Students Talking...And Listening?
Discourse about mathematics in a classroom sounds great. But, how can teachers promote it? And, how can it be effective?
In their metareview, researchers Margaret Walshaw and Glenda Anthony provide some suggestions:
 Make participation rights and obligations clear
 Support student thinking
 Finetune thinking, emphasize correct math terminology
 Shape student's mathematical argumentation
Their other suggestions include teachers modeling highlevel discourse themselves, making of conceptual connections, encouraging student selfmonitoring, and emphasizing constantly the value of "explanation, meaning, and understanding."
Though perhaps valuable by intent, I find the generality of these suggestions underwhelming...and regret they often are couched in highend jargon. Consider their claim that effective teachers "are able to bridge the students' intuitive understandings with the mathematical understandings sanctioned by the world at large." What does this mean....?
The NCTM Standards of 1989 established "communication" as an important process, with discourse being part of this process. In my experience, the key element is building student confidence in their use of mathematical language, which includes listening as well. Maybe that is part of the author's review, but I missed it...
Source: M. Walshaw & G. Athony's "The Teacher's Role in Classroom Discourse," Review of Educational Research, Sept. 2008.
