Comment by IIAOPSW | Hacker News Reader

Comment by IIAOPSW | Hacker News Reader

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Memorizing the times table is for suckers. If you can add, you can spend at most 2 additions to get 2, 3 and 4 (2x = x+x, 3x = x+x+x, 4x = (2x+2x)). Multiplying by the base of your numeral system comes for free (just add 0 to the end). Assuming subtraction just as easy as addition, I now know how to multiply by base-1 and base-2 (9 and 8 normally, 19 and 18 in this case). The last trick I need to invoke is division by 2. Assume you've ignored every other lesson in order to focus on being unreasonably fast at cutting numbers in half. So now, coupled with the append zero trick, you have a path to 5 and 10 (5x = (20x/2)/2, 10x = 20x/2). I haven't memorized anything, and I've used at most two operations, and already I can multiply by 2,3,4,5,10,11,18,19,20. With a third operation I can reach 6,8,9,12,15,17. All that's missing is 7,13,14,16. At that point the remaining part of the "table" only has 10 unique elements in it. I can cover it with a 4th and 5th op if I'm truly stuck, but at some point in doing that repeatedly I'd probably end up remembering that chunk of the table anyway. If we were still in base 10, the same tricks would get me the entire single digit table within at most two addition and/or halving operations. It only takes 3 ops if you reject my premise that halving is as easy as doubling / adding.

Sure it costs me 3 operations per multiplication, but my operations are only doubling and halving (and arguably appending zero). What I lose in number of steps I gain back by just being faster at those two specific skills. And I didn't even have to waste time memorizing stupid tables!

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

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.

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.

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.

We have them in English too: https://www.google.com/search?q=multiplication+rock

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.

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.

> 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.

> Memorizing the times table is for suckers

We humans are good at pattern recognition but we suck at mental arithmetic involving multiple steps. We are slow and error prone. Yes memorizing sucks, all schoolkids hate it, but once you have mastered it you have gained a great new skill. Instead of having to waste mental energy on calculations you just remember them and can spend your precious mental resources on higher level calculations.

You haven't understood. I'm actually better at multiplying than the average and was ahead of the class. It doesn't matter that I'm doing two addition operations per single digit multiplication, because its very easy to be more than twice as fast at doubling / halving numbers if the only thing you ever care about is doubling and halving numbers. The pain of memorizing the table is wholly unnecessary. Memorizing is for suckers.

> I'm actually better at multiplying than the average and was ahead of the class

I bet that most people on this forum were better than average in elementary school, regardless of the method they were using. I also bet that you would have been even better after memorizing. Recalling from memory is almost instantaneous, it is always faster than having some multiple step algorithm.

What did you eat for breakfast yesterday?

Was recalling that from memory "almost instantaneous"?

Recalling yesterday's breakfast is not the same as multiplication table or some other facts you've memorized. Most people don't memorize their breakfast!

edit: as an example, when someone asks "what's your name", do you not recall much faster than what you ate?

I did not memorized it and was deriving it. I was seen as good at math, cause other kids were forgetting and unable to fix situation.

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