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I read with interest, and with some dismay, the recent article "Adding It All Up" (On Assignment, Feb. 19, 2003). I'm a bit dismayed because of the continuation of this tired debate over math curricular reform. The arguments presented are the same we've heard for over a decade, and they shed no new light on the issue.

To the Editor:

I read with interest, and with some dismay, the recent article "Adding It All Up" (On Assignment, Feb. 19, 2003). I'm a bit dismayed because of the continuation of this tired debate over math curricular reform. The arguments presented are the same we've heard for over a decade, and they shed no new light on the issue.

There are three key points to keep in mind when thinking about math curricular reform. First, it is unfair and incorrect to depict the "traditional" approach to math instruction as one in which "real-life problems" are withheld from students until after they've endured rote instruction. In fact, good "traditional" math teachers have always stressed conceptual understanding through the presentation of "real life" problems.

This contention can be supported in several ways (for example, a review of mathematics textbooks and curriculum guides over the past 100 years). Most notably, it is revealed in empirical data from the late 1980s and early 1990s (National Education Longitudinal Study: 1998) that high percentages of teachers and students report emphasizing and being exposed to conceptual learning and problem-solving activity in their math courses.

Second, the advocates of reform have failed to distinguish between "traditional" instruction and "poor teaching." The NELS: 98 data also indicate that in the early 1990s, between 20 percent and 30 percent of high school students sampled were taught by math teachers who could not identify the answer to a simple algebra problem or explain why the product of two negative numbers produced a positive result. Liping Ma's comparative study of 3rd grade teachers exposed similar problems of teacher quality.

This problem of teacher quality leads to a third key point related to the construction of experimental studies of curricular effectiveness. As suggested in your article, it is extremely difficult to control for the many factors that can threaten the validity of such experiments, such as teacher quality and motivation, students' entering and dropping out of curricular programs, and so forth. Advocates of reform will always be able to find some case where students in a particular program will outperform their nonprogram peers. But such special programs have not been shown to be either portable to other situations or robust against the problem of teacher quality.

To wrap it all up, it seems clear that students are more likely to learn more math when they are exposed to mathematically knowledgeable teachers and a balanced program combining conceptual understanding with skills practice and—yes—even rote learning.

Roger C. Shouse

Associate Professor of Education

Pennsylvania State University

University Park, Pa.

To the Editor:

Critics of the National Council of Teachers of Mathematics standards ask for evidence that the new constructivist curricula and teaching methods are effective. They maintain that "research hasn't delivered nearly enough evidence to warrant schools' switching" to new approaches.

What they refuse to acknowledge is the overwhelming body of evidence collected over the past 40 years that mathematics instruction, as it has been practiced in the United States, is a failure. The Third International Mathematics and Science Study, or TIMSS, is merely the latest and most exhaustive of studies to demonstrate this.

Your article states that the TIMSS in 1996 found that 8th graders were "in the middle of the pack," and that 12th graders "fell below average." This understates the actual findings. According to "Highlights From the TIMSS," published by the National Center for Education Statistics, 8th grade U.S. students "scored below the international average in mathematics" (below all the other G7 countries), while 12th graders' performance "was among the lowest in both science and mathematics, including ... our most advanced students." Every other international comparison since the launch of Sputnik had similar findings.

These terrible results cannot be blamed on the "New Math" of the 1960s or the "fuzzy math" of the 1990s. Mathematics teaching in most American schools hasn't changed since the Second World War.

So how can anyone advocate business as usual? Pay attention to the backgrounds of those who oppose reform. Cited in your article, Michael McKeowen, a co-founder of Mathematically Correct, is a professor of medical science, while Bastiaan J. Braams is a professor of mathematics. Other critics active with Mathematically Correct have similar positions: David Klein, professor of mathematics; Wayne Bishop, professor of mathematics and computer science; David Joyce, professor of mathematics and computer science; David Gelernter, professor of computer science. And so on.

These are among the very top 1 percent of our population in math proficiency. They spend most of their professional lives working with college students in the top 5 percent of our population—the tiny minority for whom skills-based instruction was effective. They are thus well insulated from the vast majority of American students who experience mathematics as a collection of arbitrary rules, who see math as irrelevant to their lives, who learn to hate math and vow to stay as far away from it as they can. Invisible to Mr. McKeowen and Mr. Braams are the large numbers of students who fail algebra and whose failure in algebra practically dooms them to fail high school.

I have degrees in engineering and computer science, but I have also taught math full time in the Chicago public schools. I now have the privilege of working with other teachers who dedicate their daily lives to helping their students make sense of mathematics. I find it offensive that these university math professors think they have anything to tell us about what works and what doesn't work with kids.

Can we say it again, please? Traditional American mathematics instruction is a proven failure! Against that background, the existing evidence of success of the Interactive Mathematics Program and other standards-based curricula is a powerful reason to change.

Thomas McDougal

Co-Director

Chicago Secondary Mathematics

Improvement Project

Chicago, Ill.

Vol. 22, Issue 25, Page 46

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