Abstract
The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deduced from more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on the concept of chance illustrates this conflict. The interaction between teacher and students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the concept of chance is conceived of as a concrete generalization, which takes “chance” as a fixed and universalised pattern of explanation instead of unfolding potential and variable conceptual relations of “chance” or “randomness” and developing the theoretical nature of this concept in an appropriate way for students' comprehension.
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Steinbring, H. The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge. Educ Stud Math 22, 503–522 (1991). https://doi.org/10.1007/BF00312713
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DOI: https://doi.org/10.1007/BF00312713