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Paradigms of proof

Published online by Cambridge University Press:  01 August 2016

Johnston Anderson
Affiliation:
Department of Mathematics, University of NottinghamNG7 2RD
Keith Austin
Affiliation:
School of Mathematics and Statistics, University of Sheffield S3 7RH

Extract

First year mathematics undergraduates entering British universities are often very unprepared for the kind of proof activities that occur throughout undergraduate degree programmes. Their previous experiences of the idea of proof are frequently limited to situations where the ‘proof’ is simply an extended chain of calculations or algebraic manipulations. In fact, this is well-illustrated by their approach to proof by induction, where they can carry out the mechanical details of the inductive step, but have no understanding of why proof by induction works, nor what status the initialisation step and the inductive hypothesis have in the proof. There is no real grasp of what it means to prove that some assertion is true. Much time, in consequence, is spent in the first years of mathematics degree courses up and down the country attempting to bring about this understanding.

Type
Articles
Copyright
Copyright © The Mathematical Association 1995

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References

1. Anderson, J. A. Seeing induction at work, Math. Gaz. 75 (December 1991) pp. 406414.Google Scholar