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While it is possible to teach arithmetic in a purely mechanical manner, it is certainly not desirable to do so. Even for the simplest operations, it is easier to remember what has to be done if one knows the reason. For anyone who wants to go on to the other branches of mathematics, mechanical learning is fatal…It is a pity that there are schools…where arithmetic is still taught on the lines of “You do this, then you do that” –as though the subject were some form of religious ritual.

W.W. Sawyer
Mathematician's Delight, 1943