Baumdiagramme in der Wahrscheinlichkeitsrechnung: Auslöser unterschiedlicher mentaler Repräsentationen, aufgedeckt durch metakognitive Aktivitäten

Abstract

Tree-diagrams play an important role in stochastic lessons. Starting from observations of lessons, we will analyse their effect on mathematical thinking and learning processes when calculating conditioned probabilities from the point of view of cognition theoretical, contents orientated didactics. Our interest lies in the individual differences in the shaping of ideas. We explain them by individual preferences for cognitive structures. They have an effect on the selection of metaphors with which the ideas are described. A conversation during the lesson about the different interactions of individual descriptions and ideas released by the use of tree-diagrams is metacognitive by nature. In this respect the analysis of metacognitive activities forms a key to the understanding of thinking processes. © 2005 GDM - Gesellschaft für Didaktik der Mathematik.