"Are you noticing any patterns here?" What would a gesture-based 'language' of mathematics look like? I still don't know, but this paper is an interesting exploration of the relation between gestures and learning math. "Teachers can select tasks that will elicit gesturing, notice how the gesturing signals the thinking, and respond to the dynamic nature of a process conveyed by the gestures to stay with students' own ideas as they guide their mathematical understandings. To stay with student ideas, means we can use students' own ways of thinking to support their learning rather than trying to channel their thinking into some predefined process."
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