Several teachers I’ve worked with want to set a culture in their classroom that increases not just the quantity but also the quality of mathematical talk. It made me wonder… how do I recognize good mathematical talk and how would I help students see they’re doing it right?

Good mathematical arguers:

• use definitions to justify their use of mathematical objects & processes (e.g. when deciding if something is a rectangle or not, they cite the definition)
• clarify the assumptions they’re making or the criteria they’re using (e.g. I decided to do this because…)
• are accountable not just to why they think they are right, but also why other solutions are wrong, or why their answer may not be unique
• consider multiple cases
• use simpler examples to justify themselves
• think about whether their answer is reasonable and fits the original context of the problem
• is accountable to everything they noticed in the problem
• uses units and names of quantities, not just values (numbers) to talk about their thinking (e.g. I divided the total number of apples by the number of bags, not I divided 12 by 4 and got 3).

What else?

(Thanks to Ken Templeton, @ktempleton04 for the find!)

I just watched Eleanor Duckworth’s TED talk about “When Teachers Listen and Learners Explain,” especially starting at minute 10:00.

http://www.youtube.com/watch?v=1sfgenKusQk

Please watch it and tell me what you think about this question: what would have been different if they’d used actual chocolate milk?

(and yes, answers like, “it would have been stickier” or “they would have gotten stomach aches” are important answers!)