55 CUPM Curriculum Guide 2004

Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004... 1981 Recommendations for a General Mathematical Sciences Program republished in Reshaping

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.

Undergraduate Programs and Courses in the Mathematical Sciences:

CUPM Curriculum Guide 2004

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

1981 Recommendations for a General

Mathematical Sciences Program

(republished in Reshaping College

Mathematics)

1970 ~23,000 majors

1980 ~12,000 majors

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

1981 Recommendations for a General

Mathematical Sciences Program

(republished in Reshaping College

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

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

2001 Guidelines for Programs

institutional and departmental resources, physical

facilities, libraries, and services to students such as advising and co-curricular activities for majors

1999 CUPM begins to prepare for next set of recommendationsTom 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

Premise 1: Mathematics is an exciting,

dynamic field that should be recognized

as lying at the core of the entire

undergraduate curriculum.

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.

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

CRAFTY Curriculum

Foundations Project

Susan Ganter, Clemson

CRAFTY Curriculum

Foundations Project:

Voice of the Partner Disciplines

Biology: “Statistics, modeling and graphical

representation should take priority over calculus.”

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.”

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

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.”

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.”

Writing Team for the CUPM Curriculum Guide 2004

Harriet Pollatsek, chair,

Mt Holyoke College

Bill Barker, Bowdoin College

David Bressoud, Macalester

Susanna Epp, DePaul

University

Susan Ganter, Clemson

University

Bill Haver, Virginia Commonwealth

University

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

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

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

Six General Recommendations

1 Understand the student population and

evaluate courses and programs.

Assessment Practices in Undergraduate

MAA project Supporting Assessment in

Undergraduate Mathematics

http://www.maa.org/saum

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

Consortium for Mathematics and Its Applicationshttp://www.comap.com

Journal of Online Mathematics and its

Applications

Six General Recommendations

3 Communicate the breadth and

interconnections of the mathematical

sciences.

Six General Recommendations

4 Promote interdisciplinary cooperation.

Curriculum Foundations Project: Voices of the Partner Disciplines

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.”

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

Supplementary Recommendations for

Specific Student Audiences

A General education or introductory courses,

B Majors in partner disciplines, elementary &

middle school teachers,

C Majors in mathematical sciences,

D Secondary school teachers, majors preparing

for non-academic workforce, majors

preparing for graduate school

The Guide and its companion Illustrative Resources

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

This Power Point presentation can be

downloaded from

www.macalester.edu/~bressoud/talks