## Quantitative Literacy: GOALS

The foremost objective of both liberal and professional types of higher education should be to produce well-educated, enlightened citizens, who can reason cogently, communicate clearly, solve problems, and lead satisfying, productive lives.

What should every college graduate know about mathematics? What would you teach [undergraduate] students if they took only one term [or two terms] of math during their entire college career[s]?'' (For All Practical Purposes, (1988)).

No college course can make up for years of neglect or misdirection in earlier mathematics education. If the NCTM {\it Curriculum and Evaluation Standards for School Mathematics} are widely adopted and pursued relentlessly, eventually there will be no need to try. Until they are, however, remediation will be a necessary component of quantitative literacy efforts at most colleges and universities. At this level mathematics that has been encountered unsuccessfully over and over again must be presented subversively.'' Make it look fresh and different! Significant mathematical ideas and techniques should be developed within compelling applied contexts as natural, powerful tools for understanding and description. If no genuine application of a topic can be found at the appropriate level, omit it.

It has been suggested that every college mathematics course should be conceived as though it were to be the students' last--for in most cases, it will be (Reaching for Science Literacy,'' Lynn Steen, Change, July/August, '91). Understandably, the prevailing view of mathematics condemns it as nothing more than a confusing set of rules for manipulating symbols out of context and naming geometric shapes. It is seen as old, static, and intellectually confining. Any attempt to achieve quantitative literacy must refute these stereotypes by portraying mathematics as broadly useful in contemporary life connected to learners' experiences and by stressing the active, experimental, open-ended aspects of mathematical thinking and mathematical problems. It is becoming clearer and clearer that how people learn is just as important as what they learn. In order to build confidence in our students that they can read and learn mathematics on their own, it is essential that we set good examples by the pedagogical strategies we choose. Replace lectures as the primary means of delivery with more active, engaging experiences. Require teamwork, discussion and writing about mathematics. Emphasize making sense of inherently quantitative situations, problem formulation and heuristics at the expense of mechanics. Insist that calculators and computers be used routinely to carry the burden of computation and for intelligent exploration.

Any effective attack on the problem of quantitative literacy must recognize that not all mathematical roads are narrow, algebraic ones that lead to calculus. Today's routes must offer glimpses of a broad mathematical landscape with applications prominent in the foreground. To achieve some depth along the way, college students must be taught to view landmarks from a variety of perspectives-- numerical, visual, verbal and symbolic. They must learn that understanding, explanation and prediction are the real mathematical destinations, not the answers in the backs of textbooks. Unless we repeatedly immerse students in interesting quantitative settings that require drawing inferences from data, interpreting models, estimating results, assessing risks, suggesting alternatives, and even making reasonable, testable guesses, students will never see the forest for the trees.

In short, every college graduate should be able to apply simple mathematical methods to the solution of real-world problems. A quantitatively literate college graduate should be able to:

1. Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.

2. Represent mathematical information symbolically, visually, numerically, and verbally.
3. Use arithmetical, algebraic, geometric and statistical methods to solve problems.

4. Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results.

5. Recognize that mathematical and statistical methods have limits.

These five capabilities could be attained at varying levels. In particular the level intended here is beyond that normally attained in the high school experience. Explicitly college-bound high school students are generally expected to have three, and encouraged to have four, years of college preparatory high school mathematics. A quantitatively literate {\it college} graduate should be expected to have deeper and broader experiences than those who only graduate from high school. The level of sophistication and maturity of thinking expected of a college student should extend to a capability for quantitative reasoning which is commensurate with the college experience. College students should be expected to go beyond routine problem solving to handle problem situations of greater complexity and diversity, and to connect ideas and procedures more readily with other topics both within and outside mathematics.

Some guidance here can be attained from the manner in which the NCTM Curriculum and Evaluation Standards treat their school goals of problem solving, communication, and reasoning. These three standards persist throughout their K-12 curriculum but details vary between levels with respect to what is expected both of students and of instruction. This variation reflects the developmental level of the students, their mathematical background, and the specific mathematics content'' (p. 11). In one sense quantitative literacy for college students may be seen as extending the notion of mathematical power described in the NCTM Standards -- it includes methods of investigating and reasoning, means of communication, and notions of context'' (p. 5) -- to the intellectual developmental level expected in a post-secondary education. Although quantitative literacy for college students would include some mathematical content, it especially involves the ability to use concepts, procedures, and intellectual processes. It should also include a degree of versatility in approaching and solving problems.

Too big an order for a one- or two-term mathematics course? Unquestionably. Just as writing is not the sole province of English departments, neither does the responsibility for students' mathematical development rest only with mathematicians. Of course, the impetus to promote quantitative literacy , the leadership to define its elements effectively, and the energy to sustain its objectives will have to reside in the mathematical community. But mathematics must permeate the undergraduate experience the same way it permeates modern society: MATHEMATICS ACROSS THE CURRICULUM!