Lesson Study
What is the purpose of math?

Last week I went to a training session for math teachers at Martin Luther King Middle School in San Francisco. School was out, so the campus was quiet and we could park on the lower yard. It was a scorching hot day to be in the school library with the windows closed but these were dedicated teachers (and a handful of administrators).

I had the pleasure of meeting Akihiko Takahashi, one of the masters of “lesson study.” I felt like I was meeting a movie star because I had heard Dr. Takahashi’s name so many times, by so many trusted colleagues. He didn’t disappoint me with his opening presentation either! He reminded us about the purpose of math and connected a text from 1908 to the Common Core! He surprised me with his observation that many of the strategies that Japan has put in place to teach their children problem solving came from the U.S. (Japan just figured out how to implement the ideas more consistently across more schools than we have!) He had two incredibly powerful slides.

One was from early 20th century mathematician J.W.A. Young who said in a 1908 paper (p 38):

“Ten pages of mathematics understood is better than 100 pages memorized and not understood,” and “One page actually worked out independently is better than 10 pages clearly but passively understood.”

 I loved the poetic way in which Young said “less is more” and “deeper is better.” If I hadn’t seen the actually photocopy of the text on the slide with the citation, I would have thought this was an ancient Chinese proverb. I could hear my Gung Gung saying this to me. Dr. Takahashi described how this 1908 paper from an American had influenced the Japanese educational system in radical ways.

Lesson Study graphThe other powerful statement he made was through a graph. It was from the 2003 TIMMS. The Y axis was “percentage of problems answer correctly” and the X axis was “percentage of curriculum taught.” What you see in Singapore, he explained, is that a high percentage of what is tested is actually taught and the majority of students tend to answer the problems correctly. In the U.S. you see roughly the same amount of curriculum covered, but U.S. students don’t do nearly as well (meaning we teach it, but they don’t learn it). When he plotted the Japanese experience you see that a very low percentage of the curriculum tested was actually taught but their scores were close to Singapore’s in terms of correct answers. How could this be, he asked? He returned to the purpose of math. In Japan, he argued, we teach children to problem solve so that when they are faced with a problem they have never seen, they are able to reasonably work through it.

We have all the right thinking in the U.S. We just don’t seem to execute consistently well. “Lesson study” is a way of scaling best practices and engaging teachers as researchers and observers in the improvement of their own practice. I was humbled by the simple math problem that I saw Dr. Takahashi teaching to a group of 5th graders and how it made a roomful of teachers pause and consider their own practice. I couldn’t stay the whole day but I wish I could have!

A What Works Clearinghouse review found that lesson study was one of only 2 out of 643 studies that met their criteria for evidence of impact on students’ mathematical proficiency. I am anxious to see how we can help our grantee, Mills College, grow this incredibly strong cadre of “lesson study” teacher leaders into an unstoppable army of effective educators.