Would you recognize quantitative literacy if you heard it? Probably we all have encountered egregious cases of quantitative illiteracy, or as it is sometimes called, innumeracy, in the newspaper, on television, at the grocery store, or in political debate. But how would you define quantitative literacy, and more to the point, how would you broadly prepare a citizenry for the numerical and quantitative needs of the present and the future?

That's the purpose of *Mathematics and Democracy, The Case for Quantitative Literacy*. The National Council on Education and the Disciplines prepared this book with executive editor Lynn Steen. A Design Team of 16 contributors looked into the meaning of numeracy in contemporary society. Twelve of the Design Team are mathematical scientists and educators at a range of institutions. The remaining 4 of the team are from other areas of education and administration. The team wrote a 20 page prefatory "Case for Quantitative Literacy" and then invited responses from 13 authors. The respondents, including historians, mathematicians, scientists, educators, and higher education association administrators each wrote a personal essay of 4 to 6 pages addressing some aspect of the Case Statement, creating a slender volume. An Epilogue by Lynn Steen summarizes and tentatively suggests next steps. Several bibliographies provide additional reading and resources. Despite the title, which might suggest that the book is about the mathematics of social choice and fair division, the book is really about the goals and difficulties of educating a populace.

So what is quantitative literacy? It seems to be easy to recognize its absence, somewhat easy to "know it when you see it", and slippery to pin it down exactly enough to create a meaningful curriculum for it. One respondent (Alfred Manaster, page 68) says bluntly "the meaning of quantitative literacy is not well established" and the Case Statement itself says "although almost everyone agrees that quantitative literacy is important, there is little agreement on just what it is." A succinct working definition (page 68) is that "quantitative literacy is the ability to understand and reason with numerical information", to which I might add logical information and perhaps symbolic information in the form of graphs, charts and diagrams. The Case Statement explores in depth three dimensions of quantitative literacy or QL for short: the elements of QL, the expression of QL, and the skills of QL. While the result is not a definition that could be written on a matchbook cover, it is sufficient to begin exploring what to do about QL.

The Case Statement lays out several themes that are debated by the respondents. They are

- The definition of QL,
- The distinctness of QL from mathematics,
- The distinctness of QL from statistics,
- The failure (or success) of mathematics as we know it to teach QL,
- The effects of QL on policy and culture, and vice versa,
- The dependence of QL on context.

I found the essays by historians Patricia Cline Cohen and Joan L. Richards to be particularly interesting because they put a 200-year context on the current "math wars". Of course, "we haven't always done it this way" and the broad societal demand for numeracy (and mathematics) is a relatively recent development. Several of the essays by mathematicians discuss the uneasy relationship between mathematics and QL. Deborah Hughes-Hallett echoes the Case Statement (page 94) by summarizing "Mathematics focuses on climbing the ladder of abstraction, while quantitative literacy clings to context." The respondents are divided on the issue of whether the mathematical sciences are the proper place to teach QL. Lynn Steen says in the Epilogue "more mathematics does not necessarily lead to increased numeracy". But other respondents suggest that at least the mathematical sciences are in the best position to start teaching QL, saying in effect, if not us, then who?

The book is readable and engaging. I found "quotable quotes" and provocative thoughts on virtually every page. It is free of administrative or educational jargon, it is straightforward and honest. It caused me to think, and it may even cause me to change a little bit of how I teach and act. My only criticism of the book, is that it starts the debate, but offers very little in the way of concrete suggestions about what to do about increasing QL. The essays by Zal Usiskin and Larry Cuban sketch some starting principles that are likely to be controversial, but seem to me to be very sensible as trial steps.

This book is another salvo in a what should be a national discussion larger than local "math wars". A session on QL will be featured at the Joint Mathematics Meetings in January, 2002. Bernie Madison had an editorial entitled in "Quantitative Literacy: Everybody's Orphan" in the August/September 2001 Focus newsletter of the MAA. A book review in the October 2001 SIAM News featured *Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists* by Joel Best. See also a summary of recent conference activity about QL at the Project Kaleidoscope Website. The *Case* bibliography lists over 80 books and articles, most from the last 5 years, about QL.

Who should read this book? Certainly anyone concerned about a population ready to meet the challenges of a society awash in important numbers about the economy and personal finance, or about disease risks, or about environmental and energy policies. Bernie Madison said in his editorial that "these questions deserve the attention of the US mathematics faculty." This is a must-read for anyone involved with mathematics education and teacher preparation. Department chairs should take an hour or two away from the crush of day-to-day administration to read it and think carefully about the implications for their department. You may not want your dean or administrator to read this book, because it contains ideas that are not always flattering to mathematics as an educational or even professional activity.

The mathematics profession is groping about for how best to present its subject to students and the public at large. Partial answers include calculus reform, mathematics courses for liberal arts, mathematics across the curriculum, mathematical education for future teachers, and numerous other initiatives, both capitalized and not. The *Case* and the responses suggest the most important answer lies in the related but distinct direction of QL. The evidence is in the numbers!

Steven R. Dunbar (sunbar1@unl.edu) splits his time between being professor of mathematics at the University of Nebraska-Lincoln, and being Director of K-12 Programs at the MAA's American Mathematics Competitions. In the little time left over, he enjoys bicycling, gardening and occasionally writing letters to the editor about innumeracy in the newspaper.