"up to 10 x 10": have you chaps gone metric? In my Scottish school we did up to 12x12 plus "14" up to 6x14 and "16" up to 6x16, plus 14x14 and 16x16. But many of us could do it before we started school, as I suppose many of you could too.

If my kids are any indication -- NEVER. They were never forced to memorize anything in public school. All the memorizing had to happen at home or it wouldn't get done.

My class only did 10 x 10, though going up to 12 x 12 certainly doesn't take much additional effort. Concentrating on 10 x 10 does make sense, however: for those, there is no substitute, whereas once one goes further, the obvious question is where to stop. I suppose it all has to do with whether one looks upon the exercise as for its own sake, or as preparation for more complex operations.

I suppose a survey of worldwide multiplication table memorization standards might be quite interesting. My Indian and Pakistani friends are all quite keen on early memorization, for example. The Scottish pattern seems quite interesting. Why leave out 13 and 15, for example? And why 14 and 16 only up to 6x?

From my one and a half semesters teaching college-level math, I suspect that too many high-school students use their calculators as a crutch, even for such a simple job as multiplication. I suspect that many have never seen a flash-card.

So, when I tell them they can't use calculators on an algebra quiz, some panic. (I don't want to tell them that it's because most of the calculators they have can give determinants and row-echelon-form of the matrices I assign on the quiz...and I don't want to know how well they can use their calculator, I want to know whether they understand what these operations are, and can reproduce them on paper. And I don't even want to attempt to explain that the graphing calculators can also do intersections, slopes, derivatives, integrals, Taylor expansions, and other Calc stuff. They might think that the calculator is magic, when it is simply an extremely powerful hand-held computer.)

If a student memorizes the 14's and 16's up to 6x, they will probably catch on to the pattern that each one is twice the products of the same factor with 7 and 8, respectively. Thus, when they need 16x9, they'll look at 8x9=72, and double it to get 144.

The products of 15 are interesting--you can produce 15x12 quickly if you put it in this form: (10+5)x12=120+60=180. Since the 5-product is half of the 10-product, it doesn't require much extra work. Take the number, multiply by ten, and then add that to half of the 10-multiple. A talented student can do this in his head and produce the answer in approximately the same time than the student who has memorized the 15's from a multiplication table.

Leaving out 13 seems a bit odd--13 is prime, so it can't be reduced to a different set of factors. But 7x13 can become 7x(10+3), or (70+21)=91. Because the 10x part is easy, the product should be producable from the 10x10 grid. However, there's slightly more computation time spent for a non-memorizer of 13's than there is for a memorizer of 13's.

Posted by: karrde on October 9, 2006 12:22 AM

David, I suspect we added (parts of) 16 and 14 because there are 16 ounces in a pound and 14 pounds in a stone (I know you don't use "stones", but we did). Similarly, 12 is handy when you have twelve pennies to the shilling and you sell lots of items by the dozen.

A few years ago I went to a bureau de change in London and the guy at the desk (who ought to be familiar with figures, right?) used a calculator to work out how many French francs he should give me for £100 at an echange rate of 10FF = £1 !

Wow...I think I must be the only non-Brit on here.

I learned..back in the 80's up to 12x12.

I always considered that to be the standard.

We had tests where you were timed and quized on the times tables. You had to retake it until you could do all of them in under a certain amount of time.

But then again, I went to an American private school(same as your public ones in Britain).

As a bumbling idiot when it comes to advanced Math at least I can be proud that at least I've got the basics down. AND Calculus has, in fact, never had any bearing on my career.