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Member's Forum Did you have a teacher that sparked epiphanies?
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  • epiphany
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Did you have a teacher that sparked epiphanies?

dougw
dougw over 1 year ago

Did you ever have a teacher who presented material in a way that led to you have an epiphany, where the concept just clicked?

  • Like realizing that the derivative of a waveform at a point is simply the slope of the waveform at that point
  • Or understanding that the integral of the waveform is simply the area under the curve
  • Or how negative feedback makes an amplifier predictable
  • Or how a dielectric affects capacitance

What concepts do we now take for granted that when you first came across them, they were magic?

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Top Replies

  • maxpowerr
    maxpowerr over 1 year ago +2
  • electronicbiker
    electronicbiker over 1 year ago +1
    Yes - his name was Mr Woolard, he taught maths and rugby football while I was in the sixth form studying 'A' levels. Up until then I'd been pretty dumb at maths. With his teaching lots of things suddenly…
  • dougw
    dougw over 1 year ago +1
    One surprisingly useful concept that clicked after just being mentioned in an off-hand way was dimensional analysis, where one could solve problems or at least do a sanity check on answers just by figuring…
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  • battlecoder
    battlecoder over 1 year ago

    I will answer assuming that "presented material in a way that led to an epiphany" doesn't necessarily mean that the content was presented in a clear way that immediately clicked, but rather in a way that made me think and engage with the content deeply, eventually leading to an Eureka moment. And I'll do this because the only epiphanies I remember came from teachers who presented the concept in such an abstract or weirdly specific way, that the concept wasn't quite clear, until it suddenly was, several many classes later.


    One of such examples is a Pre-Calculus teacher that I had. He would focus almost entirely on the physical interpretation of each concept (Physics was his main class). He naturally presented the derivative as a "rate of change" ("rate of change" of position equals speed, "rate of change" of speed equals acceleration, etc). However, once he went over the "mathematical" definition (with very little focus on it) I suddenly realized that the derivative was the slope of a straight line drawn between two points of the function, shortening that interval until it becomes the slope of a line tangent to the curve at that point. The idea of a "slope with just one point" was pure magic. This revelation also made me appreciate Limits a lot more (because up to that point  "Limits" looked like a pointless concept). In this case it was thanks to Limits that you could take a concept that traditionally requires two points to a scenario where you only need one, by virtue of making the distance between them (tend to) zero.

    Another example of an epiphany was a class we had on Automata Theory. The teacher would teach the subject using extremely abstract examples (alphabets consisting of shapes, or colors, or just boolean values, and states that were Greek letters or more symbols). It wasn't until almost the end of the semester that I realized that if the symbols were tokens and the states were functions, I could make a language interpreter, or a compiler, or a calculator, or any sort of parser. Furthermore; replacing the symbols for observations or inputs, and the states for actions I could create a simple state-machine-based AI for robots, for example. I think it was a homework assignment involving parsing binary strings that made me realize this. Whatever the case, the vast array of applications that suddenly popped up in my head absolutely blew my mind.

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  • battlecoder
    battlecoder over 1 year ago

    I will answer assuming that "presented material in a way that led to an epiphany" doesn't necessarily mean that the content was presented in a clear way that immediately clicked, but rather in a way that made me think and engage with the content deeply, eventually leading to an Eureka moment. And I'll do this because the only epiphanies I remember came from teachers who presented the concept in such an abstract or weirdly specific way, that the concept wasn't quite clear, until it suddenly was, several many classes later.


    One of such examples is a Pre-Calculus teacher that I had. He would focus almost entirely on the physical interpretation of each concept (Physics was his main class). He naturally presented the derivative as a "rate of change" ("rate of change" of position equals speed, "rate of change" of speed equals acceleration, etc). However, once he went over the "mathematical" definition (with very little focus on it) I suddenly realized that the derivative was the slope of a straight line drawn between two points of the function, shortening that interval until it becomes the slope of a line tangent to the curve at that point. The idea of a "slope with just one point" was pure magic. This revelation also made me appreciate Limits a lot more (because up to that point  "Limits" looked like a pointless concept). In this case it was thanks to Limits that you could take a concept that traditionally requires two points to a scenario where you only need one, by virtue of making the distance between them (tend to) zero.

    Another example of an epiphany was a class we had on Automata Theory. The teacher would teach the subject using extremely abstract examples (alphabets consisting of shapes, or colors, or just boolean values, and states that were Greek letters or more symbols). It wasn't until almost the end of the semester that I realized that if the symbols were tokens and the states were functions, I could make a language interpreter, or a compiler, or a calculator, or any sort of parser. Furthermore; replacing the symbols for observations or inputs, and the states for actions I could create a simple state-machine-based AI for robots, for example. I think it was a homework assignment involving parsing binary strings that made me realize this. Whatever the case, the vast array of applications that suddenly popped up in my head absolutely blew my mind.

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