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Comment by poseid | Hacker News Reader

without training, our brains confuses numbers easily from my experience. my niece is learning multiplication tables right now, and she confuses 8 * 7 = 56. we tried to teach her these numbers with a story, or a shortcut, e.g. 5 6 7 8 . see the groups 56 and 7*8. but still she rather found this kind of symbol processing painful and preferred to play with other things. another approach we tried to show her a visual representation of the multiplication but not sure what her current progress is.

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I never memorized the multiplication table, but I also never failed a test on it. You only need to learn a fairly small portion of the table in order to infer the rest. When I see 8 * 7, I do not immediately know the answer but I do know 8 * 5 immediately and can quickly add 8 to the result twice.

This has never caused me problems.

Same here. The odd thing is, I'm usually pretty good at rote memorization, but the multiplication tables just didn't interest me or something. So, like you, I use a "multiply then add" strategy to multiply anything I don't have memorized. And it's never seemed to affect my ability accomplish anything.

I went in the opposite direction. I rote-memorized the table, and then discovered different ways to compose the numbers while playing around with them in my head later.

Of course, "multiply then add" is the only easy algorithm to use when the numbers are larger than the size of the table that you know, so most things beyond 10*10 (and some squares above that) are going to default back to that anyhow.

I remember being taught with "math manipulatives"...the result was that I intuitively grasp the relationship between numbers. Maybe that would let you physically show your niece what "eight sevens" actually looks like (and the similarity to "seven eights").

edit: something like this, but with each number 1-10 as its own block and a different color. http://www5.esc13.net/thescoop/insight/files/2012/08/MaryMat...

that looks interesting! it engages a lot of senses, trying now to google for something like that on amazon, but maybe i can print those myself with a 3d printer. or, maybe someone has open sourced a design for those cubicles already?

found the ones I used: http://store.mathusee.com/catalog/math-u-see/manipulatives/i...

Those were great! I'm pretty good at doing math in my head and my brain still visualizes numbers and their relationships based on lengths and colors. In 1970s Sweden they were called "tiostavar", "ten-sticks". They were made of high quality painted wood and very tactile and pleasant to work with. The lengths were precise so they would add up properly in any combination, and the widths were equal to one unit of length so you could make areas and volumes.

(Edit) like these: https://orsjoforskoleklass.files.wordpress.com/2014/11/img_3...

My early education used sticks and cubes like that. I don't remember different lengths with different colors, but that makes a lot of sense as a way to teach addition.

The 1000-cube fascinated me. I think the classroom only had one of them, so the teacher kept it, and we never really got to use it (and it was hard to gather 10 100-squares to build your own).

> we tried to show her a visual representation of the multiplication

I find that visual methods, open up many ways to deeper understanding of arithmetic. Even advanced topics like binomial coefficients pop up quite naturally when folling through. Here is my take on it:

http://heinrichhartmann.com/blog/2016/06/12/Box-Counting-Ari...

My kid just learned by memorizing the results in order. Like: 8, 16, 24, 32, etc. If the problem is 5x8 then she knows its the fifth number in the sequence. Did not take her a lot of time to then learn the whole formula. Now that I think about it, this is like calculating results in a hash table for easy retrieval later.

We used this video (and channel) and it helped lots:

https://youtu.be/IjPjks1R6Ng

when you get to 5x + x = 6x, you can't simply memorize a similar sequence. Knowing how the sequence is created is much more valuable than memorizing the sequence. You do loose some speed, but critical thinking is more important than speed, especially with the onset of cheap personal computers and calculators.

Often it's just a matter of developmental maturity. Childrens' minds develop at different rates and it's counterproductive to push hard on teaching concepts that they're not ready for. Try again in a year.

I made this: http://trondal.com/m Maybe it can help her.

Maybe it's because I'm on mobile but I have no idea what's happening. There a number at the bottom with some sort of countdown (I think) happening, I click a number, screen flashes red, there's a small Sudoku board on the right. Total confusion haha, can you explain?

It's not good on mobile. I tried making it language free, and relatively easy to figure out if you explore the buttons and see what happens. The top middle number is your problem. Your task is to click on the solution. If the solution is wrong, the screen flashes red. The bottom shows statistics of how much time you spend on each problem. The top left and right numbers lets you decide what factors are chosen in the problem. The sudoku board lets you toggle showing you relevant solutions based on chosen factors.

I think you succeeded. I had no idea what was going on for a few minutes and just clicked around, but it became obvious how it worked fairly quickly.

I'll give it to my 8/10 year olds tonight and see what they think. Thanks for making it! Times tables are hard slogging to memorize, and anything to make it less boring is very welcome

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