Wellesley, a liberal arts college located outside of Boston, has integrated quantitative literacy into courses and assessment.

Wellesley College Advances Quantitative Reasoning through Curricular Innovations and Assessment

In the fall of 1997, Wellesley College adopted a new approach to gauging its students' needs: it required all incoming students to take a quantitative reasoning (QR) assessment. This assessment marked the formal beginning of an innovative program that provides "basic skills" courses for those who do not pass initial assessments, advanced courses that help students understand disciplinary applications of quantitative reasoning, and workshops that offer condensed reviews of specific math skills.

In developing this program, Wellesley has been at the forefront of the movement to incorporate quantitative reasoning across undergraduate curricula. QR, unlike traditional mathematics, stresses real-world applications of mathematical concepts. As advocates point out, such practical quantitative skills are increasingly important not just to college graduates' professional success, but also to their ability to manage personal finances, understand the news, and evaluate the claims of politicians and pundits. Quantitative reasoning in this sense represents a promising way of preparing students--especially those who do not major in quantitative fields--to become mathematically literate citizens and workers.

Assessing Basic Skills

Wellesley, a small, women's liberal arts college located outside of Boston, began piloting QR tests in the early 1990s to address a perceived need for early assessment of quantitative literacy. Faculty developing the test focused on several competencies: knowledge of practical geometry and algebra, the ability to interpret and create graphs and charts, and understanding of basic statistics and probability.

The QR assessment today consists of eighteen multipart questions that cover these essential skills. But rather than taking the abstract approach of pure math, the assessment requires students to apply their mathematical skills, mostly through word problems, to realistic, hypothetical situations. According to Corrine Taylor, the director of the QR program, this emphasis on applied knowledge is a key aspect of Wellesley's approach to learning and assessment. In contrast to the way math has traditionally been taught, Taylor says, Wellesley's QR program emphasizes context and compels students "to use multiple logical, statistical, and mathematical skills" in solving real-world problems.

Since 1997, when the QR assessment was fully integrated into first-year orientation, students who do not pass the assessment--typically 6 to 10 percent of the entering class--have been required to take Introduction to Quantitative Reasoning. This basic skills course, which is taught regularly by Corrine Taylor and her colleague Jessica Polito, stresses the same essential competencies as the assessment. And like the assessment, the course contextualizes mathematical concepts--Taylor, for instance, teaches the difference between linear and exponential growth through demographic analysis and analysis of interest on loans. Students are evaluated through their coursework for mastery of such key concepts, and passing the course is equivalent to passing the basic QR assessment.

Wellesley also offers QR workshops and tutorials, although Corrine Taylor admits that the college needs to further develop this part of the program. Geared toward those students who pass the initial assessment but still need help with some basic math skills, the workshops provide opportunities for review and often complement math-intensive courses

QR in the Disciplines

The second part of Wellesley's QR requirement, the overlay component, can be completed at any point during a student's undergraduate career. Firmly rooted in the disciplines, overlay courses continue the contextualized approach of the basic skills requirement while also emphasizing the specific disciplinary applications of quantitative skills.

Wellesley students have about twenty QR overlay classes to choose from each semester, and more than a dozen departments, from biology to sociology, regularly offer the classes. Some majors require specific overlay courses; students in other majors--in the humanities, for example--can choose overlay classes that will also satisfy their distribution requirements. Every overlay course must devote at least a third of class time to QR skill development and address a number of specific topics, including the framework for data collection and analysis; the relevance and bias of data; visual, verbal, and numerical methods of representing data; ways of summarizing data; basic probability; distribution of data sets; and sampling of data.

Different departments, of course, teach about these issues through different projects, and students' work is evaluated according to their mastery of discipline-specific QR skills. For example, students in psychology overlay courses might conduct controlled experiments, students in economics courses might work with economic databases in a computer lab, and students in chemistry courses might collect and report data in a laboratory setting. Such an approach, Corrine Taylor says, provides opportunities for students to learn "in authentic contexts."

Corrine Taylor's QR classes focus the contexts in which math is used.

Making the Case for Quantitative Reasoning

Beginning this fall, all of the students enrolled in Wellesley's basic skills classes completed a pre- and post-course survey. Originally developed for Dartmouth College's Mathematics Across the Curriculum project, the survey consists of thirty-five items that measure student attitudes toward mathematics. The findings of the surveys are heartening for those who have been making the case for quantitative reasoning: in fact, Jessica Polito says, a comparison of pre- and post-course attitudes reveals positive changes in every area tested. (The surveys showed especially strong results in the category of "personal growth," which includes student responses to such statements as "Mathematical thinking helps me make intelligent decisions about my life" and "Doing mathematics raises interesting new questions about the world.") As more such data becomes available, faculty involved in the QR program will be able to better assess the effectiveness of their own teaching.

In gathering such evidence, Wellesley is contributing to a growing body of information about the effectiveness of quantitative reasoning. Campuses interested in starting QR programs and developing assessments today can draw on such evidence and can turn for support to a number of organizations dedicated to quantitative literacy. "There are a lot of really wonderful resources out there," says Corrine Taylor--including books such as Mathematics and Democracy: The Case for Quantitative Literacy, a report by the National Council on Education and the Disciplines which Taylor gave to Wellesley's president as part of her effort to build support for QR on campus.

What is the most persuasive case that can be made for the importance of ensuring students' quantitative reasoning abilities? "QR skills are universal," Taylor says. "It used to be that people could get away with saying 'I can't do numbers,' but today . . . you have to have quantitative skills to be a functioning member of society."

More information about Wellesley's quantitative reasoning program is available on the college's Web site. Mathematics and Democracy, the above-mentioned report, is available for download from the Mathematical Association of America's quantitative literacy pages.

In addition to directing Wellesley's QR program, Corrine Taylor is serving as an outside evaluator for Carleton College, which is currently integrating quantitative reasoning into its portfolio-based assessments. Carleton's writing portfolios were featured in the first story in the newsletter's series on assessment.

The Summer 2004 issue of AAC&U's Peer Review focused on quantitative literacy and explored recent trends in assessment. AAC&U also has many assessment resources available online. The association's recently released board statement, Our Students' Best Work: A Framework for Accountability Worthy of Our Mission, offers an approach to assessment that takes account of the complexity of college-level learning and the diversity of American colleges and universities.