What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students’ Mathematical Work in Classrooms.

This paper describes a tool we developed for analyzing small-group discussions in mathematics classrooms. We applied this tool to videotaped sessions of thirty groups of four students, each working together on an open-ended problem. Our analysis shows that small group discussions offer teachers and researchers important knowledge about student thinking and understanding. These insights are often invisible in the written work of the students. We also found that such student discussions frequently emulate discussions among professional mathematicians, thus creating authentic engagement experiences for the students. These findings may help bring traditionally disparate groups of thinkers together. Namely, teachers and researchers are presented with a common set of features to look for in mathematical discussions, and mathematical researchers and mathematicians are presented with striking parallels between student discussions and professional mathematical work. [ABSTRACT FROM AUTHOR]