Do You Want Me to Do It with Probability or with My Normal Thinking? Horizontal and Vertical Views on the Formation of Stochastic Conceptions

Abstract

Probability classrooms often fail to develop sustainable conceptions of probability as strategic tools that can be activated for decisions in everyday random situations. The article starts from the assumption that one important reason might be the often empirically reconstructed divergence between individual conceptions of probabilistic phenomena and the normative conceptions taught in probability classrooms, especially concerning pattern in random. Since the process of dealing with these phenomena cannot sufficiently be explained by existing frameworks alone, an alternative-horizontal-view on conceptual change is proposed. Its use for research and development within the so-called Educational Reconstruction Program is presented. The empirical part of the paper is based on a qualitative study with 10 game interviews. Central results concern the oszillation between conceptions and cognitive layers and the situatedness of their activation. In particular, diverging perspectives seem to root in contrasting foci of attention, namely the mathematically suitable long-term perspective being in concurrence to the more natural short-term attention to single outcomes. The Educational Reconstruction Program offers an interesting possibility to specify roots of obstacles and to develop guidelines for designing learning environments which respect the horizontal view.