ICME 8 - Topic Group 19

Presentation Summary

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This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8), July 14-21, 1996 in Seville, Spain..

How does a Computer Algebra System actually work to Teach and Learn Mathematics?

It has been conjectured that the use of a CAS to teach and learn secondary mathematics could give pupils a wider access to an experimental practice of mathematics and a deeper understanding of concepts in algebra and calculus. A French project including 25 teachers and 460 pupils has been achieved to study those new possibilities. Using questionnaires as well as classroom observations, we examined how those possibilities worked. We found actual benefits of the CAS, but also unexpected phenomena produced by the computational transformation of mathematical concepts when instanced inside a CAS.

First, we observed that pupils' understanding of the results obtained in a CAS were often different from the expectations of the teachers. The reason was that the teachers understood those results using their mathematical knowledge when the pupils' interpretation was closer to the explicit display. As another example, the means that a CAS brings to express functions differ subtly from the usual mathematical way. For instance, defining a piece wise continuous functions inside a CAS appeared to be a real problem to pupils. Our conclusion is that one cannot just think of a CAS as an easier equivalent to paper and pencil. On the contrary, much can be expected from the computational insight that a CAS may bring on mathematical concepts.

Jean-Baptiste Lagrange, lagrange@univ-rennes1.fr

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8 March 1996