I spent the last three weeks out of the country--in what was my first big break from my computer in a very long time. One result: I found myself watching helplessly (from my iPhone) as my blog fired off prewritten posts automatically while an article that I would have loved to have blogged about immediately sent shockwaves through the blogosphere. That article, of course, was Elizabeth Green's New York Times Magazine piece Why Do Americans Stink at Math?

Many people have critiqued this article, most recently Barry Garelick. I'd like simply to contribute a list of errata, by which I mean egregious journalist errors of the sort that define all too much education journalism.

**1. On Brazilian street vendors**

Green writes:

Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.No: the cognitive science research suggests that contextual skills of the Brazilian street vendor sort only get you so far, and that decontextualized learning, of the traditional classroom sort, are essential for abstract math. (See, for example, Anderson et al's Situated Learning and Education.)

**2. On Japanese vs. U.S. classrooms:**

In discussing Reform Math, Green writes that "..countries like Japan have implemented a similar approach with great success." Key elements of Reform Math, of course, are child-centered discovery and group work

But claims like this were debunked years ago by Alan Siegel's analysis of Stigler et al's highly influential TIMSS Videotape Classroom Study. Reviewing the raw data, Siegel reviews and analyzes the excerpts that were the basis for this study, explaining what they actually do show, as opposed to what they were claimed to show:

- The excerpts do not support the suggestion that in Japan, “[The] problem . . . comes first [and] . . . the student has . . . to invent his or her own solutions.”
- The evidence does suggest that in Japan, “Students rarely work in small groups to solve problems until they have worked first by themselves.”
- Similarly, the evidence gives little weight to the notion
that “Japanese teachers, in certain respects, come closer to implementing
the spirit of current ideas advanced by U.S. reformers than do U.S.
teachers.”
- The evidence does confirm that, “In other respects, Japanese lessons do not follow such reform guidelines. They include more lecturing and demonstration than even the more traditional U.S. lessons . . ..”

By 1995, when American researchers videotaped eighth-grade classrooms in the United States and Japan, Japanese schools had overwhelmingly traded the old “I, We, You” script for “You, Y’all, We.Where "you y'all we" entails:

a single “problem of the day,” designed to let students struggle toward it — first on their own (You), then in peer groups (Y’all) and finally as a whole class (We).But what the TIMMS video tapes of Japanese classrooms actually show, per Siegel's paper, are not you y'all we, but I you (optional y'all) I/we. The teachers go over what the class did yesterday spends a fair amount of time setting up a new problem (I); they then have students work on their own (you), with peer groups just one of several options for weaker students and not required optional (y'all); and back and forth with whole class, carefully directed by teacher every step of the way ("We," with a heavy dose of "I").

As Siegel puts it:

The excerpts show Japanese classes featuring a finely timed series of mini-lessons that alternate between grappling-motivated instruction on how to apply solution methods, and well chosen challenge exercises designed to instill a deep understanding of the solution methods just reviewed. No other interpretation is possible.

**3. On American math classes**

Green characterizes "Most American math classes" as "focusing only on procedures." She adds that American math classes don't "look much different than they did before the reforms" and that "Textbooks, too, barely changed, despite publishers’ claims to the contrary."

One has only to walk into a math class at a model elementary or middle school, or look at an Investigations or Everyday Math (etc.) textbook, to see how wrong these claims are.

Indeed, a classroom lesson the Green describes as an exemplary role model is, unfortunately, all too common:

One day, a student made a “conjecture” that reflected a common misconception among children. The fraction 5 / 6, the student argued, goes on the same place on the number line as 5 / 12. For the rest of the class period, the student listened as a lineup of peers detailed all the reasons the two numbers couldn’t possibly be equivalent, even though they had the same numerator.While her eager claims about how effective this "innovative" classroom is are supported by the vaguest and most anecdotal of "data"--if you can even call it that:

Over the years, observers who have studied Lampert’s classroom have found that students learn an unusual amount of math. Rather than forgetting algorithms, they retain and even understand them. One boy who began fifth grade declaring math to be his worst subject ended it able to solve multiplication, long division and fraction problems, not to mention simple multivariable equations. It’s hard to look at Lampert’s results without concluding that with the help of a great teacher, even Americans can become the so-called math people we don’t think we are.

**4. On the cure**

To cure our innumeracy, we will have to accept that the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work. 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.A total non sequitur, followed by the obligatory strawman caricature of traditional math.

A better way to conclude the article would have been with a quote hidden deeply within it--one by Magdalene Lampert, whose "innovative" classroom was described above:

“In the hands of unprepared teachers,” Lampert says, “alternative algorithms are worse than just teaching them standard algorithms."

## 4 comments:

That last quote is rather horrifying, since it implies that teaching the standard algorithm is a terrible thing to do.

Indeed. But that what American math "reformers" suck with their mother's milk (i.e., in ed schools).

But at least Lampert recognizes that teaching skills almost always works, with most kids and most teachers. Teaching those "reformers'" highfalutin ideas works with one teacher in fifty and one child in twenty.

Hello,

I am a Japanese and have read the NY Times article "Why Do Americans Stink at Math?", which discusses a lot about Japan.

However, I have to say that Ms. Green's account of Japanese education is very misleading, as pointed out also by Dr. Tom Loveless in the Brown Center Chalkboard blog.

So I wrote her a letter and put it in my blog: http://jukuyobiko.blogspot.jp/2014/08/big-doubts-on-ny-times-article-why-do.html

I would like to correct misunderstanding, because it is very sad to see that many people are discussing on the basis of the misleading report.

Thank you.

Watanabe Manabu: Nice article. Thanks for taking the time to share it.

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