Helping College Students Learn Mathematics

How well do college students learn mathematics, and what can faculty do to make the learning process more effective? The National Science Foundation has awarded $500,000 to the Mathematical Association of America and the University of Arkansas for a project that seeks to improve the assessment of student learning.

The three-year project, which began in January 2002, is called Supporting Assessment in Undergraduate Mathematics (SAUM). Bernard Madison, a professor of mathematical sciences at the University of Arkansas, is the principal author and national project director.

"Faculty often perceive assessment as something imposed from the outside, not as something they own and direct," says Madison. He wants to change this view, giving faculty more of a stake in assessment and making it an integral part of the teaching and learning process.

SAUM is one of only ten projects funded in a recent NSF solicitation, and it was the highest rated proposal out of 144 submitted. Madison hopes the project will increase the number of institutions that have effective assessment programs, providing a support base for college mathematics faculty in their efforts to improve teaching and learning.

The project targets six major curricular areas: the undergraduate mathematics major, courses for future teachers, courses for mathematics-intensive majors (such as engineering), developmental or remedial courses, "innovations" (reformed blocks of courses), and general education or quantitative literacy courses.

Madison hopes to reach a coherent view of course blocks rather than a narrow view of individual courses. Mathematics courses do not follow a linear progression of difficulty. In some courses, the math itself is quite basic, but the applications are sophisticated.

Madison also hopes that SAUM will pave the way for mathematics faculty to become more aware of the role of mathematics in general education. Higher education is now being subjected to the same scrutiny as elementary and secondary education has been for the past two decades. Universities are now accountable for articulating the goals of a college education and their expectations of students at each level of the process. Most such goals are cross-disciplinary, and measuring these general learning outcomes requires more complex measures than are now being employed. Such processes are inherent in the assessment methods that the SAUM project promotes.

Between 1990 and 1995, Madison chaired an MAA effort to craft new assessment guidelines, which operate on the assumption that assessment is an integral part of teaching and learning. These include setting learning goals, devising instructional strategies to reach those goals, and measuring learning.

He spent 2001 as the MAA’s Visiting Mathematician, laying the groundwork for SAUM. While teaching undergraduate mathematics courses, he had already noticed problems with the way student learning is normally assessed.

In American undergraduate education, the usual way to assess learning is through course examinations and grades. Such methods, called summative assessment, may not accurately reflect how much a student has learned, Madison says. Furthermore, they often do not show how instruction can be improved during the course or curriculum.

Formative assessment includes multidimensional methods like those in postgraduate programs. Doctoral students spend a great deal of their time presenting and discussing their own work in seminars, listening to the work of others, conversing with faculty members, and being tested by faculty committees in various areas, in addition to taking written exams and writing and defending a dissertation.

Madison thinks that formative assessment helps explain why American graduate education is indisputably the best in the world. Formative assessment produces a continuous cycle for measuring learning outcomes, where learning is constantly reviewed and enhanced. And it can be used not only to evaluate students, faculty, and academic programs, but also to target ways to improve them.

Unfortunately, large numbers of undergraduate students mean that assessment cycles may be less efficient than simple in-class tests. And previous assessment models have not always been adaptable to large and diverse institutions.

But many faculty members already use formative assessment in their daily work, Madison asserts. Perhaps unconsciously, they search for feedback from their students by listening to them and gauging their level of understanding. The challenge for SAUM is to encourage faculty to adopt this attitude as a general practice, institutionalizing broader and deeper forms of assessment.

Madison and the other members of the consortium have structured SAUM as an information campaign, which consists of forums on assessment at MAA section meetings, a series of faculty workshops, an assessment website, and various case studies of assessment programs. So far, 26 institutions are participating in workshops, and Madison hopes there will be 50 by the time the project is finished. Hundreds of others have participated in the MAA section forums. Assessment guidelines and a volume of case studies have been sent to every mathematics department in the country as part of the project, and another such mailing will be made at the end of the three years.

The workshop series will consist of 10-12 teams working over a period of two years. Workshops have already been held in conjunction with MAA meetings in San Diego (January 2002) and Vermont (July 2002). Progress reports will be presented at a meeting in Baltimore (January 2003).

More information about the project can be found at www.maa.org/SAUM/Index.html.