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The Multiplication Tables

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Al Kufr

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When I was younger I had lots of trouble memorizing my mulitplication tables and fell behind many of my other classmates. Many of my classmates could give you the answer to any problem between the tables 1 and 12 when they were asked to answer them in front of the class, but I had lots of trouble.

We learned the multiplication tables tables by rote learning. And now I have a little sister who also has trouble with her math and she is also being tought in the same way.

So my question is, what is an easier and more correct method of learning the multiplication tables?

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When I was younger I had lots of trouble memorizing my mulitplication tables and fell behind many of my other classmates. Many of my classmates could give you the answer to any problem between the tables 1 and 12 when they were asked to answer them in front of the class, but I had lots of trouble.

We learned the multiplication tables tables by rote learning. And now I have a little sister who also has trouble with her math and she is also being tought in the same way.

So my question is, what is an easier and more correct method of learning the multiplication tables?

Interesting question.

Offhand, I'd say start with the lower number tables, and work up, but I imagine you're already doing that.

For me, the thing that helps is breaking down the table problems in drills. E.g. if I were teaching someone the x6 and x8 tables, I'd want to drill them with some problems along the lines of "2 * 3 * [some number]" and "4 * [some number] * 2." Since multiplying by 6 or 8 here is the likely intermediate step, it 1) reinforces the lower tables and 2) illustrates to the person the benefit of memorizing table products in order to save time.

Don't know if this helps. I think it an interesting question, and I hope you get some other responses too.

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So my question is, what is an easier and more correct method of learning the multiplication tables?

Reason is the faculty that identifies and integrates the evidence of the senses. Mathematics is not an exception. The items in the multiplication table need to be tied to reality. One method I can think of is the following:

Illustrate some items on the multiplication table using, for example. apples. 3 x 4 is illustrated using 3 groups of 4 apples, or 4 groups of 3 apples (after counting the number of groups and the number of in each group, count through to the total). Illustrate 3 x 1, then 3 x 2, and after a while, she should get the hang of it. Then see if she can "sort of guess", even without the apples. The idea is that even when memorizing, it is easier to remember something that "rhymes" (i.e. has some regularity, like the beats of counting 3's) than something that is just arbitrary and disconnected. After a while, she should be able to remember at least some higher items, without going through one by one from the lower numbers.

There are many regularities in the multiplication table, e.g. 2 x 2 = 4, 2 x 3 = 6, then it comes back to 2 x 7 = 14, 2 x 8 = 16. When reading the table to her, try to capitalize on these regularities when dealing with higher numbers.

Also, if you notice signs of her wanting to initiate the counting herself, let her. Maria Montesorri was able to do wonders by allowing children to initiate their own education.

Hope that helps. I'm not a professional teacher, though. Just a thinker. And maybe you should try something smaller than apples. :=)

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Perhaps try finding a mathematics computer program that combines learning arithmetic with playing simple games - I remember I used to enjoy them at primary school. Also, get her to practice multiplying 2 digit numbers using a pen and paper - over time I think this will end up making her ingrain the 1 digit times tables since you need to use these implicitly to multiply bigger numbers. I think the popular idea that you shouldnt do something advanced until youve mastered the basics is incorrect - doing more advanced things often lets you practice the basics in a more interesting way, and shines light on them.

Also, dont stress about not knowing the times tables for bigger numbers (ie between maybe 6 and 10) - its not that important. As long as you can 'work out' the answers by (eg) reasoning that since 7*5 is 35 and 7*2 is 14, 7*7 must be 35+14=49. You dont need to learn the 9 times table either, since you can just do it on your fingers using that cool way you get taught in primary school. I'm currently doing a masters degree in mathematics and I still use my fingers for the 9 times table, and need to explictly work out what 7*8 and 8*6 are (I never ingrained the 8 times table). Memorisation isnt that important really as long as you know the method for working these things out. The times tables for the 'lower' numbers (1-5) are important though so youll probably need a way to internalise them.

As I said, the most important thing is to learn the basic laws of arithmetic such as associativity, so you are able to work out that 8*7 = (4*7)+(4*7) and calculate it like that. I dont think this sort of thing is taught in schools to the extent that it should be - the focus tends to be on brute memorisation rather than learning techniques for working things out. Also once youve got this internalised, multiplying big numbers shouldnt be a problem either because you can just 'see' intuitively that (eg) 56*27 = (50*27)+(6*27) = (5*270)+(6*20)+(6*7) = (5*200 + 5*70) + (120) +(42) = (1000+350)+(120)+(42) = 1512 and do it in your head in seconds. I honestly think that the focus on memorisation rather than technique at primary school is the reason why most people are terrible at arithemetic and cant do basic multiplication involving numbers bigger than (say) 20 in their heads. Also, memorisation is exceptionally boring and is probably part of the reason why a lot of people grow up hating maths, and thinking its boring. It certainly is boring, the way its taught at school.

I'm not a teacher either and know nothing about the teaching of mathematics or developmental psychology, so take all this with a large amount of scepticism.

Edited by Hal
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  • 2 weeks later...
Get a grid, numbers along the side and down, and print the products in the grid.

Better still, do not just copy the products from some table in a book. Calculate the products yourself by repeated addition and write them in the table. Then put it aside and do the same again, and again, and again, and again, etc.. Pretty soon you will remember the products instead of having to derive them.

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I've heard good things about the Trachtenberg method of speed arithmetic, which I believe doesn't use multiplication tables.

It might be worth checking out,has someone here have any comments about the method?

If it has anything to do with Michelle Trachtenberg, I'm in! ;)

mptv1.bmp

(safe for work)

Edited by JordanLand
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  • 1 month later...

I'm on board with Hal. I think it's important to see the system thats inherent there. I remember having to memorize those in 3rd grade distinctly because I was agitated that others in the class were taking too long to memorize them. I had to recite them in front of the class in the same way as you describe but thought it was easy. In retrospect I realize that I never really memorized them at all. I just figured out that 3X3 meant 3 3's

4X3 meant 4 3's and so on. So when I recited them, I just figured out each one as I went. With the larger numbers of course, it helps to break them down as Hal describes in order to keep them within the confines of your crow epistomology.

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I was always extremely slow at these types of rote learning exercises in school because I found them extremely boring and pointless. It's funny that I would still get all A's on all the tests though. :lol: I remember when I was in about 8'th grade in like pre-algebra or something and I litterally did almost none of the pointless and time-consuming homework or exercise's but still completely aced every test and the final but the jerk still failed me because I didn't do "the required work". I can't wait to get my son out of "public" schools and into a local Montessori charter school next fall just for this type of nonsense.

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