Do people really memorize the multiplication tables?

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Do people really memorize the multiplication tables?

I always thought the multiplication table was just like an education motif, like they put the alphabet on the wall way past when you need it. But now all sorts of people are telling me they memorized the multiplication table in grade school. Is that people are really doing? I don't get it, memorize what? 5*6=30? That's a priori, it just is. No one memorizes addition tables or subtraction tables. You don't need to, you do the operation. I thought "memorize the multiplication table" was just an expression people were that referred to teaching multiplication and division.

I am trying to figure out what people mean when they say they memorize the multiplication tables. Is that really what is going on in school? Can most people really not do multiplication of single digit numbers in their head? Did I actually memorize the tables someone and not realize it? Are other people actually doing the operation but calling it memorization? What is going on here?
Republicus
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Re: Do people really memorize the multiplication tables?

I see what you mean, definitely. You learn through "doing the operation", and can perhaps recall the exact operation again quickly at a later time. Children are "forced to memorise their tables at 7 years old", which is really to say that they are made to do the calculations up to about 10, 12 or 15 times tables repeatedly so that when they hear "6*7" they don't need to double 7 and then times that by three anymore (or times 7 by 10, half it and add 7), they already know the process and the result. "Memorising the tables" is practicing for practically instant recall of any operation up to a certain point.

Keep_Relentless
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Re: Do people really memorize the multiplication tables?

I get a hint from the OP that the topic is about whether mathematical entities are invented or discovered, or even more fundamental that is about the ontological status of mathematical entities. If so, it might be better to move this to the philosophy forum.

Alternatively, it could be a question about how we learn arithmetic in school (or how we should be learning arithmetic). (Note that there is apparently some society of people who never learn to count (they have only three 'numbers', 'one', 'two', 'many' as they might be translated to English, where 'two' for example, doesn't always mean '2' in the way we think of it.)

And this leads me to think about the "new math", and whether that can be the best way of learning arithmetic, or at least the arithmetic that society itself needs for most people. (Mathematicians, presumably, don't need these skills.)

Finally, I'd say, of course, children who learn their "multiplication tables" do so by memorizing them, using some or another technique. My guess is that they learn them through a process that places numbers themselves in some category of objective existence.

James
owleye
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Re: Do people really memorize the multiplication tables?

I memorized them through the twelveses. It didn't seem to harm me and it seems easier than having to actually do the multiplication in my head each time.
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Re: Do people really memorize the multiplication tables?

CanadysPeak wrote:I memorized them through the twelveses. It didn't seem to harm me and it seems easier than having to actually do the multiplication in my head each time.

Ditto. Had to do a lot of memorization of lots of other things too. French vocabulary, geological columns and times, etc. Again, a lot easier than having to go out and reinvent a lot of wheels.

Forest_Dump
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Re: Do people really memorize the multiplication tables?

Yes, the only way you just "know" that 6 x 5 = 30 is because you learned it by heart in primary school. In no sense do you just "do the calculation". Merely saying to yourself, "six times five is thirty", is NOT a calculation, nor is it an expression of a self-evident truth; it's just something you learned in school, like "The Battle of Waterloo took place in 1815".

Well, perhaps not quite like; because, after "six times five is thirty", you were probably told "seven times five is thirty-five" and, if you were a bright kid, you might have then got an inkling of the additive logical process which underpins the validity of the multiplication tables.

There is nothing a priori about the proposition that 6 x 5 = 30. The full calculation (ie proof) is in fact surprising long and non-intuitive, and critically dependent on your choice of axioms. Vary the axioms appropriately, and you can prove that 1 + 1 = 0.

In mathematics you must always beware of mistaking what is merely very familiar with what is "logically necessary" or "self-evident". But if you do happen to fall into that trap, you are at least in good company. Even the great Albert Einstein once said that it is an axiom of geometry that "a straight line is the shortest distance between two points". He was wrong, of course. It isn't an axiom, it is a theorem, a special case of the theorem that the sum of any two sides of a triangle is greater than the third side.
Alan Masterman
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Re: Do people really memorize the multiplication tables?

Imo, this type of education is a bit of a joke.

I have put hours into trying to teach my children what a multiplication and a division is, but its all completely blown off after one day with their teacher.
They don't have to know what a division is, they just have to memorise what number divides into another.
But when I ask them what is a division, all I get is a completely blank stare and, "but look at this sheet Dad its got the divisions on it."

You only have to learn the process once.
At first it is a very slow process, but with a little practice it is actually faster than trying to get a kid to sit still and memorise a bunch of meaningless numbers.

If I didn't have to put food on the table, then I'd be home schooling all my children.
But as it stands, its a battle of my teaching vs the teachings of school education, and I always lose when I'm not the Authoritarian figure on book smarts.

edy420
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Re: Do people really memorize the multiplication tables?

edy420,

Of course your kids (like mine) have been taught the shorthand version of everything. This is not entirely illegitimate. It's a question of striking a balance. Under today's educational pressures, kids have to be taken as far as possible, as quickly as possible.

When I was at high school, we just went straight into the theorems. I had no idea they were written by Euclid. The entire concept of "axiom" or "postulate" was totally missing from our education.

It would be great if we could take the time to teach our kids to question everything, to argue about the fundamentals of arithmetic, or the axioms of geometry, but the demands of modern life mean they have to get out there as quickly as possible to hustle for a living, maintain military supremacy etc, and a genuine critical understanding of ANY subject has been out of fashion since the 1960's. Grammar and punctuation haven't been taught in our schools for forty years.

Just do as much as you can to make them understand the importance of THINKING!
Alan Masterman
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Re: Do people really memorize the multiplication tables?

Alan Masterman wrote:Yes, the only way you just "know" that 6 x 5 = 30 is because you learned it by heart in primary school. In no sense do you just "do the calculation".

Absolutely. I have been trying to figure out how you would really do it any other way other than mechanically adding six objects five times (i.e., imagining 30 objects - in five rows of six?). The reality is that we do have to learn all kinds of seemingly arbitrary things like the difference between there and their or that 1 is a single object, etc. We memorize vocabulary (ever have to pass french or spanish? How else did you learn all the verbs?), math, what the signs at the side of the road mean, even what buttons to push on a calculator or computer. The trick is not in how much we need to memorize but rather in how to do it quicker and more painlessly.

Forest_Dump
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Re: Do people really memorize the multiplication tables?

Forest_Dump wrote:
Alan Masterman wrote:Yes, the only way you just "know" that 6 x 5 = 30 is because you learned it by heart in primary school. In no sense do you just "do the calculation".

Absolutely. I have been trying to figure out how you would really do it any other way other than mechanically adding six objects five times (i.e., imagining 30 objects - in five rows of six?).

When talking in childlike language, I explain it as the biggest number is the boss, the sign (x, multiplication) is the orders the boss gives and the second number is the one being told how many times to replicate or divide (or simply, being told what to do).
After a few hours of tutoring my 8 and 6 year old daughters are able to understand how to figure out 6 x 5 without memorising it.

So there are two number 30's.
The first number 30 is handed to you, in the equation 6 x 5 = 30.
It is pointless to learn this number 30 because it does not come with any understanding what so ever, and this number 30 should not be memorised.

The second number 30 comes from the question, what is 6 x 5?
It is fine to memorise this number 30, because of the way memory operates.
We can simply think of the process involved with multiplication without actually doing it, to remind our selves of the number 30.
Or if that fails you can simply redo the whole process.
But if you forget the first number 30, you fail the test.

I did a total of 3 hours home work over the period of 4 years in high school, yet I was one of 2 Maori's in the top mathematics class and I was able to pass every test handed to me. (I was the only Maori in the last year, as Hemi moved over seas)
The rest of our classroom students were all white, but if there were multiple teaching techniques, I'm sure there would have been more Maori's in the top mathematics class.
Most of my homework was for English class, and that was during lunch time for a project that I was supposed to spend two weeks on.

Many people are not able to just memorise everything handed to them.
These are the people that fail in class and where I come from, there are a lot of them.
Even in class, I was able to teach pupils my age to learn simple techniques that helped otherwise failing students.
These students who are able to learn in different ways are Imo, just as clever as someone who has good memory, but the current education system just labels them as dumb, unable to learn and are brushed aside for the students with a good memory.

The reality is that we do have to learn all kinds of seemingly arbitrary things like the difference between there and their or that 1 is a single object, etc. We memorize vocabulary (ever have to pass french or spanish? How else did you learn all the verbs?), math, what the signs at the side of the road mean, even what buttons to push on a calculator or computer. The trick is not in how much we need to memorize but rather in how to do it quicker and more painlessly.

When babies learn words, they are praised every single time the speak and so it is easy to learn by simply memorising.
But that later develops into mimicking which is another process of learning.

When adults learn a new word, they don't just memorise the word itself.
Instead we associate that word with a memory, and every time we use this memory we are reminded of the word.
This is probably the best technique for dealing with numbers too, where you associate numbers with memories.
Simply memorising 6 x 5 = 30 does not enforce the use of this memory technique.

edy420
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Re: Do people really memorize the multiplication tables?

Alan Masterman wrote:edy420,

Of course your kids (like mine) have been taught the shorthand version of everything. This is not entirely illegitimate. It's a question of striking a balance. Under today's educational pressures, kids have to be taken as far as possible, as quickly as possible.

When I was at high school, we just went straight into the theorems. I had no idea they were written by Euclid. The entire concept of "axiom" or "postulate" was totally missing from our education.

It would be great if we could take the time to teach our kids to question everything, to argue about the fundamentals of arithmetic, or the axioms of geometry, but the demands of modern life mean they have to get out there as quickly as possible to hustle for a living, maintain military supremacy etc, and a genuine critical understanding of ANY subject has been out of fashion since the 1960's. Grammar and punctuation haven't been taught in our schools for forty years.

Just do as much as you can to make them understand the importance of THINKING!

I agree whole heartedly.

This problem is the problem of people who are unable to learn using rushed education.
The current economy is all about efficiency, not realising that our society is more than a bunch of statistics.

Imo, this rubbish just has to stop, bring on the resource based economy, so we can put this nightmare in the past and laugh at how dumb we once were.

edy420
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Re: Do people really memorize the multiplication tables?

You can understand what Tennyson was talking about when he gazed at the water, and still memorize Break, Break, Break, for later recitation or quoting.
You can understand how to arrive at 7X8 and still find it easier to refer to in memory than working it out.
It's a chore one time and a convenient short-cut for the rest of your life.
Serpent
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Re: Do people really memorize the multiplication tables?

It's a two-step program. First comes getting an understanding of what multiplication is - a fast way of adding. Then, to save a lot of time working out what 7 added 9 times is, memorize it - and all the others. In second grade? I never heard of it but I suppose it could be if you stuck to the lowest numbers. We memorized the multiplication tables and I've never broken out in hives for having done so. I still had trouble with 8 x 7, though. Never could remember that one. So, take 4 x 7 and double the 28. Aha! Two alternate skills. Nothing wrong with that. Variety is the spice of life.

Of course, there are our math geniuses who don't need any tools or crutches. They just see the answer immediately. Bless them For the rest of us ...... memorize.

More: Cure for insomnia? Count by 7s without reciting the whole table. Still awake? County by 9s. Lots of fun. If the boredom doesn't put you to sleep, try reciting the states in alphabetical order. With their capitals. Memory - a tool of the brain's wiring? Used for shortcuts. Use it or lose it.

Oops! Slippery soap box again.
vivian maxine
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Re: Do people really memorize the multiplication tables?

Interesting thread, but a bit older. I memorized all the multiplication and addition tables - and I find it allows me to solve simple math problems quickly like a calculator. I do not understand what the OP means by "just do the operation". So 6 x 7 is 42 to me - what is the operation method for solving it? I wasn't even aware there was an alternative beside just drawing 6 rows of 7 and counting them, or counting by sixes 7 times.

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Re: Do people really memorize the multiplication tables?

My mother once bought nine booklets that cost \$3 each, from a secondary school student who had never been exposed to old-fashioned pedagogics. She waited, somewhat bemused, holding her three ten dollar bills, while the girl laboriously stacked nine \$3.00's in her ledger and added them up. Not three nines, mind you! She was just curious to see how long it would take to work out the change.
It's not always a matter of either/or; sometimes it's neither/nor.
Serpent
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Re: Do people really memorize the multiplication tables?

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Riyan
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Re: Do people really memorize the multiplication tables?

Serpent » August 18th, 2016, 3:06 pm wrote:My mother once bought nine booklets that cost \$3 each, from a secondary school student who had never been exposed to old-fashioned pedagogics. She waited, somewhat bemused, holding her three ten dollar bills, while the girl laboriously stacked nine \$3.00's in her ledger and added them up. Not three nines, mind you! She was just curious to see how long it would take to work out the change.
It's not always a matter of either/or; sometimes it's neither/nor.

It took a while - I'm slow, too - but it just occurred to me why the girl added nine 3's instead of three 9's. She'd memorized counting by 3's. We all did. OK. Most of us did. Counting by 2's, 3's, 5's and 10's. I don't think we ever memorized counting by 4, 6, 7, 8 or 9. That came later as we gained understanding. For some, it never came.

Something easy she was using. If she was slow at it, her teachers had cured her of counting on her fingers. :-(
vivian maxine
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Re: Do people really memorize the multiplication tables?

No, I think it's just that it didn't occur to her to take a shortcut. She wasn't counting by three's; she was making out a receipt as she had been shown. If it was two booklets, she's have written
\$ 3.00
\$ 3.00
\$ 6.00
We, and my mother's generation more than mine, had been shown labourious ways to do things and then more efficient ways to arrive at the same thing. It did require some memory work... but, in her 70,s, she could still draw a pretty accurate outline of Europe and put in the capitols. Exercising memory, both early and often, is a worthwhile investment in the long-term functionality of one's brain.

By the time my kids were in high-school, they did everything the hard way: Show all your work; nothing taken for granted. It's more a function of our society's attitude toward children - we give them more and expect less of them and worry that they grow up too fast.
Serpent
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Re: Do people really memorize the multiplication tables?

vivian maxine » October 3rd, 2016, 1:27 pm wrote:
Serpent » August 18th, 2016, 3:06 pm wrote:My mother once bought nine booklets that cost \$3 each, from a secondary school student who had never been exposed to old-fashioned pedagogics. She waited, somewhat bemused, holding her three ten dollar bills, while the girl laboriously stacked nine \$3.00's in her ledger and added them up. Not three nines, mind you! She was just curious to see how long it would take to work out the change.
It's not always a matter of either/or; sometimes it's neither/nor.

It took a while - I'm slow, too - but it just occurred to me why the girl added nine 3's instead of three 9's. She'd memorized counting by 3's. We all did. OK. Most of us did. Counting by 2's, 3's, 5's and 10's. I don't think we ever memorized counting by 4, 6, 7, 8 or 9. That came later as we gained understanding. For some, it never came.

Something easy she was using. If she was slow at it, her teachers had cured her of counting on her fingers. :-(

Possibly, the commutative property of multiplication is not so intrinsically and obviously perceived...
If you have 9 items - each with value 3 - you add up three, nine times.
I suspect it is not directly intuitive that adding up nine, three times, gets you to the same result.

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Re: Do people really memorize the multiplication tables?

You are probably right, neuro. If you don't intuit one math, you don't intuit another. For some of us math just doesn't lend itself to intuition. I once had a clerk in a dry goods store insist on measuring out a piece of material by putting the 1 of the yard stick at the edge of the material. Nothing would convince her that she was wrong. Counting starts at 1, she insisted. I solved the problem by ordering a yard and a half instead of one yard.
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Re: Do people really memorize the multiplication tables?

vivian maxine » October 13th, 2016, 7:58 am wrote:You are probably right, neuro. If you don't intuit one math, you don't intuit another. For some of us math just doesn't lend itself to intuition. I once had a clerk in a dry goods store insist on measuring out a piece of material by putting the 1 of the yard stick at the edge of the material. Nothing would convince her that she was wrong. Counting starts at 1, she insisted. I solved the problem by ordering a yard and a half instead of one yard.

You still paid for the extra inch you never received. Now, if that was expensive drapery in 54" width, that clerk was stealing a noticeable amount of money from you, and a great whack of money from all customers over a year.
Serpent
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Re: Do people really memorize the multiplication tables?

Serpent » October 13th, 2016, 9:33 am wrote:
vivian maxine » October 13th, 2016, 7:58 am wrote:You are probably right, neuro. If you don't intuit one math, you don't intuit another. For some of us math just doesn't lend itself to intuition. I once had a clerk in a dry goods store insist on measuring out a piece of material by putting the 1 of the yard stick at the edge of the material. Nothing would convince her that she was wrong. Counting starts at 1, she insisted. I solved the problem by ordering a yard and a half instead of one yard.

You still paid for the extra inch you never received. Now, if that was expensive drapery in 54" width, that clerk was stealing a noticeable amount of money from you, and a great whack of money from all customers over a year.

Fortunately, it wasn't. Just an inexpensive piece of cotton I needed for something. But I don't think she was stealing anything. She simply learned to count from 1 and misunderstood that when it comes to measurement. I do not remember zero being stressed for any thing.

But, you know what? Even today, after we've acknowledged the importance of zero, some math systems are still making light of it by calling it nothing more than a place holder. Seems to me it's a bit more than an unimportant place holder. It is a ten which you soon find out if you have to borrow or add to.

So much for my math. Am I wrong?
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