The first foci of elementary school students dealing with prognosis tasks in interviews
The nature of stochastics is not only characterized by its relationship as a model of the real phenomena described by it as well as by its usage to find hypotheses to be tested in reality, but also by its peculiar characteristic of modeling the relation between model and real phenomena. Stochastic prognoses can be one key concept for ele- mentary school stochastics to implement the fundamental idea of the specific nature of stochastics. Stochastic prognoses may be characterized as reflexive statements containing the structural components focus, evaluation and justification. Examples are given to illustrate these components. The paper outlines some a priori determined conceptional requirements for stochastic prognoses to give a first orientation of what can be expected from primary school children. It is assumed that the topics, ques- tions and problems stochastics is concerned with, are part of a culture that a child is just entering. To learn more about the ways in which primary school students under- stand and express stochastic prognoses, a series of half-structured interviews with 3rd graders (age 8-9) were videotaped and transcribed before and after a series of lessons. This contribution concentrates on the foci that children might adopt when dealing with prognosis tasks in interviews for the first time. An overview of the reconstructed types of foci is given and illustrated by examples. The stochastic foci reconstructed so far may be classified as simple foci that could be further described as sequential or aggregate foci. A case study of one child in a pre-interview shows what and how foci might be articulated when being confronted with the new semiotic means of a list.
Judith Stanja studied mathematics and history of science at the Georg- August University of Göttingen (Germany) and at Lund University (Sweden) with an emphasis on stochastics. Currently, she is working on her Phd in mathematics education at the University of Duisburg-Essen (Germany). Her research interests include early stochastic learning, con- straints for the development of stochastic knowledge, and representations.