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:

- Mathematics at work is crucial, as employers have been telling us;
it also varies enormously, and provides many examples of application, of
"usefulness," and "relevance." Mathematics at work often involves a
complex series of applications of relatively low-level mathematics or
application to ill-defined problems. The complexity of the application is
more important than the sophistication of the "school" mathematics. In
other cases some relatively primitive mathematical understanding would
help workers interpret better what they do. For example, few people--and
not very many doctors--understand the variability inherent in medical
tests. As a result their inferences are often wrong.
- People employ mathematical thinking to extract information from
graphs, charts, maps, newspaper articles, and other visual devices that
display information. (Some of these competencies have been incorporated
into the concept of "document literacy" developed by the Educational
Testing Service.) Without such facility, individuals may not be able to
understand what they need for civic purposes, or parental
responsibilities, or simply for daily life.
- In many social and natural sciences, algebraic expressions and
geometric displays are used to model complex phenomena. But the notion of
modeling in general, and mathematical modeling in particular, is
difficult. My economics students have a hard time moving from the reality
of economic phenomena to simplified models and back again, and traditional
"school math" in no way prepares them to do this.
- Many aspects of "common sense" and "judgment"--competencies in scarce
supply in work as well as other settings--require aspects of mathematical
thinking even though formal calculations may be irrelevant: strategic
thinking in the face of uncertainty, rough calculation of expected
outcomes, probabilistic estimates, and rudimentary benefit-cost
comparisons.
- "Street mathematics" can be seen in many contexts: merchants who
mentally calculate prices and negotiate discounts; children who
strategize about sports competitions; even school drop-outs who thrive
in a drug economy. Many of these individuals have failed "school
mathematics," yet clearly demonstrate a kind of mathematical power in
contexts that are meaningful to them.
- Just as there is escapist reading and both reading and writing for
aesthetic purposes, so there is escapist mathematics (puzzles and games)
and a kind of "mathematics for art"--golden rectangles, classic
proportions, tessellations, symmetry, Escher. In recent years, chaos
theory and fractals have stimulated the public imagination. Yet these
pleasurable uses of mathematics are unavailable to most people because
"school math" requires that they progress through a lot of boring stuff
before they can understand the fun stuff.

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.*

*Last Update: *02/28/96