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The art of explanation

By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity—to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathe­matics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m com­plaining about the lack of mathematics in our mathematics classes. [29]

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