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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Joined June 2012

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    1. Dave Richeson‏ @divbyzero Jan 23
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      Replying to @abusch38 @RobJLow @ef_math

      I believe that. Students forget all kinds of math as they progress, but "don't leave a square root in the denominator" is rock solid in all their brains—like it is "don't divide by zero." I'm exaggerating, but not too much. They get very uncomfortable when I tell them it is OK

      1 reply 0 retweets 1 like
    2. Dave Richeson‏ @divbyzero Jan 23
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      Replying to @divbyzero @abusch38 and

      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.

      1 reply 0 retweets 4 likes
    3. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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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.

      1 reply 0 retweets 3 likes
    4. Eddie Fuller‏ @ef_math Jan 23
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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.

      1 reply 0 retweets 3 likes
    5. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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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.

      1 reply 0 retweets 1 like
    6. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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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.

      1 reply 0 retweets 1 like
    7. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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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.

      1 reply 0 retweets 1 like
    8. Andrew Busch‏ @abusch38 Jan 23
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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.

      1 reply 0 retweets 0 likes
    9. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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      Replying to @abusch38 @ef_math and

      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.

      1 reply 0 retweets 1 like
    10. Laurens Gunnarsen‏ @MathPrinceps Jan 23
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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.

      2 replies 0 retweets 0 likes
      Laurens Gunnarsen‏ @MathPrinceps Jan 23
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      Replying to @MathPrinceps @abusch38 and

      Indeed, it's hard to name a subject more generally reviled than math, and I defy you to name one of which more people are proud to acknowledge their ignorance. Any pedagogical enterprise with a track record like that has proven itself a thorough-going failure.

      4:13 PM - 23 Jan 2020
      0 replies 0 retweets 0 likes

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