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> Why are you advocating memorization? Because it's something kids do really well and it's something to take advantage of when learning at that age. In other w

by rdtsc 8y ago

> Why are you advocating memorization? Because it's something kids do really well and it's something to take advantage of when learning at that age. In other words, it's better to memorize the multiplication table then find insights into how it work later, and do proofs and make connections with calculating an area of a rectangle etc. A lot of the tricks and insights don't mean anything to the children if they didn't already do many examples the rote, repetitive way and in a lot of cases the "insights" are often a distraction as well. Those should come later. Even more interesting is when children see or discover these tricks or rules on their own, then they become really memorable to them. I don't have many samples work with, but I have observed this over the years based on my own experience, my kids and my extended family members and I have noticed the same patterns.

coretx 8y ago
Although I tend to mostly agree with your main argument, the example you presented ( memorizing multiplication tables ) is a bad one. My mind was blown when I found out how they teach multiplication to children in Japan. Link: ( Vedic method ) https://www.youtube.com/watch?v=z4X98Mnj0tc https://www.youtube.com/watch?v=z4X98Mnj0tc The superiority of the teaching method shows to be significant when compared to other teaching methods elsewhere and even remains noticeable when children encounter higher levels of math.
- dhimes 8y ago
  This is similar to the "Lattice Method" that they taught (still teach?) here in the US. I can't stand it. The students simply learn an algorithm, without developing a sense of place value and an intuition for "how numbers work." Sure, they can quickly multiply large numbers and it's a cool "party trick." But they aren't learning math. Might as well use an iPhone.
  - butmath 8y ago
    Fair point that memorizing an algorithm doesn't necessarily advance the student's intuition for how numbers work, but keep in mind that you're replying on a subthread about how learning a general algorithm is an improvement over memorizing multiplication tables. Ideally, we teach children the intuition for mathematics. Just memorizing arithmetic algorithms isn't ideal, but it's surely better than memorizing finite arithmetic tables.
    - rmah 8y ago
      I don't think it is better to learn some shortcut algo at a young age. Memorizing your times tables up to say 10 * 10 or 12 * 12 is fundamental to understanding multiplication. Remember, the brain is not a turing machine, it's an associative memory machine. Facts are the foundation of knowledge. First memorize the times tables. Then learn the long method. Then learn the shortcuts. IMO, of course.
      - dhimes 8y ago
        I agree with you. To do multiplication by any non-parlor-trick method you have to be able to multiply single-digit numbers. If you don't memorize the table then every time you do larger numbers the process becomes that much more of a chore. Now, that is not to say that you should forego understanding multiplication. But forcing student to memorize the basics (like forcing them to memorize verb forms) (1) makes their life easier later on and (2) gives them the chance to spot patterns themselves.
- rdtsc 8y ago
  > The superiority of the teaching method shows to be significant when compared to other teaching methods elsewhere and even remains noticeable when children encounter higher levels of math. I was mainly talking about addition and multiplication up to 10x10. Looking through all the tricks and hacks they teach the kids in an attempt to simplify ideas seems very wasteful as the brain at that age is so good at memorizing things. ut the schools don't seem to be taking advantage of that. They think like adults in the sense of "oh let's introduce this abstract idea and prove it and derive the specific examples from it". Yes, a college kid or high school would do well there, but in earlier grades I haven't seen it work. It's a bit like learning a language. An adult might do well to start learning about grammar rules, tenses, cases etc, a kid might do better hearing a lot of example and deriving the rules on their own. Later they might find out that there are 8 tenses, 4 cases, predicates, adjectives etc.
jimmaswell 8y ago
Memorizing the multiplication table is a useless waste of time and I recognized as much when they tried to make me do it and I refused. Nobody needs to know 8x7 off the top of their head. What's really important is estimation techniques to tell if something passes a sanity check, like reducing things to powers of 10/etc and seeing if they're close to the result you got on a calculator, like how 123x456 should be close to 50000 (100x500)
- CamperBob2 8y ago
  How in the world are you supposed to estimate products of large numbers if you don't know the products of small ones?
  - jimmaswell 8y ago
    You'll pick up on a few as you go along and that's all you need.
    - grimjack00 8y ago
      So, you'll memorize them.
      - jimmaswell 8y ago
        A few that you need, on an ad-hoc basis, instead of front-loading a bunch of calculations you're probably never going to use.
        Dylan16807 8y ago
        Memorizing every combo of 2-9 x 2-9 is only 36 numbers. That doesn't seem like a big waste of time to me. If you do common ones like 2, 3, 5, and squares, that already covers most of them and you only have 10 left to remember them all.
- CharlesColeman 8y ago

by rdtsc 8y ago

coretx 8y ago

Although I tend to mostly agree with your main argument, the example you presented ( memorizing multiplication tables ) is a bad one. My mind was blown when I found out how they teach multiplication to children in Japan. Link: ( Vedic method ) https://www.youtube.com/watch?v=z4X98Mnj0tc https://www.youtube.com/watch?v=z4X98Mnj0tc The superiority of the teaching method shows to be significant when compared to other teaching methods elsewhere and even remains noticeable when children encounter higher levels of math.

dhimes 8y ago
This is similar to the "Lattice Method" that they taught (still teach?) here in the US. I can't stand it. The students simply learn an algorithm, without developing a sense of place value and an intuition for "how numbers work." Sure, they can quickly multiply large numbers and it's a cool "party trick." But they aren't learning math. Might as well use an iPhone.
- butmath 8y ago
  Fair point that memorizing an algorithm doesn't necessarily advance the student's intuition for how numbers work, but keep in mind that you're replying on a subthread about how learning a general algorithm is an improvement over memorizing multiplication tables. Ideally, we teach children the intuition for mathematics. Just memorizing arithmetic algorithms isn't ideal, but it's surely better than memorizing finite arithmetic tables.
  - rmah 8y ago
    I don't think it is better to learn some shortcut algo at a young age. Memorizing your times tables up to say 10 * 10 or 12 * 12 is fundamental to understanding multiplication. Remember, the brain is not a turing machine, it's an associative memory machine. Facts are the foundation of knowledge. First memorize the times tables. Then learn the long method. Then learn the shortcuts. IMO, of course.
    - dhimes 8y ago
      I agree with you. To do multiplication by any non-parlor-trick method you have to be able to multiply single-digit numbers. If you don't memorize the table then every time you do larger numbers the process becomes that much more of a chore. Now, that is not to say that you should forego understanding multiplication. But forcing student to memorize the basics (like forcing them to memorize verb forms) (1) makes their life easier later on and (2) gives them the chance to spot patterns themselves.
rdtsc 8y ago
> The superiority of the teaching method shows to be significant when compared to other teaching methods elsewhere and even remains noticeable when children encounter higher levels of math. I was mainly talking about addition and multiplication up to 10x10. Looking through all the tricks and hacks they teach the kids in an attempt to simplify ideas seems very wasteful as the brain at that age is so good at memorizing things. ut the schools don't seem to be taking advantage of that. They think like adults in the sense of "oh let's introduce this abstract idea and prove it and derive the specific examples from it". Yes, a college kid or high school would do well there, but in earlier grades I haven't seen it work. It's a bit like learning a language. An adult might do well to start learning about grammar rules, tenses, cases etc, a kid might do better hearing a lot of example and deriving the rules on their own. Later they might find out that there are 8 tenses, 4 cases, predicates, adjectives etc.

jimmaswell 8y ago

Memorizing the multiplication table is a useless waste of time and I recognized as much when they tried to make me do it and I refused. Nobody needs to know 8x7 off the top of their head. What's really important is estimation techniques to tell if something passes a sanity check, like reducing things to powers of 10/etc and seeing if they're close to the result you got on a calculator, like how 123x456 should be close to 50000 (100x500)

CamperBob2 8y ago
How in the world are you supposed to estimate products of large numbers if you don't know the products of small ones?
- jimmaswell 8y ago
  You'll pick up on a few as you go along and that's all you need.
  - grimjack00 8y ago
    So, you'll memorize them.
    - jimmaswell 8y ago
      A few that you need, on an ad-hoc basis, instead of front-loading a bunch of calculations you're probably never going to use.
      - Dylan16807 8y ago
        Memorizing every combo of 2-9 x 2-9 is only 36 numbers. That doesn't seem like a big waste of time to me. If you do common ones like 2, 3, 5, and squares, that already covers most of them and you only have 10 left to remember them all.
CharlesColeman 8y ago