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Math and Learning

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President Clinton was right to congratulate the nation's 4th grade students on their accomplishments following the release in June of the Third International Mathematics and Science Study, or TIMSS. The study showed that American 4th graders ranked second in the world in science, though only 8th in math. But TIMSS also raises a deep concern, particularly in mathematics. By the 8th grade, our students have fallen to 28th place in the international mathematics rankings. That is, between the 4th and the 8th grades, U.S. students have slipped from a bit above average to well below average in math. What is being done in classrooms across the globe that doesn't happen in the U.S. classroom? A fuller look at the TIMSS results is needed.

The Third International Mathematics and Science Study does far more than rank student performance: It documents the multiplicity of reasons for our nation's trouble in mathematics. It discloses an unfocused curriculum that, in trying to cover too much ground, slides by math fundamentals. It reveals that our math textbooks are poorly written and pedagogically unsound. And it strongly implies that America's teaching corps is simply ill-prepared to meet the demands of today's math classroom. TIMSS explains why parents, employers, and colleges have complained that high school graduates are glaringly deficient even in the three R's.

Political leaders of both parties have certainly recognized the need to address this crisis. America 2000, initiated by President Bush and adopted in somewhat different form as the Goals 2000 Act signed by President Clinton, calls for national standards in every educational discipline. President Clinton is calling for nationwide student testing to help track the need for, and success of, math reforms.

Recognizing the need for exemplary mathematics education, the National Council of Teachers of Mathematics, with support from the National Science Foundation, has formulated national mathematics standards. Individual states, as well as many cities and school districts, have seized on these guidelines and are implementing reforms.

But these "reform" standards face the same pitfalls the international math and science study describes--a lack of focus and the repercussions that come from poor teaching. Instead of concentrating on a thorough understanding of core areas, they take instruction for our technological society as requiring a wide variety of topics past the traditional core. Never mind that this calls for more and better preparation by a teacher corps already working past the borders of their training. Never mind that the new pedagogy, developed at a cost of millions of dollars, turns out to require more, not less, teacher ability, effort, and knowledge to be successful.

These are not merely theoretical concerns, as California found out the hard way. A California "framework" for the study of mathematics was drawn up, implemented--and the country watched the state's mathematical performance nose-dive. The California framework, and the NCTM standards, are in the process of revision. Fortunately, the TIMSS results are now here to act as a guide.

In any case, standards alone cannot put American students into the top bracket by 2000. The Third International Mathematics and Science Study warns unequivocally: U.S. students need to work toward a better, deeper understanding of mathematics--the "how" and "why" behind the equations. Without a clear, consistent vision for teaching math, there is little chance for any of our children to ever meet these standards. And this vision must start with the people whose job it is to impart knowledge to them: the teachers.

Politics has effectively frozen out of math education what would be a powerful resource—the American mathematics-research community.

This brings us to teacher training and certification, and to the colleges and universities that train teachers. How often have I heard faculty members moan that "if only" a requirement could be put in place that pre-service teachers get at least a grade of B in their undergraduate math courses? Or--for that more lofty level of teacher preparation, a master's degree--that the required math courses in the teacher training program "had to be" watered down? The American Federation of Teachers has been fighting a lonely battle asking for content quality in courses and better teaching knowledge in performance. It is time the AFT got some allies.

These are both national political questions and university-style political questions. Politics has effectively frozen out of mathematics education what would be a powerful resource--the American mathematics-research community. This community is not just world-class; indeed, it is No. 1 in the world. It is time its views were taken seriously by the education establishment. These mathematicians are perfectly capable of drawing up wonderful curricula and writing comprehensive, understandable textbooks. One excellent example is the Gelfand Outreach Program in Mathematics, based at Rutgers University. This program's creator and director is a famous research mathematician, a member of the National Academy of Sciences, and a recipient of a MacArthur Foundation "genius" award. Professor Israel M. Gelfand has written high-school-level textbooks that outshine those written under the aegis of the famous Japanese research mathematician Kunihiko Kodaira. But Mr. Gelfand's books are almost unknown in this country, while Mr. Kodaira's are used throughout the Japanese school system. It is not merely coincidental that Japan places third in the TIMSS 8th grade findings, while the United States places 28th.

The TIMSS project will release its 12th grade findings next spring. Preliminary indications already warn that the United States will make an even poorer showing than at the 8th grade level. The problem is systemic, and covers every level of math education.

Given the opportunity, the mathematics and mathematics education communities can make great strides in better preparing elementary and secondary teachers for the demands of the 21st century. If we can find consensus on our vision for mathematics education, we can begin to make real change happen. The solutions are out there--now we need to focus our attention on where to look.


Madge Goldman, the president of the Gabriella and Paul Rosenbaum Foundation in Chicago, has been a leading advocate in the private philanthropic community for the funding of basic mathematical research in the United States and around the world. She lives in Bryn Mawr, Pa.

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