by F. James Rutherford, 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.*

Students are taught mathematical formulas on the assumption that they will then be able to apply them correctly in any appropriate context. But how are people supposed to recognize an appropriate context when they see one? How are they supposed to know which quantities are the correct ones to use in a given context? Are light-years distance or time? What about microns? Is it okay to express the speed of an elevator as "floors/minute"? Are "shares of stock sold/hour" on the New York Stock Exchange and "gallons of water/minute" flowing at some point in the Colorado River measures of speed, even though distance is not involved? For that matter, is a year always the same amount of time?

The truth is that people have difficulty using context-free knowledge and skills in everyday situations. It is instructive that the two rates most people can manipulate with some mathematical ease have to do with automobile speed and wages. The more abstract the mathematical construct, the less likely it is to be used in the practical affairs of everyday life.

This argument that quantitative literacy is contextual has significant educational ramifications. It suggests, for one thing, that the starting place for deciding what constitutes quantitative literacy is less mathematics itself than the contexts in which people are most likely to encounter the need for mathematical insights and skills. It also leads to the radical possibility that much of the teaching of mathematics--something different from the application of mathematics already learned--ought to take place in subjects other than mathematics. The latter proposition is, however, not likely to be warmly embraced either by mathematics teachers (who take the teaching of mathematics to be their rather exclusive responsibility) or by the teachers of other subjects (who believe they have more than enough to teach already and lack training in teaching mathematics).

To begin with, it is important to overcome the widespread belief--fostered all too often by the way mathematics is taught--that mathematics is only another name for computation ... . This misconception interferes with seeing mathematics as a science in its own right, as a science of abstract patterns and relationships that may sometimes be quantitative but can also be logical, spatial, temporal, functional, or, as is often the case, a combination of such forms.

From the perspective of science, quantitative literacy includes understanding the nature, importance, and limitations of measurement ... . To achieve such insights, students need to have extensive experience taking measurements in many different contexts--measurements that are used for computation that serves some sensible question that students care about or that are used to critique the mathematical treatment of quantities by others. This should happen in all classes where quantitative data are used--science and social studies, of course, but also (and especially) in mathematics, the natural refuge of measurement-free numbers.

* Jim Rutherford is chief education officer for the American
Association for the Advancement of Science and director of Project 2061,
a nationwide project intended to reform the teaching of K-12 science.
He can be reached by e-mail at*` jrutherf@aaas.org. `

*Last Update: * July 17, 1997