Focus on Calculus
A Newsletter for the Calculus Consortium Based at Harvard University
Winter 1997, Issue No. 12

IN THIS ISSUE
Preparing TAs to Teach Reformed College Algebra at the University of Missouri
Sandi Athanassiou

Calculus in Inner City High Schools: Equity and Reform
Robert W. Case

"New and "Old" Calculus:
Student Reactions and Comments

Sheldon P. Gordon

Brief Calculus for Business, Social Sciences, and Life Sciences
Patti Frazer Lock

Sixth Conference on the Teaching of Mathematics
Upcoming Workshops
From the Publisher
About this Newsletter

Global Review Faults U.S. Curricula

Gretchen Vogel, Science Magazine


It's a student tradition to blame a bad grade in science or math on a teacher who didn't spend enough time explaining the material. Although most parents don't buy that excuse, a new international study suggests that U.S. elementary- and secondary-school students may have a point. Being taught from a syllabus that's "a mile wide and an inch deep," says one report, could be one reason why U.S. students do relatively poorly on international achievement tests.

The Third International Mathematics and Science Study (TIMSS), which [in October] released its first set of four reports, is a 5-year international project to compare curricula and achievement in 50 countries. ... The new reports examine the international teaching of science as well as mathematics, offer in-depth case studies from six countries, and compare the U.S. results to the rest of the world. The first student achievement results and reports on curricula in many other countries [were] released in November.

The first report reveals marked differences in the way math and science are taught around the world, says William Schmidt, a statistician at Michigan State University and U.S. coordinator for the study. The U.S. curriculum, described in a report entitled "A Splintered Vision: An Investigation of U.S. Science and Mathematics Education," attempts to cover many more topics in a single year than the international average. Teachers respond by trying to teach a topic a week, says education professor Marcia Linn of the University of California, Berkeley, an adviser to the TIMSS study, but that approach "denies students the opportunity to find out what it is like to have a deep understanding of any subject." That approach may be reflected in the lower scores of U.S. students on standardized math and science tests, Schmidt says.

In recent years, standards issued by the National Council of Teachers of Mathematics, the American Association for the Advancement of Science (publisher of Science), and the National Research Council have tried to address the problem, which includes broad, unfocused textbooks. While the standards are on the right track, Schmidt says, they end up as part of a "babble of voices," sending conflicting messages about which topics to cover. Local school authorities, in attempting to please everyone, add to existing teaching guides without dropping anything, he notes.

The decentralized U.S. educational system compounds the problem, say the authors. Although the system has many advantages, they cite the need to win consensus at the local level as a further source of curriculum overload. Linn agrees. "It's a lot easier for a committee to add topics than to drop them from the curriculum," she says.

Schmidt says the report calls for making tough choices on what to omit. "We leave the debate over how to do that to the public and to Congress," he says. "But there are no magic bullets."

Reprinted with permission from Science, Vol. 274, October 18, 1996. Copyright 1996 American Association for the Advancement of Science.)


More is less?
The graph below shows that the U.S. covers topics about 2.5 grades longer than the international median number of grades. Topics such as geometry, fractions, and functions linger for years in the U.S. math curriculum, leaving too little time for in-depth coverage.



Graph is adapted from "Splintered Vision: An Investigation of U.S. Mathematics and Science Education," by William H. Schmidt, Curtis C. McKnight, and Senta A. Raizen, Kluwer Academic Publishers Group (in press).

Editor's Note
The TIMSS is a sweeping international study conducted between 1991 and 1995. It assessed the intended curriculum (what textbooks and frameworks say students should learn), the implemented curriculum (through video, case study, and teacher survey data about what is taught and how), and the attained curriculum (through achievement tests to 500,000 students ages 9, 13, and 18). These three aspects of the study provide a complex picture of the relationship between curriculum and achievement that can inform math and science education reform. The study provides a portrait of American mathematics education early in the wave of reforms that have taken hold in the last few years, and the findings reveal many of the issues mathematics educators are seeking to address.

For more information about TIMSS, visit the TIMSS site on the Web.



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