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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. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      Ok I have to say something about learning and teaching for a sec #iteachmath. The thing is that if somebody is trying to learn how to do something, or how to take hold of an idea with their mind, we don't really know ahead of time what is going to achieve that. It might be 1/

      1 reply 3 retweets 5 likes
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    2. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      the same lesson / exercise / whatever that worked for somebody else, but it really might not. Some ways of approaching a given learning goal will work and some won't, and you can't really know ahead of time what will work, even if educator experience, research, etc. can be 2/

      2 replies 0 retweets 4 likes
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    3. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      useful guides. It is never a learner's fault that a particular approach to learning is not working for them -- it is no evidence of defect -- for all learners in all areas at all times, some approaches will work and some won't, so when you discover that an approach isn't work- 3/

      1 reply 0 retweets 2 likes
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    4. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      ing, that's *always* normal (even if *this particular* approach worked for many learners before). When an approach doesn't work, *we are learning something new* about what will work with this learner in this context. We should always be *grateful*. 4/

      1 reply 0 retweets 2 likes
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    5. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      Yesterday, a student asked me a question, and then asked me if it was a dumb question. No it's not a dumb question! Furthermore, an earnest question *is never dumb*! I am trying to help you learn something, and every earnest question is *good information for me* in exploring 5/

      1 reply 0 retweets 4 likes
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    6. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      with you how to solve the fundamentally new, open problem of how you will learn this thing you don't know yet. btw, correction, good information for *us*. We are together on the frontier of human knowledge: yes, other people already understand Y, but nobody on earth knows 5/

      1 reply 0 retweets 3 likes
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    7. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      the process by which YOU will come to understand Y. We are out here doing original research together! And your question cannot be dumb because it is *good data for our research*. How will we figure this out together if not via such data? 6/6

      1 reply 0 retweets 4 likes
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    8. Dr Ben Blum-Smith‏ @benblumsmith 3 May 2019
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      p.s. lol don't let them tell you mathematicians can count or anything. 9/8

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    9. Laurens Gunnarsen‏ @MathPrinceps 3 May 2019
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      Replying to @benblumsmith

      All this is very well, but it effectively argues for a one-on-one approach to teaching and learning, which is prohibitively expensive. The real problem is how to optimize a one-on-many approach, which will always be less flexible and sensitive (and so will fail some learners.)

      1 reply 0 retweets 0 likes
    10. Laurens Gunnarsen‏ @MathPrinceps 3 May 2019
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      Replying to @MathPrinceps @benblumsmith

      Game designers are essentially pedagogues; their job is to ensure that players enjoy gaining complex skills through prolonged participation in a demanding activity. They cannot and do not hope to succeed with every possible purchaser of their products. Nor, alas, can we.

      1 reply 0 retweets 0 likes
      Laurens Gunnarsen‏ @MathPrinceps 3 May 2019
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      Replying to @MathPrinceps @benblumsmith

      When you're aiming at a mass market, and can't meticulously redesign your product to accommodate the peculiarities of each potential customer, you must be guided by statistical data. The question isn't what works for everyone -- nothing will -- but what works best for most.

      9:13 AM - 3 May 2019
      1 reply 0 retweets 0 likes
        1. New conversation
        2. Laurens Gunnarsen‏ @MathPrinceps 3 May 2019
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          Replying to @MathPrinceps @benblumsmith

          Japanese master teachers of elementary mathematics depend upon statistical data on student responses to diverse pedagogical stimuli obtained by classroom observations undertaken by all their colleagues nationwide. These data guide a never-ending process of successive refinement.

          1 reply 0 retweets 0 likes
        3. Laurens Gunnarsen‏ @MathPrinceps 3 May 2019
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          Replying to @MathPrinceps @benblumsmith

          Similarly, teams of experimental psychologists observe in painstaking detail the moment-by-moment responses of playtesters to various preliminary versions of games. These data likewise guide a systematic process of successive refinement, which optimizes for depth of engagement.

          1 reply 0 retweets 0 likes
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