Mathematics Curricula in 2010:
What Should Students Know?

What are your views on the mathematics curriculum? What are your expectations of graduates? CUPM (The Committee of the Undergraduate Program in Mathematics) is seeking advice from the community of mathematicians. At the January 2001 meetings, an MAA Report appeared with preliminary recommendations (along with several papers presenting views of individual mathematicians) in order to stimulate discussion. CUPM would like to hear from those who have thought about, discussed, and experimented with curricula. Write to CUPM at CUPM-curric@maa.org.

A History of Curriculum Review
Each year since the 1950's, a little over 4% of 22-year olds major in mathematics, science, or engineering. It is striking that this percentage has changed very little even though education itself has undergone major transformations in this time. Over this same period, the proportion of this percentage majoring in mathematics has slowly declined. I think students are still very interested in mathematics, but they prefer to couple this mathematics with other disciplines where they see their opportunities. Mathematics has responded to the diversity of its students in several ways. The 1981 CUPM report recommended the creation of a mathematical sciences major with the flexibility to serve a broad range of student interests. By 1991, universities varied so greatly that the curriculum report was both brief and less specific than before. The volume "Models That Work" reported case studies of successful majors distinguished by their differences. In "Confronting the Core Curriculum," MAA addressed broadening the curriculum to meet the needs of students in the first two years. This rapid summary brings us up to date. Since it is no longer possible to specify required courses for the major, CUPM has decided to address the expectations of students. What is it that we expect mathematics or mathematical science majors to know upon graduation? What skills and experiences should they have? What should they be able to do?

Expectations from Other Disciplines
Frequently, students in other mathematics-intensive majors make up the majority in advanced undergraduate mathematics courses. Successful departments have found that they can attract these students by offering mathematics in form, content, value, and interest to these students. The CUPM is cooperating with AMS and other professional societies to investigate faculty expectations. CRAFTY (The CUPM Subcommittee on Calculus Reform and the First Two Years) is holding a series of invited conferences where mathematicians meet with faculty in other disciplines to discuss the mathematical needs of those disciplines. Eight reports have been written that appear on the Web at
http:// academic.bowdoin.edu/math/faculty/ barker/dissemination/Curriculum_Foundations, and additional details will be posted on the MAA Online Web page. But just a few highlights: Computer scientists have watched as much of the mathematics they need has disappeared from both the high school and college curriculum. Engineers and physicists give a list of mathematical skills, but also ask for other reasoning capabilities from students. The number of disciplines requiring mathematics is growing, as is the depth of mathematics required. Many disciplines offer their own mathematical curricula embedded in their courses, but they still expect a great deal from mathematics departments.

Framework for Curriculum Review
What then is the shape of CUPM thinking? First, the committee is trying, for the first time, to describe the curriculum in terms of expectations of students. Second, this description is to be given in the form of a planning process so that a department can shape a curriculum suited to the needs of its students. Because this represents such a large departure from past curriculum documents, CUPM is becoming far more involved with the community and with other disciplines. The following outlines six broad areas of consideration in curriculum planning.

General Expectations about Mathematical Knowledge and Skills
Close to our own discipline are recommendations about the mathematical content knowledge that we expect students to understand. But as a second critical foundation, we also expect a level of skill development. A new third dimension has been added as technology has grown in importance. Employers expect graduates to be able to read, write, and speak about mathematics, both for their expert colleagues and for others whose background is not in mathematics. We expect our graduates to enjoy mathematics and to be emissaries for it in later life. What classroom experiences foster the attainment of goals like these?

A Responsibility to Future Teachers
The country is encountering critical shortages of mathematics and science teachers. Every department should discuss the role of their program in the preparation of future teachers of mathematics and science.

Extra-Curricular Learning Experiences
Because motivation so strongly influences learning, these kinds of experiences have fostered a large number of loyal students. What parts of the environment outside the classroom should a department address? What actions benefit students?

Assessment
Departments can recognize their goals and gather information that indicates progress. How are students assessed? Is assessment compatible with departmental goals? Is the department recruiting, retaining, and graduating the expected audience? Are graduates reporting satisfaction with their preparation?

The Role and Responsibility of the Department

Doesn't it seem reasonable that students graduating from widely differing types of institutions should possess knowledge and skills that are recognizable as preparation in mathematics? If the faculty is to assist students in meeting our expectations, then what are the needs of the faculty? How should expectations be set and fulfilled so that faculty members enjoy their careers and grow as teachers and mathematicians?

Issues for the Discipline
What tools will promote careful planning? What contact should be fostered with other professions? What information and support should be provided by the professional societies? Your participation in the CUPM planning process will insure a report that is constructive and useful to departments. Foster discussions of expectations in your department. Bring faculty from other mathematics-intensive disciplines into the discussions. Look carefully at the needs of prospective teachers and of students planning careers in business. Gather information about your own program and programs at like institutions. Share the results with CUPM.

References
AMS Task Force on Excellence, Towards Excellence, AMS, 1999. John A. Dossey, ed., Confronting the Core Curriculum, MAA Notes 45, 1998. Alan C. Tucker, ed., Models That Work, MAA Notes 38, 1995. Lynn Arthur Steen, ed., Heeding the Call for Change, MAA Notes 22, 1992. NSF DPRA, The State of Academic Science and Engineering, NSF 90-35, 1990. Lynn Arthur Steen, ed., Reshaping College Mathematics, MAA Notes 13, 1989.