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sapinker's profile
Steven Pinker
Steven Pinker
Steven Pinker
Verified account
@sapinker

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Steven PinkerVerified account

@sapinker

Cognitive scientist at Harvard.

Boston, MA
pinker.wjh.harvard.edu
Joined January 2010

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    Steven Pinker‏Verified account @sapinker Jul 30

    Why is calculus so fearsome? It's not the concepts (differentiation is just rate; integration = accumulation). It's that for many, building blocks from algebra, trig aren't 2nd-nature. Basic cog psych: Complex learning requires chunking, automatization.https://news.harvard.edu/gazette/story/2018/07/masters-of-calculus-come-prepared-harvard-study-shows/ …

    7:46 AM - 30 Jul 2018
    • 214 Retweets
    • 684 Likes
    • ɴᴀᴀᴛɪꜱᴋᴀ andrew t. lane 🦉☕️ Dev Banerjee Michael Demür Cody Ms. Behaving Brain Saloni 🎃 Lilith Felix
    41 replies 214 retweets 684 likes
      1. New conversation
      2. Michael Talley‏ @Mike_Talley5 Jul 30
        Replying to @sapinker

        There is also another level conceptually that students must go to in order to learn calculus. It is the first time you really have to confront infinity in a meaningful way. For the first few thousand years of mathematics, the greatest minds couldn’t make sense of it.

        1 reply 1 retweet 16 likes
      3. Dr. Tien Chih‏ @TChihMath Jul 31
        Replying to @Mike_Talley5 @sapinker

        https://www.smbc-comics.com/comic/how-math-works …

        2 replies 3 retweets 19 likes
      4. Michael Talley‏ @Mike_Talley5 Jul 31
        Replying to @TChihMath @sapinker

        This is fantastic.

        0 replies 0 retweets 2 likes
      5. End of conversation
      1. bslatner‏ @bslatner Jul 30
        Replying to @sapinker

        Having failed or dropped Calc 1 three times, I can tell you that derivatives and integration were NEVER taught to me in those terms. Only the mechanics of the operations were taught, never the why. Trig, by contrast, with its obvious practical applications, was super easy for me.

        0 replies 2 retweets 17 likes
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      1. LaurieEndicottThomas‏ @LaurieEThomas Jul 31
        Replying to @sapinker

        In my book Not Trivial, I explain that Jaime Escalante's AP Calculus program (Stand and Deliver) succeeded because he started by enriching the junior high school math program.http://nottrivialbook.com 

        0 replies 2 retweets 6 likes
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      1. Jim Kennedy‏ @scuba_jim Jul 31
        Replying to @sapinker

        I also think in high school it is viewed as advanced math that most can’t do. Dumbing down of expectations. :(

        0 replies 1 retweet 5 likes
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      1. Renaissance Man‏ @Renaissanc3Mann Jul 30
        Replying to @sapinker

        It's because textbook authors are pretentious douchebags who write books to impress their Rockefeller Foundation masters. Skipping 5 steps and assuming the student realizes a Taylor Expansion was employed is not the best way to introduce integration.

        0 replies 1 retweet 3 likes
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      1. Justin Painful Death 🗡 🗡‏ @crashfrog Jul 30
        Replying to @sapinker

        When I took calculus - and I took it a bunch of times - we spent a lot of time algebraically integrating functions without really talking about how we built a world based on computers entirely because so few real-world equations have solvable integrals.

        0 replies 0 retweets 5 likes
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      1. New conversation
      2. Peter Laudenslager‏ @peterl Jul 30
        Replying to @sapinker

        I found calculus concepts very easy to understand. Memorizing and recognizing all the trig identities was brutal and limited my performance later in the class.

        1 reply 0 retweets 7 likes
      3. 1 more reply
      1. Nullus Maximus‏ @NullusMaximus Aug 1
        Replying to @sapinker

        Algebra should be taught in elementary school, as soon as children have learned to multiply and divide. Geometry/trigonometry soon after.

        0 replies 1 retweet 1 like
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      1. Andrew J Cleary‏ @AndyCleary Jul 30
        Replying to @sapinker

        If it were *taught* as concepts like rate and accumulation, I don't think it would be so hard. Instead, in my experience, it is taught purely through symbols and formulas... Too abstract.

        0 replies 0 retweets 4 likes
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      1. Charmantides‏ @Charmantides Jul 30
        Replying to @sapinker

        Its the abstraction and the nomenclature. As said by Pratchett, Stewart and Cohen our brains do calculus almost automatically, and faster than machine if trained. Like catching a cricket ball.

        0 replies 1 retweet 1 like
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      1. New conversation
      2. Sean Maley‏ @ProfMaley Jul 30
        Replying to @sapinker

        Teaching calc for 8 years, this is exactly what I tell students on day 1. (In order to encourage review, not to scare them off)

        1 reply 0 retweets 1 like
      3. Renaissance Man‏ @Renaissanc3Mann Jul 30
        Replying to @ProfMaley @sapinker

        Please god when introducing a new topic, explain in the easiest way imaginable--the shitty classes I took would have oopsilons and missing lines of Taylor Expansions. In the engineering industry, you will literally never play algebra games. Visual graphical concepts are paramount

        0 replies 0 retweets 2 likes
      4. End of conversation
      1. New conversation
      2. Dr. Dan Cady‏ @DanCady Jul 30
        Replying to @sapinker

        The most beautiful thing in social science is represented by Y = { 1/[ σ * sqrt(2π) ] } * e-(x - μ)2/2σ2

        1 reply 0 retweets 0 likes
      3. Mark Virag‏ @MarkVirag Jul 31
        Replying to @DanCady @sapinker

        I never memorized that formula but you know it’s printed on the 10 DM note next to Euler’s picture

        3 replies 0 retweets 2 likes
      4. Dr. Dan Cady‏ @DanCady Jul 31
        Replying to @MarkVirag @sapinker

        I did not know that! I've used the formula in so many programming activities, that I've fallen in love with it.

        1 reply 0 retweets 0 likes
      5. Mark Virag‏ @MarkVirag Jul 31
        Replying to @DanCady @sapinker

        How to cheat on your stats final (in Germany)pic.twitter.com/6KVIIYskYe

        2 replies 0 retweets 3 likes
      6. P-Brane‏ @BraneRunner Jul 31
        Replying to @MarkVirag @DanCady @sapinker

        That’s Carl Friedrich Gauss, not Leonhard Euler.

        2 replies 0 retweets 0 likes
      7. Mark Virag‏ @MarkVirag Jul 31
        Replying to @BraneRunner @DanCady @sapinker

        Yeah thanks didn’t have the bill in front of me when I jotted the first tweet. Naturally it would be Gauss

        1 reply 0 retweets 1 like
      8. 1 more reply

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