Publishers want textbooks to be acceptable to the majority of buyers, without being objectionable to anyone, even people who might be wrong. Things get watered down. Authors are encouraged to make the safest choices. Change is difficult. And yet, we fight...
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Replying to @mathgrrl @stevenstrogatz
But the earliest methods of presentation were often the best. The Babylonian approach to quadratic equations is superior to the modern one. Euler's textbook on elementary algebra is vastly superior to any now in use. We have regressed.
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And make no mistake about it: regression is change. We seem quite capable of changing for the worse; why can't we change for the better? Why can't we even return to superior pedagogical practices of past times? Ptolemy's approach to trigonometry remains hard to improve on.
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Replying to @MathPrinceps @stevenstrogatz
Sounds like you should write that book! I am sure many would appreciate it. The best authors have a fire in their belly
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Replying to @mathgrrl @stevenstrogatz
A very near approach to pedagogical optimality may be made simply by cribbing shamelessly from the great past masters (who, pretty much by definition, knew exactly what they were doing.) If it were up to me, I'd probably mostly just try to update Euler's notation and language.
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I would contend that this is a good way to gather hypotheses about what would work. I would recommend combing this with a build-test-fix engineering cycle on the proposed materials at various levels of detail.
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This is a sound notion, but it is costly and hard to do. Absent any reason to believe that all the effort and expense might eventually lead to something widely and successfully used, no one bothers to make the attempt. Those who know don't speak, and those who speak don't know.
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Its worse than that. There have been efforts that have demonstrated results. See also the work of Roland Fryer. But the political process of selecting educational practices is not driven by what works. Hence the system we have.
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It's worse than that. Our teacher corps lacks the subject matter understanding prerequisite to the successful execution of even the most mathematically sound and politically popular of reforms. And making better teachers takes (much) more time and money than we have.
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And we need to pay our teachers more, on top of all that
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But even the best, and best-paid, teachers cannot succeed consistently -- or often, even -- with students who are hungry, terrified, and struggling to make sense of even the most accommodating forms of spoken English. We must recognize that no teacher is a super-being.
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okay but also pay them more :)
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