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Articles > Back to Basics–Wrong Answer for Math
Back to Basics–Wrong Answer for Math
by John Dossey
San Francisco Chronicle, September 5, 1997
A cellular phone company offers customers two plans. The first charges a $25 monthly service fee and 45 cents per minute, while the second has a $50 monthly service fee but charges only 25 cents per minute. Which is the better deal for you?
Answering this question requires knowing some basic arithmetic, but it also involves more sophisticated mathematical thinking. That's because the answer depends on how many hours a month you are likely to use the phone.
Such problems are typical of the real-life math challenges that schools must prepare students to handle. The question of how teachers can best do this is a source of controversy.
Some people back a clear-cut focus on "basics." All responsible educators agree that students must master fundamental math skills. But "basics" is also used as a code word for classroom methods biased toward memorizing, rote learning and downloading of information from an active teacher to passive students.
This approach has been tried and has failed. Long-standing reliance on "drill and kill" methods is a major reason why U.S. students have fared so poorly in international comparisons of student achievement. It is the demonstrated failure of this approach that has inspired the movement to improve math teaching in American schools.
Also, although students need the basics, they also need much more. Not only should they know how to solve story problems in a book, but more important, they should learn how to apply their knowledge to solve a myriad of everyday challenges. In the phone problem, for example, memorization of procedures and arithmetic skills will not by themselves allow a student to calculate that 125 minutes is the point at which the second plan becomes more economical. Before doing the calculation, students must first figure out what to multiply and divide in the first place. In other words, they must know how to "think" mathematically.
Beginning in 1989, the National Council of Teachers of Mathematics has worked to set standards for teaching and assessment. The NCTM standards emphasize problem-solving rather than rote learning, active rather than passive learning, and the need for students to be able to articulate the mathematical principles with which they are working.
The council's standards have slowly made their impact felt in U.S. classrooms. Research carried out as part of the Third International Mathematics and Science Study found that most eighth grade math teachers in the United States knew of the new standards, agreed with them, and had taken steps to incorporate more elements, such as problem-solving activities. And several high-quality texts exemplifying the standards are now on the market.
In the eight years since the standards were released, U.S. students' performance has risen. Data from the National Assessment of Educational Progress, which samples the performance of fourth, eighth, and twelfth-graders, show progressive improvement in all three grades between 1990 and 1996, the gains have been particularly strong in knowledge of math fundamentals between 1990 and 1996; the proportion of students performing at or above the basic level increased. These figures should silence any claims that U.S. schools are neglecting to teach basics.
U.S. math students are also faring better in relation to their peers in other countries. The Third International Mathematics and Science Study [TIMSS] showed U.S. fourth graders, on average, scored higher than those in 26 other countries.
However, we still have a long way to go. Given the gains of recent years, it would be tragic if, instead of pushing to further implement standards-based math instruction, schools succumbed to those who want to roll back the clock, barred textbooks that reflect the new approach and condemned U.S. students to discredited forms of teaching.
John Dossey, an Illinois State University math professor, is past-president of the National Council of Teachers of Mathematics (NCTM), and author of several secondary-school math programs.
© 1997 San Francisco Chronicle
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