Bansho Mathematics

The publication of the Third International Mathematics and Science Study (TIMSS) in the 1990s was considered a groundbreaking look at mathematics instruction around the world, particularly in Germany, Japan, and the United States ( As one might expect, the international rankings of various countries in comparison to one another is of some interest to educational researchers. Of particular note was the United States, placing well below countries such as Singapore, Korea, Japan, France, Australia, Hungary, and Ireland (Hiebert and Stigler, 4). James W. Stigler and James Hiebert summarized portions of the study, in particular the videotapes of math lessons from Germany, Japan, and the United States in their book The Teaching Gap.

Oftentimes, I have found parents wondering about the particular math program used at a school. Certain specific programs have garnered particular buzz. However, I would argue that it is not the program that we should be asking our teachers about. A speciifc program is simply a teacher’s guide, student textbooks, and a series of prescribed lessons plans. While many are quite good, it is impossible for any program to perfectly match the needs of any particular class. Instead, we need to be asking about the teachers, and their knowledge of mathematics instructional practices. We need to look at the differences between procedure-centered and problem-solving centered classrooms, and whether or not our teachers know how to approach mathematics problems from many different angles with their students.

I would like to share an anecdote shared in The Teaching Gap. The authors speak of a professor who, when asked to note the differences between the instructional practices of the three aforementioned countries, noted that,

“In Japanese lessons, there is the mathematics on one hand, and the students on the other. The students engage with the mathematics, and the teacher mediates the relationship between the two. In Germany, there is the mathematics as well, but the teacher owns the mathematics and parcels it out the students as he sees fit, giving facts and explanations at just the right time. In U.S. lessons, there are the students and there is the teacher.
I have trouble finding the mathematics. I just see interactions between the students and teachers (Hiebert and Stigler, 25-26).”

What this professor likely noted is the difference between teaching students a procedure and then asking them to repeat it, and helping students truly understand the concepts and relationships behind mathematics. It is this deeper understanding of the concepts that is so important in my own classroom. I sometimes believe that there is some misconception about the Japanese mathematics classroom. The picture painted in The Teaching Gap is quite different from what we might expect. After sumamrizing last day’s lessons, the teacher is seen to present one to three really good problems for the day, that students work on individually. The teacher then engages the students in discussion about the problem-solving that took place, and the efficiencies of the various solutions are discussed. Finally, the teacher summarizes the key points and strategies found throughout the day. Not being assigned homework is typical (Hiebert and Stigler, 30).

Contrast the above engagement with mathematics with what we may see in a typical classroom. A teacher reads out instructions from the teacher’s guide, and the students follow along on the board, perhaps with a few volunteers coming forward to complete simple questions as the teacher brings them up. Students then go off to their workbooks to complete many more questions of the same type. As noted, here we see an interaction between students and teachers – a following of procedures – but are the students really doing mathematics?

The Japanese problem-solving lesson plan, known as Bansho, has been adopted for use in the Ontario classroom by many math experts across the province. In Japanese Bansho, the entire board is used, filled with the problem, student solutions, and teacher/student notes regarding attempted strategies (
The Ontario version of Bansho includes a focus on collaborative problem-solving and “strategically coordinated discussion (

Bansho Mathematics allows teachers to focus on the big ideas of mathematics, as opposed to focusing on minute procedures. By focusing on these big ideas in a problem-solving context, students have a much better understanding of mathematical concepts. They learn to do mathematics as a whole, as opposed to simply following a certain type of procedure for each type of problem. It is trickier to teach, and the problems are more difficult than what are found in most standard textbooks. However, the rewards can be great. Moreover, Bansho Mathematics, either in the Japanese or the Ontario style, can be used in conjunction with any program. As I stated earlier, it is not the program that makes the math class effective, it is the teacher’s knowledge and the instructional practices.

In our Grade Two classroom, we commonly use this type of problem-solving approach to mathematics. Students are learning to classify their mathematics strategies by discussing and comparing them with their peers. Bansho is not about labelling strategies with a grade; rather, it is about assessing the efficiencies of all valid strategies. I keep various student artefacts from our Bansho lessons on the Mathematics Strategies wall in my classroom. If anybody is interested in this type of mathematics instruction, please feel free to drop in at any time.

Paul Lacey, O.C.T., Spec. Hons. B.A., B. Ed. (P/J)
Member of Ontario Association for Mathematics Education (OAME)
Member of Toronto Educators Association for Mathematics (TEAMS)

Works CIted and Consulted

American Mathematical Society. “The Third International Mathematics and Science Study.” Notices of the AMS. American Mathematical Society, May 1996. Web. 21 Sept. 2012. <>.

“Bansho (Board Writing).” Ontario Ministry of Education. Ontario Literacy and Numeracy Secretariat, Feb. 2011. Web. 21 Sept. 2012. <>.

Kubota-Zarivnij, Kathry. “Using (Ontario) Bansho.” Web. 21 Sept. 2012. <>.

Stigler, James W, and James Hiebert. The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom. New York: Free Press, 2009. Print.