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— W. W. Sawyer"When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination. Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination."
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Text is linear; it is black and white; it doesn't zoom around the page in 3-D; it isn't intelligent by itself; in fact, in terms of immediate reaction it is quite boring. I can't imagine a single preliterate was ever wowed at the first sight of text, and yet text has been the basis of arguably the most fundamental intellectual transformation of the human species. It and its subforms, such as algebra, have made science education for all a plausible goal.
— Andrea diSessa
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Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.
— Archimedes
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