A bunch of people have been sending me links to a USA Today article about a math professor who wants to change math education. Specifically, he wants to stop teaching fractions, and de-emphasize manual computation like multiplication and long division.
Frankly, reading about it, I’m pissed off by both sides of the argument.
On one side, you’ve got Professor DeTurck, who wants to abolish fractions, in favor of teaching children only decimals. This is a perfect example of an out-of-touch academic making idiotic proposals.
To be abundantly clear, I don’t think that academics are, in general, out of touch, clueless, ignorant fools. I’m not a subscriber to the “ivory tower” view of academia. But like any other group, academics have idiot members who do their best to reinforce the negative stereotypes about the group.
But Professor DeTurck has clearly not actually looked at how kids learn about numbers. In fact, I don’t think he’s looked at how normal people actually understand numbers. Many (most?) adults actually don’t really understand decimals. Try asking a random adult what
20% means – you’ll get some astonishing answers.
Back in grad school, my wife and I moved between two different apartments in the same
complex. The rent in one was $600. The rent in the other was $650. We moved on the 12th day
of january. When we moved, the rental agency said we needed to pay the pro-rated difference
between the two rents. By their calculation, that meant that we owed them $60. I tried
arguing with the agent: how can pro-rating 19/31 of $50 be larger that $50? And the
idiot agent kept answering: “I plug the number into my computer, and that’s what it says.” No
matter how many times I kept pointing out: “the difference between the rents is $50. If we
moved in on the first, that meant we needed to pay $50 for the month. If we moved in after
the first, we’d by paying part of that $50.” And the agent agreed with me. So we
moved in on the 12th. That means we should be paying part of $50. Again, the agent
agreed. So how much do we owe? $60. Is $60 part of $50? According to the agent “My
computer says it is.”. Eventually, I gave up in disgust.
Dr. DeTurck argues that the scenario above is fine and dandy. He doesn’t think that understanding what parts means, or how numbers work is worth teaching to kids. Just let
them use calculators and decimals.
The understanding of numbers starts with whole numbers. From there, you move from whole to parts. Fractions are parts. Kids understand fractions in terms of a very tactile representation of parts. 1/2 means what you get cut something into two equal pieces: each piece is one half of the original. 1/3 is what you get when you cut it into three equal pieces. And so on. It’s very concrete, very tactile. It matches our natural intuitions about things: “I want a cookie for a snack, but my mommy says I can’t have one because it’s too big. So can I have a piece of one?” That’s how my kids learned the basic idea of fractions.
According to Professor DeTurck, they should have learned “Can I have 0.5 cookies?”
Abandoning fractions to teach only decimals does exactly the opposite of what we should do in teaching math. The biggest problem, in my experience, with how math is taught is that we focus on mechanics to the exclusion of understanding. Switching to pure decimals without fractions is carrying that to a ridiculous extreme. What does 0.3 mean? It means 3/10 – three parts of something split into 10. If you do away with the fraction, then the decimal representations are meaningless. You can’t explain what they really mean without using fractions – because they’re just an alternative way of writing fractions. So what Professor DeTurck’s proposal comes down to is: teach math without providing any intuition for what things mean. Just throw the decimals at kids, and let them solve problems with calculators. None of it means anything. It’s just fiddling around with meaningless symbols.
How is that improving math education?
DeTurck also wants to de-emphasize manual computation. He doesn’t think kids need to know how to do long division, or multiplication, or square roots. After all, why should they do
those things by hand? A calculator can do it!
The reason to know how to do it by hand is because doing it by hand teaches you to understand what it means, and how it works. If DeTurck’s proposals are accepted by schools, what will happen is that kids will end up with even less of a sense of what numbers all mean!
On the other side, many of the responses I’ve seen have been like this one from the
USA Today article: “Math is hard. The idea that somehow we’re going to make math just fun is just a dream.”
Math is fun! It’s idiots like DeTurck and friends who ruin the fun of it, by turning it into nothing but repetitive rote exercises that don’t mean anything. Anyone who says that math can’t be fun should be eternally banned from teaching math.
Last year, I went to my daughter’s first grade class, and did a project with them, where each kid made a four-column abacus. Then I showed them how to add big numbers on the abacus. They were so excited! The idea of being able to do it was thrilling, and the idea that they made this thing that let them do it, they were so happy, having so much fun. That’s how math should be. Of course there’s rote – just like there is for reading. You’ve got to memorize some things, you’ve got to learn the skills, and practice them. And practice isn’t always fun. But teaching math should make time for the joy of being able to do something new – and make sure that it’s taught as something fun.
I look at my daughter’s second grade class now. She’s got a wonderful teacher. And the teacher really does make math fun for the kids. Sure, it’s hard sometimes. But it’s also fun, and she’s great at making the kids see that.
Both DeTurck and his quoted opponent don’t believe that you should do that. DeTurck thinks it should be nothing but rote. And his opponent thinks it should be hard, not fun.
They’re both idiots.