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 deducted from former 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 introducing the chance concept illustrates this conflict. The interaction between teacher and his students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the chance concept is conceived of as a concrete generalization, which takes "chance" as a fixed and universalized pattern of explanation instead of unfolding potential and variable conceptual relations of "chance" or "randomness" and developing the theoretical mature of this concept in an appropriate way for students' comprehension.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education