Yes, Curriculum and Pedagogy Matter (Maybe)

This week’s NY Times Magazine has an article “Why Do Americans Stink at Math” that breathlessly focuses on the need for changing how we teach math and what math we teach–that is, pedagogy and curriculum. While the article, perhaps so it could be published at the NYT, repeats some Things We All Know and Yet Are Untrue™ (e.g., Shanghai’s PISA test scores are overinflated, while the U.S. scores should be higher as they overweight poor students), it does remind people that there’s more to education that just busting teachers unions.

There are glowing descriptions of a Japanese educator who is trying to improve the U.S. mathematics curriculum–it sounds like a good system (and is somewhat similar to the way I was taught math in grade school). I’m inclined to agree with the article: after all, I have argued many, many, many times that what you teach (curriculum) and how you teach (pedagogy) matter. It’s also important that we train teachers in how to use these methods–just dropping off some books and materials won’t cut it (though that would be a good start…). This, of course, costs money. And I agree wholeheartedly that “We will have to come to see math not as a list of rules to be memorized but as a way of looking at the world that really makes sense.”

But happy stories aren’t necessarily good policy.

One problem I have with the article–again, an article I want to agree with–is the counterfactual of Massachusetts. Keep in mind that the mathematics described in the article is largely grade school and junior high school math, so even if one is inclined to take the PISA data at face value, the TIMMS data (which test fourth and eighth graders) are far more relevant. In those data, Massachusetts does as well as Japan. As far as I’m aware, Massachusetts teaches math using the same god-awful methods everyone else in the U.S. does, so it’s not clear that pedagogy matters so much. It might have much to do with Massachusetts being one of the best places to be a child in the U.S.

The article also doesn’t present any data that the methods, when used in the U.S., increase math proficiency. Seems kinda important.

This is what happens when reporters parachute in to a very complex area and then fixate on a storyline. Though if it leads to some improvements in teaching, that’s probably a good thing.

Related note on how not to commit journalism: A lot of people have fixated on this part of the story:

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

First of all, that was three decades ago–many grade school parents hadn’t been born yet or were infants. It says absolutely nothing about how kids would handle this question today. But it’s SHOCKING!!! This is pretty shitty journalism (more like fear-mongering). Second, there are no comparative data. Were people in other countries just as stupid in the early 1980s? Dunno. Third, speaking of which, thirds are weird. While that’s not an excuse, I’ll speculate that people would have done better with halves, fourths, or fifths. Thirds are weird, and people just don’t use them that often.

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3 Responses to Yes, Curriculum and Pedagogy Matter (Maybe)

  1. Min says:

    Is the US an innumerate society? Yes. Has it always been innumerate? Probably. Certainly within my lifetime. Have we gotten better? Yes. I remember the math curriculum when I was in school, and I see online what students are learning now. Middle school kids are already a year or two ahead of where we were back then.

    If we are innumerate, it is because we do not value numeracy. How many pundits, our public intellectuals, admit, almost with pride, that they could not balance their checkbooks? How many NYT editors and columnists could pass 8th grade math? Do they care?

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  3. Jim Sweeney says:

    The only reason we teach fractions to kids is because we refuse to switch to the metric system. We’re still dealing with 3/8 inch or 1/4 cup, when we should be using 1 cm or 60 ml. Manipulating fractions is trivial once you’ve mastered algebra, but instead it’s taught as a separate subject, and it’s a major stumbling block for kids. I used to know another mathematician who had the same view.

    If we want to continue using binary divisions we should use octal and write 3/4 as 0.6, or 0.C in hexadecimal. It makes addition and multiplication trivial. We can do this. We have the technology.

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