## Forms of Mathematical Interaction in Different Social Settings: Examples from Students’, Teachers’ and Teacher–Students’ Communication about Mathematics

Source: *Journal of Mathematics Teacher Education, Volume 12, Number 2* / April 2009, pages 111-132.

This study investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional discourse while observing and analyzing young students mathematical interaction followed by teacher’s intervention. The teachers’ joint professional discourse is about a combined learning and talking between two students before an intervention by their teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting 2). The joint professional teachers’ discourse constitutes setting 3.

This combination of social settings 1 and 2 is taken as an opportunity for mathematics teachers’ professionalization process when interpreting the students’ mathematical interactions in a more and more professional and sensible way.

The epistemological analysis of mathematical sign-systems in communication and interaction in these three settings gives evidence of different types of mathematical talk. These types are explained depending on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher and by the expectations of the students.