Mathematically productive discourses among student teachers

This article reports research that focuses on the characteristics of mathematically productive discourses (MPD) while student teachers are working collaboratively on a geometry problem in a problem-solving context. Analyses from the discourses of two groups of students are presented in order to illustrate mathematically non- productive and productive discourses respectively. A definition of MPD is presented and used as an analytical tool to identify critical characteristics of sequences of productive discourses. This definition involves the following five criteria: 1) Student utterances, stimulating a monitoring utterance, 2) the monitoring utterance, 3) student responses, stimulating a second monitoring utterance, 4) the second monitoring utterance, 5) further elaborations, advancing the mathematical discussion among the students. The article also discusses the difficulty of concluding when a discourse is productive or not, especially when students are challenged to work on complex problems in which a solution is not usually reached within a school lesson.