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.

Computer-based constructive introduction to group theory

A constructive introduction to the elementary group theory using a computer "Permutation group" program is proposed. The psychological background of this approach is the conviction that understanding of abstract algebra cannot be achieved by students on the basis of pure logical reasoning. It is necessary to enrich and to develop students individual mental experience of work with groups and it must be a diverse and multiform experience. With the help of the above mentioned computer program students (age 15-16) develop their group theory intuition and come to different notions and theorems of group theory such as generators system and defining relations, orders of subgroups and elements, the Lagrange theorem and others more effectively through accumulating facts and hypothesizing. Only upon accumulating some experience of work with the help of computer program the students are set the task of giving a proof or a counterexample for different hypotheses by means of logical reasoning. At last the concluding stage of students understanding forming (age 16-17) is independent programming for solving different problems which appear during the work with permutation group. I am convinced that working out an effective computer program for work with a permutation group is a good test for the level of understanding of elementary group theory. Commentary: In conclusion I would like to mention that the visual aspect of individual mental group theory experience of students needs a special computer support and my work is going in this direction on but it is not completed yet.

Sam Rososhek, gelfman@mpi.tomsk.su

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