Undergraduate Programs in the Mathematical Sciences: CUPM Curriculum Guide 2004

1. 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. Supported by grants from NSF and the Calculus Consortium for Higher Education The Mathematical Association of America

2. Historical Background to the Guide Committee on the Undergraduate Program in Mathematics (CUPM) established in 1953 (as CUP). Curriculum guidelines published in 1965 with update in 1972 described the program needed to prepare for doctoral study The Mathematical Association of America

3. 1981 Recommendations for a General Mathematical Sciences Program (republished in Reshaping College Mathematics) 1970 ~23,000 majors 1980 ~12,000 majors Alan Tucker, Chair The Mathematical Association of America

4. 1981 Recommendations for a General Mathematical Sciences Program (republished in Reshaping College Mathematics) • Meet needs of average students • Emphasize development of reasoning skills • Interactive teaching, guide students • Use applications to illustrate and motivate • Introductory courses should appeal to a • broad audience The Mathematical Association of America

5. 1981 Recommendations for a General Mathematical Sciences Program (republished in Reshaping College Mathematics) • All majors should take • Statistics • Discrete Mathematics • Modeling • A 2-course upper division sequence The Mathematical Association of America

6. 1991 The Undergraduate Major in the Mathematical Sciences (published in Heeding the Call for Change) 1970 ~23,000 majors 1980 ~12,000 majors 1990 ~13,000 majors Lynn Steen The Mathematical Association of America

7. 1991 The Undergraduate Major in the Mathematical Sciences (published in Heeding the Call for Change) • Reaffirmed 1981 recommendations, added • Emphasis on writing, speaking, team work • Includeconcentrations in applied mathematics • Take advantage of technology • Pay attention to advising The Mathematical Association of America

8. 2001 Guidelines for Programs and Departments in Undergraduate Mathematical Sciences Contains statements on planning and periodic review, faculty and staffing, curriculum and teaching, institutional and departmental resources, physical facilities, libraries, and services to students such as advising and co-curricular activities for majors. The Mathematical Association of America

9. Tom Berger 1999 CUPM begins to prepare for next set of recommendations Math Math Ed Stat 1970 ~23,000 1980 ~12,000 2,000 600 1990 ~13,000 3,000 1000 2000 ~11,000 5,000 1100 The Mathematical Association of America

10. Premise 1: Mathematics is an exciting, dynamic field that should be recognized as lying at the core of the entire undergraduate curriculum. The Mathematical Association of America

11. 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. The Mathematical Association of America

12. 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 The Mathematical Association of America

13. CRAFTY Curriculum Foundations Project Susan Ganter, Clemson Bill Barker, Bowdoin The Mathematical Association of America

14. CRAFTY Curriculum Foundations Project:Voice of the Partner Disciplines Biology: “Statistics, modeling and graphical representation should take priority over calculus.” The Mathematical Association of America

15. CRAFTY Curriculum Foundations Project:Voice of the Partner Disciplines Chemistry: “It is desirable that calculus courses address multivariable problems from the outset.” “Logical, organized thinking and abstract reasoning are skills developed in mathematics courses that are essential for chemistry.” The Mathematical Association of America

16. CRAFTY Curriculum Foundations Project:Voice of the Partner Disciplines 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 very important … It is more important than esoteric computational skill.” The Mathematical Association of America

17. CRAFTY Curriculum Foundations Project:Voice of the Partner Disciplines Business & Management: “When in doubt, mathematics faculty should cover less material—and treat the material covered with respect—imparting to the students a sense of the importance of the mathematics.” The Mathematical Association of America

18. CRAFTY Curriculum Foundations Project:Voice of the Partner Disciplines Electrical Engineering: “The mathematics required to enable students to achieve these skills should emphasize concepts and problem-solving skills more than emphasizing repetitive mechanics of solving routine problems.” The Mathematical Association of America

19. Writing Team for the CUPM Curriculum Guide 2004 Harriet Pollatsek, chair, Mt. Holyoke College Susanna Epp, DePaul University Bill Barker, Bowdoin College Susan Ganter, Clemson University David Bressoud, Macalester College Bill Haver, Virginia Commonwealth University The Mathematical Association of America

20. 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 The Mathematical Association of America

21. 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 The Mathematical Association of America

22. New themes, CUPM 2004 • Look outward and include non-majors • Know students, create appropriate goals, evaluate courses and programs (assessment) • Emphasize mathematical thinking and communication in all courses, incremental approach • Promote interdisciplinary cooperation,joint majors • Alternative routes to the major • Provide support for faculty working on these changes Provide examples of good practice! The Mathematical Association of America

23. 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 Assessment Practices in Undergraduate Mathematics, Gold et al. 1999 The Mathematical Association of America

24. 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. The Mathematical Association of America

25. 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 The Mathematical Association of America

26. Six General Recommendations 4. Promote interdisciplinary cooperation. Curriculum Foundations Project: Voices of the Partner Disciplines The Mathematical Association of America

27. 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 Mathematical Association of America

28. 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 The Mathematical Association of America

29. 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 Mathematical Association of America

30. 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 The Mathematical Association of America

31. This Power Point presentation can be downloaded from www.macalester.edu/~bressoud/talks The Guide and its companion Illustrative Resources are available at www.maa.org/cupm The Mathematical Association of America