I’ve had something on my mind for a long time that greatly bothers me: the multiplication table. This is because I think that education should be fun — full stop. Memorizing the multiplication table is not fun. But more than that, I believe they are the source of most people’s hatred of math. At the same time, I’ve long thought that one should probably know them. And that created a conflict in me because I thought that it was really only possible to know them by memorizing them. But the other day it occurred to be what hogwash that is.
To begin with, I’m really good at math. Yet I’m pretty flaky on the multiplication table. I remember in the sixth grade, I had this teacher who seemed more like a drill sergeant. And he used to do this thing where he would go desk by desk asking each student one question, “Seven times eight?” He went sequentially through the table and the desks, so I always calculated which question I would get so I could figure it out and say it the moment he asked me. In that case, there was clearly some mathematics education going on for me, but it had nothing to do with the multiplication table.
The rationale for knowing your multiplication table is that if you know them, then you can do things like multiply and divide arbitrarily large numbers. But if that’s true, why were we taught the table from 1 through 12? It should have been 1 through 9, right? You can calculate 11×12 — you don’t need to memorize that it is 132. And I think the reason for it is that it was a way to fill the curriculum. It didn’t take long enough to force the students to learn up to 9×9, so they went up to 12.
And as you get into higher math, you don’t even much deal with numbers. And for people like me who are naturals at math, it never is about numbers but rather elaborate games you make up. You think about things like the way the nines go down by one as you go up the table, and elevens go in the opposite direction. If you are lucky, you get introduced to octal and start seeing numbers in a whole new way. But you are unlikely to ever play with numbers if they are forced on you in the same way that the ordering of the alphabet is. (I am still quite fuzzy about which letters go before others without the help of the song.)
Multiplication is just a matter of counting. I have never memorized what 6×7 is. Instead, I know that 6×6 is 36, and so I know 6×7 must be 6 more than that, which is 36+6, which is 42. I don’t find this fun, but I did think it was a nifty trick when I was a kid — one I was never taught. And I fear that many if not most children memorize their multiplication table without having a profound sense that all they are doing is counting. That’s sad.
As everyone should know, math is extremely abstract. That’s why I say it is the closest thing to theology, and certainly it is the closest I ever get to God. But the mindless memorization of the multiplication table is not just boring. For many students, it turns math into alchemy. Sure, it’s abstract. But much more, it is mysterious in the same way God is: unknowable. And why even try?
There is no need for children to learn the multiplication table. I have a simple proof:
- What is 9×9?
- 9×9 = 9+9+9+9+9+9+9+9+9.