Quantiative Thinking at Macalester Today

Macalester's QT graduation requirement

Findings from pilot project, 2002–06

Workshops and outreach

The Original Proposal

Quantitative Thinking at Macalester Today

Quantitative Literacy (QL) is not mathematics. It has almost nothing to do with mathematics as taught at the college level. It is about gaining the ability and habit to seek out quantitative information, to be able to analyze and critique it, and to use it in our public, personal, and professional lives. By its nature, QL is interdisciplinary. It appears in political debate and polling, in issues of health care, in understanding the choices we face with regard to the environment, in grappling with the complexities of poverty, education, and social action. QL recognizes the fact that quantitative information in the real world is messy, complex, often incomplete, sometimes overwhelming, and not infrequently appears to be contradictory. At a basic level, the methods needed to think critically about this information use nothing beyond high school mathematics: ratios, percentages, rates, simple probabilities. But basic does not mean easy. There is still a lot to learn about how to choose and think about quantitative information when it is outside the idealized world of the mathematics classroom.

There is national recognition that QL is one of the fundamental abilities that informed citizens should have. In 2001, the National Council on Education and the Disciplines convened a national conference on QL. Its recommendations are contained in Mathematics and Democracy: The Case for Quantitative Literacy. Among those contributing to this conference was Carol Schneider, President of the Association of American Colleges and Universities (AAC&U). The AAC&U has continued to support QL efforts. Their publication, Peer Review, featured an article on QL in summer 2003, and devoted the entire issue to QL for summer 2004. It is worth noting that Macalester’s QM4PP program was cited in both issues.

Macalester’s QL program, Quantitative Methods for Public Policy (QM4PP) has always focused on quantitative literacy in the context of case studies that illustrate how its tools can be used to illuminate debate over real policy issues. In the first year of the program, 2002–03, the focus was on the school voucher debate. In subsequent years, the program has drawn on several policy issues, especially surrounding immigration but also including public health issues such as mad cow disease as well as various approaches to dealing with terrorism. This focus on public policy was the primary reason that this program received a $400,000 grant from the US Department of Education’s Fund for the Improvement of Post-Secondary Education, and a smaller grant from the National Science Foundation in 2002.

Initially, the program was intended to be a 2-credit supplement that students would take in conjunction with another course, providing the quantitative insights that would tie into the policy questions being studied in, for example, a course in sociology or political science. By 2004–05, it was clear the coordination with other classes was problematic, and the decision was made to offer as a variety of stand-alone courses. As part of the development of such courses, this spring Erik Larson and Andrew Latham are teaching Practical Policy Analysis, a course cross-listed between Political Science and Sociology. Beginning next year, Raymond Robertson and David Bressoud will be teaching Quantitative Thinking for Policy Analysis, a course cross-listed between Economics and Mathematics.

Macalester's QT Graduation Requirement

In the fall of 2005, the faculty adopted new graduation requirements that include a requirement in quantitative thinking (QT) that is built on what we have learned from the QM4PP program. Students will have the option of satisfying this requirement either through an intensive course in quantitative thinking such as Practical Policy Analysis or Quantitative Thinking for Policy Analysis, but they will also have the option of taking several courses that are less quantitatively intensive but will give them the opportunity to experience quantitative thinking in a variety of contexts.
There are six areas of competency that constitute the goals of the QT requirement:

• Describing the world quantitatively: rates of change, linear & exponential growth, descriptive statistics, presentation of data.
• Evaluating sources and quality of data: assessing reliability of measurement, sources of bias and error.
• Association and Causation: weighing statistical significance, determining importance of findings, knowing when and how to infer causation.
• Trade-offs: weighing the benefits and costs of different options, especially in the area of policy analysis; recognizing that there is seldom a single correct solution and learning to use quantitative analysis to help evaluate different options.
• Uncertainty and Risk: interpret and use conditional probability to compare and balance risks, draw valid conclusions from conditional probabilities, understand limitations and potential pitfalls of conditional probabilities.
• Estimation, Modeling, Scale: understand scale and relative nature of “big” and “small,” be able to estimate and work with order of magnitude approximations, appreciate value and limitations of models constructed by abstracting out detail, importance of sensitivity of the model and necessity to report assumptions.

Starting with the class of 2011, which enters in September, 2007, students will be required to take either

• A course designated Q3 in which all of these topics are covered and almost all of the course is devoted to these quantitative topics, or
• A Q2 course that deals with at least half of these topics and at least half of the course is devoted to these topics PLUS another Q2 course or a Q1 course that covers some of these topics, or
• Three Q1 courses that each cover some of these topics.

In addition to the courses described above, several courses that will qualify for QT designation now exist or are being created. These include Introductory Statistics, Principles of Economics, Introduction to Environmental Science, Environmental Geology, Introductory Journalism, and Media Institutions.

[return to top]

Findings from pilot project, 2002–06

While analysis of our assessment tools is still ongoing, preliminary results suggest that there is little evidence that the single session in quantitative reasoning each week had a significant impact on student ability to reasoning quantitatively. In fact, our most successful assessments were formative, learning what would not work at Macalester:

• The attempt to create a course that operates as supplement to other existing courses suffered from the difficulty of articulating it with these other courses that had very different goals.
• We learned a lot about how to teach large classes (>100 students) effectively, especially by using anonymous electronic feedback during class to engage students, but we still ran up against the expectation that at a small college such as Macalester, classes should be small. Many students were turned off by the large class format.
• A single meeting per week for 1 1⁄2 hours was not sufficient.
• As a pass/fail course, students were not sufficiently invested.
• Any attempt to teach quantitative reasoning requires that students work with real data. This means that we need time spent in computer labs.

There were several very successful aspects of the program.

• Tying quantitative reasoning to policy analysis was popular and stimulated student interest. Students really were interested in how simple quantitative concepts could help to illuminate difficult questions that they consider important.
• The entire process clarified for us the importance of emphasizing the concept of trade-offs, the realization that most policy questions do not have a single correct answers, but that any solution brings both benefits and costs. Comparing the pluses gained in one area to the minuses in another is seldom clean and easy. Students are reluctant to wrestle with these complexities. A program such as ours that forces them to do this wrestling is very useful.
• The process helped us to identify the six critical areas described under Research and Education Activities and to build a collection of case studies that are being used in our successor classes that will meet the new graduation requirement.
• Over the course of our grant, 45 of the 155 faculty at Macalester College participated in some way in the QM4PP program. This greatly raised the visibility of Quantitative Reasoning at Macalester and clarified for many of our faculty its central importance. When the faculty voted on this graduation requirement in fall, 2005, the vote was almost unanimous in favor.
• The many workshops sponsored under this program have helped to build a strong network of faculty across the country and in a broad variety of disciplines that are working to build programs in Quantitative Reasoning. This has helped to jump-start much of the work of the National Numeracy Network and the Mathematical Association of America’s SIGMAA QL, two organizations devoted to fostering collaboration in building QR programs.

[return to top]

Workshops and outreach

Over the course of this program, Macalester has held eight workshops:

May 22–23, 2002. Initial Planning Workshop

24 participants, including 15 faculty from Macalester College and others from the Humphrey Institute at the University of Minnesota, Duke University, Grinnell College, Carleton College, Lawrence University, and St. Olaf College.

January 9, 2003. Initial Assessment and Follow-Up Planning Workshop

24 participants including 16 faculty from Macalester College, faculty from the University of Minnesota, Grinnell, and Samford University, and representatives from Senator Dayton’s office, Representative McCollum’s office, the Jewish Community Center, and AHANA.

May 19–21, 2003. Planning Workshop to Develop Case Studies on Immigration Policy

49 participants, including 26 faculty from Macalester College, faculty from Duke, Occidental, Augsburg, University of Minnesota, Lawrence, University of Nevada-Reno, a high school teacher, and represents from Ramsey County Government, HACER, AHANA, MN State Government, Wilder Foundation, MN Council of Churches, and Western Initiative for Neighborhood Development.

January 30–February 1, 2004. Pew Midstates Science and Math Workshop on Quantitative Reasoning Initiatives

40 participants, including faculty from Macalester College, Hope College, Colorado College, Duke University, Carthage College, Hollins University, Carleton College, Kalamzoo College, Lawrence University, Hamline University, Colleg eof St. Catherine, Gustavus Adolphus College, Knox College, Beloit College.

May 17–18, 2004. Policies Affecting the Immigrant Experience in Minnesota — also used as an opportunity for significant modifications to the QM4PP program

25 participants, 22 faculty from Macalester, also faculty from Duke, University of Minnesota, and Evergreen State University

June 21–25, 2004. Workshop for High School Teachers on Immigration in America: Understanding the Numbers

25 participants, 17 high school social science teachers representing 11 high schools, 2 Macalester faculty, 2 guest speakers, 4 immigrant students

June 14–19, 2005. MAA PREP workshop on Creating and Strengthening Interdisciplinary Programs in Quantitative Literacy and national meeting of National Numeracy Network

46 participants, 3 presenters from Macalester College plus faculty teams from Johnson State College, Colby-Sawyer College, Hollins University, DePauw University, Mount St. Mary College, Augsburg College, Central Michigan University, Dartmouth College, University of South Florida, Carleton College, individual faculty from Duke University, Carthage College, LaGuardia Community College, Rockford College, Luther College, Bowdoin College, Raritan Valley Community College, University of Arkansas, Trinity College (Hartford), University of St. Thomas, Ithaca College, Wellesley College, and a representative from the American Sociological Association.

May 15–16, 2006. Workshop on preparing case studies for use in quantitative thinking courses and on assessment of QT.

Expecting about 20 participants.

In addition, Macalester has recently joined with Carleton, St. Olaf, and Grinnell in the Collaborative for Assessing Liberal Learning, sponsored by the Teagle Foundation. Each of these four schools has four teams of four faculty each, one team for each of four broad goals: writing, global understanding, critical thinking, and quantitative reasoning. The purpose of the collaborative is to share and collaborate on strategies for assessing student learning in each of these four areas. Because of its record of work in QR, Macalester College is leading the four QR teams.

Outreach

In addition to the workshops, outreach from this program has included an article on the QM4PP program to appear in an upcoming MAA Notes volume, Current Practices in Quantitative Literacy. Other outreach has included:

• David Bressoud and Steve Holland had a poster on the program at the FIPSE Project Director’s meeting in Denver in December, 2003.
• David Bressoud had a poster on the program at the annual joint meetings of the American Mathematical Society and the Mathematical Association of America held in Phoenix in January, 2004.
• Daniel Kaplan ran a workshop on the program at an NSF DUE CCLI conference in Washington, DC in April, 2004. The resulting article “Mathematics for Citizens”, will appear in the proceedings of this conference.
• David Bressoud gave a presentation on the program at a faculty seminar at Hollins University in Roanoke, VA in May, 2004.
• Steve Holland gave a presentation on the program at a workshop sponsored by the American Sociological Association in Washington, DC in June 2004.
• David Bressoud participated as a represent of the QM4PP program at a steering committee meeting of the National Numeracy Network held at Dartmouth College in June, 2004.
• David Bressoud gave a presentation on QM4PP at the Pacific Northwest Section meeting of the Mathematical Association of America held in Anchorage, Alaska in June, 2004.
• Daniel Kaplan gave a presentation on the program at the PREP (Professional Enhancement Programs of the Mathematical Association of America) Workshop on Quantitative Literacy held at Sleeping Lady Retreat Center in Washington state, August 2004.

[return to top]