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The depressing thing about arithmetic badly taught is that it destroys a child’s intellect and, to some extent, his integrity. Before they are taught arithmetic, children will not give their assent to utter nonsense; afterwards they will. Instead of looking at things and thinking about them, they will make wild guesses in the hopes of pleasing a teacher…. The essential quality for a mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire it later.

W.W. Sawyer
Mathematician's Delight, 1943