by Martha J. Siegel, Professor, Towson University
I serve as chair of the Mathematical Association of America’s (MAA’s) Committee on the Undergraduate Program in Mathematics (CUPM). Approximately every ten years, CUPM publishes a new curriculum guide, with the primary goal of assisting mathematics departments with their undergraduate offerings. Over five years in the making, the 2015 Curriculum Guide to Majors in the Mathematical Sciences encourages departments to engage in a process of review and renewal, by examining their own beliefs, interests, resources, mission, and particularly their own students in designing or revising a major in mathematics or, more generally, in the mathematical sciences. In the remainder of this blog post, we discuss the history, development, process, and key characteristics and recommendations of the 2015 Guide.
CUPM has a long and distinguished history, going back to curriculum reports in the 1950’s. The CUPM recommendations of 1991 were limited to the mathematics major and can be found in the report, Heeding the Call for Change. The CUPM Curriculum Guide 2004 addressed the entire undergraduate mathematics curriculum, with a particular emphasis on service courses of the first two years and pedagogical methods. In 2011, when we began thinking about preparing this guide, we decided to revisit the undergraduate mathematics major, as almost 25 years has passed since the MAA has done an in-depth study of the mathematics major. The 2004 Guide included important basic principles that apply to all mathematics courses. However, the applications of mathematics have expanded so much of late that CUPM felt it important to address the full scope of majors in the mathematical sciences.
At national meetings over the last five years, CUPM has held numerous focus groups, presented ideas to groups of chairs and coordinators of undergraduate mathematics programs, and solicited advice from directors of graduate programs, at both Master’s and doctoral levels. Several years of these discussions of content and cognitive goals have led to a consensus of what might be considered the fundamental components of any mathematical sciences bachelor’s level program. The draft of the 2015 Guide was submitted to the member organizations of CBMS, and many CBMS members created Association Response Groups that sent us valuable suggestions and comments. We were pleased with the response and have incorporated almost all of their advice.
The recommendations and principles in the Curriculum Guide are meant to drive a process of intentional design within a framework of basic cognitive and content goals that have been agreed upon by the mathematical community across many types of institutions. As the title reflects, this report is intended as a guide, not as a prescription. It is not an accreditation document. The members of CUPM and the Curriculum Guide Steering Committee found fundamental agreement as to what should be the core of any mathematical sciences major. From the many applied fields to the doctoral programs in pure mathematics, we heard much the same basic ideas. Although we spent quite a lot of time refining the words in the recommendations, there was very little disagreement on the principles. Nevertheless, CUPM emphasizes that each department is expected to examine its own program(s), mission, students, resources, and interests as it considers its own goals and pathways. At its August meeting in 2014, the Board of Governors of the MAA approved the Cognitive and Content Recommendations discussed in the Overview of the 2015 Guide and also reaffirmed the Principles of the 2004 Guide.
The real planning and intentional structure of the mathematics major derives from the cognitive and content goals and from recognizing that a department must design courses in the core to advance students toward the mathematical maturity that is the sum of the stated goals.
We believe that a successful major program offers a program of courses to gradually and intentionally lead students from basic to advanced levels of critical and analytical thinking, while encouraging creativity and excitement about mathematics. This requires that students be expected to do more each semester to develop and grow so that they achieve the goals eventually. This is the essence of the generic mathematics major. Each department should incorporate the core goals by offering their own intentional design of appropriate experiences and electives for their students. The Overview section of the 2015 Guide is the closest we get to “defining” the major.
There are many parts to the current Guide. There is a downloadable brochure, which briefly explains the contents and can be used to discuss the main points with administrators and others. A printed abbreviated version of the 2015 Curriculum Guide will be sent to all department chairs. The bulk of the details on all the course areas and program areas will appear online only. Carol Schumacher of Kenyon College co-chaired the Curriculum Guide Steering Committee and is co-PI with me and Michael Pearson of the MAA on the NSF grant [DUE-1228636] and the Educational Advancement Foundation grants that made this project possible. Paul Zorn is the editor, and has generously offered wise counsel to Carol and me in preparing all of the disparate parts for distribution.
The Introduction and the Overview are essential reading. They describe the context and essential components of the report and the recommended goals for all mathematical sciences. Although this Guide makes recommendations about a great variety of programs that center on new and developing applications of mathematics, CUPM urges departments to continue to offer an option for a major in mathematics that is perhaps considered traditional in scope and purpose. Some departments call this the “pure” mathematics track; some call it the preparation for doctoral programs in mathematics. Such programs should rely on educational processes that lead to mathematical maturity, should cultivate appreciation for mathematics for its own sake, and, while incorporating some applications of the theory, they are centered on the theoretical nature of the subject. All undergraduate major programs in mathematics/mathematical sciences have common elements however, and the cognitive and content goals reflect those common threads.
Focus groups and MAA SIGMAAs (MAA’s special interest groups) generated many ideas for an in-depth view of undergraduate course areas, and of course, provided a modern look at the many applied areas that beckon mathematicians. The Mathematical Sciences in 2025, a publication of the Board of Mathematical Sciences and Its Applications of the National Research Council, provided CUPM with many examples of fast-growing career opportunities for mathematicians. The INGenIOus Report in 2014 added to the call for career-readiness in college graduates. These resources and the members of the Curriculum Guide Steering Committee were instrumental in the selection of the many Course Areas and Program Areas featured in the report. Invitations to the members of the nearly 40 Study Groups were informed by the Steering Committee, as well.
Some MAA committees provided a natural resource as, for example, the American Statistical Association-MAA Joint Committee on Statistics or the CUPM Subcommittee on Mathematics Across the Disciplines. Of particular importance are the reports on the Preparation of High School and Middle School Teachers, which are reports from the MAA’s Committee on the Mathematical Education of Teachers. CUPM is pleased that more than 200 individuals have contributed to these group reports. The willingness of the mathematical community and many of our colleagues in allied fields to commit their time to this project has been very gratifying. I urge everyone to read these reports. They represent the views of a large and varied group of mathematicians and scientists who teach undergraduates.
Because a successful department is more than just its course and program offerings, the Guide contains a large section on matters “beyond the curriculum.” These are essential departmental and institutional policies that advance and enhance undergraduate major programs. These include articles on recruitment and retention, assessment, and placement, for example.
In some ways, the most interesting CUPM discussions were focused on Review and Renewal, the “how” to go about making change, particularly focused on meeting our cognitive and content goals. We believe that a healthy mathematical sciences program should incorporate intentional evolution and continual improvement. Every mathematical sciences department should have and follow a strategic plan that acknowledges local conditions and resources, but is also informed by recommendations from the greater mathematical community. The process of planning and renewal should be guided by consultation both within the department and with outside stakeholders at the institution and beyond. Departments should assess their progress in meeting cognitive and content goals through systematic collection and evaluation of evidence. The process of program review and departmental responsibilities in renewal are discussed in our report.
The most radical feature of this CUPM Guide is that it is meant to be dynamic in that we expect CUPM will add resource material to the Course and Program Areas regularly and do a thorough review of several course and program areas each year. Rather than trying to write a guide to the undergraduate curriculum and the major every decade, CUPM hopes to maintain an on-going revision and renewal process of its own that is directed at all of the course and program areas. We invite members of the mathematical community to submit ideas such as projects, resources, and videos, so that they can be posted online appropriately. We are preparing a submission procedure at this time. CUPM’s mission is to provide a current, meaningful, and useful resource for the design and improvement of the undergraduate major, and we welcome your input.
Feel free to contact me with your comments and suggestions at msiegel@towson.edu.