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Linear Algebra: a Privileged Context to Develop Abstract Notions Using Spatial Intuition

Mario Lavoie, Jean Brousseau, Jean-François Goulet

Université du Québec à Rimouski

Situation

Educational books dealing with analytic geometry, such as Swokowski 1, present the geometry of 2D and 3D spaces and introduce vectors and their methods. However, a lot of methods developed for 2D and 3D spaces use the cross-product that does not generalize to space dimensions greater than three. On the other hand, educational books presenting linear algebra for engineers, such as Kreyszig 2, introduce notions in a more or less abstract manner without attempting to make the link with analytic geometry. In those books, no examples are given and no problems are presented concerning spaces of four, five, or six dimensions, for example, even though concrete problems within the engineering field require such expertise (cf. 3 Brousseau, Lavoie and Goulet). A good opportunity is lost to develop abstract concepts using spatial intuition.

Proposed abstract learning situations

The learning situations listed below, which are not exhaustive, could enable students to use spatial representations to learn abstract notions of linear algebra. The main notions of linear algebra that will be investigate are linear independence, basis, linear systems of

Proceedings of the 2002American Society for Engineering Education Annual Conference & Exposition Copyright Ó 2002, American Society for Engineering Education

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Lavoie, M., & Brousseau, J. (2002, June), Linear Algebra: A Privileged Context To Develop Abstract Notions Using Spatial Intuition Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--11325