Focus on What Students Know, Not Just on Correct Answers
Students’ need to understand mathematics in order to apply it effectively is clearly demonstrated in a study by Carraher, Carraher, and Schliemann (1985, cited by Sutton & Krueger, 2002), in which context-embedded problems were much more easily solved (98 percent correct) than ones with partial context (74 percent correct) or especially than ones with mathematical operations without context (37 percent).
Students must have opportunities to make transparent, to themselves and others, what they already know and understand so that this prior knowledge can be a foundation for new learning. Furthermore, teachers who use knowledge of common student errors and misconceptions can build opportunities to reveal thinking and help students change their conceptions (Donovan & Bransford, 2005). Formative assessments allow teachers to gather information about student thinking.
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