Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004 This is the first CUPM report to address the entire undergraduate mathematics curriculum, for all students. It is the result of four years of work including extensive consultation with hundreds of mathematicians as well as faculty from biology, chemistry, economics, engineering and other partner disciplines. The MAA’s Committee on the Undergraduate Program in Mathematics has been publishing recommendations on the undergraduate curriculum in mathematics at roughly ten-year intervals since the early 1950’s. Through the 1970’s, these reports focused on preparing students for graduate work in mathematics. Beginning with the 1981 recommendations, attention has shifted to all majors in the mathematical sciences. This is the first report to consider not just what is appropriate for our majors, but how the undergraduate mathematics curriculum should meet the needs of all students. The Guide was published in February, 2004. It consists of 22 recommendations, organized into six general recommendations followed by sixteen recommendations intended for courses aimed at particular audiences. The Guide should not be read as an admonishment of what must be done, but rather as goals toward which we should strive. How they are achieved will depend very much on local circumstances. Supported by grants from NSF and the Calculus Consortium for Higher Education The Mathematical Association of America

Premise 1: Mathematics is an exciting, dynamic field that should be recognized as lying at the core of the entire undergraduate curriculum. From a peak of almost 25,000 in the late 1960s, the number of bachelors degrees in mathematics per year dropped to 10,000 in the late 1970s. Despite strong growth in the sciences and engineering, the number of majors has stayed between 10,000 and 11,000 since then. CUPM believes that there have been missed opportunities to convey to students the dynamic nature of mathematics as it is practiced today and its importance across a wide range of disciplines. Each department will need to interpret these recommendations in the light of its own circumstances, considering the students with whom they work, the resources that are at their disposal, and the strengths and weaknesses of their own faculty. Because of this variability, each recommendation is followed by an extension discussion of how it might play out in a variety of situations and contexts. The Mathematical Association of America

Premise 1: Mathematics is an exciting, dynamic field that should be recognized as lying at the core of the entire undergraduate curriculum. Premise 2: Excellence is achieved by focusing on the outcomes we want of our students and tailoring the program to the specific needs of our students within the context of our institution. From a peak of almost 25,000 in the late 1960s, the number of bachelors degrees in mathematics per year dropped to 10,000 in the late 1970s. Despite strong growth in the sciences and engineering, the number of majors has stayed between 10,000 and 11,000 since then. CUPM believes that there have been missed opportunities to convey to students the dynamic nature of mathematics as it is practiced today and its importance across a wide range of disciplines. Each department will need to interpret these recommendations in the light of its own circumstances, considering the students with whom they work, the resources that are at their disposal, and the strengths and weaknesses of their own faculty. Because of this variability, each recommendation is followed by an extension discussion of how it might play out in a variety of situations and contexts. The Mathematical Association of America

Preparing for the Guide Focus groups at Joint Math Meetings 2000, 2001 & Mathfest 2002—over 500 participants Panel discussions at meetings Invited papers, September 2000 Reports from AMS, AMATYC, ASA, NCTM This Guide was a corporate effort. Not only is it based on the input of hundreds of mathematicians as well as faculty in the partner disciplines, multiple drafts of the Guide were reviewed by specially established Association Review Groups for AMS, AMATYC, ASA, and NCTM. The Mathematical Association of America

CRAFTY Curriculum Foundations Project Susan Ganter, Clemson In preparation for the writing of the Guide, CRAFTY held ten workshops around the country to which the leaders in undergraduate education in partner disciplines such as Biology, Economics, and Engineering came together to create sets of recommendations for the mathematical community. Reports from eighteen different disciplines are collected in the Curriculum Foundations Project, also published in February, 2004 and available at www.maa.org/CRAFTY. This volume is intended to facilitate discussions with the partner disciplines at each individual institution, providing a starting point for meaningful dialog about the actual needs of the students majoring in these departments. Bill Barker, Bowdoin The Mathematical Association of America

CRAFTY Curriculum Foundations Project: Voice of the Partner Disciplines Biology: “Statistics, modeling and graphical representation should take priority over calculus.” Physics: “Courses should cover fewer topics and place increased emphasis on increasing the confidence and competence [of] students…Conceptual understanding of basic mathematical principles is more important than esoteric computational skill.” This slide quotes from two of the workshops, giving examples of the kinds of recommendations made by the partner disciplines. The Mathematical Association of America

Common themes in CUPM 1981, 1991, 2004 Reasoning and analytical skills Interplay of applications, problem solving and theory Broad, flexible major for diverse student goals Take advantage of technology Recruit and nurture majors; good advising Include data analysis and discrete mathematics in major Much of Guide reiterates points made in previous CUPM reports. This slide highlights the recommendation, first made by CUPM in 1981, that every mathematics major should be required to take a course in statistics that emphasizes data analysis and should be required to take a course in discrete mathematics. The Mathematical Association of America

Six General Recommendations 1. Understand the student population and evaluate courses and programs. MAA project Supporting Assessment in Undergraduate Mathematics http://www.maa.org/saum Each of the six general recommendations are very rich. These summary slides highlight one facet of or resource for the recommendation. Assessment, knowing who our students are, what they need from our programs, and how well we are meeting those needs, is the essential starting point. This slide presents two valuable resources for aid in uncovering this information. Assessment Practices in Undergraduate Mathematics, Gold et al. 1999 The Mathematical Association of America

Six General Recommendations 2. Develop mathematical thinking and communication skills. Mathematics: “The most important task of the first two years is to move students from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction, and formal proof. The sooner this can be accomplished, the better.” —Curr. Fdns. Proj. One of the Curriculum Foundations workshops, held as MSRI, brought together representatives from mathematics doctoral programs to talk about what their students really need to learn in undergraduate mathematics, especially in the first two years. The quote given on the slide summarizes the main point of their report. The Mathematical Association of America

Six General Recommendations 3. Communicate the breadth and interconnections of the mathematical sciences. Consortium for Mathematics and Its Applications http://www.comap.com Journal of Online Mathematics and its Applications http://www.joma.org Instructors should strive in every course to find ways to communicate the vitality and importance of mathematics in the world today. This slide highlights two of the resources that are available to assist in this. The Mathematical Association of America

Six General Recommendations 4. Promote interdisciplinary cooperation. Curriculum Foundations Project: Voices of the Partner Disciplines This recommendation speaks for itself. The Guide describes many of the ways in which interdisciplinary cooperation can be fostered. The Mathematical Association of America

Six General Recommendations 5. Use computer technology to support problem solving and to promote understanding. “The view of programming as consisting only of if-then, do-while, and a few other structures is several decades behind the current state of the art …If a person needs to learn a programming language in the future, the best basis is to know one of the state-of-the-art languages of today.” The Guide intentionally does not recommend any specific technologies. The use of computers (including graphing calculators) has now been well tested in the classroom and there is considerable of evidence for what works. How technology should be used will depend on the particular circumstances of the institution, its students, and its resources, but there is no longer an excuse for not taking advantage of the pedagogical benefits that technology can bring. One issue that the Guide addresses is that of learning computer programming. The Guide recommends that majors who will go directly into the workforce will need a course in programming, and majors who will go on to graduate school will need a course in computer programming. In both cases, they need a course that teaches programming as it is practiced today. The Mathematical Association of America

Six General Recommendations 6. Provide faculty support for curricular and instructional improvement. “There should be clear standards of excellence for those whose greatest achievements are in teaching or other educational activities, and faculty who meet those standards should share in faculty rewards, both financially and through promotion in rank.” AMS report Towards Excellence None of these recommendations can be implemented without faculty time and energy. Faculty efforts devoted to improving the undergraduate curriculum need to be recognized and rewarded by the college or university. This is a point made very forcefully by the AMS in its report Towards Excellence, quoted above, and fully endorsed by the MAA. The Mathematical Association of America

Supplementary Recommendations for Specific Student Audiences General education or introductory courses, Majors in partner disciplines, elementary & middle school teachers, Majors in mathematical sciences, Secondary school teachers, majors preparing for non-academic workforce, majors preparing for graduate school. The Guide includes an additional sixteen recommendations that address the needs of particular audiences of our students. The third collection consists of recommendations relevant to all majors in the mathematical sciences. The final collection contains recommendations that are appropriate for particular subsets of the mathematical sciences majors. The Mathematical Association of America

Illustrative Resources A web-based supplement to CUPM Guide Illustrative Resources describes courses, programs, curricular materials, articles, etc. that illustrate ways the recommendations can be implemented at varied institutions. The Guide and its companion Illustrative Resources are available at www.maa.org/cupm A lot of work has been done at many different colleges and universities. We need to take advantage of what has been learned by others. To this end, the Guide is supplemented by the Illustrative Resources, a collection of short descriptions of programs and initiatives at a wide variety of institutions, together with references and links to further information. This currently exists on the CUPM website, organized according to the recommendations in the Guide. CUPM is in the process of turning this resource into a fully searchable, edited, and constantly updated database that will be part of the MAA’s Mathematical Digital Library, MathDL. The Mathematical Association of America