Mathematical Discourse

"Techniques for Small Group Discourse" from Teaching Children Mathematics

The subject of this article is using mathematical discourse in classrooms, including discourse between teachers and students and between students and other students. Two case studies highlighted two different teachers' responses to their students, who had just worked on problem solving in small groups. Some of the teachers' comments were helpful, in that they facilitated mathematical discourse, critical thinking and responsibility for learning; others of their comments hindered these qualities. The helpful responses from the teachers included requiring explanations from the students to help them reason through the math processes on their own instead of relying on the teacher. They also listened to the students' justifications, but did not evaluate them. Instead, one of the teachers in particular, turned to another group and encouraged their input. This promoted more mathematical discourse, while helping the students to take ideas from each other to note their own errors. One unhealthy response given by one of the teachers was that she did not allow her student to struggle and struggle with her own thought process. Instead, she jumped in and redirected her thinking so that she then figured out the answer using the teacher's preferred method. Not only did this hinder deep understanding contrived from the student's own reasoning, it halted mathematical discourse that could have stretched the student's understanding.

I definitely agree with the purpose of the article - that mathematical discourse improves student understanding and that teachers should be facilitators. It is my hope that I will allow time for my future students to engage in conversation and exchange ideas when working through math problems. Teaching math in this manner may not unveil immediate leaps in testing, but in the long run, I am sure that student understanding and achievement will increase.