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Empirical research on probability concepts

Bentz, H. J., & Borovcnik, M. G.
University of Klagenfurt

A frame of an interplay between intuitions of individuals and abstract theories is developed. Within this frame difficulties in learning/understanding a theory may be described by a breakdown in communication between the intuitive level of individuals and the "official" language of theory (used in class). It is, however, the scope of pertaining empirical research on probability concepts to investigate such intuitive imaginations. We will show that the interpretation of results is a precarious task and cannot successfully be done without regarding this interplay between intuitions and mathematics frame. Among the major problems are: Understanding of concepts and problem solving strategies are on different levels. It is hard to get information about the concept level in probands. The spectrum of intuitions covered be the investigations so far is very narrow, a huge percentage of diagnosing items referring to the symmetry view, few being related to the frequency aspect, hardly any to subjectivist ideas. The narrowness of the view on probability leads you inextricably into puzzles and troubles and may cause a breakdown in communication between interviewer and interviewed. The results of the discussion are directly transferred to the teaching situation. Some clues for improving teaching in class may be drawn from it.