by Shirley Malcom, American Association for the Advancement of Science
Excerpted with permission from "Why Numbers Count: Quantitative Literacy for Tomorrow's America," Copyright (c) College Entrance Examination Board, 1997. All rights reserved.
Many years ago Lucy Sells identified mathematics as the "critical filter" for education. Is that metaphor still apt?
I would say that mathematics is even more of a critical filter then ever. If anything it has ceased being just a gatekeeper for entry into college majors and has become the determiner of participation in courses of study at the high school level such as advanced, vocational, and technical programs. Whether your employer is willing to invest in your retraining or upgrading of skills may also be a function of your attitude about and willingness to work at mastering mathematics.
Do you believe that prospective students of science should study different mathematics in high school from that which vocational students study? Can the same curriculum serve all students in high school?
I really chafe at the idea that different students need different mathematics. Let's say we should have the same standards, the same mathematics concepts with very different examples. We may need to emphasize different topics (going more deeply into statistics, for example, for technical education students who may need these skills in manufacturing settings). Whether that must equate to providing different curricula depends on the attitudes and skills of the teachers and the willingness to accommodate any kind of difference.
I do not believe that the shop students need less mathematics, however. Studies such as What Work Requires of Schools (the SCANS report) and America's Choice: High Skills or Low Wages (the report of the Commission on the Skills of the American Workforce) emphasize that curricular ghettos will not work in the new economic reality. Mathematics needs to make explicit connections with other subject areas, with the world of work and with people's regular lives.
What about honors courses, and special programs for the gifted and talented? Don't these children deserve courses appropriate to their abilities and interests?
Let me tell you about an experience I had just a few months ago. I was visiting a high school in a university town where the science teachers had decided on their own that there was really no difference between honors and regular pre-college courses. The way they were taught, they were really the same course. In their view, tracking was not compatible with where they wanted to go with standards.
Well, the community, especially the university faculty, was up in arms. They perceived this as a move to endorse watered-down science. And besides, they said, not all these kids are equally motivated, and not all of them are this or that. They couldn't possibly imagine their children being in the same classes with these others. It was really heavy. People were not speaking with each other, and I got e-mail asking if I really understood that I was getting into. You wouldn't believe the posturing that I encountered.
It really took people by surprise when I didn't come at the issue from the perspective of tracking. Instead, I asked what things we want all children to know and be able to do? Where are the standards taking us? Most people did agree that slicing the student population into horizontal bands is not particularly helpful if your goal is to move towards those standards.
But as you know, mathematics is the most tracked of all subjects, and most mathematics teachers believe strongly that tracking leads to the most effective education for all students. Does tracking in mathematics classes enhance or diminish the prospects for a quantitatively literate population?
The issues in mathematics are particularly problematic. Tracking supports mathematics education as we have known it--topic specific, disconnected from rich examples, a race through the concepts and the textbook. Let's face it; this stuff is just a lot easier for some people to master than for others.
Teachers seem to allow very little variation in the way mathematics is taught and presented. If you made real changes in the way mathematics is taught, you'd find interesting surprises, both about people's capacity to learn but also about mathematics itself. You'd discover lots of "unfound" mathematics that happens to exist in the world, and in people's minds, but not in the textbook. We've barely begun to examine the deep implications of how we must rethink the discipline and the way that it is taught in order to be inclusive. The linear topical approach may not support the way most people really operate. This idea of turning content on its head to fit the subject to the audience is the real uncharted territory of mathematics education.
Shirley Malcom is director of education and human resources programs at the American Association for the Advancement of Science. She also serves on the National Science Board and the President's Council of Advisors on Science and Technology. She can be reached by e-mail at firstname.lastname@example.org.
Last Update: July 17, 1997