Volume IV: What works, what matters, what lasts

2004 Curriculum Guide from CUPM

Committee on the Undergraduate Program in Mathematics


Mathematics is universal: it underlies modern technology, informs public policy, plays an essential role in many disciplines, and enchants the mind. At the start of the twenty-first century, the undergraduate study of mathematics can and should be a vital and engaging part of preparation for many careers and for well-informed citizenship.

From that opening statement, CUPM leaders call on mathematicians and mathematics departments to rethink the full range of their undergraduate curriculum and co-curriculum to ensure the best possible mathematical education for all their students, from liberal arts students taking just one course to students majoring in the mathematical sciences.

The MAA Board of Govenors approved the following recommendations at their Mathfest 2003 meeting. These recommendations can be seen not only as a roadmap for planning the future of mathematics departments, but also as a template for use by those pursuing excellence in all STEM departments. If conversations between mathematics and partner disciplines are to be encouraged, these recommendations provide some talking points for collegial conversations [Note recommendation 4]. Further, these recommendations also serve as a check-list from which institutional leaders can determine the quality and character of the STEM departments on their campus [Note recommendation 6].

Recommendation 1: Mathematical sciences departments should

  • Understand the strengths, weaknesses, career plans, fields of study, and aspirations of the students enrolled in mathematics courses;
  • Determine the extent to which the goals of the courses and programs offered are aligned with the needs of students as well as the extent to which these goals are achieved;
  • Continually strengthen courses and programs to better align with student needs, and assess the effectiveness of such programs.

Recommendation 2: 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. More specifically, these activities should be designed to advance and measure students’ progress in learning to:

  • State problems carefully, modify problems when necessary to make them tractable, articulate assumptions, approacite the value of precise definition, reason logically to conclusions, and interpret results intelligently;
  • approach problem solving with a willingness to try multiple approaches, persist in the face of difficulties, assess the correctness of solutions, explore exammple, pose questions, and devise and test conjectures;
  • Read mathematics with understanding and communicate mathematical ideas with clairtyh and coherence through writing and speaking.

Recommendation 3: Every course should strive to

  • Present key ideas and concepts from a variety of perspectives;
  • Employ a braod range of examples and applications to motivate and illustrate the material;
  • Promote awareness of connections to other subjects (both in and out of the mathematical sciences) and strengthen each student’s ability to apply the course material to these subjects;
  • Introduce contemporary topics from the mathematical sciences and their applications, and enhance student perceptions of the vitality and importance of mathematics in the modern world.

Recommendation 4: Mathematical sciences departments should encourage and support faculty collaboration with colleagues from other departments to modify and develop mathematics courses, create joint or cooperative majors, devise undergraduate research projects, and possibly team-teach courses or units within courses.

Recommendation 5: At every level of the curriculum, some courses should incorporate activities that will help all students progress in learning to use technology

  • Appropriately and effectively as a tool for solving problems;
  • As an aid to understanding mathematical ideas.

Recommendation 6: Mathematical sciences departments and institutional administrators should encourage, support and reward faculty efforts to imporve the efficacy of teaching and strengthen curricula.