Quantitative Literacy and SIAMApril 3, 2002
A national forum, Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, was held in Washington, DC, on the tropical weekend of December 1-2. Sponsored by the National Council on Education and the Disciplines (NCED) at the Woodrow Wilson National Fellowship Foundation, the forum was hosted by the Mathematical Sciences Education Board in cooperation with the Mathematical Association of America. It was attended by a diverse group of 100 policy experts, administrators, and secondary and college mathematics teachers, who listened to invited speakers, were heard in discussion and break-out sessions, and contributed to a white paper that will summarize the conclusions of the forum. I was one of the few SIAM members---perhaps the only one---in attendance, so I thought a report to SIAM members might be in order.
The idea of quantitative literacy has been around for well over a decade. Books by Sheila Tobias, in 1978 , and John Paulos, in 1988 , were like voices in the wilderness, raising an early warning about quantitative literacy. Concerns about quantitative literacy were expressed by the economic and labor sector in such early reports as What Work Requires of Schools: A SCANS Report for 2000 , arguing for higher quantitative skills across the work force. More recently, the case for quantitative literacy was made in reports commissioned by the American Mathematical Association for Two-Year Colleges, MAA, and The College Board [4,5,7]. The recent forum coincided with the NCED's release of the monograph Mathematics and Democracy: The Case for Quantitative Literacy , which eloquently restates the case with some urgency. The proceedings of the forum and nine commissioned papers will appear in subsequent volumes.
Any discussion of quantitative literacy begins with a basic question: What is it? Most forum participants were not overly concerned about a concise definition of quantitative literacy; some preferred the terms "numeracy," "quantitative reasoning," or "mathematical literacy." Many agreed that quantitative literacy (like pornography) is easy to recognize, even though it may be difficult to define. Participants were in agreement, however, about certain aspects of quantitative literacy.
One approach is to cast quantitative literacy as a collection of skills-basic mathematical, statistical reasoning, critical thinking, and problem-solving skills. Like literacy itself, these are survival skills, needed by any person who wants to understand and make decisions in a complex world flooded with data. Some forum participants cited the citizenship side of quantitative literacy: In order to function as a citizen, one must possess the skills needed to read a decent newspaper and to make informed voting decisions. For some participants, quantitative literacy is not only a collection of skills, but also a frame of mind-a feeling of comfort and confidence when it comes to basic quantitative thinking and discourse.
Others pointed to historical or cultural aspects of quantitative literacy: It provides students with an idea of the power and utility of mathematics, and makes them aware of how it has shaped the society in which we now live. Some participants emphasized the distinction between quantitative literacy and mathematics, pointing out that quantitative literacy is neither a discipline of its own nor a subdiscipline of mathematics. Whereas mathematics tends to be hierarchical and abstract, quantitative literacy is broad, outreaching, and practical because of its interfaces with other disciplines. Indeed, it was stated repeatedly during the forum that quantitative literacy is mathematics in context; it is mathematics as it arises in diverse real situations.
Another approach is to be prescriptive about quantitative literacy. It is possible to list mathematical themes associated with quantitative literacy, together with representative situations in which they might arise. Themes frequently suggested for inclusion in the list include:
- Critical and logical thinking---for navigating the media, avoiding deception by advertisers, and understanding ballot initiatives.
- Number sense, estimation, and percentages---for handling currency exchanges; understanding economic situations, such as the Social Security debate; and maintaining perspective on such quantities as the federal debt or world population.
- Statistical reasoning---for reading statistical studies and evaluating them critically.
- Basic financial concepts---for assessing loan options and comparing investment plans.
- Exponential and linear modeling---for understanding the behavior of populations, prices, tumors, and drugs in the blood.
- Elementary probability---for assessing travel and health risks, understanding lotteries and medical tests, and making decisions about insurance policies.
The list is hardly exhaustive, but it makes the point that quantitative literacy should be viewed as an essential part of all disciplines. It involves relatively elementary skills applied to what are often sophisticated situations. For students, it is vital to their success in future courses, their careers, and in fact their lives.
When it comes to implementing quantitative literacy programs at colleges and universities, the forum provided few specific conclusions. But some key observations suggest why teaching quantitative literacy courses is a challenge. While the calculus reform of the 1990s produced lasting changes, it had little impact on non-calculus-bound students. These students form the primary audience for quantitative literacy initiatives (although it may be wrong to assume that calculus-bound students are necessarily quantitatively literate). Calculus reform involved students with relatively homogeneous needs and backgrounds, and mathematicians could confidently lead the charge. By contrast, quantitative literacy courses involve students with far more diverse needs and backgrounds, and this group makes up a large majority of all students in mathematics and statistics courses. These students come from the entire academic spectrum, and for that reason, a quantitative literacy "reform" must involve not only mathematics faculties, but faculties from that same broad spectrum.
Forum participants agreed that in its ultimate expression, quantitative literacy should be woven throughout the undergraduate curriculum, with threads in many courses. Seen on this scale, an emphasis on quantitative literacy will involve a significant shift in perspective on the part of teachers and a rethinking of content for many courses. Realistically, change of this enormity will occur slowly, and only if there is a constant pressure to maintain quantitative literacy as an institutional priority. Forum participants were in general agreement about the role of the mathematics/statistics community in implementing a quantitative literacy program: Through the professional societies and through the efforts of individuals on their own campuses, mathematics/statistics educators must initiate and sustain this collaborative effort.
Realizing the time scale involved in integrating quantitative literacy throughout the curriculum, some forum participants urged a more immediate and incremental approach. Many colleges and universities already offer individual quantitative literacy courses (often called general education or liberal arts mathematics), and there is a wealth of material available to support such courses. These courses often capture the spirit and purpose of quantitative literacy. If these single courses evolve into course clusters, which are further integrated into core curricula, then progress will be made in establishing full quantitative literacy programs.
Given this account of quantitative literacy, perhaps it's evident how SIAM-at least its education wing-might contribute. If pressed to describe quantitative literacy in a few words, one might claim that it is applied elementary mathematics. SIAM's long tradition of outreach and service to other disciplines is entirely consistent with the spirit of quantitative literacy. Its diverse membership and its mission of promoting applied mathematics make SIAM a natural participant in the quantitative literacy conversation. At the organizational level, SIAM should be aware of the progress of the quantitative literacy "movement," and become engaged as opportunities arise. At the same time, individual members should know that the quantitative literacy discussion will inevitably come to their campuses, and should be ready and willing to get involved. The process of integrating quantitative literacy into the undergraduate curriculum will be long and challenging, but SIAM has much to gain and much to offer by being a partner.
 J.A. Paulos, Innumeracy: Mathematical Illiteracy and Its Consequences, Vintage Books, New York, 1988.
 L.A. Steen, ed., Mathematics and Democracy: The Case for Quantitative Literacy, prepared by the National Council on Education and the Disciplines, 2001.
 S. Tobias, Overcoming Math Anxiety, Houghton Mifflin, New York, 1978. Revised edition, W.W. Norton, New York, 1993.
 Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, American Mathematical Association for Two-Year Colleges, 1995.
 Quantitative Reasoning for College Graduates: A Complement to the Standards, Mathematical Association of America, 1995.
 What Work Requires of Schools: A SCANS Report for 2000, Secretary's Commission on Achieving Necessary Skills (SCANS), U.S. Department of Labor, Washington, DC, 1991.
 Why Numbers Count: Qualitative Literacy for Tomorrow's America, The College Board, 1997.
William Briggs is a professor of mathematics at the University of Colorado at Denver.