Teaching pills 1: Primary Maths. The easy way to multiply

What I love of maths teaching is that you are, may be more than in any other subject, teaching a way of thinking. To be honest I don't really know how multiplying is usually taught in the UK, but in my country in most cases it's still regretfully taught as a memoristic skill, with tables from 1 to 10 that children need to memorize and repeat until they automatically can throw up the result of any single-digit multiplication. In my opinion this is not only a rough and boring way of learning something, it also denies the opportunity of logical and deductive thinking to the children and spoils a chance to reinforce their self-confidence and their understanding of how maths work, the relationship between adding and multiplying, substracting and dividing, and so on. In short, wrong way of multiplying teaching. Moreover, it is hard, takes time and can create an ugly -and mistaken- impression that maths are boring. I bet I can teach any kid who pays attention to multiply in just one session and making it fun. I have tried it before with kids in Nicaragua, kids who had a fairly large lack of previous knowledge -which might have been good, at the end- and most of them got it quickly and, with a few hours of practising, were able to do it by themselves. Of course I haven't "invented" (though "discovered" would be more accurate) this teaching strategy, I am sure it's broadly used, with subtle differences, all over the world. Twenty-five years ago I was taught to multiply with part of this at my school Aire Lliure, which used to be -at least at its origin- an impressive education cooperative, a school based on a sort of libertarian pedagogy, teching how to think instead of what to think. I became a fan and I have just completed it.

Here it comes: My easy way of multiplying that promotes deductive thinking is based in two well-known mnemonic rule -the 9 and 5 rule- which most teachers use to teach to multiply by 5 and 9; the natural ability of mentally adding few times (up to 4); and memorizing just two multiplications: 6x6= 36 and 7x8 = 56. Once you know this, and supposing you are able to add and substract, you have all you need to mentally deduce any single-digit multiplication. Children don't need to memorize anything else and, more important, they'll feel good every time they deduce an unknown one, reinforcing their confidence and their maths liking, which may be really useful for their future.

I guess most of you have got it straight away, but I'm going to explain it with a bit more of detail just in case anyone studied laws -sorry, solicitor and lawyer friends, I know the truth can be painful. First, the mnemonic rules: You all know multiplying by five is easy, just the half ten (v.gr. 8x5 = [the half ten of 8] 40). Most of you might also know that multiplying by nine is very easy indeed, just the previous ten and what's missing to get to nine. It is to say: if you want to multiply, for instance, 6x9, you take the previous ten of six (5, fifty-something), and the unit is what's missing to make nine: 4. So, 6x9= 54. This works. Ok, we've got every single number multiplied by 5 or 9. Then, adding up to four times can be done mentally without effort. So, we have deduced every single digit multiplied by 1 to 5 and by 9. Now we have these two ops, 6x6=36 and 7x8=56, which we'd better memorize (we could eventually add them but I have realized it's a bit tricky for children) and now we have a supporting point to get to every single-digit multiplication directly or by just adding or substracting the number once. Think about any single-digit multiplication, let's say 6x7? the child mental process would go: Ok, I know 6x6=36, so if I add 6 I'll have 6x7! 36+6=42. Good. 8x3? Ok, eight and eight, sixteen, and eight twenty-four. Easy. 8x6? Humpf, well I know 8x7=56, so if I substract 8 I'll have 8x6 -> 56-8=48. Or either I know 6x6=36 I add six twice and I'll have 8x6 -> 36+6=42 +6= 48. And so on, and so forth.

 It's a perfect system, and despite it may look a bit complicated in writing it's very easy indeed to do mentally. What I love of this teaching strategy is that it focus not in memoristic learning but in deductive abilities. It relates multiplying to adding, which is nice, and to substracting also, which is even better because it gives the child a more comprehensive understanding of mathematic relationships, but the important point is that it reinforces a lot their self-confidence and transforms the maths in a deductive game, something that is worth and fun. As it should be.