Don't Believe It

Don't believe it. "Reform math" in the U.S. does not mirror what these successful countries use.

Here are some issues that are often overlooked:

• The use of calculators is common in "reform math". In fact, the 1992 California Math Framework advocates their availability for all grade levels at all times, including use for homework, class work and tests. This is NOT true in Japan, where calculators are not used until later grades, and even then not used much.

• Most "reform" programs push "applications" very strongly. They want all practice to occur in the context of "real-world" problems. They emphasize the concrete over the abstract. However, the symbolic abstraction that gives power to mathematics is not the enemy. The TIMSS videotape study showed that the proportion of abstract presentations was high in both Germany and Japan (86%). These successful countries do NOT expect all mathematics to be learned in the context of applications.

• The Japanese texts do NOT look at all like the "reform" texts in this country. If anything, they look more like the antithesis of "reform". Translations of the Japanese texts are available in this country, some supplied by UCSMP. They contain clear explanations and procedures, for example, rather than leaving all these matters up to the children to discover. Many new U.S. programs push a "don't tell" approach, even admonishing parents NOT to teach solution methods to their children. By contrast, the program in Japan is more likely to give explicit solution methods.

• The Japanese classroom does NOT emphasize group activity. The kids spend perhaps 20% of their time in groups -- and when they do the purpose is often to gather work to use as examples for whole-class presentation.

• The Japanese system is NOT "student-directed" or "student-centered" but rather the progress of the class is carefully designed and directed by the teacher.

• In Japan and Singapore, they do value the correct answer, NOT just the process or the effort.

• The Japanese kids get plenty of drill. They practice in class and at home, and some in after-school school (juku). They have workbooks for this purpose. Also, there is reason to believe that not all of this practice shows up as "homework" in TIMSS data. While the "reform math" advocates do NOT want drill, students in Japan are very competent in their math facts and use of operations. This success comes with practice.

• The "reform math" folks do NOT want a strong focus on proof in mathematics, and their programs evidence the gradual deletion of proof from the curriculum over the years. In fact, the TIMSS study report indicates ... "It is likely that the kind of mathematics that students learn is related to the nature of the mathematics that they are asked to study. Although constructing proofs and reasoning deductively are important aspects of mathematics, American students lacked opportunities to engage in these kinds of activities. None of the US lessons included proofs, whereas 10 percent of the German lessons and 53 percent of Japanese lessons included proofs." "In a separate analysis of 30 lessons from each country conducted by a group of experienced college mathematics teachers, 62 percent of Japanese lessons were found to include deductive reasoning, compared to 21 percent in Germany and zero percent in the US."

• Part of the REAL difference between the U.S. and Japan is the organization of schools. Teachers concentrate on their subject matter lessons much more. The focus on the content of the lessons is the subject of the film Polished Stones. Such a focus is NOT typical in the U.S. under either "traditional" or "reform" designs.

• There is a great tendency on the part of the "reform" movement to avoid details about just what a student should know and be able to do in each year of the curriculum. The NCTM Standards are "...without specific recommendations for homework, grades, or any one part of the educational enterprise." This is part of the REAL difference between the U.S. and other countries. There are national standards in both Japan and Singapore. In Japan, these standards are not very detailed, but they really don't need to be because they have a standardized curriculum.

• The new "integrated" forms of high school mathematics we see in U.S. are NOT similar to the programs found in countries like Japan, where the "integrated" nature is fundamentally different. In one sense, "integration" is essential -- that is including algebraic thinking in geometry and vice versa. This is the case in Japan. However, they concentrate on algebra for part of the year and geometry for the rest of the year. By contrast, "integrated" mathematics in some of the new U.S. high school programs doesn't concentrate on algebra or geometry at all. Instead, the focus is on specific problems. The hope is that students will absorb sufficient mathematics knowledge secondary to the process of dealing with varied "non-routine" problems. Success in Japan cannot be used to justify this new form of "integrated" mathematics.

• There are REAL cultural differences between these Asian countries and the U.S. population, not to mention many other variables that cannot be directly addressed by the TIMSS data. These important factors are downplayed or ignored by much of the rhetoric that has come out since the TIMSS study. In fact, the TIMSS should be taken as a descriptive study on a grand scale, but not one that permits solid causal inferences.

• "Unfortunately, there are indications that U.S. teachers are weaker in subject-matter preparation and knowledge than teachers in other countries." (A Splintered Vision, by William Schmidt, Curtiss McKnight and Senta Raizen). This concern is not often mentioned in connection with the TIMSS reports, but awareness of this issue is becoming more acute in the U.S. today.