In my last “smart and thoughtful post” (the parlance that edu-pundits use when they refer to each other’s writings), I talked about “understanding vs procedure”. The quote at the end from a teacher in New Zealand seemed to ruffle the feathers of some who took to Twitter to state that they believed otherwise.
In all these discussions of “understanding”, those who believe it is not taught and that students are doing math without knowing math rarely if ever explain what they mean by understanding in terms of how it translates or transfers to problem variations or new areas in math. For example, a student who has learned the invert and multiply rule for fractional division may not be able to explain why the rule works, but may have an understanding of what fractional division represents. The student then uses the latter to solve problems requiring fractional division.
Anna Stokke, a…
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