Abstract
A method for analyzing everyday mathematics teaching is presented which permits to take into account the different levels of mathematical meaning within teacher-students interactions. By means of graphical diagrams conceptual structures of the development of mathematical meaning in the classroom are visualized. These new diagrams permit to display the chronological course of teaching and at the same time global patterns. The actual epistemologica! analysis of lessons about elementary probability (in grades 5, 6 and 7) reveals the following central result. There are mainly two basic types of interactive development of mathematical knowledge: 1) Some lessons display graphical patterns indicating teacher-student work simultaneously and parallel on different levels of meaning. This characterizes an open, systemic and anticipating type of teaching process. 2) Other lessons result in graphical diagrams indicating a strictly linear succession caused by working only separately on different levels of meaning in isolated teaching phases. This charaterizes a linear, consecutive and deductive type of teaching process.
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