Monday, July 28, 2008


Innumeracy: Why can't Johnny add?

Last week, I was in a local cafe, ordered a few things, and got a bill that came to 9 dollars and 46 cents. I gave the barista a ten, she entered the number into the cash register, and it told her I was owed 54 cents in change. As she did that, I’d found a penny, said, “Here’s a penny,” and gave it to her.

She cheerfully took the coin and put it in the register. But then she started picking up and putting down coins, touching all the coin bins in the drawer, making one false start after another in an attempt to give me my change. She had no idea what to do, and thanked me when I said, “55 cents.”

This isn’t a one-off occurrence, of course, but just the latest — it happens all the time, and you’ve all surely run into it too. It’s easy to blame over-reliance on automation (“In my day, why, you had to make change the old-fashioned way, by hand. And, by gum, you knew how! In the snow. Uphill in both directions.”), but, while that might be a factor, it’s not that simple. Consider another story:

About 25 years ago, I went into a record store[1] a few weeks before Christmas, and picked up a bunch of records, some for myself and some to give as gifts. The total came to about $80. The store had a mechanical (not computerized) cash register, and a sheet of paper next to it that helped the cashier — in this case, a 16-year-old high-school student, hired to help for the pre-Christmas rush — figure the sales tax.

Only, the tax table on the crib sheet only went up to $70, and, as in the more recent story, the cashier was at a complete loss. For a moment, I thought she was going to ask me to put a couple of records back, or maybe ring them up separately, in order to bring the total below $70. But she called the manager over, and the manager showed her how to use the calculator to multiply the total by .05 — I would have looked up the tax on $70 and on $10, and then added them, but either way works (though the manager’s method requires her to know the tax rate, and to do rounding, so it’s arguably harder).

The issue here isn’t that the cashier in 1983 didn’t know how to add 70 and 10 to get 80, or that the barista in 2008 couldn’t add 54 and 1 to get 55. It’s that neither knew how to solve the problem, and it comes down to a common word, derived from Arabic: algebra. It scares many people, and many think it’s irrelevant to them — they’re not going to be accountants or math teachers, after all.

But thinking that knowing algebra is irrelevant to you is like thinking that knowing how to read is irrelevant because you’re not going to be a writer nor teach literature. Simple algebra is a basic skill that everyone needs every day, and innumeracy is as crippling as illiteracy in many ways.

A $45 item is on sale for 30% off. How much will I have to pay for it? Algebra.

Gasoline costs $4.39 per gallon. I have $25. How many gallons can I get? Algebra.

An 8.5 ounce can of peas sells for 50 cents. A package of frozen peas is 89 cents for 16 ounces. Which is cheaper per ounce? Algebra.

The restaurant bill, including tax, comes to $37. How much should I leave for a tip? Algebra.

How much change do I get back if I pay $10.01 for $9.46 worth of goods? Algebra.

It’s basic, and we have to teach it effectively. There’s just no excuse for a normally functioning student to get to high school — and even graduate — without having a working knowledge of this real-world sort of mathematics. And NCLB competency tests won’t get us there.

[1] Yes, LPs, twelve-inch black vinyl things. No Internet, no Amazon-dot-com. It was the Dark Ages.


Anonymous said...

I only hope those were 33 rpm LPs and not 45's!


The Ridger, FCD said...

If gas costs $4 a gallon, and a station five miles away is selling it for $3.95, and I get 12 miles to the gallon, am I really saving money when I drive over and back to pump 20 gallons?

W.M. Irwin said...

It seems to be a little more than just not knowing algebra, Barry. Unless someone stops and performs the math on paper, those examples you cited are going to require some mental computation (with some estimating probably needed in some cases). And along with that, the ability to store a partial solution to the problem temporarily in memory for later recall to make the final solution. Some people have never developed this ability! And then there are those who have no attention span to speak of, anyway.

Barry Leiba said...

Bill: Yes, while the stories I told involve dead-simple things, the examples I gave are harder to do in one's head. But my point was that these are the problems we need to know how to solve, and that too many people don't know how to approach them.

Julio Cesar: He-he-he... yes, LPs. (I did have some 78s when I was a kid, though.)