"...US students strongly prefer the procedurally oriented lessons to
those that emphasize conceptual understanding. In fact, almost all of
them see weakness in a Japanese lesson because the teacher fails to
"explain" the mathematics in the lesson. Apparently, they identify
explaining mathematics with prescribing methods of solution - which was
not done in the Japanese lesson. When the Japanese students were being
helped to understand why the mathematical conclusions were correct, the
students didn't recognize this very different meaning of "explain."
"...students should appreciate that the essence of mathematics depends
on proofs to justify conclusions, and they need to reconginze when, for
whatever reason, their knowledge is incomplete."
How very far from hither to thither.
Geoff Hagopian
Palm Desert, CA
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