeton University Press (1957).Google Scholar
6. Hersh, R., Proving is convincing and explaining, Educational Studies in Mathematics, 24 (1993) pp. 389–399.CrossRefGoogle Scholar
7. Schoenfeld, A.H., Learning to think mathematically: problem solving, metacognition, and sense making in mathematics, in Grouws, D.A. (ed.), Handbook of research on mathematics teaching and learning, Macmillan (1992) pp. 334–370.Google Scholar