Epistemic issues in classroom mathematical activity: There is more to students' conversations than meets the teacher's ear

We report on a comparative investigation of student mathematical activity in two settings of a secondary mathematics classroom: peer interaction in small group and group interaction with the teacher. Our framework draws on the understanding of school mathematics as activity in between the historicity of knowledge and the situatedness of norms. We propose the term epistemic issue to refer to instances of knowledge about the construction and justification of school mathematics knowledge whose use is traceable in student activity. A major finding points to the presence of a number of epistemic issues during peer work and their omission in the communication of this work to the teacher; a phenomenon we call epistemic shift. To illustrate this finding and the methods of analysis, we take data from a group of students during a lesson of probability and the lesson-based video stimulated recall interview. We finish by discussing some implications for the development of the mathematical culture of the classroom.