Negative x Negative = Positive? Abstract Proofs

Last time we looked at explanations for the product of negative numbers in terms of various concrete models or examples. But it really requires a mathematical proof, as we’ll explain and demonstrate here, first with a couple different proofs, then with the bigger picture, giving the context of such proofs.

When Parameters Become Variables

(An archive question of the week) I’m looking for past questions that led to deep discussions. This week, we have a case where a student realized he was doing algebra by rote, not thinking about what variables really mean. This realization was triggered by a step that many students stumble over, where parameters change their …

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