ABSTRACT
A key issue in modern mathematics teaching at all levels of schooling is captured by Lacampagne’s (1993) assertion that “Mathematical discussion should be a daily part of classroom activity!” (p. 7). However, this demand produces a number of basic questions that raise very fundamental considerations for Didaktik der Mathematik, the Didaktik of mathematics, with its focus on hermeneutic approaches, epistemological embedding, and structuralist thinking. There are questions about:
The content of the discourse: What is possible when we try to reflect on mathematics in the classroom? What are the most appropriate ways of speaking about mathematics? Do we have a broad range of possibilities for such reflection and discourse?
The personal interests and capabilities of the students: What are they able to do? What are they able to capture? What can be transformed into simpler questions without losing its authenticity—and how can this problem be dealt with (see Kirsch, chap. 15, this volume)?
The overall structure of the lessons: What setting is appropriate for such discourse? Are there methods to facilitate it? What is the role of the teacher in such discourse?
