Are geometric concepts of vectors bookable? An analysis of the didactic transpositions in mathematics textbooks
Résumé
In Germany, the use of vectors is traditionally introduced in lower secondary education in Physics and in upper secondary education in Mathematics. In this curriculum, a geometric point of view plays an important, but somewhat unclear role whereas at the beginning of the Bachelor’s degree programmes structural-symbolic approaches dominate in courses like “analytic geometric and linear algebra”. Based on an analysis of Mathematics textbooks in upper secondary education from a point of view of geometry, differential geometry, and dynamical systems, the underlying geometric concepts are worked out as praxeologies. Some typical problems in working with vector geometry relate to the change between different conceptual models in the organisation of the textbooks.
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