by Calvin C. Moore, University of California, Berkeley
California has taken the lead in upgrading mathematics education for
the 21st century. But while reforms are gradually taking hold, the majority
of classrooms still rely on a traditional mathematics curriculum, that,
as one cynical observer remarked, is largely composed of eight years of
15th century arithmetic, two years of 17th century algebra and one year
of 3rd century B.C. geometry.
The situation is further complicated by this summer's legislative debates over education. It seems that some critics are convinced that the state's current curriculum frameworks, and the recently blocked statewide assessment effort,would wreak havoc in the classroom. According to them, students need more basic skills and less problem-solving experience in mathematics. They claim a revival of the "back to basics" movement will solve our problems, which include low test scores at the kindergarten through 12-grade levels, and an increase in remedial courses for college students.
There are indeed, growing complaints from business and industry concerning the lack of math skills among students entering the workforce. Those complaints focus not just on basic skills, but more importantly on students' inability to put isolated facts together to solve problems or to engage in what we describe as higher level thinking and reasoning.
We in the universities see the same problems with students coming to us. As we confront the scientific and technical challenges of the Information Age, the need to extend mathematical literacy beyond a small cadre to include all levels of the work force has never been more acute.
But let's set the record straight. The reforms demand that children master basic skills, for without these, they cannot proceed at all. Where the reforms differ from traditional practice is that they no longer subject children to years of mind-numbing drill and the manipulation of symbols and formulas, to which students attach little or no meaning. Instead the reforms insist that children build on their basic skills to develop problem solving skills involving real problems -- not superficial exercises. In short, students are asked to start doing some real mathematics.
Mathematics is a growing, evolving, and vigorous body of scientific knowledge that is often described as the science of patterns -- a way of thinking that helps to analyze complex patterns in the world around us and to bring order and simplicity to it. The role of mathematics is to produce economy of thought, just as a machine produces economy of physical effort. Mathematics is an unusually powerful tool for solving problems, not only in science and engineering , but in many other fields as well, and for analyzing and bringing order to the complex world in which we live. We want our students to think mathematically, and to discover that mathematics, while based on abstractions, is closely related to the real world of solving problems.
Such reforms demands more of students by asking them to think and reason on a higher level than ever before. They ask teachers to have high expectations for all their students. And they emphasize that learning is an active process. Students should not be memorizing mathematics passively, but rather using their knowledge to solve problems. If you use what you know, you'll remember it.
These reforms in mathematics education began with the establishment of standards for curriculum and instruction by the National Council of Teachers of Mathematics. Such standards are a way of holding up a flag and saying this is where we want to go. They provide a yardstick to let us know how well our students are being prepared for the 21st century. Our State Mathematics Framework is aligned with the NCTM standards. A number of innovative curriculums and curricular modules based on these standards have been developed and are being implemented gradually and thoughtfully in many school districts.
But the standards only establish goals; they indicate where we should be going, not how to get there. They do not tell us how to teach, but they do tell us whether we're "measuring up." Standards and their implementation should be strictly limited to the core academic curriculum, for when they have been extended to embrace opinions, values, and attitudes or feelings of students, we run the risk of jeopardizing the original purpose of reform.
The technological future invites our children to explore the essence of mathematics, which is to describe and understand the order that underlies apparently complex and diverse situations . Why block that road to the future? If we recognize the wisdom of sustaining mathematics reform efforts now, we will see in the next generation a society of productive wage-earners and decision-makers who can tackle the complex and diverse problems of our time.
Calvin Moore is Professor of Mathematics at the University of California at Berkeley. This article is reprinted from the Sacremento Bee, October 18, 1995.