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I'm wondering if you are serious or not - it's hard to tell. It's really pretty obvous why the "1" from one column goes into the next column over to the left,

I'm wondering if you are serious or not - it's hard to tell. It's really pretty obvous why the "1" from one column goes into the next column over to the left, isn't it?

yardie 17y ago
If you have to use the same rules as the standard multiplication method then how is this anymore elegant than doing it the old fashioned way. So instead if counting numbers now you count dots, how revolutionary
- Avshalom 17y ago
  because to perform 312 * 123 you draw 12 lines, count a total of 36 intersections and perform a single addition. you did not have to actually know any multiplication. and the rules for are hung on a visual framework instead of just being "the rules." No one said it was revolutionary (well maybe some youtube commenters..)
  - bitwize 17y ago
    No, fuck you. The rules aren't just "the rules". They are directly derivable from the property of distributivity of multiplication over addition. E.g., 12 * 39 = 12 * (30 + 9) by the property of place value, and hence 12 * 39 = (12 * 30) + (12 * 9) by distributivity. Then you do the same thing again with the 12s to get the two subresults, and... well, you get the idea. This is the basis of the standard algorithm, and it is derived directly from the properties of multiplication itself. But this line thing... this is a trick. And, might I add, a trick that may actually cause more work and use up more scratch-paper space for the figurer. Using a "visual framework" without meaning is no way to teach math. The point is that the standard algorithm is the shortest path from point A to point B, and that is why it should be taught first and foremost.
    - cilantro 17y ago
      Easy there. (This isn't actually a youtube comment thread!) This is just a visual metaphor for standard mutiplicaton process. They are fundamentally the same thing. I personally think the way in the video has the potential to help children assimilate the process faster and/or better than otherwise.
    - Avshalom 17y ago
      Wow, I'm sorry, did cross hatching molest you as a child or something? But please explain to a child the difference between abstract rules and directly derivable properties of distributivity of multiplication over addition. See how much of a difference there is to a first grader between "It's a fundamental property of mathematics" and "Because I said so." >But this line thing... this is a trick. Yes, yes it is. And seeing as all any one has said is it's a elegant (under certain circumstances) trick, why are you so hostile. No one here has proposed replacing the k-12 math curriculum with happy fun line counting time. EDIT: okay the sibling post may have said something that could possibly be construed as supporting the addition of this to the standard curriculum. Still not advocating replacement.

I'm wondering if you are serious or not - it's hard to tell. It's really pretty obvous why the "1" from one column goes into the next column over to the left, isn't it?

yardie 17y ago

If you have to use the same rules as the standard multiplication method then how is this anymore elegant than doing it the old fashioned way. So instead if counting numbers now you count dots, how revolutionary

Avshalom 17y ago
because to perform 312 * 123 you draw 12 lines, count a total of 36 intersections and perform a single addition. you did not have to actually know any multiplication. and the rules for are hung on a visual framework instead of just being "the rules." No one said it was revolutionary (well maybe some youtube commenters..)
- bitwize 17y ago
  No, fuck you. The rules aren't just "the rules". They are directly derivable from the property of distributivity of multiplication over addition. E.g., 12 * 39 = 12 * (30 + 9) by the property of place value, and hence 12 * 39 = (12 * 30) + (12 * 9) by distributivity. Then you do the same thing again with the 12s to get the two subresults, and... well, you get the idea. This is the basis of the standard algorithm, and it is derived directly from the properties of multiplication itself. But this line thing... this is a trick. And, might I add, a trick that may actually cause more work and use up more scratch-paper space for the figurer. Using a "visual framework" without meaning is no way to teach math. The point is that the standard algorithm is the shortest path from point A to point B, and that is why it should be taught first and foremost.
  - cilantro 17y ago
    Easy there. (This isn't actually a youtube comment thread!) This is just a visual metaphor for standard mutiplicaton process. They are fundamentally the same thing. I personally think the way in the video has the potential to help children assimilate the process faster and/or better than otherwise.
  - Avshalom 17y ago
    Wow, I'm sorry, did cross hatching molest you as a child or something? But please explain to a child the difference between abstract rules and directly derivable properties of distributivity of multiplication over addition. See how much of a difference there is to a first grader between "It's a fundamental property of mathematics" and "Because I said so." >But this line thing... this is a trick. Yes, yes it is. And seeing as all any one has said is it's a elegant (under certain circumstances) trick, why are you so hostile. No one here has proposed replacing the k-12 math curriculum with happy fun line counting time. EDIT: okay the sibling post may have said something that could possibly be construed as supporting the addition of this to the standard curriculum. Still not advocating replacement.