Elementary Stochastic Seeing in Primary Mathematics Classrooms—Epistemological Foundation and Empirical Evaluation of a Theoretical Construct

Abstract

This contribution presents a first conception and empirical testing of the theoretical construct elementary stochastic seeing (else). This notion serves to focus on a basic idea of the evolving stochastic thinking and it could be an orientation for the learning of stochastics at the primary school level. In consideration of the specific nature of stochastic knowledge, as well as from a semiotic and an epistemological perspective, some fundamental characteristics of the construct “else” are elaborated. The interplay between (recorded) empirical observations of outcomes of random experiments and (relational) symbolic interpretations of artefacts in elementary stochastics—as for instance diagrams and lists—is of great importance. The diagrams and lists should serve as instruments for the learning child and are an integral part of an intervention that should stimulate the transformation of initial perspectives on and interpretations of these artefacts and so offering him/her, in this way, an approach to grasp the particularity of stochastic prognoses. As a starting point, we take the transformation of artefacts to mathematical signs into consideration. Episodes of a clinical interview videotaped in a pilot study are qualitatively analysed in order to describe how young students (grade 3) may use and interpret these artefacts and what kind of connections they are able to construct between their interpretations.