4 ms·

> For instance, you can multiply by 8 by doubling three times. So instead of trying to figure out 12x8, just double 12 three times: 24, 48, 96 This can be more

> For instance, you can multiply by 8 by doubling three times. So instead of trying to figure out 12x8, just double 12 three times: 24, 48, 96 This can be more generally thought of as using exponentiation. 12 * 8 = 12 * 2^3 Using the more general rule, again. 12 * 9 = 12 * 3^2. Or 12 * 3 * 3.

cgriswald 10y ago
I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. 12 * 8 = 10 * 8 + 2 * 8 = 96 12 * 9 = 12 * 10 - 12 = 108 That said, most of the things in the article are things I've picked up more or less automatically. If you could train yourself to do them, I think it could help, but I think most people who do them just figured them out on their own. I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Those who memorize do worse on tests, because if they forget, they can't just apply their knowledge. They also seem to forget the material faster after the class. Those who learn the concepts are usually okay, even if they forget a detail they can often work it out. I also think that someone who needs to memorize that 3/5 = 0.6 is unclear on some deeper concept somewhere. Edit: formating
- discombobulate 10y ago
  > I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. Sure. It's just another tool. > I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Do you find the best students are fluent with the techniques and have an understanding? It would seem to me, spending time pondering meaning also has the benefits of remembering 'building blocks'; because they're the primitives involved in the struggle for understanding.
  - cgriswald 10y ago
    There are three components: facts, techniques, concepts. Being fluent with techniques is not strictly necessary, but is generally important and can aid in helping to understand concepts by demonstrating relationships. But a student who prioritizes concepts is probably better off than one who only understands techniques.[0] My objection to the article is that it is advocating memorizing facts. Figuring out that 3/5 == 0.6 is trivial if you already understand the concepts and knowing that 3/5 == 0.6 is pointless if you don't know what it means. [0] - Anecdotally, I breezed through calc 1 in high school. First done with every test, always aced those tests, never studied. Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing.
    - discombobulate 10y ago
      > Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing. I suppose so. If you wrote some code to carry out the rules, you wouldn't say the computer knows anything.
    - dwringer 10y ago
      If you were always first done and aced your tests, but think you had no idea what you were doing, then think how everyone else must have felt.
- deleted 10y ago
  [deleted]
- mathiium 10y ago
  128=(11+1)8=88+8=96 1111128 = 1111118+8=888896

cgriswald 10y ago

I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. 12 * 8 = 10 * 8 + 2 * 8 = 96 12 * 9 = 12 * 10 - 12 = 108 That said, most of the things in the article are things I've picked up more or less automatically. If you could train yourself to do them, I think it could help, but I think most people who do them just figured them out on their own. I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Those who memorize do worse on tests, because if they forget, they can't just apply their knowledge. They also seem to forget the material faster after the class. Those who learn the concepts are usually okay, even if they forget a detail they can often work it out. I also think that someone who needs to memorize that 3/5 = 0.6 is unclear on some deeper concept somewhere. Edit: formating

discombobulate 10y ago
> I find both of these easier and faster using other methods. Maybe just because I've been doing them since childhood. Sure. It's just another tool. > I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Do you find the best students are fluent with the techniques and have an understanding? It would seem to me, spending time pondering meaning also has the benefits of remembering 'building blocks'; because they're the primitives involved in the struggle for understanding.
- cgriswald 10y ago
  There are three components: facts, techniques, concepts. Being fluent with techniques is not strictly necessary, but is generally important and can aid in helping to understand concepts by demonstrating relationships. But a student who prioritizes concepts is probably better off than one who only understands techniques.[0] My objection to the article is that it is advocating memorizing facts. Figuring out that 3/5 == 0.6 is trivial if you already understand the concepts and knowing that 3/5 == 0.6 is pointless if you don't know what it means. [0] - Anecdotally, I breezed through calc 1 in high school. First done with every test, always aced those tests, never studied. Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing.
  - discombobulate 10y ago
    > Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing. I suppose so. If you wrote some code to carry out the rules, you wouldn't say the computer knows anything.
  - dwringer 10y ago
    If you were always first done and aced your tests, but think you had no idea what you were doing, then think how everyone else must have felt.
deleted 10y ago
[deleted]
mathiium 10y ago
128=(11+1)8=88+8=96 1111128 = 1111118+8=888896