I think we are teaching mathematics the wrong way around. Instead of "this is how we solve a quadratic function; this is how we graph a function; coincidentally, the graph of a quadratic function is a parabola", start from the parabola; the quadratic function is its specification
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It's as if we taught music by starting with finger exercises, then teaching the manipulation of lots of complicated notation, and mentioning in passing that it could theoretically help with all that singing and instrumental playing that we are doing intuitively every day.
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Indeed, in the case of music, we begin “the teaching" by singing and tapping the lid of a closed piano. We expect content and meaning to emerge. Then we add technique in order to make own copy. The content is often lost..., but just for a while, to the luckiest people.
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