7 ms·

It is still extra mental steps, memorising times table is relatively trivial. The costs of having these extra steps really add up for more complicated problems

It is still extra mental steps, memorising times table is relatively trivial. The costs of having these extra steps really add up for more complicated problems that involve multiplication

jacquesm 4y ago
Memorizing the multiplication table is a shortcut that works for small numbers, memorizing a quick method for multiplication works for all numbers. The table is just an optimization that can come in handy in the same way that cache memory is handy: it gives you the same answer but only for a limited set of data and in a faster way. Eventually you'll have to venture out of cache memory to reach the rest of the space and if cache memory is all you have you're in trouble. So if you can learn only one of the two the method is the better one, so learn that one first, then memorize, as much or as little as you feel like. Up to 20x20 is doable, much larger is useful for squares, powers of two and some other numbers for order-of-magnitude checks but when I'm lazy I'll just break out the calculator. It's useful to be able to do this in your head up to a certain point and beyond I'll use a tool just because it is convenient and faster.
hnbad 4y ago
I'd object to the idea that memorizing times tabes is relatively trivial as I've always had trouble memorizing anything. But I too realized a lot of the times tables are basically "free": the only ones I felt I really had to memorize were 2, 3, 5 and 7 (incidentally, the primes). In fact, I still struggle with the 7 sequence because we learned the times tables in two batches (1-5 and 6-10) and 7 was the only one in the second batch that required actual effort and at the age I mistook the other ones being trivial to deduct with me having become better at memorizing times tables. In retrospect, batching it as learning the primes first (including 1 to ease you into it) and then the rest of the numbers second would have probably helped me a lot by avoiding the feeling of "what the heck, why do I suddenly suck at this again when I just thought I had gotten good at it". But of course the concept of primes is off-limits when teaching basic arithmetic so even hinting there's something special about those numbers was apparently taboo. EDIT: Additionally I'd argue out of the primes, 5 is almost free because of how numbers are represented in decimal (i.e. it just alternates between 0 and 5 and the digits in front of that go up every other time) and doubling is fairly intuitive to reason about (take what you have and add the same amount again) so it's just 3 and 7 that are weird.
- charlieyu1 4y ago
  I guess my case is different because we have multiplication songs in Cantonese. (Not really a song, just multiplication facts.) It takes like 30 seconds to read a full column, and kids were taught to read aloud a column at a time. So just plain old repetition, but easy to catch on after a while. A few short practices everyday in a week would be 15-20 repetitions on a single column, which is a fairly good starting point, and very short practices would minimise mental burdens.
  - saalweachter 4y ago
    We have them in English too: https://www.google.com/search?q=multiplication+rock https://www.google.com/search?q=multiplication+rock
IIAOPSW 4y ago
Then you haven't realized how well what I wrote actually scales. In base 10, 2 operations gets you the whole of single digit multiplication (versus memorizing the whole table just to get it down to 1). It also gets you to 11, 12, 20, 21, 19, 30, 40 (by various use of the append 0 trick to multiply by 10 for free anywhere you want). Now try to work out which multiplications are possible within 3 additions/subtractions? How about 4? You should find the accessible fraction of the number line grows exponentially. Memorizing the whole multiplication table for 2 digit numbers isn't practical. That's a 100x100 table. But a small number of adding, doubling, and halving steps can get you anywhere you want in that table.
watwut 4y ago
It is superior, because you can apply the same knowledge on larger numbers and later on general equations. Memorized table is just one pony trick to get result faster in limited amount of situations. And once you forget it, which you are guaranteed to forget, then you will need to derive numbers anyway. Also, it was NOT easy to memorize it. It was hard. Which is why I started to use derivation as s kid, once I realized it is possible. I always did well in math, it did not harmed me at all.
viraptor 4y ago
> memorising times table is ... ... a different experience for different people and I wish we just accepted that and provided multiple ways to deal with it rather than assuming it's something we have to memorise. And maybe also paid attention if those having issues memorising it don't have more general memory issues that need addressing.

It is still extra mental steps, memorising times table is relatively trivial. The costs of having these extra steps really add up for more complicated problems that involve multiplication

jacquesm 4y ago

Memorizing the multiplication table is a shortcut that works for small numbers, memorizing a quick method for multiplication works for all numbers. The table is just an optimization that can come in handy in the same way that cache memory is handy: it gives you the same answer but only for a limited set of data and in a faster way. Eventually you'll have to venture out of cache memory to reach the rest of the space and if cache memory is all you have you're in trouble. So if you can learn only one of the two the method is the better one, so learn that one first, then memorize, as much or as little as you feel like. Up to 20x20 is doable, much larger is useful for squares, powers of two and some other numbers for order-of-magnitude checks but when I'm lazy I'll just break out the calculator. It's useful to be able to do this in your head up to a certain point and beyond I'll use a tool just because it is convenient and faster.

hnbad 4y ago

I'd object to the idea that memorizing times tabes is relatively trivial as I've always had trouble memorizing anything. But I too realized a lot of the times tables are basically "free": the only ones I felt I really had to memorize were 2, 3, 5 and 7 (incidentally, the primes). In fact, I still struggle with the 7 sequence because we learned the times tables in two batches (1-5 and 6-10) and 7 was the only one in the second batch that required actual effort and at the age I mistook the other ones being trivial to deduct with me having become better at memorizing times tables. In retrospect, batching it as learning the primes first (including 1 to ease you into it) and then the rest of the numbers second would have probably helped me a lot by avoiding the feeling of "what the heck, why do I suddenly suck at this again when I just thought I had gotten good at it". But of course the concept of primes is off-limits when teaching basic arithmetic so even hinting there's something special about those numbers was apparently taboo. EDIT: Additionally I'd argue out of the primes, 5 is almost free because of how numbers are represented in decimal (i.e. it just alternates between 0 and 5 and the digits in front of that go up every other time) and doubling is fairly intuitive to reason about (take what you have and add the same amount again) so it's just 3 and 7 that are weird.

charlieyu1 4y ago
I guess my case is different because we have multiplication songs in Cantonese. (Not really a song, just multiplication facts.) It takes like 30 seconds to read a full column, and kids were taught to read aloud a column at a time. So just plain old repetition, but easy to catch on after a while. A few short practices everyday in a week would be 15-20 repetitions on a single column, which is a fairly good starting point, and very short practices would minimise mental burdens.
- saalweachter 4y ago
  We have them in English too: https://www.google.com/search?q=multiplication+rock https://www.google.com/search?q=multiplication+rock

IIAOPSW 4y ago

Then you haven't realized how well what I wrote actually scales. In base 10, 2 operations gets you the whole of single digit multiplication (versus memorizing the whole table just to get it down to 1). It also gets you to 11, 12, 20, 21, 19, 30, 40 (by various use of the append 0 trick to multiply by 10 for free anywhere you want). Now try to work out which multiplications are possible within 3 additions/subtractions? How about 4? You should find the accessible fraction of the number line grows exponentially. Memorizing the whole multiplication table for 2 digit numbers isn't practical. That's a 100x100 table. But a small number of adding, doubling, and halving steps can get you anywhere you want in that table.

watwut 4y ago

It is superior, because you can apply the same knowledge on larger numbers and later on general equations. Memorized table is just one pony trick to get result faster in limited amount of situations. And once you forget it, which you are guaranteed to forget, then you will need to derive numbers anyway. Also, it was NOT easy to memorize it. It was hard. Which is why I started to use derivation as s kid, once I realized it is possible. I always did well in math, it did not harmed me at all.

viraptor 4y ago

> memorising times table is ... ... a different experience for different people and I wish we just accepted that and provided multiple ways to deal with it rather than assuming it's something we have to memorise. And maybe also paid attention if those having issues memorising it don't have more general memory issues that need addressing.