In 2001, the National Council on Education and the Disciplines (NCED) published

*Mathematics and Democracy: The Case for Quantitative Literacy,* which set the stage for the Mathematical Sciences Education Board to host a forum that December, co-sponsored by NCED and the MAA, titled Quantitative Literacy: Why Numeracy Matters for Schools and Colleges. Proceedings of the forum were published by NCED under the same title, and distributed along with

*Mathematics and Democracy* as MAA Notes #44 and #43. In

*Achieving Quantitative Literacy,* Lynn Steen summarizes the results of that forum, including numerous and generous quotations from presenters.

While *Achieving Quantitative Literacy* is that synopsis, its primary value to the educational community is likely to be that it is a superb introduction, overview, and inspiration for anyone who wants to know what QL is and why something needs to be done about it. With his usual grace and style, and possessing a view of Quantitative Literacy that is both broad and deep, the author has provided a small volume (only 115 pages) that makes clear the urgency for QL, that characterizes the enterprise of QL, and that calls for broad institutional commitments to interdisciplinary infusion of QL throughout college curricula.

Briefly, Quantitative Literacy is about reasoning in context and about making judgments based on real-world data and having real-world consequences. For example, if an article describes the size of a population as a "percent more than" another known group, can you calculate what that population is? From a newspaper graph that shows changes in the price of a stock, can you tell when the price was at its highest? If you are tested positive for a disease that has a low incidence, how worried should you be? If a drug is reported to have a side effect of doubling the risk of heart attack and stroke, should you stop taking the drug or is there other information that would be useful in making that decision? These examples demonstrate some of the reading and reasoning skills described as Quantitative Literacy.

Part I of *Achieving Quantitative Literacy* begins with a statement of the Five Findings of the forum, upon which the subsequent chapters elaborate. The Findings are:

- Many students finish their education ill prepared for the quantitative demands of contemporary life.
- The increasing importance of quantitative literacy is not sufficiently recognized by the public or by educational, political, and policy leaders.
- The lack of agreement on QL expectations at different levels of education makes it difficult to establish effective programs for QL education.
- QL is largely absent from our current system of assessment and accountability.
- Faculty in all disciplines need significant professional support in order for them to enhance the role of quantitative literacy in their courses.

Although there has been general agreement for millennia that mathematics is a useful skill for everyday life, Steen begins by making clear that the 21^{st} century will require the use of quantitative reasoning to a degree not previously even imagined. The ubiquity of technology, and especially its use of large databases and computer modeling, means that "success in the new information economy requires a new set of problem-solving and behavioral skills ... [including] the ability to make sense of real-world situations and to make judgments grounded in data [pp. 9-10]." Questions of social policy and civic health will require quantitative methods of analysis; individuals will need these skills to control their own lives and to participate in social decision making. Throughout, Steen makes clear that QL is a concern for both personal quality of life and for the survival of democratic society.

The focus on personal and societal well-being makes clear that Quantitative Literacy is not simply a set of "basic skills" that can be taught in a single academic course: it is a cumulative knowledge responsive to the dynamics of real life problems and experiential data, requiring the ability to develop appropriate analytic strategies and apply quantitative tools in context.

This is not to suggest that at present QL is widely taught in schools and colleges, or even that it a likely outcome of what is taught. Many college students finish a required mathematics course believing that the mathematics they have seen has little to do with their life outside the classroom. (Steen notes in a fascinating sidebar that while patterns in twentieth century college enrollments reflect increasing democratization of higher education, and while other disciplinary curricula have evolved over that century, college mathematics curricula have remained largely static, in a design emphasizing the priorities of an age when the college population represented a primarily elite class.) This is not to say that revised versions of presently required college courses should not be implemented for the new literacy (and examples of several institutional programs are found in Part II), but the reader is alerted early on that no single course, modified or not, will be able to provide the repeated exposures in a variety of contexts that the development of a functional quantitative literacy will require.

Those who are looking for a definitive list of "the QL skills" will not find it in this volume, but rather will find characterizations of Quantitative Literacy: QL requires, above all, "engagement with the world;" it includes "the ability to apply quantitative ideas in unfamiliar contexts;" and it requires "flexible thinking that adapts readily to new circumstances [p. 24]." Quantitative Literacy involves "sophisticated thinking with elementary mathematics more often than elementary thinking with sophisticated mathematics [p. 9]." QL is not a discipline but a way of thinking, a habit of mind.

Given that Quantitative Literacy is concerned with making sense of quantitative information found in contexts, and that the relatively recent phenomena of computer modeling and data collection create new contexts almost daily, it should not be surprising that a precise consensus of the skills comprising the QL tools has not yet evolved. In fact, it is easier to highlight counterexamples: QL is not College Algebra and is not likely to be found in such a course; QL is not Calculus, and the funneling of high school and college students into a Calculus track may well be counterproductive for such literacy; QL is not merely deductive reasoning. But beyond what Quantitative Literacy is not, QL programs will require challenging, college-level thinking, and must not be perceived to be "lower-track" or remedial mathematics.

Even without a consensus definition of QL skills, directions are emerging and some topics are generally accepted: ratios, percentages, probabilities, interpretation of information presented in graphical form, the language of statistics. To wait for more precision could tempt the community to reduce the QL enterprise to that of designing a single QL course with an ideal syllabus, but given that QL is inextricable from contexts, such an effort may itself be at odds with the QL task. Instead, Professor Steen calls for Quantitative Literacy to have a presence in the college curriculum analogous to the place it will have in today's students' lives: occurring in multiple and unexpected applications, wherever quantitative data and questions arise.

This perspective sets the stage for thinking about the implementation of Quantitative Literacy as a curricular component of higher education. It must be embedded in and infused throughout college curricula. It will deal with real questions, where they occur. It will use quantitative reasoning to make real-life judgments. It will be visited and re-visited, in multiple contexts and with increasing depth. And to reach this goal, broad institutional commitment will be required.

How will we get there? And what will be the role of mathematics? Mathematicians are obviously not the only educators who will need to address QL; in fact, they may not be the best qualified to teach it. Data-driven real-world problems are usually messy, often with unclear assumptions to be ferreted out and evaluated, using techniques far removed from what is learned in much of graduate mathematics education. The colleagues in the disciplines will be needed to explicate the issues and the methods of their professional areas for mathematicians, who may have to learn to listen in a new way. Because of the interdisciplinary composition of QL, no particular discipline has a natural leadership role in implementing a pedagogy. Nonetheless, the public accurately perceives mathematics' special foundational role for QL, and, while interdependent with colleagues across the curriculum, mathematics departments will necessarily bear a special responsibility for nurturing QL programs.

A particular difficulty for QL will be the problem of assessment. Because standardized test items are "generally decontextualized by design," meaningful assessment of QL "challenges the very notion of 'test' as that term is ordinarily understood [p. 57]." Nonetheless, "quantitative literacy must develop accepted methods of assessment if it is to achieve its goals [p. 59]," and Steen recommends the policy goal suggested by NSF director Rita Colwell of establishing benchmarks for QL proficiency as students move throughout their K-16 education.

Part I of this report concludes with Responses to the Five Findings of the Forum, including directions and clear suggestions for action. Many of these recommendations are viable starting points for a department or interdisciplinary task force that is ready to pursue Quantitative Literacy on its own campus.

Part II is the hands-on section of this volume. The first chapter contains a number of dialogues between mathematical insiders and skeptical outsiders that Steen has edited from e-mail discussions following the Forum. They will be helpful for the reader who anticipates conversations with colleagues, both in setting the stage for outsiders' perceptions of mathematics and the need for QL, and for challenging mathematicians' commonly held assumptions.

Having resisted definitions, Steen now provides a chapter of sample problems taken from QL course and assessment materials at a variety of institutions, including the examples cited above. The problems range from number sense (what is the approximate population of the United States? of the world?) to reading graphs (what characteristics do the clusters of points on a scatterplot represent?), to interpreting tabular data (what is the significance of this particular entry in a table compared to the other entries?), to percentages (should a company's change in participation in a retirement plan from 30% to 90% be reported as a 60% increase or a 200% increase?), to actual newspaper excerpts that call for analysis of their conclusions (do the 93% of those Chicago students who qualify for bussing to better schools but elect not to take it really prefer to attend a failing school?). The examples given make vividly clear the difference between what have been called (textbook) "exercises," i.e. problems that have been decontextualized, and (real) "problems."

Part II ends with brief descriptions of QL programs at six of the institutions that have joined forces to form the National Numeracy Network. The programs vary, each in keeping with the needs and resources of its home institution. Each is available as a resource to interested institutions, and contact persons are listed.

*Achieving Quantitative Literacy* appears ten years after the 1994 report of the CUPM Subcommittee on Quantitative Literacy, a five-year project chaired by Linda Sons. That report, which is available at http://www.maa.org/QL, includes a recommendation for two-tiered college Quantitative Literacy programs consisting of foundation experiences followed by continuing application experiences. In the decade since the report, a modest number of colleges (are known to) have implemented a variety of QL programs, and in 2004 the MAA established a Quantitative Literacy SIGMAA and the National Numeracy Network was founded. The QL SIGMAA maintains a webpage that is reachable through http://www.maa.org/SIGMAA, and which contains links to a variety of resources. A particularly rich site containing downloadable interdiscplinary material is found at Dartmouth http://math.dartmouth.edu/~mqed. Another link reaches Professor Steen's summaries of QL activity at 25 institutions, including contact persons for each and URLs for several of the programs.

So who needs this book? If you are a teacher of mathematics at the school or college level, you need to read this book. If you are on a committee to investigate or implement Quantitative Literacy at your institution, you need to give copies to all your committee members--and to your Dean and President as well. If you want to convey the spirit of QL to a skeptical colleague, give them this book.

Whether your institution has already established a Quantitative Literacy requirement or is just now investigating such a program, this reviewer highly recommends membership in the National Numeracy Network and the QL SIGMAA, and attendance at their sponsored sessions at the national MAA meetings. The members of both of these groups are most generous in sharing their experiences, insights and materials, much of which can be found through the mentioned websites.

The great accomplishment of *Achieving Quantitative Literacy* is that it articulates the urgent need with an eloquent philosophy of education and democracy, and a vision that is both compelling and awesome; yet it never forgets that the real-world mathematical/QL problems to be solved are everyday tasks that will often be contextually messy. As the Responses to the Findings demonstrate, the real-world implementation of QL education will also require everyday tasks that are not always elegant, and not always comfortable for mathematicians. Professor Steen says in the Preface that the purpose of *Achieving Quantitative Literacy* is "to pervade undergraduate education with a consciousness of the importance of QL." We hope that its readers will make that so.

Charlotte Chell is Professor of Mathematics and Computer Science at Carthage College in Kenosha, WI. She has served as Chair of Mathematics and Chair of the Division of Natural Science at Carthage. Her training is in mathematical logic, and her current interests are in quantitative literacy and applications of mathematics.