*Lewis & Tsuchida (1998) quoted a Japanese teacher as saying, “A lesson is like a swiftly flowing river; when you’re teaching you must make judgments instantly” (p. 15). Recognizing shared student thinking as a teachable moment is one of the instantaneous judgments that are made during lessons. Recognizing the pedagogical and mathematical value in students’ thinking in the moment is a difficult step in the process of using students’ thinking, even for experienced teachers (Chamberlin, 2005).*

The teacher was teaching mathematics in a class.

“in order to subtract, things have to be in the same denomination. for instance, we couldn’t take two apple from three oranges, or five dogs from 6 cats. do you understand?”

the class seem to understood until one little boy asked, “But teacher,” he said, “how come we can take four quarts if milk from three cows?”

Learning how to orchestrate an effective classroom discussion is quite complex and requires attention to various elements. The goal of which is to keep the cognitive demand high which students are learning and formalizing mathematical concepts, not for them to tell their answers and get a validation from the teacher

As students describe and evaluate solutions to tasks, share approaches, and make conjectures, learning occurs in ways that are otherwise unlikely to take place. Similarly, students come to see the varied approaches in how mathematics can be solved and see mathematics as something they can do.

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The value of student talk cannot be overemphasized.

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