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Exploring "Multiple Mathematics"

by W. Norton Grubb, University of California, Berkeley

In the analysis of literacy, the notion of "multiple literacies" has become common. People use reading and writing in many different forms--at work, at home, in trying to get information from various print and electronic media, for amusement and pleasure as well as for more utilitarian goals. The sophistication and tone of different literacies vary; assumptions about form and about what an individual can infer differ as well, and so some understanding of literacy in its different forms is valuable. In fact, the multiple literacies that people employ are often quite different from conventional "school literacy," which usually involves the reading of well-known literature; standard exercises in detailing plot, character, and theme; and familiar drills with synonyms, homonyms, sentence completion, and grammar. For all those who were turned off to Shakespeare in high school, the pain associated with "school literacy" is easily remembered.

The idea of literacy in many different contexts can just as easily be applied to mathematics. Mathematical thinking and calculation (both formal and informal) arise in different ways in various settings. These "multiple mathematics" can be quite different from "school mathematics" with its rigid progression through arithmetic, algebra I, geometry, algebra II, and calculus. In this standard curriculum, which is best suited to the preparation of college mathematics majors, the use of mathematics is ripped from any context and divorced from the various ways people do use mathematics (or could use it if they didn't find it so forbidding). And so--like the concept of multiple literacies--articulating the different worldly manifestations of mathematics might help us appreciate better both the sterility of the standard curriculum and possibilities for alternatives.

When I--an economist, but no expert in mathematics--think about the multiple ways ordinary people use mathematics, the following come to mind:

There are surely many other forms of mathematics. As the advocates of multiple literacies stress, the ways in which a subject is encountered are varied, sometimes hidden, often subtle and unsuspected, often providing opportunities for instruction that are otherwise lost. Indeed, by simply articulating a notion of "multiple mathematics," we may stimulate a search for the forms it might take in many walks of life. This is an urgent project for mathematicians, mathematics educators, and all those who mourn the sorry state of mathematics in this country.

Now, I would never argue that "multiple mathematics" should displace conventional school mathematics. Some advocates of whole language and literacy "in context" have gotten into trouble with parents and legislators for saying (or appearing to say) that drill should never be used, or that grammar and spelling are unimportant, or that standard literature is "irrelevant." So too in mathematics: it would be silly and extremist to argue that drills on formal operations or facility with algebraic and geometric representations are unimportant.

The trick is to devise curricula that use different approaches to support one another-- that introduce modeling as a way into the power of algebraic representation; or that examine gambling and the vagaries of the weather to begin the study of probability and stochastic thinking; or that examine the mathematics used at work to demonstrate its relevance and provide facility with application. In this way the notion of "multiple mathematics" could help inspire curricula with greater range, power, and motivation without abandoning the school mathematics that has left so many behind.

W. Norton Grubb, Site Director of the National Center for Research in Vocational Education (NCRVE), is a member of the faculty of the School of Education at the University of California, Berkeley 94720; He can be reached by e-mail at norton_grubb@maillink.berkeley.edu; or by fax at 510-642-3488.




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Last Update: 02/28/96