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..

Necessity to build a theoretical framework for designing a CBILE : the APLUSIX system example for the factorisation of polynomial expressions

We have realised a CBILE called APLUSIX for training students to factor polynomial expressions. This system has been experimented since 1990. The students' interactions have been recorded and analysed for modelling the students off-line to see how they learn the domain. Our purpose is to present the work realised for building the framework used to develop the system. This work is called 'didactic transposition + computational transposition' by didacticians (e.g., N. Balacheff) and 'modelling' by AI people. In the case of the factorisation task, it has been achieved by building a theoretical framework with an important formal component. This framework borrows elements to psychology, didactique, computer science and artificial intelligence. Some of these elements have cognitive features and lack computational features. Conversely, others have computational features and lack cognitive features.

The interaction mode of the APLUSIX system differs from the usual paper-pencil mode for factoring polynomial expressions: at each step, the student chooses an operator to apply to a sub-expression and the system makes the calculations. This mode aims at focusing on the learning of matching and strategic knowledge. It allows to give exercises with strategic difficulties to the student, and requires to have a theory concerning the strategy to solve theses exercises. We have developed such a theory in the framework we have built.

Jean-Francois Nicaud, Jean-Francois.Nicaud@irin.univ-nantes.fr

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8 March 1996