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Applying abstract math to concrete physics comes much more naturally than generalizing from concrete physics to abstract math.
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In the words of K. Anders Ericsson, the world’s leading expert on expertise, novices improve as long as they are, “1) given a task with a well-defined goal, 2) motivated to improve, 3) provided with feedback, and 4) provided with ample opportunities for repetition and gradual refinements of their performance.”
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You need a particular kind of practice—deliberate practice—to develop expertise. When most people practice, they focus on the things they already know how to do. Deliberate practice is different. It entails considerable, specific, and sustained efforts to do something you can’t do well—or even at all.92
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The alternative? For starters, give students numerous and diverse options. Instead of making students study yet another American poem, expose them to Japanese graphic novels. Rather than forcing kids to perform one more play, show them a few films from the 1980s. When you run out of ideas, assign a random Wikipedia article. If you want to help kids discover what emotionally “clicks” for them, trial and error beats academic tradition cold. Anyone who calls Japanese comic books and old movies “useless” should check their double standard. How are comic books and movies any more useless than poems
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