INTRODUCTION

INTRODUCTION

Louise Hainline, Peter Lesser, Myra Kogen, George Brinton

The Problem of Quantitative Literacy

Fifty years ago, “literacy” was defined as having a fourth-grade education, literally being able to read. Today, literacy requirements go far beyond this minimal ability. There have also been requirements for the ability to reason about numbers and data, sometimes called quantitative literacy, but increasingly also referred to as “numeracy” (a British term that is finding more common usage in the U.S.). Over the last 50 years, the skills required by an individual to be considered quantitatively literate, or if you prefer, numerate, have also increased markedly.

In this age of computers, we are awash with data of all kinds: data on medical issues, new drugs and treatments, crime statistics, federal and state budget information, data on voting patterns, marketing and business, personal finances, high-stakes educational testing and expenditures on schooling, environmental issues, sports, and public policy and on and on. The availability of data on the Internet alone is staggering. Data penetrate every aspect of our lives, both personal and work-related.

Considering this deluge of numbers and their importance to so many aspects of our lives, one would think that equipping students to deal effectively with all this information would be at least as high a priority for educational institutions as literacy training is in helping students to deal with verbal information. Yet many educated adults are, truth to tell, functionally innumerate. Their ability to deal with concepts like graphical displays of information, quantitative estimates of risk, rates of change vs. change in rates, and the logic of statistical analysis is inadequate for the reasoning and decisions required of them.

The issue is not merely pedantic. It has been contended that an innumerate public is a danger to very core of our democracy. Individuals unable to draw their own conclusions from data are constrained in many cases to having conclusions fed to them by politicians and the media, if not by demagogues and the unscrupulous. Further, Lynn Steen, an early leader in the national discussion about numeracy, has noted that an innumerate citizen today is as vulnerable to exploitation as an illiterate peasant was in the pre-Gutenberg 15^th century. To be innumerate in this day and age is very likely to be confined to the lowest rungs of our economic and social ladder. The ability to handle capably the masses of data we encounter every day separates the rich from the poor, the powerful from the weak, the boys from the girls, and minority from majority cultures. Let’s look at how this situation of educated but innumerate individuals may have come about, and what steps various organizations are taking to address the problem of the quantitative reasoning competency of our citizens.

The first reaction of many people when this issue is introduced is that mathematics education has failed, or that students just need more classes in mathematics. The prevailing view of many participants in quantitative literacy discussion is that this impulse is wrong. Mathematics and quantitative reasoning are not the same thing. College level mathematics instruction in the US has generally followed the familiar ladder of algebra, trigonometry, geometry, and calculus, a sequence that prepares students to appreciate the discipline of mathematics as an abstract system of numbers and pure Platonic forms. Mathematics as typically taught is decontextualized and abstract, and, in fact, that is its power. Traditional undergraduate mathematics does not normally deal with measurement, and it does not focus on numbers in specific contexts. Although mathematics is more than algorithms, proofs and procedures, it is typically not taught as a form of reasoning about data.

But reasoning about data is exactly what is called for in quantitative literacy, specifically reasoning about concrete information in a particular context. Quantitative literacy, numeracy, although it involves numbers, is not the same as mathematics. Nor is it watered down mathematics. Many mathematicians immediately dismiss quantitative literacy as “remedial.” It is not. It is a form of reasoning that uses tools from mathematics, logic, and other fields to draw conclusions about information from specific contexts. Quantitative reasoning calls, for example, for knowledge of statistics, which is not normally part of the traditional mathematics ladder (except possibly theoretical statistics for mathematics majors which is not the same thing).

The result is that we often find that even students who major in mathematics don’t have an easy time recruiting the power of mathematics in specific disciplines. This happens even in the sciences where one might expect to find the most quantitatively sophisticated students; students’ inability to apply quantitative knowledge to specific scientific contexts is a frequent complaint from science faculty. A common solution is for each field to add its own courses on mathematics “in the discipline,” to provide the framework that students in that major need to use their math skills for practical ends in that field. Thus we encounter mathematics and statistics courses in economics, political science, psychology, sociology, health, computers, engineering and the sciences. Whether this really enhances students’ ability to apply mathematical reasoning in a flexible way across the range of contexts in which it is needed is an open question. One senses that this just creates separate “columns” rather than a generalized skill in analysis that fits all the requisite situations.

If quantitative literacy is not the same as traditional mathematics, then who is responsible for it in the modern university with its strong disciplinary and departmental separations? Bernard Madison, a founding member of the National Numeracy Network, recently called quantitative literacy “everybody’s orphan.” In recent years the “Writing across the Curriculum” model posits that teaching students to write effectively is the responsibility of all departments and faculty, not just English departments. This argument has been instrumental in moving forward an interdisciplinary agenda for teaching writing in the disciplines. The analogy between writing and numeracy is strong. A national movement similarly argues that quantitative literacy is not the responsibility just of mathematics departments, but one that must be shared. The real difficulty is what in psychology has been called “diffusion of responsibility.” If too many entities are responsible, in effect no one takes responsibility; each assumes someone else will do the job. Who will shelter the orphan of quantitative reasoning is still an open question.

The goal, some argue, is not to require more, higher, mathematics from more students, but to teach people how to apply relatively simple mathematical tools in complex situations. Certainly some students, in engineering, the sciences, and economics, may need higher, abstract mathematics. But the argument that most students need more practice in application, and perhaps less mathematics, is highly controversial at the moment, with some advocating that students only need basic arithmetic and simple algebra, that knowing about polynomials and differential equations really does not help people deal with the contexts that all educated citizens need to understand. Others argue just as strongly that this is lowering standards in a harmful way. What is at stake, among other things, is who among our faculty can reasonably play a role in teaching quantitative literacy, and what format this teaching should take. There are many models. Some colleges are creating separate Quantitative Reasoning courses. Others are opting for an approach that infuses quantitative reasoning into the widest possible range of courses. The vast majority haven’t done anything yet. The jury is out on whether one model is more effective than another.

The path to creating a numerate citizenry is becoming a high-profile issue on the national scene. Input has come at various times from organizations such as the National Science Foundation, the National Research Council/National Academy of Sciences, the Mathematics Association of America, and Project Kaleidoscope, among others. The most recent public statement is from the National Council on Education and the Disciplines, a component of the Woodrow Wilson Foundation, which takes as its mission “a national reexamination of the core literacies” (which NCED defines as quantitative, historical, scientific and communicative), essential to the coherent, forward-looking education all students deserve. NCED has just established the National Numeracy Network, an organization that is attempting to generate widespread discussion of the problem and to explore possible model solutions. A year ago, they published an excellent book, edited by Lynn Steen, called Mathematics and Democracy: The Case for Quantitative Literacy, a collection of essays developing many of the points raised here. A serious reexamination of what kind of quantitative training, at what level and in what areas, and using what mathematics everyone needs for numeracy promises to be one of the more interesting discussions in higher education for the next several years. We at Brooklyn College became involved in this discussion some five years ago.

The Brooklyn College Quantitative Reasoning Project

The Brooklyn College QR project was conceived in 1995 when Louise Hainline, then Acting Dean of Graduate Studies and Research, convened a group of faculty to consider submitting a grant proposal to the National Science Foundation for funding in support of science and math education. It was decided to focus on quantitative reasoning across the undergraduate curriculum and to propose a program that would take advantage of the unique features of the Brooklyn College Core Curriculum. We had the idea that if quantitative reasoning were infused throughout the Core curriculum, wherever appropriate, rather than being the sole domain of the sciences, it would help to break down barriers separating math and science from other liberal arts disciplines. The hope was that this approach would impress upon students the idea that quantitative reasoning is a powerful and useful way of thinking about the world in a wide variety of contexts. It has an important role to play in the understanding of social sciences, arts and humanities, just as it does, of course, in the natural sciences. At least some of our faculty members were complaining that they felt constrained to avoid quantitative material because their students both lacked the requisite math skills and were exceedingly negative in their attitudes towards quantitative reasoning.

Louise Hainline, Myra Kogen and Peter Lesser wrote the grant proposal entitled “Quantitative Reasoning Across the Core Curriculum” that was funded beginning in July, 1997, under the NSF’s Institution-wide Reform program. NSF intended that our $200K, two-year grant would start a process that would ultimately be taken over by the College and would result in significant, sustained reform of the educational experience provided to our students. Five years later, our Quantitative Reasoning Across the Core project has had, we believe, significant impact on the thinking of many faculty at Brooklyn College. However, the transition from a grass-roots effort involving several dozen faculty members to an institutional effort involving virtually all remains a goal for the future. The Transformations Seminar, represented in this collection,

was certainly an important step along the way.

During the past five years, participants in the QR project have engaged in a wide variety of activities. We have run numerous faculty discussion groups and workshops, have presented our work at various on-campus meetings or seminars, have participated in several major conferences, have surveyed the attitudes of Brooklyn College faculty towards quantitative reasoning, and have organized a day-long symposium on QR. Some of the highlights:

— The project sponsored a survey of all Brooklyn College faculty to determine their attitudes and perceptions regarding QR.

— The project co-directors (Louise Hainline, Myra Kogen, George Brinton, Peter Lesser) participated in and gave presentations at various outside conferences on quantitative reasoning. Sponsors of those conferences included:

American Association of Higher Education (Wash. D. C., Nov., 1998)

Borough of Manhattan Community College (May, 1998)

Richard Stockton College (March, 1999 and August, 2000)

— The project sponsored a day-long symposium (May, 1999), “Quantitative Literacy Across the Curriculum,” featuring speakers from other colleges and programs. Dorothy Wallace, director of the NSF-funded project at Dartmouth College, was the keynote speaker. Among the other speakers were Jeffrey Bennett and William Briggs, authors of a textbook on Quantitative Reasoning.

— Project participants gave a presentation at the Core Seminar (June, 2000) which included the following talks: Peter Lesser, history of the QR project at BC; Louise Hainline, results from the faculty survey; Michael Kahan, “Making Sense of Polling and Sampling” (Core 3); Jocelyn Wills, “Mapping the Industrial Revolution” (Core 4); Jonathan Adler, “Moral Motivation and The Prisoners Dilemma” (Core 10).

— The project co-sponsored the 3^rd Annual Building Bridges Conference at Brooklyn College (May, 2001), titled “Quantitative Literacy: The New Challenge.” Featured speakers included Jaime Escalante and John Allen Paulos. Presenters/discussion leaders included Fred Greenleaf and Andre Adler from NYU, Louise Hainline and George Brinton representing the Brooklyn College QR project.

— Louise Hainline, Peter Lesser and two faculty participants in the QR project presented papers in a Faculty Day Symposium (May, 2002) titled “Quantitative Reasoning: Can We Teach It? Should We Teach It? A Symposium in Memory of Professor Michael Kahan.”

— A QR Task Force, chaired by Peter Lesser, met during the 2001-2002 academic year to consider the possibility of introducing a QR general education requirement at Brooklyn College along the lines followed by a number of other colleges across the country. The task force will report to the Provost and faculty during the Fall, 2002 semester.

— The QR project co-directors participated in Transformations, Session VI: Quantitative Reasoning in Courses for First-Year Students.

The Transformations Seminar

In the fall 2001 annual Transformations Seminar, sponsored by the Dean of Undergraduate Studies, ten Brooklyn College faculty members from across the disciplines, the four Quantitative Reasoning Project coordinators and the Dean of Undergraduate Studies met regularly throughout the semester to share ideas on quantitative reasoning and deliver formal workshop presentations. The articles in this collection are a product of these discussions. During the workshop the participants discovered that they had many concerns in common. It was agreed that students’ difficulties with quantitative reasoning interfere with their learning in many disciplines.

Though participants in the Seminar were given complete freedom to define quantitative reasoning for their own purposes, all of the presentations assume that reasoning about data is of central importance. The wide variety of contexts and applications reflected in the following summaries demonstrates that at the college level, instruction in quantitative reasoning is most appropriately applied across the curriculum.

The importance of numeracy in significant areas of daily life was understood by the ancients. In “Nomen et Numerus: Quantitative Reasoning in the Field of Classics,” C. L. H. Barnes reminds us that since antiquity, quantitative reasoning has played an important role in the exercise of civic responsibility and government, in the engineering of public works and in architectural design.

In the nineteenth century, as John Blamire points out in “Quantitative Reasoning: Core Biology 8.1,” statistical inference made possible the discovery of genetics. His students extend this insight to the discovery and understanding of other biologically important mechanisms.

Robert Cherry’s “Approaches to Quantitative Reasoning” demonstrates some applications of fundamental problem-solving skills to the economics of modern life, and observes that these skills have wide application elsewhere, from baseball to student grades.

Reasoning about exam scores receives further attention in Marvin J. Kohn’s “A Quantitative Reasoning Project for Math 1.95,” an account of a project that fosters creativity and skepticism in the context of mathematics for elementary education majors.

The application of logic and avoidance of fallacy are always requirements of sound reasoning, whether the data under scrutiny are numbers or facts. In her “Quantitative Reasoning in Evaluative Listening,” Mary Ann Messano-Ciesla examines the logical context for students of speech, with reference to the importance of listening.

We revisit the preparation of elementary school teachers in Eleanor Miele’s “A New Emphasis on Quantitative Reasoning in a Science Education Course.” The gathering and interpreting of data in these exercises integrate mathematics and science in such a way as to sharpen student awareness of stereotypic thinking, an important issue in the humanities and contemporary life.

Another area of modern life with which we are all concerned, provides the context of Jerry Mirotznik’s “Quantitative Literacy and Public Health.” The health of a community cannot be assessed without numbers, and the ability to think critically about numbers, to apply logic and avoid fallacy, can make a profound difference in our ability to deal with death, disease and disability.

In science as in public health, the concept of probability is often essential to reasoning. But it is not, as we have seen in the context of speech and listening, always expressed numerically. Wayne Powell and David Leveson remind us of this in “The Unique Role of Introductory Geology Courses in Teaching Quantitative Reasoning.” In geology and other disciplines, “weighing data and appreciating implications of scale, location and spatial relationships are critical.”

By modeling the energy content of a forest, Micha Tomkiewicz, in “QR—Global Warming,” shows us how a course might employ mathematical tools in a critical examination of this important environmental issue.

Finally, Noson S. Yanofsky discusses assignments which use statistics, graphs and numeric concepts to teach quantitative reasoning in the second course of a four-course sequence in computer programming.