by Diane Kue
How students solve a problem—whether it is a standalone equation, expression, or a word problem—can be quite perplexing, especially when answers are unexplained. Students’ approaches and strategies vary, and their foundations of knowledge span a wide spectrum. It is probably truer than not that a mathematics teacher has come across the following scenario:
Teacher: How did you solve this problem?
Student: I don’t know. I just did it.
Whether the answer to a problem is correct or not, the pedagogical dilemma in this scenario is gaining access to student thinking so we can address misconceptions and incompleteness as necessary and validate or guide further application. But how do we get our students to use language to convey their mathematical thinking?
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