Does getting the answer mean understanding the concept?
Concept questions in physics and geometric intuition in linear algebra reveal gaps that procedural success can hide. Neither approach rules out calculation practice.
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What does explaining an answer to a peer reveal? →Collaborative learning gains a concrete mechanism when students have to explain their reasoning to one another. Agreement on an answer alone tells the teacher less.Why do experts miss the step a beginner needs? →Familiarity can hide prerequisites. Compare the techniques each speaker uses to expose the gap between what a presenter assumes and what a learner can reconstruct.Can you reconstruct the area formula? →A formula is easier to transfer when a learner can rebuild the reasoning that produced it. Compare a memorized answer with a representation that makes the derivation visible.
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good problem solving does not necessarily mean understandingwe almost always get computers to handle that half,