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.
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This is fantastic.
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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.
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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
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I also think in high school it is viewed as advanced math that most can’t do. Dumbing down of expectations. :(
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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.
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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.
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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.
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Algebra should be taught in elementary school, as soon as children have learned to multiply and divide. Geometry/trigonometry soon after.
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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.
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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.
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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)
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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
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The most beautiful thing in social science is represented by Y = { 1/[ σ * sqrt(2π) ] } * e-(x - μ)2/2σ2
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I never memorized that formula but you know it’s printed on the 10 DM note next to Euler’s picture
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I did not know that! I've used the formula in so many programming activities, that I've fallen in love with it.
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That’s Carl Friedrich Gauss, not Leonhard Euler.
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Yeah thanks didn’t have the bill in front of me when I jotted the first tweet. Naturally it would be Gauss
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