Slide1 : 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 Mathematical Association of America Supported by grants from NSF and the Calculus Consortium for Higher Education Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004
Slide2 : The Mathematical Association of America 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
Slide3 : The Mathematical Association of America 1981 Recommendations for a General Mathematical Sciences Program (republished in Reshaping College Mathematics) Alan Tucker, Chair 1970 ~23,000 majors
1980 ~12,000 majors
Slide4 : The Mathematical Association of America 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
Slide5 : The Mathematical Association of America 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
Slide6 : The Mathematical Association of America 1991 The Undergraduate Major in the Mathematical Sciences (published in Heeding the Call for Change) Lynn Steen 1970 ~23,000 majors
1980 ~12,000 majors
1990 ~13,000 majors
Slide7 : The Mathematical Association of America 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
Include concentrations in applied mathematics
Take advantage of technology
Pay attention to advising
Slide8 : The Mathematical Association of America 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.
Slide9 : The Mathematical Association of America 1999 CUPM begins to prepare for next set of recommendations Tom Berger 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
Slide10 : 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.
Slide11 : 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.
Slide12 : 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
Slide13 : The Mathematical Association of America CRAFTY Curriculum Foundations Project Susan Ganter, Clemson Bill Barker, Bowdoin
Slide14 : 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.”
Slide15 : The Mathematical Association of America 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.”
Slide16 : The Mathematical Association of America 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.”
Slide17 : The Mathematical Association of America 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.”
Slide18 : The Mathematical Association of America 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.”
Slide19 : The Mathematical Association of America Writing Team for the CUPM Curriculum Guide 2004 Harriet Pollatsek, chair, Mt. Holyoke College Bill Barker, Bowdoin College David Bressoud, Macalester College Susanna Epp, DePaul University Susan Ganter, Clemson University Bill Haver, Virginia Commonwealth University
Slide20 : 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
Slide21 : 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
Slide22 : The Mathematical Association of America 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!
Slide23 : The Mathematical Association of America Six General Recommendations
1. Understand the student population and evaluate courses and programs. Assessment Practices in Undergraduate Mathematics, Gold et al. 1999 MAA project Supporting Assessment in Undergraduate Mathematics
http://www.maa.org/saum
Slide24 : 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.
Slide25 : 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 Six General Recommendations
3. Communicate the breadth and interconnections of the mathematical sciences.
Slide26 : The Mathematical Association of America Six General Recommendations 4. Promote interdisciplinary cooperation. Curriculum Foundations Project: Voices of the Partner Disciplines
Slide27 : 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.”
Slide28 : 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
Slide29 : 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.
Slide30 : The Mathematical Association of America The Guide and its companion Illustrative Resources are available at www.maa.org/cupm 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.
Slide31 : The Mathematical Association of America The Guide and its companion Illustrative Resources are available at www.maa.org/cupm This Power Point presentation can be downloaded from www.macalester.edu/~bressoud/talks