Mathematically Correct
Released Jan. 16, 1997

Math Lessons from Japan
The TIMSS and the Truth
For the Record - LA Times page A3, 1/15/97
Math teaching--A Jan. 5 article in The Times on
math instruction stated incorrectly that a Reform
curriculum called the Interactive Mathematics Program
is widely used in Japan. It is not.

For a bit of description of what is the truth ...

Jim Stigler of the UCLA psychology department was very actively involved in the Third International Mathematics and Science Study (TIMSS) that received a great flurry of press recently but will be getting deeper and more reasoned consideration for years to come. His involvement was, and is, to oversee a video project of what actually goes on in typical US mathematics classrooms versus that of some of our international competitors in the study. Summaries of what was done in that project along with order information for a CD-ROM of the actual videos are available at the Videotape Classroom Study Website.

Also very helpful in getting a better picture of the line that did and will continue to get a lot of coverage, US mathematics and science education is a mile wide and an inch deep, is the on-line pre-publication draft, A Splintered Vision: An Investigation of U.S. Science and Mathematics Education.

Prof. Stigler will more than likely be writing an article for the popular press that addresses some or all of the following perceptions that he shared with me recently but until that appears ...

Does the Japanese curriculum and classroom look like Mathland at the elementary school or at the secondary level, IMP, where it was reported on 1/5/97 in the LA Times that this curriculum was "in widespread use" in Japan? No, I never said that. (This comment would be consistent with the LA Times correction above.) The Japanese classroom doesn't look like a traditional US classroom either. It looks, well, Japanese. Some aspects of the Japanese mathematics pedagogy that he reports as being true, however, are the following.

The lessons are of a "problem solving" nature but they are usually not so-called "real world" problems, they are mathematics problems in a verbal setting with a definite right answer implied. Students are actively involved in solution approaches and formulation with alternative solution ideas discussed extensively. These are not, however, student directed situations. The classrooms are very teacher directed. The instructor has studied the problem extensively and is aware of the various approaches that will be offered. An important part of the lesson is discussing these various solutions, including their strengths and weaknesses. These are not independent projects that are expected to be accompanied by a lengthy student essay on the various strategies failed and ultimately successful as is common in reform movement pedagogy in the US today. The instructor knows and the instructor weighs the various strategies offered and all students are expected to know the optimal ones and why to reject inferior ones.

Along the way, some of this instructor direction is done in a lecture mode although it would not be fair to characterize the setting as primarily lecture. The current reform movement cliche, to be "a guide on the side" instead of "a sage on the stage", is simply not an apt description of instruction in Japanese classrooms. The instructor is clearly the "sage" whether guiding or lecturing. During the student solution stage, instructors are well aware of the approaches being chosen and offer helpful advice and critical comments. Overall, Japanese instructors do more traditional lecturing than is common in US precollegiate classrooms.

Regarding basic number facts, Japanese students are much more competent than US students. The facts are over-learned to a point where they are simply not a problem. Calculators are not allowed to replace oral or pencil and paper computations in lower elementary school where this competence is consciously sought and achieved nor are graphing calculators in widespread use at the secondary level.

Although there is no national broad screen assessment such as the ITBS, schools are well aware of the nation-wide grade-level standards that are clearly presented and expected to be achieved. Teachers make up school wide exams collectively and the same exam is given to all of the students in the school at each grade level. Concepts that appear to be problem areas on comparison with the national standards are carefully addressed with a great deal of discussion and eventual action to rectify them. Teachers are not free to "do their own thing" but are expected to implement the collective wisdom to the best of their ability.

Prof. Stigler does not feel, however, that the ubiquitous "standardized tests" of the US are inherently bad. Performance on such exams does correlate very well with the kind of exams given in Japanese schools as evidence by the fact that their students do appreciably better on our exams, never having seen them in advance, than do ours where time has often been spent, perhaps wasted, in exam preparation.

As far as suggestions from the Japanese data to improve US education, Prof. Stigler is a strong advocate of the need for clearly presented and easily understood national, grade-level standards. Although he doesn't endorse the interpretations that E. D. Hirsch, Jr. has given to some of the references to research on teaching in The Schools We Need and Why We Don't Have Them, Stigler definitely endorses Hirsch's strong belief in grade-level specific content standards.

Adding my own footnote to Stigler's position, I am reminded of NCTM president Gail Burrill's quote in their November News Bulletin on the subject of TIMSS, The study reinforces the recommendations for mathematics education that NCTM has been encouraging through our Curriculum and Evaluation Standards, which was published in 1989. Since nothing close to grade-level standards, nor competence assessment Japanese style, nor even expertly guided content teaching strategies are presented in this document - and probably will not be in its replacement in the year 2000, the statement would appear to be more wishful thinking than fact. It is reminiscent of the quote that came out of the curricular division of NSF that IMP is widely used in Japan. The quote does support a philosophy but it is clearly in error and the country doesn't need more smoke and mirrors; it needs to emulate and improve upon programs that do work. The real Japanese one does.

Wayne Bishop
Professor of Mathematics and Computer Science
California State University, Los Angeles