An American way of teaching

A class of sixth-graders at the Murch Elementary School in Washington, D.C., 1943. (Photo: Library of Congress)A class of sixth-graders at the Murch Elementary School in Washington, D.C., 1943. (Photo: Library of Congress)

This essay is part of the larger radio documentary Teaching Teachers, which you can listen to in its entirety on this website or on our podcast feed (iTunes).

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In 1993, a group of researchers set out to do something that had never been done before. They would hire a videographer to travel across the United States and record a random sample of eighth-grade math classes.

“Our goal was to find out what an average eighth-grader would experience when they got up in the morning, went to their local school and had math class,” says James Hiebert, a professor at the University of Delaware and one of the researchers who worked on the study.

No one really knew what American teaching looked like. The routine for most teachers at the time was: Go in your classroom and shut your door. Typically the only people who saw you teach were your students, maybe a student teacher or a classroom aide. No one had ever attempted to videotape teaching on a wide scale like this.

The videographer recorded 81 classes. Here’s one of the videos, of an eighth-grade math class in the United States, circa 1994.

The video study was part of a larger research project called the Third International Mathematics and Science Study (TIMSS). Funded largely by the U.S. government, the goal was to see how American students were doing in math and science compared to students in 40 other countries. As part of the project, more than half a million students around the world took tests to assess their math and science knowledge.

The researchers were not expecting American students to fare well; previous international comparisons had already shown that American students were behind their international peers. But many of the researchers involved in planning the TIMSS study believed that just worrying about low test scores would not help educators or policymakers figure out how to improve those scores. They wanted to understand the reasons for low achievement. For that, they needed to know more about what was going on in American classrooms. What did teaching and learning look like?

For comparison, they needed to know what teaching and learning looked like in other countries. Were there differences? Could those differences explain anything about the achievement gap between American kids and kids in other nations?

One of the nations researchers wanted to know more about was Japan. Japanese students were doing remarkably well on international comparisons of math and science achievement.

So the researchers sent a videographer to record a random sample of eighth-grade math classes in Japan too. Here’s one of those videos.

The videographers in Japan and the United States would record a class, ship it off to the researchers, and then go to another school to record another class.

“FedEx got a lot of business during these studies,” says Hiebert.

The FedEx packages were headed to UCLA, where researchers watched the videotapes (with English subtitles for the Japanese lessons). Then they discussed what they’d seen. It could take a day to get through a single lesson. But eventually the researchers were able to develop a coding system that allowed them to compare teaching across the various classrooms.

Here’s what they found: Teaching in the United States looked very different from teaching in Japan. And what was perhaps more remarkable is that teaching within each country looked pretty much the same. In other words, most eighth-grade math teachers in the United States were teaching math pretty much the same way. And most eighth-grade math teachers in Japan were teaching pretty much the same way. But there was an American way of teaching math, and there was a Japanese way of teaching math, and these ways of teaching were distinctly different.

Differences Between Teaching in Japan and the United States

The researchers came up with a name to describe the way students in the United States were being taught math. They called it “learning terms and practicing procedures.” Teachers would present definitions of terms and demonstrate procedures for solving specific problems. Students would then be asked to memorize the definitions and practice the procedures. It was a bit of a lather, rinse, repeat approach, and the actual math students were asked to do was not very advanced. Watch the video above, and you will see this approach in action.

The researchers concluded that the American teaching approach did not require students to do much mathematical thinking and reasoning. Students did not appear to be learning the math in a very deep way.

In Japan, teachers would ask students to come up with their own procedures for solving problems. A typical class might begin with the teacher giving students a word problem, like in the video above. The students come up with as many ways as they can to solve the problem. Then students present their methods to the class, and the teacher guides them in a discussion of the mathematics behind each method. The idea is to lead the class towards increasingly sophisticated ways of solving the problem. The researchers came up with a name to describe Japanese teaching. They called it “structured problem solving.”

The researchers concluded that the American teaching approach did not require students to do much mathematical thinking and reasoning. Students did not appear to be learning the math in a very deep way.

At one point in the American video above, a student is struggling to remember the difference between supplementary and complementary angles. The teacher suggests a little trick to remember. Complementary angles add up to 90 degrees, and supplementary angles add up to 180 degrees.

“C comes before S in the alphabet. Ninety comes before 180,” says the teacher. “Complementary: 90. Supplementary: 180.”

I remember learning lots of little tricks like this in my math classes growing up. There’s nothing wrong with learning tricks if they help you remember things. The problem is when the math students are asked to do doesn’t get much beyond this kind of memorization. In the American math classes, it rarely did.

The Japanese approach to teaching required students to develop a more sophisticated understanding of mathematics. Students in Japan did memorize terms and formulas, and teachers did explicitly demonstrate procedures for solving problems, but there was significantly more time devoted to having the students apply this knowledge, on their own, to new and challenging problems. The students learn there are multiple ways to solve a math problem; it’s not just about memorizing a procedure the teacher taught you.

The Benefits of Struggle

One of the most remarkable differences between teaching in Japan and teaching in the United States, according to the video study, was how much time teachers gave students to grapple with problems on their own.

“Mathematical ideas are difficult. They require struggling.”
–James Hiebert

At one point in the American lesson above, the teacher tells students he is going to give them a “couple of minutes” to do some problems on their own. They have a worksheet with 40 problems on it. The students start working, and the teacher walks around the room to check on their progress.

But it takes just 40 seconds for the teacher to interrupt the class to say, “OK, you want some prompting on this one?” He goes to the board to demonstrate a procedure, and in the process gives the class the answers to three of the problems.

In the Japanese lesson above, students spend almost the entire class period working on one word problem. The teacher begins by going over the word problem. This takes a little less than four minutes. Then students work, on their own, for close to fifteen minutes. The teacher walks around, looking at their work, and asking questions like, “How did you obtain this?” and “Is there any method that’s simpler? Can you please find that?”

In Japan, the researchers noticed, it was typical for students to struggle with a task before the teacher intervened. In the United States, it was typical for teachers to intervene at the first sign of confusion or struggle.

Hiebert says there are big differences between how teachers in the U.S. and teachers in Japan tend to think about the value of struggle. In the United States, the idea is: Math is best learned in a smooth, mistake-free way.

“The longer kids are confused, the more demoralized they’ll become, the more mixed up they’ll become,” says Hiebert. “So, you want to jump in and prevent confusion.”

But, he says, “mathematical ideas are difficult. They require struggling.”

The Japanese approach to teaching embraces this idea.

“Confusion is an expected part of what (students) are going to confront,” says Hiebert. Letting kids be confused and then have that “aha” moment where they figure something out results in deeper learning of mathematical ideas and concepts, he says.

Explaining Achievement Differences

The TIMSS study was released in 1996. It showed that Japanese students scored among the best in the world in math, topped only by Singapore and Korea. Students in the United States were in the middle of the pack, scoring below the international average.

The question the researchers who did the video study had wanted to be able to answer was, why? Why was math achievement so poor among American students? Did it have anything to do with the way students were being taught?

Their study could not provide definitive answers to these questions. There are many factors that may affect student achievement, including school resources, poverty rates, and family education level. There’s no way to say for sure that the way students in Japan were being taught was the reason they were doing better in math.

But the researchers believed they had gathered enough evidence through the video study to suggest that teaching was playing a significant role.

The next question was: how did Japanese teachers learn to teach this way?

And what would it take to get American teachers to teach more like that?

To find out what the researchers discovered, click here to read about Japanese lesson study.

To learn more about the TIMSS video study and what researchers learned about American teaching, check out The Teaching Gap by James Hiebert and James Stigler.

This essay is part of the larger radio documentary Teaching Teachers, which you can listen to in its entirety on this website or on our podcast feed (iTunes).

Episode: Teaching Teachers