Wow, this is great, thank you! What a wonderful break-down of pedagogies. I especially like your last paragraph; “Students are trained not to worry about being good at math. Mathematics is a huge discipline and it is impossible for anyone to know most of what there is to know. There will always be someone who knows more than you and who can work faster, and who cares anyway? We do mathematics because it is fun, beautiful, and is a means of solving interesting and important problems. We learn to appreciate the beauty of mathematical ideas and the joy of feeling our minds at work.”
At first glance, this attitude seems universal, but then I realize that it depends on the audience. A highly motivated student who puts a ton of pressure on himself or herself to be perfect at the expense of creativity and perseverance would benefit from this; a student failing to put in the work required to be more efficient at basic calculations might take this as an excuse.

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