David M. Bressoud September, 2005
Recommendation A1: Offer suitable courses.
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All students meeting general education or introductory requirements in the mathematical sciences should be enrolled in courses designed to
• Engage students in a meaningful and positive intellectual experience;
• Increase quantitative and logical reasoning abilities needed for informed citizenship and in the workplace;
• Strengthen quantitative and mathematical abilities that will be useful to students in other disciplines;
• Improve every student’s ability to communicate quantitative ideas orally and in writing;
• Encourage students to take at least one additional course in the mathematical sciences.
One of the characteristics that distinguishes this CUPM Curriculum Guide from previous sets of CUPM recommendations is the attention paid to the students we teach who do not intend to major in mathematics. One of our most important audiences consists of the math-averse, those who feel that they are constitutionally incapable of doing mathematics, consider it irrelevant to their interests, or have had a bad experience with mathematics. According to the CBMS [1], more than 75% of students taking mathematics in college are taking courses classified as “remedial” or “introductory”. Many if not most of these students qualify as math-averse. They would rather not be there.
This is the first of three recommendations that the CUPM Curriculum Guide makes for the courses aimed at these students. It makes the case that we need to be clear about what mathematics these students actually need. For many of them, a course in quantitative literacy (aka quantitative reasoning, quantitative thinking, numeracy) will serve far better than a repeat of algebra.
Quantitative literacy is “the power and habit of mind to search out quantitative information, critique it, reflect on it, and apply it in one’s public, personal, and professional life” (National Numeracy Network [2]). The mathematics can be very simple. It is the ability to work in context that makes this a demanding discipline, and for quantitative literacy, context is everything. The goal is to empower students to reason with the complex quantitative information that is omnipresent in today’s world.
Many colleges and universities are wrestling with how to teach this. It is not the unique domain of mathematicians. The American Sociological Association in now encouraging its members to promote quantitative literacy. The National Numeracy Network includes geographers and geologists, physicists, economists, biologists, and statisticians as well as sociologists and mathematicians. The MAA’s Special Interest Group on Quantitative Literacy [3] was established as a forum for the exchange of information on innovative ways to develop and implement QL curricula. The MAA has made available two of the most useful publications on quantitative literacy, Mathematics and Democracy: The Case for Quantitative Literacy [4] and Achieving Quantitative Literacy: An Urgent Challenge for Higher Education [5].
Macalester College is developing its own program in quantitative thinking [6], assisted by funding from the Department of Education’s Fund for the Improvement for Post-Secondary Education and from NSF Department of Undergraduate Education. We have identified several key components of quantitative thinking and created lessons to teach them. These include:
• Trade-offs Identifying and working through the complexities of conflicting goals. One of the weaknesses we observe in many of our students is a tendency to latch onto a single worthwhile goal and to ignore the effect that maximizing that single good has on other desirable ends. Recognizing the difficulty of balancing competing goals motivates the need for quantitative thinking.
• Rates and comparisons How the quantities composing a rate can inform or mislead a discussion. Understanding the distinction between aggregate and differential rates, total and partial rates, and knowing when each is appropriate.
• Change over time Exponential versus linear growth and decay. Compounding. Restricted growth. Limits to prediction and extrapolation.
• Variability and bias Distinguishing among what is normal, what is average, what is typical. Knowing how to assess the reliability of measurements.
• Causation and association Understanding the difference and why an insubstantial association might still pass the test of “significance”. Recognizing the hallmarks of reliable research.
• Uncertainty and risk Assessing, comparing, and balancing risks. Ability to understand conditional statements and probabilities and draw on them to assess risk.
• Estimation, modeling, and scale Ability to do “back of the envelope” calculations. Recognizing the usefulness and limitations of models. Knowing that big and small are not absolutes but always relative.
What I have described is not a traditional mathematics class. In fact, it is not clear where such a class belongs or who is best trained to teach it. But quantitative literacy is a set of capabilities that every educated person should possess, and it is a first step in demonstrating to the math-averse the importance of mathematics. If mathematicians do not promote quantitative literacy, who will?
[1] Includes 2-year and 4-year colleges and universities.
At 4-year institutions, it is over 60%. Tables E.2 and TYR.4 in Statistical
Abstract of Undergraduate Programs in the Mathematical Sciences in the United
States: Fall 2000 CBMS Survey, David J. Lutzer, James W. Maxwell, Stephen B.
Rodi, editors, American Mathematical Society, Providence, RI, 2002.
[2] taken from the Vision Statement of the National Numeracy Network, www.math.dartmouth.edu/~nnn/
[3] SIGMAA QL website is at pc75666.math.cwu.edu/~montgomery/sigmaaql/
[4] Mathematics and Democracy: The Case for Quantitative Literacy, Lynn Arthur Steen, editor, National Council on Education and the Disciplines, Woodrow Wilson national Fellowship Foundation, 2001.
[5] Lynn Arthur Steen, Achieving Quantitative Literacy: An Urgent Challenge for Higher Education, MAA Notes #62, Mathematical Association of America, Washington, DC, 2004.
[6] Quantitative Methods for Public Policy, www.macalester.edu/qm4pp
Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?
Submit resources at www.maa.org/cupm/cupm_ir_submit.cfm.
We would appreciate more examples that document experiences with the use of
technology as well as examples of interdisciplinary cooperation.
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |