First, go read Elizabeth Green’s article, “Why Do Americans Stink at Math?”. It’s great.

I think her point about practice is really interesting. Quote below:

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.

This definitely rings true, but I’ve also heard many teachers being given “discovery math” curricula (TERC comes to mind) saying that they didn’t build in enough time for practice. I think Green is right that in American classrooms there is too much time spent on practice and not enough on critical thinking and productive struggle, but I also think it’s important to temper that with a healthy amount of practice, including independent practice, to maximize retention.

This makes me think about Steven Leinwand, who presented today at Twitter Math Camp, and praised the NCTM Teaching Practices, summarized in this image:

Made me think about the difference between choosing problems and tasks, which is much of what gets shared in the MTBoS, and the practices that teachers use to facilitate those tasks, which gets much less attention and is much more difficult to capture and communicate.

Green gets at that in her article as well. She writes:

If teachers weren’t able to observe the methods firsthand, they could find textbooks, written by the leading instructors and focusing on the idea of allowing students to work on a single problem each day. Lesson study helped the textbook writers home in on the most productive problems. For example, if you are trying to decide on the best problem to teach children to subtract a one-digit number from a two-digit number using borrowing, or regrouping, you have many choices: 11 minus 2, 18 minus 9, etc. Yet from all these options, five of the six textbook companies in Japan converged on the same exact problem, Toshiakira Fujii, a professor of math education at Tokyo Gakugei University, told me. They determined that 13 minus 9 was the best. Other problems, it turned out, were likely to lead students to discover only one solution method. With 12 minus 3, for instance, the natural approach for most students was to take away 2 and then 1 (the subtraction-subtraction method). Very few would take 3 from 10 and then add back 2 (the subtraction-addition method).

I think this is awesome, and it makes me think of the challenges we have in the MTBoS of sorting through all of the awesome material that gets shared and figuring out what is relevant and helpful for each teacher personally. Would love to see a project in the US along those lines, using the Common Core standards.

Finally, one of the fundamental problems (I think) in education reform: the necessity of collaboration in the United States, and the challenges in making it happen:

In Japan, teachers had always depended on

jugyokenkyu, which translates literally as “lesson study,” a set of practices that Japanese teachers use to hone their craft. A teacher first plans lessons, then teaches in front of an audience of students and other teachers along with at least one university observer. Then the observers talk with the teacher about what has just taken place. Each public lesson poses a hypothesis, a new idea about how to help children learn. And each discussion offers a chance to determine whether it worked. Withoutjugyokenkyu, it was no wonder the American teachers’ work fell short of the model set by their best thinkers. Withoutjugyokenyku, Takahashi never would have learned to teach at all. Neither, certainly, would the rest of Japan’s teachers.…

And other countries now inching ahead of Japan imitate the

jugyokenkyuapproach. Some, like China, do this by drawing on their own nativejugyokenkyu-style traditions(zuanyan jiaocai, or “studying teaching materials intensively,” Chinese teachers call it). Others, including Singapore, adopt lesson study as a deliberate matter of government policy. Finland, meanwhile, made the shift by carving out time for teachers to spend learning. There, as in Japan, teachers teach for 600 or fewer hours each school year, leaving them ample time to prepare, revise and learn. By contrast, American teachers spend nearly 1,100 hours with little feedback.