Quantitative Literacy Resources

The need for Quantitative Literacy (QL) is generally accepted.  But the content and teaching of QL is under active discussion and debate.  The quotes from the following publications present some of that discussion.

While four of the seven booklets are edited by Lynn Arthur Steen (pictured above) and two more are co-edited by Bernard Madison and Lynn Steen, they all contain ideas presented by many people.  In the Steen-Madison books, Robert Orrill (to name just one) worked tirelessly in support of QL as have the members of the Mathematics and Democracy Design team and the members of the National Numeracy Steering Committee. [Note: this US National Numeracy effort is different from the National Numeracy Strategy in the UK.].  [While the following are all quotes from the listed publications, this page has not been reviewed or approved by any of those mentioned on this page.]

General Comments on Numeracy and QL:

• Numeracy takes years of study and experience to achieve.

• An innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg's time.

• In the twenty-first century, literacy and numeracy will become inseparable qualities of an educated person.

• It is time for a change, time to recognize the unique quantitative requirements of universal education in the computer age. 

• The essence of QL is to use mathematical and logical thinking in context.

Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education  (2008). 
Editors: Bernard L. Madison and Lynn Arthur Steen

"Innovative and more effective quantitative literacy education is urgent both as a part of revitalization of liberal education and as a response to the increasing quantitative reasoning demands of US society. In the information age of today and tomorrow, lives are increasingly governed by numbers. The ubiquity of data and analyses of data require one to use sound quantitative reasoning to cope intelligently with the requirements of citizenship, job and family, and to be prepared for a healthy, happy and productive life. But quantitative reasoning for the practical circumstances of life is not part of the school or college curriculum - even for those taking a large complement of mathematics and science courses. In particular, it is not part of the college education of prospective teachers, and it is not a major part of the current national agenda reshaping school curricula. Achieving a quantitatively literate citizenry requires serious changes in the education of teachers and the curricula they teach. Thus, the need for a conference on Quantitative Literacy and Its Implications for Teacher Education." - From the letter of invitation to conference participants

"Innovative and more effective quantitative literacy education is urgent both as a part of revitalization of liberal education and as a response to the increasing quantitative reasoning demands of US society. Thus, the need for a conference on Quantitative Literacy and Its Implications for Teacher Education.  " MAA Bookstore.

"This volume contains the broadest interpretation yet of quantitative literacy (QL) as it should play out across the school and college curriculum. Nine commissioned essays on QL and teacher education by scholars in eight academic disciplines both challenge and expand more traditional views of QL. These essays, introductions by editors Bernard Madison and Lynn Steen, and brief summaries of discussions summarize the proceedings of a June 2007 multi-disciplinary conference held at Wingspread Conference Center and sponsored by the MAA's NSF-funded PMET project." MAA 2008 Fall/Winter Catalog

Conference Steering Committee Stanley Katz, Princeton University Bernard L. Madison, University of Arkansas Robert Orrill, National Council on Education and the Disciplines Richard Scheaffer, University of Florida Carol Geary Schneider, Association of American Colleges and Universities Lynn Arthur Steen, St. Olaf College Corrine Taylor, Wellesley College Alan Tucker, State University of New York at Stony Brook

Order from the MAA Bookstore.  See under Quantitative Literacy or search on title. Not available under author.
PDF available from QL page.

Humanism and Quantitative Literacy, Robert Orrill  "Humanists seem always to have kept a worried eye on quantification."
    "Opposition to quantification has become deeply-seated in the heritage of humanism."

Arguing with Numbers: Teaching QR through Argument and Writing, Neil Lutsky
     "Mathematicians are least-well prepared to deal with the meaning of socially-constructed numbers, which is the essence of QL."

Fractions and Units in Everyday Life, Alan Tucker

Quantitative Literacy and School Mathematics: Percentages and Fractions, Milo Schield

Quantitative Literacy for All: How Can We Make it Happen, Hugh Burkhardt  "If QL is not taught in Mathematics, it will not happen."  

Current Practices in Quantitative Literacy (2006)  Editor, Richard Gillman

"Current Practices in Quantitative Literacy present a wide sampling of efforts being made on campuses across the country to achieve our common goal of having a quantitatively literate citizenry. Colleges and universities have grappled with complicated issues in order to define quantitative literacy within their own communities and to implement appropriate curriculum. It is clear that any quantitative literacy program must be responsive to the local conditions of an institution including its mission, its student clientele, its history and its resources.

Although the programs and courses described in this volume only represent a sample of what is happening in the community, some trends do seem to be apparent. There is consensus that the mathematical skills necessary to be quantitatively literate include elementary logic, the basic mathematics of financial interest, descriptive statistics, finite probability, an elementary understanding of change, the ability to model problems with linear and exponential models, estimations and approximation, and general problem solving. It is clear that many of our students enter college with minimal mastery of these skills and their application.

The essays suggest that we have moved forward a long way in our understanding of quantitative literacy and our ability to implement effective programs to teach it. Read the stories of other institutions who have worked through some of these issues and begin a dialogue on your own campus."  Source:  MAA Bookstore Review  

Order from the MAA Bookstore. (Search on Gillman)

Introduction: Rick Gillman

Some Historical Notes: Linda Sons

Issues, Policies, and Activities in the Movement for Quantitative Literacy: Susan L. Ganter

What Mathematics Should All College Students Know?: William L. Briggs

Quantitative Methods for Public Policy: David Bressoud

The Quantitative Requirement at Juniata College: John F. Bukowski

Quantitative Literacy at Dominican University: Paul R. Coe and Sarah N. Ziesler

The Quantitative Reasoning Program at Hollins University: Caren Diefenderfer, Ruth Doan and Christina Salowey

A Decade of Quantitative Reasoning at Kalamazoo College: John B. Fink and Eric D. Nordmoe

Interconnected Quantitative Learning at Farmingdale State: Sheldon Gordon and Jack Winn

Quantitative Reasoning Across the Curriculum: Beth Haines and Joy Jordan

Mathematics Across the Curriculum: Rebecca Hartzler and Deann Leoni

Math Across the Curriculum at UNR: Jerry Johnson

The Quantitative Literacy Program at Hamilton College: Robert Kantrowitz and Mary B. O’Neill

Quantitative Reasoning at the University of Massachusetts Boston: Maura Mast and Mark Pawlak

Contribution of a First Year Mathematics Course to Quantitative Literacy: Aimee Ellington and William Haver

Increasing the Relevance to and Engagement of Students in a Quantitative Literacy Course: Sarah J. Greenwald and Holly Hirst

Quantitative Reasoning: An Interdisciplinary, Technology Infused Approach: David Jabon

Advising, Assessment, and Other Issues

About the Editor

Achieving Quantitative Literacy (2004)  MAA or Amazon
An Urgent Challenge for Higher Education (edited by Lynn Arthur Steen)

Literacy includes "prose, document and quantitative literacy."

"Document literacy refers to reading charts and tables."  p. xi.

"Quantitative literacy refers to interpreting and reasoning with numbers." p. xi

"The essence of QL is to use mathematical and logical thinking in context." p.47

QL skills involve "sophisticated reasoning with elementary mathematics rather than elementary reasoning with sophisticated mathematics." p. 9

"Because of their education and training, most teachers are not prepared for or comfortable with the mathematics required for quantitative literacy." p.47

"According to Johnny Lott, former president of NCTM, it is simply unrealistic to expect that teachers of other subjects will either know or understand what might be considered quantitative literacy." p. 47

"QL advocates need to be very clear about what all students need to know and be able to do, starting with where it fits into the mathematics program."  Janice Somerville, p.3.

Earlier innovative, QL-type courses "had one thing in common that contributed to their remaining a small elective rather than a major requirement -- they were designed specifically to focus on ideas -- generally QL-like ideas -- rather than techniques.    This made them more difficult for teachers to teach and for students to master, and for that reason they thrived only in special niches out of the mainstream of college mathematics." p. 39

"Thus, on both sides of the school-college boundary, policy related to quantitative literacy is inextricably tied with mathematics and statistics." p. 33

"In reality, data analysis -- what most statisticians actually practice -- is typically more than the average person needs to be an informed citizen, intelligent consumer or skilled worker.  What everyone needs is typically called statistical thinking or statistical literacy, a crucial component of quantitative literacy." p. 43

"Although most adults see probabilistic and statistical arguments every day, few have any preparation to make sense out of them." Deborah Hughes Hallet, p. 43

Not withstanding the importance of quantitative literacy to health, politics, work and personal finance, in our discipline-dominated education system, QL has neither an academic home or an administrative promoter." p. xi

"Although mathematics certainly cannot bear the sole burden of quantitative literacy, it is the discipline best suited to play a leadership role." p.44

"It may well be that with regard to our democratic conception of higher education, it is undergraduate mathematics that is most out of date."  p. 5

"It is time for a change, time to recognize the unique quantitative requirements of universal education in the computer age."  p.9

Reviewed in The American Statistician (2006) V 1.    "Many of the problems that are cited as reasons why typical citizens need to be quantitatively literate are in fact subtle and difficult. A good example mentioned in the book is that of false positives in screening for cancers. Can a QL curriculum be expected to emphasize basic skills also introduce such tough cases? And how can we measure whether the students are essentially literate? It is in the development of tools for the assessment of quantitative skills that statisticians have some experience and perhaps can offer assistance in solving this problem."

Reviewed in the MAA online by Charlotte Chell:  "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."

Quantitative Literacy: Peer Review 2004
Everything I learned about Numbers..., I learned in College  by Lynn Arthur Steen

"QL is anchored in context; the objects of QL are data."

"Quantitative reasoning relies on concepts first introduced in middle school --averages, percentages, graphs."

"Averages, like percentages, are also a source of mysteries."

"my point is that QL is sufficiently sophisticated to warrant inclusion in college study and, more important, that without it students cannot intelligently achieve major goals of college education."

"Quantitative literacy is not just a set of precollege skills.  It is as important, as complex, and as fundamental as the more traditional branches of mathematics."

"One clear priority has emerged: the need to develop benchmarks for quantitative literacy that can guide both curriculum and assessment in grades 10-16."

Other Related Publications

• Quantitative Literacy: Why Numeracy Matters for Schools and Colleges  Conference review. Focus, 2/2002 (MAA Online 2004)

• Numeracy: The new Literacy for a Data Drenched Society   10/1999 Educational Leadership

Quantitative Literacy
Why Numeracy Matters for Schools and Colleges (2003) MAA or Amazon

Edited by Bernard L. Madison and Lynn Arthur Steen

"Quantitative literacy, in my view, means knowing how to reason and how to think and it is all but absent from our curricula today."  Users of quantitative information "have to learn how to think for themselves, and that is what an education in quantitative reasoning can teach them."  Gina Kolata (1997)

"The attention to quantitative reasoning that she [Gina Kolata, see above] thinks so essential to sound judgment simply does not exist in the academic programs of most of our schools and colleges.  Robert Orrill

"To expand the conversation about QL, the NCED subsequently sponsored a national forum, Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, held at the National Academy of Sciences in Washington D.C. on December 1-2, 2001.  This volume represents the proceedings of this Forum and includes papers commissioned as background for that Forum, essays presented at that Forum, and selected reactions to that Forum."  Bernard Madison

• "Numeracy lies at the intersection of statistics, mathematics and democracy.  Like statistics, numeracy is centered on interpretation of data; like mathematics, numeracy builds on arithmetic and logic.  But the unique niche filled by numeracy is to support citizens in making decisions informed by evidence."  " Numeracy is largely an approach to thinking about issues that employs and enhances both statistics (the science of data) and mathematics (the science of patterns).  Yet unlike statistics, which is primarily about uncertainty, numeracy is often about the logic of certainty.  And unlike mathematics, which is primarily about the Platonic realm of abstract structures, numeracy often is anchored in data derived from and attached to the empirical world."   Lynn Steen, p. 62-63.

• "Quantitative Literacy (QL), the ability to use numbers and data analysis in everyday life, is everybody's orphan.  Despite every person's need for QL, in the discipline-dominated K-16 education system in the United States, there is neither an academic home nor an administrative promoter for this critical competency."  p. 153  Bernard Madison

• "In reality, full-bore data analysis is more than most people need to deal with the statistical issues of everyday life and work."  P. 146 "Many statisticians would probably disagree with the statement in Mathematics and Democracy that QL is "not the same as statistics."  Indeed many think that a very large part of QL is statistics..." p.147   "Those experienced with teaching statistics suggest that one way to garner administrative support [for QL across the curriculum] and foster institutional change is to tie much of QL to the statistics curriculum, everywhere it is housed."  p.149   "Statistics and quantitative literacy have much in common.  Although few would disagree with this, statisticians would probably argue that QL is mainly statistics while mathematicians and mathematics educators tend to argue that QL is only partly statistics. p. 151  Richard Scheaffer

• "Statistical methods are about logic as well as numbers.  For this reason, as well as on account of their pervasiveness in modern life, statistics cannot be the business of statisticians alone, but should enter into the schooling of every educated person.  To achieve this would be a worthy goal for statistics in the coming decades."  Porter, 2001

• "many aspects of statistical thinking are not about numbers as much as about concepts and habits of mind.  For example, the idea of a lurking variable upsetting an apparent bivariate relationship with observational data is a conceptual idea, part of statistical thinking, but not particularly about numbers." p. 150 Richard Scheaffer.

TABLE OF CONTENTS:

Background Papers:

• Introduction:  The Many faces of Quantitative Literacy, Bernard Madison.

• Need for Work and Learning:  The Many Faces of Quantitative Literacy, Bernard Madison; Democracy and the Numerate Citizen, Patricia Cohen; The Democratization of Mathematics, Carnaevale and Desrochers; What Mathematics should "Everyone" Know and Be Able to Do, Arnold Packer; Quantitative Literacy in the Workplace, Linda Rosen.

• Curriculum Issues: Data Shapes, Symbols: Achieving Balance in Scholl Mathematics, Lynn Steen; Mathematics for Literacy, Jan de Lange; The Role of Mathematics Courses in the Development of Quantitative Literacy, Deborah Hughes-Hallett; The Third R in Literacy, Richardson and McCallum. 

• Policy Challenges:  Articulation and Mathematical Literacy: Political and Policy Issues, Michael Kirst;  "Get Real!"  Assessing for Quantitative Literacy, Grant Wiggins; Statistics and Quantitative Literacy, Richard Scheaffer; Articulation and Quantitative Literacy, Bernard Madison.

Forum Papers:

• Need for Work and Learning: Addressing Societal and Workforce Needs, David Brakke; Making Mathematics Meaningful, Arnold Packer; Grounding Mathematics in Quantitative Literacy, Johnny Lott; Quantitative Literacy: A Science Literacy Perspective, George Nelson; Learning and Work in Context, William Steenken; Of the Teachers, by the Teachers and for the Teachers, Roger Howe; Impediments to and Potentials for Quantitative Literacy, J. T. Sutcliffe.

• Policy Perspectives: Say What you Mean (and Mean What You Say), Janis Somerville; Education Policy and Decision Making, Margaret Cozzens; Policies on Placement and Proficiency Tests: A Community College's Role, Sadie Bragg; Standards are Not Enough: Challenges of Urban Education, Judith Rizzo; Creating Networks as a Vehicle for Change, Susan Ganter.  

• International Perspectives: Numeracy in an International Context, Lynn Steen;  Quantitative Literacy and Mathematical Competencies, Morgan Niss; Defining Mathematical Literacy in France, Michel Merle;  What Mathematics for All?, A. Geoffrey Howson; Numeracy: A Challenge for Adult Education, Mieke van Groenestijn; The Role of Mathematics in Building a Democratic Society, Ubiratan D'Ambrosio. 

• Reflection Papers:  Why Are We Here?,  Jeanne Narum; Quantitative Literacy Goals: Are We Making Progress?, Rita Colwell;  What Have We Learned.. and Have Yet to Learn?, Hyman Bass;  Reflections from several forum participants.

Mathematics and Democracy
The Case for Quantitative Literacy (2001) Edited by Lynn Steen  MAA or PDF

"Despite its occasional use as a euphemism for statistics in school curricula, quantitative literacy is not the same as statistics. Neither is it the same as mathematics, nor is it (as some fear) watered-down mathematics.  Quantitative literacy is more a habit of mind, an approach to problems that employs and enhances both statistics and mathematics. Unlike statistics, which is primarily about uncertainty, numeracy is often about the logic of certainty. Unlike mathematics, which is primarily about a Platonic realm of abstract structures, numeracy is often anchored in data derived from and attached to the empirical world. Surprisingly to some, this inextricable link to reality makes quantitative reasoning every bit as challenging and rigorous as mathematical reasoning." 

"In the twenty-first century, literacy and numeracy will become inseparable qualities of an educated person."

• "Numeracy takes years of study and experience to achieve."

• "Although quantitative literacy is a recent and still uncommon addition to the curriculum, its roots in data give it staying power."

• "Numeracy will thrive similarly because it is the natural tool for comprehending information in the computer age."

• "Numeracy embodies the capacity to communicate in this new language."

• "colleges seem to have no clear vision about the goals of quantitative literacy or the means by which these goals can most readily be achieved."

• "Numeracy is not the same as mathematics, nor is it an alternative to mathematics."

• MAA Online Book Review of "Mathematics and Democracy"

  ---

  Why Numbers Count 
  Quantitative Literacy for Tomorrow's

  America (1997)  Edited by Lynn Steen  College Board

  "Numeracy is the new literacy of our age"

  "The relentless quantification of society continues unabated."

  "In short an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg's time."

  "The ascendancy of quantitative information has changed profoundly not only the environment in which we live and work, but also the entire framework of civic life."

  "The tendency to reduce complex information to a few numbers is overwhelming--in health care, in social policy, in political analysis, in education. ... Although the widespread availability of data should enrich public discourse, inevitable over-simplifications and misinterpretations may ultimately cheapen it. ... Instead of enhancing Jeffersonian democracy, limited numeracy can easily shift the balance to a technocracy.

  "Innumeracy thus becomes another means of disenfranchisement: by reinforcing the idea that truth is relative and unknowable, people with the least defenses against charlatans will be most vulnerable."

   

  Numeracy and Quantitative Literacy (Table of Contents)
  Why Numbers Count: Foreword by Robert Orrill,  The New Literacy by Lynn Steen,  Defining Quantitative Literacy, 
  The Triumph of Numbers: Civic Implications of Quantitative Literacy by Theodore Porter.  "Rarely do they [students] learn what a stratified sample is, or how an unemployment rate is determined, or what the smog index measures. The sorts of numbers that modern citizens are likely to confront in their lives as citizens and voters have little place in the modern curriculum."
  Civic Numeracy: Does the Public Care?  by Deborah Wadsworth,  Making Mathematics The Great Equalizer by Shirley Malcom (AAAS),
  Numeracy: Imperative of a Forgotten Goal by Iddo Gal, Thinking Quantitatively about Science by James Rutherford (AAAS)
  Mere Literacy is not Enough by George Cobb,  Solving Problems in the Real World by James Pollak, 
  Quantitative Practices by Peter J. Denning     Organizing Mathematics Education around Work by Gary Hoachlander

1994: MAA Quantitative Reasoning for College Graduates

The report (in its Part 2) presented this over-arching goal:

• 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.

The report (in its Part 2) presented this goal for quantitative literacy:

• 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.

The report in its Part 2 asserted that:  "A quantitatively literate college graduate should be able to

• interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.

• represent mathematical information symbolically, visually, numerically and verbally.

• use arithmetical, algebraic, geometric and statistical methods to solve problems.

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

• recognize that mathematical and statistical methods have limits.