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Why Americans Stink at Math

9/25/2014

 
This column originally appeared at RealClearEducation.com on July 29, 2014

Over the weekend the New York Times Magazine ran an article titled “Why do Americans Stink at Math?”  by Elizabeth Green. The article is as much an explanation of why it’s so hard not to stink as an explication of our problems. But I think in warning about the rough road of math improvement, the author may not have even gone far enough.

The nub of her argument is this. American stink at math because the methods used to teach it are rote, don’t lead to transfer to the real world, and lead to shallow understanding. There are pedagogical methods that lead to much deeper understanding. U.S. researchers pioneered these methods and Japanese student achievement took off when the Japanese educational system adopted them.

Green points to a particular pedagogical method as being vital to deeper understanding. Traditional classrooms are characterized by the phrase “I, we, you.” The teacher models a new mathematical procedure, the whole class practices it, and then individual students try it on their own. That’s the method that leads to rote, shallow knowledge. More desirable is “You, Y’all, We.” The teacher presents a problem which students try to solve on their own. Then they meet in small groups to compare and discuss the solutions they’ve devised. Finally, the groups share their ideas as a whole class.

Why don’t US teachers use this method? In the US, initiatives to promote them are adopted every thirty years or so—New Math in the 60’s, National Council of Teachers of Mathematics Standards in the late ‘80’s--but they never gain traction. (Green treats the Common Core as another effort to bring a different pedagogy to classrooms. It may be interpreted that way by some, but it’s a set of standards, not a pedagogical method or curriculum.)

Green says there are two main problems: lack of support for teachers, and the fact that teachers must understand math better to use these methods. I think both reasons are right, but there’s more to it than that.

For a teacher who has not used the “You, Y’all, We” method it’s this bound to be a radical departure from her experience. A few days of professional development is not remotely enough training, but that’s typical of what American school systems provide. As Green notes, Japanese teachers have significant time built into their week to observe one another teach, and to confer.



Green’s also right when she points out that teaching mathematics in a way that leads to deep understanding in children requires that teachers themselves understand math deeply. As products of the American system, most don’t.

Green’s take is that if you hand down a mandate from on high “teach this way” with little training, and hand it to people with a shaky grasp of the foundations of math, the result is predictable; you get the fuzzy crap in classroom that’s probably worse than the mindless memorization that characterizes the worst of the “I, we, you” method.

But I think there are other factors that make improving math even tougher than Green says.

First, the “You, Y’all, We” method is much harder, and not just because you need to understand math more deeply. It’s more difficult because you must make more decisions during class, in the moment. When a group comes up with a solution that is on the wrong track, what do you do? Do you try to get the class to see where it went wrong right away, or do you let them continue, and play out the consequences of the their solution? Once you’ve decided that, what exactly will you say to try to nudge them in that direction?

As a college instructor I’ve always thought that it’s a hell of a lot easier to lecture than to lead a discussion. I can only imagine that leading a classroom of younger students is that much harder.

There are also significant cultural obstacles to American adoption of this method. Green notes that Japanese teachers engage in “lesson study” together, in which one teacher presents a lesson, and the others discuss it in detail. This is a key solution to the problem I mentioned; teachers discuss how students commonly react during a particular lesson, and discuss the best way to respond. That way, they are not thinking in the moment, but know what to do.

The assumption is that teachers are finding, if not the one best way to get an idea across, then a damn good one. As Green notes, that often gets down to details such as which two digit numbers to use for particular example. An expectation goes with this method; that everyone will change their classroom practice according to the outcome of lesson study. This is a significant hit to teacher autonomy, and not one that American teachers are used to. It’s also noteworthy that there is no concept here of honoring or even considering differences among students. It’s assumed they will all do the same work at the same time.

The big picture Green offers is, I think, accurate (even if I might quibble with some details). Most students do not understand math well enough, and the Japanese have offered an example of one way to get there. As much as Green warns of the challenges in Americans broadly emulating this method, I think she may underestimate how hard it would be. It may be more productive to try to find some other technique to give students the math competence we aspire to.

Francis Poissant
9/25/2014 11:37:44 am

Hi, I exactly agree with you that it is difficult to use that method of discovery (You, Y’all, We). It sounds as an sociocontructivist approch of teaching and what we sould say it's that kind of approch is not effective an give usually worst result than an instructional approch as many serious studies point out. It is summarised in the last years by the autralian John Hattie (Visible Learning: A Synthesis of Over 800 Meta-Analyses) who explain what are effective teaching strategies base on experimental results, not only on some far away cases.

As ususally we have here an agglomeration of traditionnal an some of his new ways to achieve a good instruction in maths and others mathers...

I'm teaching math and I see that leave child searching for their understanding takes too much wasting time than guide them to the effective knowledges. When the are more confident of their knowledges, you can give them a challenge and it could be good for a better understandings, but not at the start. The find tune of teaching is to challenge at the good time when they are ready for it. Or, challenge step by step, with many strategies. Here, we have a classic opposition of two methods to reach at the conclusion that one is good and the other is completly bad. Real life is more complex than that.

A common argument of that network of thinkers is to take an so far away culture (here Japonese) suppose to apply their so good approch. No one can really verify the point...Someone can explain what really the japonese method use actually, not the official, but the real thing. We should ask for investigation, for sure.

Sorry for my bad english.

Jamea Mannion
9/26/2014 06:13:44 am

Interesting piece. One quibble - "the Japanese"? How about "our colleagues in Japan"?!! Please don't feel the need to approve this comment, but I do think you might reword that last paragraph =]

Gabriella
9/27/2014 12:35:04 pm

I agree with Mr. Poissant. It would take much more time than we have to teach math by expecting students to reinvent the wheel at eMoreover, I and nearly everyone I know hated small group work as yet another waste of time; I suspect their enduring popularity stems from the fact that they give teachers a much needed break, but that's hardly a good reason.

Gabriella
9/27/2014 12:41:08 pm

Sorry, that should say "the wheel at every step."
I also think the vilification of lecturing has gone too far. Some of the most electrifying moments I had as a student came during lectures. I still remember sitting on the edge of my seat in tenth grade during a series of lectures in which our teacher explained Rutherforf, Bohr, and Heisenberg's experiments bombarding gold foil with electrons, and what they revealed about the structure of the atom. (I am not a scientist.)

Gabriella
9/27/2014 12:46:41 pm

(When I go back to edit what I've written the whole text box freezes and allows me only to delete characters, not to add.)
Anyway, to finish what I was saying: that's just one example. Given that lectures, especially when punctuated by give-and-take with students, are an effective and enjoyable method of teaching, I wish there were some acknowledgement of this fact and some discussion of how to give a good lecture, explain ideas, when to ask questions, how to deal with wrong answers. That would all be very helpful. As it is, whenever I'm observed I have students do groupwork for at least part of the lesson, because I know that the powers that be look kindly upon it and in fact will never question it, even though I feel in my bones that it is a waste of time.

Christopher Stephens link
9/29/2014 06:34:36 am

Thanks for this post. I've struggled to implement the "You, Y'all, We" method in my classes (I"m also a college instructor though my subject is philosophy). Naturally, I find myself "covering less material" in my classes, but my hope is that they're understanding what we do cover better. I've not yet done my own research to find out if this is so (though I'd like to), but I'm just relying on the research of so many others who have studied student centered learning.
My plea to those such as Gabriella and Francis who are skeptical is to look carefully at this research (and at the success in places like Japan). If we're serious about improving our students' competence in math and other subjects, we have to rely as much as possible on good empirical studies rather than on anecdote or gut intuition.

Of course this doesn't mean we should get rid of lectures altogether or that they don't have their place...

Don Gwinn link
9/29/2014 07:58:01 am

I feel a bit of desperation when I look at ideas like this, and when I looked at the original article a couple of weeks ago, I remember thinking we ought to figure out how to implement the Japanese approach (which is kind of a deceptive way to label it--as mentioned, it became a "Japanese approach" because the Japanese actually took the ideas and ran with them, while American schools made some effort and then went back to business as usual.)

My guess is that there are other barriers. I don't know what the average work week for a Japanese school teacher looks like, but I wouldn't be surprised to find that a Japanese student in many schools spends the same amount of time at school as the average teacher in the U.S. Don't get me wrong, I know how hard we work, but I'll still bet that it's not the same. How hard would it be to change that, nationally?
When we hear that they have "time built into their work week" for that kind of rigorous collaboration, I ask the question: What did they give up in favor of that time? Did something else have to come out of their week (for instance, did they hire more teachers to reduce class loads?) or does the average Japanese teacher simply spend more time per week working with colleagues than the average American teacher?

As for alternative techniques, that raises another question: what alternatives? If American and Japanese culture are too far apart (at least in the schoolhouse) for American schools to make a Japanese model work, who else can we look at next? Where is the nation that has school systems at least somewhat similar to the U.S., but has greater success teaching math? I confess I don't know, nor am I sure where to start looking. I suppose if we agree that we'll consider rankings on international math measures as markers of successful math instruction, that would mean looking for countries that rank above the U.S. but are culturally similar, preferably with similar school cultures.

Canada, for instance, appears to have kicked our asses for us in the last round of PISA. Could that be a place to look for successful strategies in schools closer to what we have in the U.S.? Obviously, Canada is not the same as the U.S., and for all I know about the Canadian school system (nothing, other than a few church-state details) it could be that their methods would seem more alien than anything Japan uses. But maybe not?

Daisy
9/29/2014 09:15:01 pm

What about the direct instruction, or whole class interaction, method of teaching mathematics? This gets high ratings in all of Hattie's work and some recent research suggests it might be one of the reasons Chinese pupils outperform English pupils. http://www.bera.ac.uk/bera-in-the-news/teaching-methods-explain-the-china-england-results-gap-in-maths

Manabu Watanabe
10/1/2014 09:39:37 am

I am a Japanese and have read the NY Times article, 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 the misunderstanding of Japanese education spreading in your country.

Francis Poissant
10/1/2014 03:13:33 pm

Interesting Mr. Watanabe! You wrote a really clarifying point of view on your blog on the situation in Japan. Hope your destinator and others will read.

Manabu Watanabe
10/2/2014 02:11:22 am

Thank you for reading it.

I am anxious about the possibility that this misunderstanding may be reversely imported to Japan and confuse educational debates here.

So I would be grateful if you could let your friends know this fact.

Ian Lynch link
10/5/2014 02:51:25 am

Maybe the answer is to turn all school teachers into Juku :-)

http://thelearningmachine.co.uk/how-to-pay-teachers-100k-per-year/


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