We Don’t Need to Memorize the Multiplication Table

Octal Multiplication TableI’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.

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.

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:

  1. What is 9×9?
  2. 9×9 = 9+9+9+9+9+9+9+9+9.
  3. QED.

Political Science 101 for Political Reporters

Bill ClintonI’m a big fan of Brian Beutler. And I agree with his conclusion in his recent article, The Trump Crack-Up Is Just the Beginning of the Republican Civil War. His point is that even if Trump loses the general election badly, the Republican Party won’t change. But he pushed one of the most common and ignorant claims about the Democratic Party, and more generally political science.

According to Beutler, after the three presidential losses (1980, 1984, and 1988), the Democratic Party reassessed itself and decided that it had to move to the right. Thus brought Bill Clinton and victory. That’s a nice narrative. But it’s totally wrong. Carter wasn’t a liberal. He was the beginning of the emergence of what would become the New Democrats. What’s more, he was — as were Walter Mondale and Michael Dukakis after him — part of that new breed of Democrats who weren’t really ideological but just technocratic.

We look back on them now as liberal, not because of their policies, but because they lost. Remember, I was around during Bill Clinton’s term. And according to the conservative movement, he wasn’t just liberal, he was a radical — a communist, even. That’s because Democrats are always leftist radicals in the minds of conservatives. And this is why it makes no sense to try to take welfare “off the table.” Did Bill Clinton ending welfare as we know it make the Democratic Party any less prone to attacks that it was the party of welfare recipients? Of course not!

It would have been very surprising if the Democrats had won any of those races, because the fundamentals were not only against them, they were against them forcefully.

But as I’ve shown elsewhere, and as is documented with scientific precision in Lynn Vavreck’s book, The Message Matters, the economic fundamentals favored the Republicans in 1980, 1984, and 1988. It would have been very surprising if the Democrats had won any of those races, because the fundamentals were not only against them, they were against them forcefully. Carter eked out a slight victory in 1976 because the fundamentals were only against him slightly.

Neither the nation nor the Democratic Party base was begging for the Democratic Party to move to the right in 1992. Bill Clinton was not the answer to the previous three elections. He was, however, a gifted politician in a party that had mostly been taken over by conservative elites. The only thing the party was responding to was the desires of powerful people in or aligned with the DLC.

I find this stuff really annoying because it just isn’t hard. My job — what people are willing to pay me for — is technology writing. If you want me to make Fortran 77 interesting and understandable, I’m your man. I have a basic understanding of computer science and programming. But political writers generally don’t know anything about political science. And it is particularly sad in the case of Brian Beutler, because he’s both smart and insightful. But how about learning a little about the science of it? Instead, it is just fine to depend upon what everyone “knows” — which turns out to be untrue.

So yes, the Republican Party won’t change even if Trump only manages to get 30% of the vote. But the Democratic Party is no different. What’s more, why is the presidency such a big deal? Does political science teach us that the presidency is all that matters? No, of course not. And as it is, 31 state legislatures are controlled by Republicans, compared to just 11 by Democrats! They also control the Senate and the House. And after the next election, they will almost certainly still control the House — and might control the Senate. It seems to me that the Republican Party is doing okay.

This all disturbs me. But we aren’t going to change it unless we can see the truth and look clearly at the political science. And believing that Bill Clinton was a response to political changes in the country is perhaps the biggest part of the problem. Because now conservatives win even when the Republican Party loses. And someone as smart as Brian Beutler should understand that.