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Nutting your way through a Standard Quadratics Exercise: Example 1 (Tanton)

Of course every educator would choose thinking for their students over memorization, but the pressures of the rigid curriculum make this hard to accomplish for teacher and student alike. Here's a very concrete example of how to approach a classic unimaginative textbook question from algebra II in a way that really promotes personal reliance on common sense, on "nutting your way" through things, being confident to flail and nonetheless find success. The content is not at all relevant to real life (let's admit it a la Dr. Hacker) and one should question why this content is labored so in the curriculum. But if we teach intentionality in thinking skills and problem solving, then the curriculum, I believe, would be a truly meaningful experience for all. One solves problems in real life by taking time, flailing, and nutting your way through. That's the real story of math too!
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