Mathematics and Mathematical Sciences in 2010: What Should Students Know?
By Tom Berger and Harriet Pollatsek
The question of what students should know is critical for the MAA Committee on the Undergraduate Program in Mathematics (CUPM) as it works to develop a new Curriculum Guide for departments, planned for late 2002. The situation today is much more complicated than in the decades when CUPM began formulating curricular recommendations. Institutions and students are more diverse, the number of mathematical sciences majors is falling, teacher shortages in mathematics and the sciences are becoming acute, the range of mathematics courses taught at the undergraduate level has increased dramatically, and the need for mathematical knowledge at the undergraduate level has grown significantly. The goal of the new Curriculum Guide is to help departments respond effectively to the current challenges in ways appropriate to their particular institutional settings and missions.
Last summer, CUPM solicited a dozen position papers on the undergraduate mathematics curriculum, and in September 2000 it held a conference with the authors. A study document entitled Mathematics and Mathematical Sciences in 2010: What Should Students Know? includes the position papers and some preliminary recommendations resulting from the conference. It is available on MAA Online in .PDF format at /news/cupm_front.pdf; a print version may be ordered as an MAA Reports volume. Both the conference and the publication were generously funded by the Calculus Consortium for Higher Education (CCHE). We regret that the CCHE acknowledgment was missing in some early distribution copies of the volume.
This month, CUPM is sending a questionnaire to a sample of mathematical sciences departments in an effort to obtain data and examples to help shape, illustrate, and support the final recommendations of the Curriculum Guide. If you receive a copy of the CUPM questionnaire, we urge you to respond, and if you know of a department that is engaged in successful program development or one gathering useful data to inform its planning, please let CUPM know about it.
As we move forward, we must consider what actions and expectations are appropriate for the different student populations whose needs we serve: (1) our own majors, including those preparing for careers in teaching, for direct entry into business, industry, or government, for graduate study in the mathematical sciences, and for graduate or professional study in other areas; (2) students preparing for majors in fields that make extensive use of the mathematical sciences; and (3) students who take only one or two courses in our departments. We are especially concerned about the needs of future teachers and recommend that all MAA members read the draft report prepared by the Conference Board of the Mathematical Sciences, Mathematical Education of Teachers, may be purchased from either the AMS or the MAA. The CUPM study document includes the following preliminary recommendations.

Students should achieve mastery of a rich and diverse set of mathematical ideas and should experience mathematics as an engaging field with contemporary open questions.

Students should be able to think analytically and critically, to formulate and solve problems, and to interpret their solutions. They should understand and appreciate the value and validity of careful reasoning, precise definition, and close argument.

Students should have experience applying knowledge from one branch of mathematics to another and from mathematics to other disciplines.

Students should be able to use a variety of technological tools.

Students should be able to communicate mathematics both orally and in writing; they should be able to read mathematics.
An Invitation from CUPM
We invite you to read the full study document Mathematics and Mathematical Sciences in 2010: What Should Students Know? Please discuss it with colleagues in your department and at your MAA sectional meetings, and send us feedback. We are particularly interested in responses to the following questions for the different groups of students you serve.

Do the proposed recommendations identify the crucial issues and principles for a mathematics curriculum? What is missing? What should be deleted?

Which mathematical ideas are most important, and how do we create thematic links among them? Which courses should students take in the first two years? Where should geometry and visualization fit in?

How do we help students develop their critical thinking abilities?

How can we best form productive alliances with other disciplines? The CUPM subcommittee on Calculus Reform and the First Two Years has conducted a series of workshops with faculty from other disciplines in the Curriculum Foundations project. The CRAFTY CF reports appear at http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum_Foundations/. How can we translate what we learn from the CF project into effective and feasible programs?

How does technology best serve student learning? How much technology should we incorporate into our curriculum to prepare our students for the workplace? How should institutions and departments support faculty in learning how to make pedagogically effective use of technology?

How can we assist departments in making assessment productive and helpful, integral to their work and not just an activity done at the end of a project or to please a dean?

What can departments do to counter declining enrollments in upper level courses and shrinking numbers of majors? What can be done to encourage more women and minorities to study mathematics and enter our profession? How can student recruitment, retention, and satisfaction be improved?