3 ms·

Well said and all, but notation is a destroyer of understanding, if you are not well versed in reading math. There is a very abrupt jump in the video from the p

by jonsen 11y ago

Well said and all, but notation is a destroyer of understanding, if you are not well versed in reading math. There is a very abrupt jump in the video from the pleasant down to earth demonstration using picture language when the "cold" math notation is just thrown at you in the end.

ColinWright 11y ago
If you are not well versed in reading math then you have two options. One is to forever remain fuzzy and imprecise in your understanding, the other is to learn the notation you need, see how it matches your internal understanding, and then use it as an enabler. If the notation destroys your understanding, then you didn't understand it in the first place, you only had a vague sense of satisfaction with a pseudo-understanding. This is akin to thinking you understand an algorithm, but not being able to code it. I have every sympathy with people who find the notation a barrier, because so did I. Over the years, indeed, the decades, I have come to appreciate notation as a way of concisely expressing deep and complex ideas. Try not using notation - your brain quickly turns to mush as you try to follow hundreds of words that could otherwise be expressed in a mere dozen symbols. Archimedes in "Measurement of the circle" wrote: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle. Today we would write: Area = (1/2)⋅r⋅(2πr)= π⋅r^2 People have a phobia about notation, but the solution isn't to avoid notation, it's to show that it is powerful, and that overcoming the phobia is one way of gaining access to that power. Edited to change the example from Newton's Principia to Archimedes
- jonsen 11y ago
  My point was, that the way notation is just thrown at you in the video can only add to the phobia for the uninitiated. The video is clearly aiming at basic pedagogic explanation, and it is all destroyed in the end. The math versed who easily read that math without explanation do not need the bead juggling. The pedagogy fails in the end.
  - ColinWright 11y ago
    The explanation of the theorem has got as far as it can go by that point. There's a choice to be made. Avoiding notation means that those who could now connect the explanation with things they have already seen is lost. Avoiding notation also means that it's just all been a show, and there's no real take away except that, well, this guy played with beads an counted things. If someone is truly notation-phobic then there is nothing to be done. Having the notation means that those in the middle ground have a chance to see real maths in action, and may be inspired to do more. The genuinely notation-phobic will never advance in math. For those who know the theorem this is a cute visualisation. People will only learn when they are ready, and all pedagogy needs to be targeted at those who are ready for it. I suspect we agree more than people reading this might think, but we might disagreed over the perceived purpose of the video. I see it as getting people engaged with the thought processes, and then showing that it's really math, and look, here are the formulas that come out of it. It's an opportunity to learn about the formulas. For the genuinely notation-phobic, there is no real hope, except for them to see that this is a cool thing their phobia is preventing them from understanding better, so maybe getting over the phobia would be worthwhile. I could do a complete case analysis, but this isn't the place, and I don't have the time. Would you suggest not having the notation at all? What would then be the point of the video? Who would gain?
    - jonsen 11y ago
      Yes, we agree a long way. I'm sure the video works well in its intended greater context, as you describe here. My points are about taking the video at face value out of context, which is probably what lead to clear-as-muds comment.
      - britcruise 11y ago
        Hey there, I created this video. It was just one part of a longer lesson I was trying on "Random Algorithms" because it involved Fermat's primality test...so in this case we really needed that formula to try it out which is why I added it at the end. https://www.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/randomized-algorithms-prime-adventure-part-8 https://www.khanacademy.org/computing/computer-science/crypt...

by jonsen 11y ago

ColinWright 11y ago

If you are not well versed in reading math then you have two options. One is to forever remain fuzzy and imprecise in your understanding, the other is to learn the notation you need, see how it matches your internal understanding, and then use it as an enabler. If the notation destroys your understanding, then you didn't understand it in the first place, you only had a vague sense of satisfaction with a pseudo-understanding. This is akin to thinking you understand an algorithm, but not being able to code it. I have every sympathy with people who find the notation a barrier, because so did I. Over the years, indeed, the decades, I have come to appreciate notation as a way of concisely expressing deep and complex ideas. Try not using notation - your brain quickly turns to mush as you try to follow hundreds of words that could otherwise be expressed in a mere dozen symbols. Archimedes in "Measurement of the circle" wrote: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle. Today we would write: Area = (1/2)⋅r⋅(2πr)= π⋅r^2 People have a phobia about notation, but the solution isn't to avoid notation, it's to show that it is powerful, and that overcoming the phobia is one way of gaining access to that power. Edited to change the example from Newton's Principia to Archimedes

jonsen 11y ago
My point was, that the way notation is just thrown at you in the video can only add to the phobia for the uninitiated. The video is clearly aiming at basic pedagogic explanation, and it is all destroyed in the end. The math versed who easily read that math without explanation do not need the bead juggling. The pedagogy fails in the end.
- ColinWright 11y ago
  The explanation of the theorem has got as far as it can go by that point. There's a choice to be made. Avoiding notation means that those who could now connect the explanation with things they have already seen is lost. Avoiding notation also means that it's just all been a show, and there's no real take away except that, well, this guy played with beads an counted things. If someone is truly notation-phobic then there is nothing to be done. Having the notation means that those in the middle ground have a chance to see real maths in action, and may be inspired to do more. The genuinely notation-phobic will never advance in math. For those who know the theorem this is a cute visualisation. People will only learn when they are ready, and all pedagogy needs to be targeted at those who are ready for it. I suspect we agree more than people reading this might think, but we might disagreed over the perceived purpose of the video. I see it as getting people engaged with the thought processes, and then showing that it's really math, and look, here are the formulas that come out of it. It's an opportunity to learn about the formulas. For the genuinely notation-phobic, there is no real hope, except for them to see that this is a cool thing their phobia is preventing them from understanding better, so maybe getting over the phobia would be worthwhile. I could do a complete case analysis, but this isn't the place, and I don't have the time. Would you suggest not having the notation at all? What would then be the point of the video? Who would gain?
  - jonsen 11y ago
    Yes, we agree a long way. I'm sure the video works well in its intended greater context, as you describe here. My points are about taking the video at face value out of context, which is probably what lead to clear-as-muds comment.
    - britcruise 11y ago
      Hey there, I created this video. It was just one part of a longer lesson I was trying on "Random Algorithms" because it involved Fermat's primality test...so in this case we really needed that formula to try it out which is why I added it at the end. https://www.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/randomized-algorithms-prime-adventure-part-8 https://www.khanacademy.org/computing/computer-science/crypt...