The wrong way to teach math?

This post is by James.

I recently ran into a New York Times article by Andrew Hacker, provocatively titled “The wrong way to teach math?”  You can read it at the link here.  Looking at his other published works, which includes “Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids – and What We Can Do About It” and an article called “Is Algebra Necessary?” published in the New York Times, it’s clear he’s made a bit of a career challenging common assumptions in math education.  This article is more of the same.

I doubt I agree with all of his conclusions, but I found this article to be a very good read, and I agree with many of its important points.  If I had to summarize it in a single sentence, it would be:

“We need to teach people how to solve practical word problems rather than advanced mathematics.”

If you’ve read the rest of this site, you can tell that somewhat agree with the spirit of this statement.  My opinion is that if you can’t solve word problems, you can’t really do math.  Nobody is fluent in a language if they can’t speak it with somebody they don’t know in a situation they’ve never seen before.

My biggest qualm with the article is that I think it underplays the advanced mathematics more than it should and overplays the success we have in K-12.  For instance, near the end of the article, he says:

We teach arithmetic quite well in early grades, so that most people can do addition through division.  We then send students straight to geometry and algebra, on a sequence ending in calculus. Some thrive throughout this progression, but many are left behind.

I would argue that ideally, the arithmetic curriculum should be more similar to that of geometry so that when students hit geometry, it isn’t a big change but a continuation of what they’ve been doing the whole time.  Real-world arithmetic is very much as complex as geometry and we need to stop hiding that fact.

On the other hand, if we had to have either the current math education system or Andrew Hacker’s system, I would probably go with his as being more practical.  I don’t think those are the only two choices, though.

Despite this qualm, he makes really good points about the kind of math people actually run into in real life.  He teaches a class at Queens College which he calls “Numeracy 101,” which focuses on making students fluent in real-world math.  This includes vital things like being able to read a graph of real-world data without being scammed by clever tricks often used by big companies and governments.  It also includes the ability to estimate how much something would cost.  If you want more details, I suggest that you read the article.

So what do you think?  I’m pretty sure he’s overstated his case, but I can’t argue that the kind of things he’s talking about teaching are pretty useful.

Edited for clarity.

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