Some mathematicians do indeed have a sort of "Well, I suffered; so must everyone else" attitude. It's a rationalization for doing nothing.
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Replying to @MathPrinceps @thegymnosophist and
I expect they no more know how to fix curricula than I know how to do their mathematics. And yes, some hazing may be involved.
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Replying to @kdhowe1 @thegymnosophist and
But you see, they don't even try to figure out what to do, and their involvement is vital. These are smart people. They really know the art.
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Replying to @MathPrinceps @kdhowe1 and
When you're trying to teach an art, it's crucial to have an intimate personal acquaintance with its practice. Violinists must teach violin.
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Replying to @MathPrinceps @thegymnosophist and
For the virtuosos that is true. For the beginners, what is needed is someone with a moderate knowledge of both math and pedagogy.
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Replying to @kdhowe1 @thegymnosophist and
Actually, beginners need someone with an exceptional knowledge of both math and pedagogy. Beginners are especially demanding to teach well.
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Replying to @MathPrinceps @kdhowe1 and
The failure of such persons to participate in the education of beginners largely explains the alienation of beginners from mathematics.
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Replying to @MathPrinceps @thegymnosophist and
I have yet to find that my struggles with PDE are limiting my ability to teach 11-year olds. 2/2
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Replying to @kdhowe1 @thegymnosophist and
I fear we are failing to communicate. I am saying that no one can teach a practice who lacks direct experience of that practice.
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Replying to @MathPrinceps @kdhowe1 and
This is a very general statement. It does not refer to you personally. I do not know what experience you may have of mathematical practice.
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And about this I frame no hypotheses (although it is hard for non-mathematicians to gain meaningful experience of mathematical practice.)
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