to leave an expression as 1/sqrt(2), and most of them ignore my invitation. That tells me that it is firmly implanted in the high school curriculum. Speaking only for myself, I think that should change.
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Replying to @divbyzero @abusch38 and
Any system of mathematics education that inculcates a widespread and stubborn disposition to mistake a pure convention for a fundamental law is fatally flawed. We might dismiss as accidental this single instance of perversity, were there not so many others, equally flagrant.
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Replying to @MathPrinceps @divbyzero and
Exactly. PEMDAS. Always put the function in standard form. It takes time to unspool these beliefs and get to the actual mathematics. It seems to be a part of the strength of active learning/IBL. Students get back some of the power that they lose to (unneeded?) simplifications.
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Replying to @ef_math @divbyzero and
Alas, the essence of the problem is that the teacher corps, lacking real mathematical understanding, often cannot distinguish between conventions and axioms. Which is in turn a consequence of the irresponsible, self-serving indifference of mathematicians, who merely shrug at it.
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Replying to @MathPrinceps @ef_math and
Mathematical teaching ought to have at least a passing resemblance to mathematical practice, with which only mathematicians are sufficiently acquainted to convey. But mathematicians (vastly) prefer to do mathematics, and to view pedagogy as a fraught and futile backwater.
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Replying to @MathPrinceps @ef_math and
Most mathematicians are indifferent even to the mathematical misery of their own children in school, or, if not actually indifferent, insufficiently motivated to try to do anything material about it. A little discreet hand-wringing is usually enough to assuage their consciences.
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Replying to @MathPrinceps @ef_math and
I think it has more to do with curriculum than secondary teachers not knowing. Their stuff. If the textbook manufacturers put everything in simplest form, the teacher is not going to fight that fight.
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It's everything, really. The dysfunction is comprehensive. Writing textbooks means accepting constraints intolerable to great mathematicians, so only mediocrities get involved. Teaching teachers is hard, so most math teachers are poorly prepared. Teaching is hard. And so on.
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Replying to @MathPrinceps @abusch38 and
Really a challenge to name any part of the "system" that consistently works well, for anyone. It's a train wreck, and has been for decades. Most people have just given up, and kids in the classroom can tell. Everybody's taken lots of math classes. Nobody remembers any of it.
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Replying to @MathPrinceps @ef_math and
There’s a group of math teachers on Twitter
#mtbos. Basically, we’re trying to ‘suck less’ together.1 reply 1 retweet 1 like
Yes, I've noticed. And of course I'm rooting for you. But the task before you is not unlike that of chopping down the Amazonian rain forest with a machete. Another metaphor I often use: trying to reform mathematics education is like trying to reform the Soviet economy.
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