Today we visited the offices of Tokyo Shoseki, the largest textbook company in Japan. In the morning we received an overview of Japanese mathematics textbooks by Mr. Toshinari Ogasawara, Chief Editor of the mathematics textbook department. I will try to sum up some of the main points of his presentation below.

There are six major math textbooks in Japan. These textbooks are very similar. According to Mr. Ogasawara, this is due to the fact that the other companies have copied Tokyo Shoseki’s textbooks because of their coherence and excellent sequencing. These textbooks were written based on lesson study findings. Textbook company executives attend large lesson study open houses in Japan and also consult many published lesson research lesson findings to learn what to incorporate into their textbooks. This is one reason why Tokyo Shoseki’s mathematics textbooks are the most widely used math textbooks in Japan.

Several years ago, a new subject called “integrated studies” was added to the Japanese curriculum. In addition, Saturday school was eliminated. Therefore, the number of class hours per year dedicated to mathematics teaching was reduced. Now, 1st graders spend 114 hours, 2nd graders 155 hours, and 3rd through 6th graders 150 hours in math classes per year respectively (1 hour = one 45 min. lesson). Japanese students generally have math class 3 to 4 times per week, depending on the grade level. As a result, textbook companies had to reduce the content of the math textbooks and move certain topics into higher grades. This has created somewhat of an outcry among Japanese educators and because of that, the Ministry of Education is revising the curriculum to possibly include more hours of mathematics in the near future.

Perhaps the first reaction one gets when looking at Japanese math textbooks is that they are thin, lightweight paperbacks with colorful cartoon illustrations. The total number of pages ranges from 120 to 210 per grade level. This is vastly different from the 500 to 600+ pages found in typical, heavy U.S. textbooks. (I couldn’t help thinking that if for some reason the number of hours devoted to math education were reduced in the U.S., we wouldn’t bother reducing the content.) This embodies the Japanese philosophy of teaching a few important math topics per year in depth instead of what is typically done in the U.S.—teaching many topics per year superficially. Japanese textbooks are also inexpensive and they are given to the children to keep. We saw many instances at the schools we have visited of kids writing in their textbook, something unheard of in the U.S. (unless they’re writing graffiti!)

Another characteristic of Japanese elementary math textbooks is that they are designed so teachers can teach the subject without having any special knowledge. Elementary school teachers in Japan typically teach every subject (except gym, art, music, etc.) so they are generalists, not specialists. Teacher’s guides for the textbook offer suggestions on how to teach each lesson based on the results of actual research lessons. Examples are given of questions that may be asked by students according to various stages of learning as well as helpful hints on how to deal with these questions and typical student responses and errors. They even include diagrams on how to organize the chalkboard.

Not only are the teacher’s guides useful, but the textbooks themselves are also very helpful for teachers. Oftentimes, teachers will teach lessons without using the textbook because the textbook pages include pictures of children solving the problems in several different ways. These illustrations are given to help both the teacher and the students. When a student is stuck and cannot think of a strategy, the teacher will oftentimes tell the student to look at the textbook to get ideas. In addition, several textbook pages often show pictures of what the teacher’s chalkboard should look like.

As noted above, Japanese textbooks have many pictures and colorful, cartoon illustrations. These illustrations, however, have a purpose and are not just for show as is often seen in U.S. elementary textbooks. In Tokyo Shoseki’s textbook, there is friendly cartoon space creature who gives helpful hints or states important mathematical ideas. This makes the textbooks very child friendly. Instead of statements like “solve the problem below” Japanese textbooks say “Let’s solve the problem below,” reflecting the philosophy of whole class, student-centered problem solving. (I was wondering if the kids might think that “let’s” is referring to them and the friendly space creature though!)

In the past, math teaching in Japan focused on implementing knowledge thoroughly by direct instruction (“cramming” was the word Mr. Ogasawara actually used.) In recent years, however, the focus has shifted to having students understand the process of solving a problem by thinking for themselves. Therefore, Japanese textbooks focus much on problem solving and having students find various solution methods as well as analyzing the merits of each method. An example that was shared was a page from the 6th grade textbook (English version available at http://www.globaledresources.com) that showed pictures of three students finding the area of a trapezoid by transforming it in different ways. One child is seen dividing the trapezoid into two triangles, another attaches a congruent trapezoid upside down to one side to create a parallelogram with twice the area of the trapezoid, and another child cuts the trapezoid at half of its height and rotates it to create a parallelogram with the same area as the trapezoid. Each of these methods can be used to derive the formula for the area of a trapezoid. The teacher’s guide also offers various other possibilities students might try. I think that this type of approach is largely absent in most U.S. math textbooks (in fact, all the ones I’ve ever seen!)

Textbooks are revised every three to four years in Japan, but before they begin the revision process, the textbook company surveys up to 2000 university scholars and teachers to ask for ideas on how to improve the textbooks. These ideas are then incorporated into the new version. This is very important because Japanese mathematics textbooks tend to improve slowly over time reflecting the philosophy of continually polishing and improving upon what has been learned. Different U.S. textbooks tend to offer radically different approaches and tend to “throw out the bay with the bath water” (at least that’s this particular blog writer’s opinion). It seems to me that we don’t share this idea that improving math teaching and learning is a long-term process based on the results of actual classroom research.

After Mr. Osawagara’s talk, Dr. Tad Watanabe gave the LSIP participants a workshop on geometry in elementary Japanese textbooks. In this workshop he showed us how to use set-squares and compasses to construct parallel and perpendicular lines and draw polygons. Most of us were commenting on how we had little experience in this area in elementary school and witness little of it still today. Japanese students are encouraged to use these tools to draw accurate rectangles, parallelograms, rhombuses and many other figures. How many 3rd graders do you know who can draw an accurate isosceles triangle using a compass and a ruler (or adults, for that matter)? Well, in Japan they do (and we also did, and, yes, it was a lot of fun)!

After the workshop, we were invited to a wonderful Bento Box lunch at Tokyo Shoseki’s company cafeteria. Afterwards, we had a tour of their one-of-a-kind textbook history museum where we saw school textbooks from the 18th century on up (and even earlier examples of wooden panels of math problems). It was interesting to find out that teaching mathematics through story problems has a very long history in Japan. These story problems often involved animals. Even very old textbooks have cartoon illustrations of animals for the problems. One textbook from the 1930’s had an illustration of 8 frogs who jumped into a pond but only 7 came out. The panic-stricken friends jumped back in and pulled their half-drowned friend to shore. Now that makes for an interesting math problem!

Domo (which basically can mean anything from hi to bye to thanks and just about anything else—good word to know if don’t know what to say!)

Bill Jackson

Tokyo, Japan

June 28, 2007

July 3, 2007 at 3:20 am |

Interesting post. Regarding the early geometric drawing skills, I see this on our math team. Quite often, the Asian students will explain a problem geometrically, including why a problem is impossible. Now I know why, to American students, it seems like such an advanced method of instruction / intuition, but to the Asians, it is second nature.