In 1997, I attended a series of workshops on the Third International Mathematics and Science Study (TIMSS). That study compared math achievement in over 40 countries in grades 4, 8 and 12. Singapore and a handful of East Asian countries performed extremely well, much better than the United States, which had a mediocre performance. I was an 8th grade teacher at Public School No. 2 in Paterson, New Jersey at the time. At the workshop we watched videotapes of 8th grade mathematics lessons from Japan, Germany and the U.S. The U.S. lesson looked very familiar. The teacher showed his students how to do a procedure and then they practiced while the teacher helped individual students. This is commonly referred to as the “I do, we do, you do” approach. The Japanese lesson looked very different, however. The teacher began the lesson by posing a rich problem. Then the students solved the problem based on what they had learned previously and shared different solution methods. Important mathematical points of the lesson were brought out through class discussion of the various methods. The students looked very engaged and they even clapped for each other. After watching the video, I felt that my students were getting shortchanged and I became determined to learn how to teach like that Japanese teacher! Making this change, however, would not be easy. The lessons in the heavy 600+ page textbook I was using did not begin with problem solving. In fact, the word problems were the last thing on the page and often times we were so busy practicing procedures that we didn't even get to them. I decided to teach my lessons backwards by posing one of the word problems at the bottom of the page and then asking the students to solve it, share and discuss their methods. I explained to my students what I was trying to accomplish and even showed them the TIMSS videotapes. I was amazed at how quickly they adjusted to the new methodology and how engaged they were. They were actually starting to like math. They even began to clap for each other after they presented their solutions! I soon realized, however, that there was much more to good math teaching than merely imitating the steps of the Japanese lesson. I got involved in a math study group begun by our principal to study the TIMSS data, read books and articles, and explore how to improve mathematics instruction. This led in 1999 to a partnership with researchers from Teachers College and a Japanese school in Greenwich, CT to conduct lesson study, a process where groups of teachers plan, observe and discuss actual classroom lessons. I also traveled to Japan to observe mathematics classes and learn about the Japanese school system.

When I began working with the Japanese teachers, I soon realized three important reasons why they were such good math teachers: (1) They have a high level of math content knowledge. Later I found out that Japanese primary school teachers teach all grades from first to sixth.

(2) They use thin, lightweight paperback textbooks that were much more focused and coherent than our heavy hard cover books. (3) They work collaboratively to improve their teaching throughout their careers by conducting lesson study. When we began conducting lesson study at our school we found that it was difficult to develop engaging and focused lessons like the Japanese teachers taught because of our unfocused textbooks. This led us to textbooks from Singapore. Like the Japanese textbooks they were thin and lightweight and addressed fewer topics per year with depth and coherence. They were also very kid friendly with simple cartoon drawings that highlighted important mathematical ideas. One of the things we liked the most about them was a very effective method to solve complex problems using pictoria[cw1] l diagrams called bar models. In 2000, we decided to adopt mathematics textbooks from Singapore in grades K-8. At that time there were no U.S. editions and the books used British spellings and had word problems with strange foods like durians and rambutans. But these things did not impede students' understanding of the mathematics.

With the adoption of Singapore math textbooks combined with lesson study, math teaching began to improve at our school. But there were also challenges. We realized that in order to teach math well we needed to improve our mathematical content knowledge so we invited knowledgeable others to conduct workshops for our teachers. We also realized that our math content knowledge was improving just by teaching lessons from the textbooks. Later we found out that the textbooks were intentionally designed in a way that teachers could acquire mathematical content knowledge because most Singaporean teachers only receive two years of post-secondary education before entering the classroom, and Singaporean elementary teachers are not math specialists.

I also came out of the classroom to become the school's math facilitator. In small group meetings, we conducted lesson study, studied the textbooks, and solved problems together using bar models. I'll never forget the time we were solving a difficult 6th grade problem with first grade teachers and one teacher jumped up a shouted excitedly, "I got it!" She was so excited that she was finally getting it after not having a good mathematics learning experience herself as a child. The lesson study process was instrumental in allowing us to study the materials together and discuss how to craft good lessons.

In 2008, I left the Paterson school district to become a district wide math staff developer in the Scarsdale, NY public schools to assist with the implementation of Singapore Math. It was interesting to me that Scarsdale, one of highest performing and most innovative school districts in the country, was interested in adopting Singapore math. Before making the decision, they spent time researching and piloting the program. They concluded that even though their students were doing well already in comparison to most students nationwide, they needed to continually improve mathematics instruction. This was a very wise decision in my opinion and the implementation was very successful. Teachers, students and parents were enthusiastic about the program and many groups of teachers also conducted lesson study. One Scarsdale fifth grade teacher said, "Singapore math has given me the opportunity to love teaching math. In turn, my students love math and impress me every day as they become incredible mathematicians."

After my time in Scarsdale I dedicated my career to helping schools throughout the country and even in other countries learn these techniques to improve the teaching and learning of mathematics. Singapore and Japanese math textbooks are focused, rigorous and coherent but just using better textbooks does not guarantee improvement. When they are combined with effective training for teachers and collaborative professional learning such as lesson study, however, mathematics teaching can improve and students from all backgrounds can improve their abilities, confidence and achievement in mathematics.

Bill Jackson is an author, educator and consultant. He is the lead author of the latest Singapore Math series Dimensions Math.

© Bill Jackson

This article was originally composed in 2010. The latest revision was in March 2020.

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