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Sun Aug 17, 2014, 05:45 AM

Why Do Americans Stink at Math?


Takeshi Matsuyama was an elementary-school teacher, but like a small number of instructors in Japan, he taught not just young children but also college students who wanted to become teachers. At the university-affiliated elementary school where Matsuyama taught, he turned his classroom into a kind of laboratory, concocting and trying out new teaching ideas. When Takahashi met him, Matsuyama was in the middle of his boldest experiment yet — revolutionizing the way students learned math by radically changing the way teachers taught it.

Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun.

Takahashi quickly became a convert. He discovered that these ideas came from reformers in the United States, and he dedicated himself to learning to teach like an American. Over the next 12 years, as the Japanese educational system embraced this more vibrant approach to math, Takahashi taught first through sixth grade. Teaching, and thinking about teaching, was practically all he did. A quiet man with calm, smiling eyes, his passion for a new kind of math instruction could take his colleagues by surprise. “He looks very gentle and kind,” Kazuyuki Shirai, a fellow math teacher, told me through a translator. “But when he starts talking about math, everything changes.”


It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.


By focusing only on procedures — “Draw a division house, put ‘242’ on the inside and ‘16’ on the outside, etc.” — and not on what the procedures mean, “I, We, You” turns school math into a sort of arbitrary process wholly divorced from the real world of numbers. Students learn not math but, in the words of one math educator, answer-getting. Instead of trying to convey, say, the essence of what it means to subtract fractions, teachers tell students to draw butterflies and multiply along the diagonal wings, add the antennas and finally reduce and simplify as needed. The answer-getting strategies may serve them well for a class period of practice problems, but after a week, they forget. And students often can’t figure out how to apply the strategy for a particular problem to new problems.


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.” (American schools, meanwhile didn’t look much different than they did before the reforms.) Japanese students had changed too. Participating in class, they spoke more often than Americans and had more to say. In fact, when Takahashi came to Chicago initially, the first thing he noticed was how uncomfortably silent all the classrooms were. One teacher must have said, “Shh!” a hundred times, he said. Later, when he took American visitors on tours of Japanese schools, he had to warn them about the noise from children talking, arguing, shrieking about the best way to solve problems. The research showed that Japanese students initiated the method for solving a problem in 40 percent of the lessons; Americans initiated 9 percent of the time. Similarly, 96 percent of American students’ work fell into the category of “practice,” while Japanese students spent only 41 percent of their time practicing. Almost half of Japanese students’ time was spent doing work that the researchers termed “invent/think.” (American students spent less than 1 percent of their time on it.) Even the equipment in classrooms reflected the focus on getting students to think. Whereas American teachers all used overhead projectors, allowing them to focus students’ attention on the teacher’s rules and equations, rather than their own, in Japan, the preferred device was a blackboard, allowing students to track the evolution of everyone’s ideas.

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Response to eridani (Original post)

Sun Aug 17, 2014, 06:07 AM

1. yep, contrary to what i was taught in school, there is usually


'More than one way to skin a cat' as my dad used to say...too bad I didn't know this in elementary school before my self esteem was shaken and faculty expectations for me carved in stone. I was in my 20's before an employer who needed me to understand fractions, decimals, and percentages showed me his method...it was almost instantly I could do much of it in my head. To this day some of my coworkers marvel at my head math...especially younger people who are almost completely dependant on electronic math brains.

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Response to eridani (Original post)

Sun Aug 17, 2014, 08:27 AM

2. The New Math Was NOT a Failure


Where do you think all the computer nerds came from? The SMSG after school program was my first introduction to logic and set theory, in 5th grade. It was by invitation, for those who had mastered arithmetic functions.

The better question to ask is why American students are so weak at basic arithmetic...

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Response to Demeter (Reply #2)

Mon Aug 18, 2014, 02:15 AM

7. For students not mathematically gifted it was a failure

As the article points out, that was because non-nerd teachers had very little help learning to implement it. It certainly isn't impossible, as the Japanese have shown.

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Response to eridani (Original post)

Sun Aug 17, 2014, 08:34 AM

3. Because they think the teachers can make them learn it if only the teachers do the right things.

Getting ready for the new year to start and this article actually kind of hit a nerve so RANT ON!

Frankly I have a cynical take that the NYTIMES article is fringe "blame the teachers" nonsense.

Oh if ONLY our teachers worked harder or did something different it would ALL be better.

Wishful thinking and pretending that the process is just "Teacher does A -> students learn 10%, Teacher does B -> students learn 90%"

Any classroom strategy will inevitably fail when confronted with a lack of personal motivation. Almost any (or even the lack of a) classroom strategy will work when sufficient motivation is present.

Sure, individual teachers can change things slightly through the personal charisma they have but frankly it is a small effect on the main driving factors here:

1) On the "I don't believe you front" 1/3 of a typical American classroom will reject evolution on religious grounds and who have been told that education is a form of elitism -- so right there you have a group of people who value dogma over reason and who will simply not excel at any kind of rigorous thinking.

2) On the "too cool for school" front, we have "math is hard" Barbie and you have "I didn't need it so why does my kid" parents. It's okay to struggle because they have been indoctrinated to believe it is irrelevant and won't matter after graduation.

3) On the "why work harder than we have to front": You have flat old intellectual laziness -- it's hard so avoid the pain and don't do it. Besides, the time can be spent on activities connected with actual aspirations like making it big as music or athletic stars and after you make it big who cares!

4) On the peer pressure front I have seen students who one-on-one show an intense driving interest who immediately fold up and repudiate it to avoid losing coolness with their peers who have already been lost through 1-3.

OTOH here is an example of absolutely NO classroom technique yielding results that put those of the article to shame:

A few years back I was reading a biography called "Battleship Sailor" about a guy who was a radioman at the end of World War II as the fleet cut literally thousands of radiomen while decommissioning a large fleet no longer needed. How did they determine who got to stay in the Navy? Grades from a series of classes. These twentysomethings badly wanted to keep those good jobs (most entered from poverty from the depression) but they came to understand that staying required the highest grades out of huge classes where the teachers didn't care if they passed or failed. The author talks about what kinds of math these high school educated kids were forced to do without acknowledging that he was describing 3rd year electrical engineering math for a group of kids who hadn't had the two years of calculus and vectors we'd normally expect in preparation. They did it too -- without tutors and without teachers. Motivation was enough to get them to perform THREE YEARS above their grade level.

It's all about motivation.

The article ignores this, and cynically I'd say it is because some drivers behind it would like to sell the solution. It ignores a far more likely explanation in that the Japanese students have been convinced that their future depends critically on their performance in math and the American students have been indoctrinated to believe that it doesn't matter in the end.

Once motivated the tactics sound superior, but the tactics are a second order effect here and I am completely sick of pretending that the first order effects don't exist.

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Response to Pholus (Reply #3)

Mon Aug 18, 2014, 02:19 AM

8. I thought that the article emphasized that teachers need HELP to implement--

--good math teaching, which they have never really gotten.

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Response to eridani (Reply #8)

Mon Aug 18, 2014, 06:40 AM

9. I am a professor in the hard sciences...

and have waited anxiously for years to see where my children were going to "fall off the wagon" when the curriculum and teachers would fail them. After all, everyone told me it was going to happen. My colleagues all warned me to put my kids in private schools because of it. Television media every year talks about failures in the education system and "Waiting for Superman" was supposed to depict the failure the system was.

You know what I found examining things first hand?

That the curriculum was thoughtful and elegant. In second grade the foundations were laid so that intuitively the students understood the "two equation two unknown" problem that personally I do not remember getting until algebra. My eldest child is a full two years ahead in math compared to my own time in school, having just finished a geometry course in 8th grade. We had a talk about the quadratic equation last year, three years ahead of when it was introduced for me.

I have yet to encounter a teacher whose math credentials were a problem or whose enthusiasm was questionable.

The only criticism I would level after nine years of watching is that the newfangled "intuitive" way they teach of doing division involves a grouping method which is computationally awkward for larger than four digit numbers where the old fashioned "algorithmic" method scales to arbitrary number sizes. I made sure my child knew the method that your NYTIMES article specifically pans ("put numbers in the house" simply because it always WORKS.

Now what I have seen plenty of are failures on the parts of my fellow parents who allow their children to screw off because that's what they did or because they won't need math given what they'll be doing. I have seen the subject dismissed by parents and children as "unnecessary" and "geeky." And I have seen a deluge of popular media totally decrying the importance of the subject -- "Math is hard" Barbie came from somewhere, right? Never mind the role it plays in developing critical thinking skills -- if it ain't what you do every day it ain't necessary -- that is the mindset at work here.

Nope, solving this "education problem" has never been about teachers and curriculums. The right wanted unions destroyed and the corporate elements saw education tax dollars as a huge profit center. So "blame the teachers" breaks the union and "blame the curriculum" opens up business opportunities.

Note that I am not saying that this particular mathematical "tactic" is a bad thing -- just highly disputing two things about it.

1) that it will be a panacea and questioning the motives behind its publicity.
2) that it actually improves comprehension over the long term as a student advances from grade school to higher mathematics.

Articles like this that indicate that education is all wrong and that we just merely need to "wake up" annoy the heck out of me because this particular one of America's problems, like so many others, is about self motivation -- not about its teachers doing something simple wrong. I don't see that changing.

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Response to eridani (Original post)

Sun Aug 17, 2014, 10:19 AM

4. And do even worse at critical thinking


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Response to rock (Reply #4)

Mon Aug 18, 2014, 12:36 PM

10. Obviously if you read some of responses to threads on DU

1 + 1 = 10 think it through.

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Response to eridani (Original post)

Sun Aug 17, 2014, 01:19 PM

6. this is a good friend of mine. trying to get it right in chicago.

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