Friday, July 1, 2016

MAA and Active Learning

There is a general perception among both research mathematicians and those working in our partner disciplines that—with a few exceptional pockets such as the community of those promoting Inquiry Based Learning (IBL)—the mathematical community is only now beginning to wake up to the importance of active learning. In fact, the MAA’s Committee on the Undergraduate Program in Mathematics (CUPM) began to promote the use of active learning in 1981 and has never ceased. It is a cry to which many have responded, but which has recently been rediscovered and promoted with urgency as chairs, deans, provosts, and presidents have come to realize that the way mathematics instruction has traditionally been organized cannot meet our present needs, much less those of the future. I was reminded of the origins of MAA’s support for active learning after encountering a particular piece of misleading data in Andrew Hacker’s The Math Myth, an unpleasant little book filled with half-truths, deceptive innuendo, and misleading statistics.

Hacker argues that the “math mandarins” cannot even attract students to major in mathematics and supports his argument with the fact that the number of Bachelor’s degrees in mathematics earned by US citizens dropped from 27,135 in 1970 to 17,408 in 2013. As a percentage of the total number of Bachelor’s degrees, the drop is even more impressive: from 3.4% to 1.0%. These numbers are symptomatic of Hacker’s deceptive use of data.

The first thing that is deceptive about these numbers is that they suggest a steady erosion of interest in mathematics. In fact, as Figures 1 and 2 show, the drop was precipitous during the 1970s, with the total number of Bachelor’s degrees in mathematics bottoming out in 1981 at 11,078, showing some recovery in the ‘80’s, followed by a steady decline until 2001 when it dipped back below 12,000, only 0.94% of Bachelor’s degrees. Since then, the growth has been reasonably strong, rising to 20,980 (of whom 2,438 were non-resident aliens) in 2014. That was back up to 1.12%.

(Note: The sharp increase in the early 1980s is almost certainly due to the high unemployment the United States was then suffering. Similarly, the noticeable increase in slope around 2010 is most probably a product of the unemployment rate that peaked in 2009.)

The other thing that is deceptive is the choice of when to start. The year 1970 came at the end of a strong national push for young people to enter mathematics and science. We had begun that decade in 1960 with only 11,399 mathematics degrees, though admittedly that was 2.9% of the total. Much of the loss during the ’70’s may be attributed to the creation of computer science majors. Bachelor’s degrees in computer science rose from 2388 in 1971 to 15,121 in 1981. Much, but not all. In fact, many members of the mathematical community were alarmed by this drop. Therein begins the story that is far more important than Hacker’s data.

CUPM was established in the early 1950’s to bring order to the chaotic assortment of courses that constituted mathematics majors across the country. In 1965 this committee of leading mathematicians published A General Curriculum in Mathematics for Colleges, which codified what by then was becoming the standard undergraduate major, beginning with three semesters of calculus and one semester of linear algebra. CUPM’s concern was almost entirely what to teach, not how to teach it. That changed in 1981 when Alan Tucker’s CUPM panel published Recommendations for a General Mathematical Sciences Program.

Concerned about the precipitous fall in the number of majors as well as enrollments in upper division courses, the attention in this report was focused on the goals of an undergraduate major and how they could be achieved. It laid out a five-point program philosophy that included an appeal to use active learning:
  1. “The curriculum should have a primary goal of developing attitudes of mind and analytical skills required for efficient use and understanding of mathematics … 
  2. “The mathematical sciences curriculum should be designed around the abilities and academic needs of the average mathematical sciences student … 
  3. A mathematical sciences program should use interactive classroom teaching to involve students actively in the development of new material. Whenever possible, the teacher should guide students to discover new mathematics for themselves rather than present students with concisely sculptured theories. (My italics.) 
  4. “Applications should be used to illustrate and motivate material in abstract and applied courses… 
  5. “First courses in a subject should be designed to appeal to as broad an audience as is academically reasonable …” 
 In the 1991 CUPM report, The Undergraduate Major in the Mathematical Sciences, chaired by Lynn Steen, the third point from 1981 was expanded to a clearer articulation of active learning.
III. Interaction. Since active participation is essential to learning mathematics, instruction in mathematics should be an interactive process in which students participate in the development of new concepts, questions, and answers. Students should be asked to explain their ideas both by writing and by speaking, and should be given experience working on team projects. In consequence, curriculum planners must act to assure appropriate sizes of various classes. Moreover, as new information about learning styles among mathematics students emerges, care should be taken to respond by suitably altering teaching styles.
The next report, CUPM Curriculum Guide 2004, chaired by Harriet Pollatsek, continued to build on the theme of how we teach. In this iteration, CUPM expanded its vision to all of the courses taught by departments of mathematics, insisting that “Every course should incorporate activities that will help all students progress in developing analytical, critical reasoning, problem-solving, and communication skills and acquiring mathematical habits of mind.”

This emphasis continues in the most recent CUPM guide, 2015 CUPM Curriculum Guide toMajors in the Mathematical Sciences, co-chaired by Carol Schumacher and Martha Siegel and edited by Paul Zorn. It begins with four “Cognitive Recommendations:"

  1. Students should develop effective thinking and communication skills. 
  2. Students should learn to link applications and theory. 
  3. Students should learn to use technological tools. 
  4. Students should develop mathematical independence and experience open-ended inquiry.

Throughout these decades, MAA has done more than issue recommendations. All of these reports have been backed up by MAA Notes volumes that have pointed to successful programs and explained how such instruction can be implemented within specific courses. (For a list of all Notes volumes, click here.) The Notes began in 1983 with Problem Solving in the Mathematical Sciences, edited by Alan Schoenfeld. MAA has run workshops as well as focused sessions and presentations at both national and regional meetings. Project NExT, MAA’s program for new faculty now in its third decade, has always had an emphasis on introducing newly minted PhDs to the use of active learning strategies.

It is hard to say whether these measures have been responsible for arresting and reversing the slide in the number of majors. Economic factors have certainly played a role. But MAA publications and activities have established a depth of experience and expertise within the mathematical community. Now that there is broad recognition of the importance of active learning strategies in the teaching and learning of undergraduate mathematics, we are fortunate to have this foundation on which to build.


Duren, W.L. Jr., Chair. 1965. A General Curriculum in Mathematics for Colleges. Berkeley, CA: CUPM.

Hacker, A. The Math Myth: and other STEM Delusions. New York, NY: The New Press.

Pollatsek, H., Chair. 2004. CUPM Curriculum Guide 2004. Washington, DC: MAA. departments/curriculum-department- guidelines-recommendations/cupm/cupm-guide- 2004

Schoenfeld, A.H., Editor. 1983. Problem Solving in the Mathematical Sciences. Washington, DC: MAA.

Schumacher, C.S. and Siegel, M.J., Co-Chairs, and Zorn, P., Editor. 2015. 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences. Washington, DC: MAA. departments/curriculum-department- guidelines-recommendations/cupm

Steen, L.A., Chair. 1991. The Undergraduate Major in the Mathematical Sciences. Washington, DC: MAA.

Tucker, A., Chair. 1981. Recommendations for a General Mathematical Sciences Program. Washington, DC: MAA. Reprinted on pages 1–59 in Reshaping College Mathematics, L.A. Steen, editor. Washington, DC: MAA,