AMS-MER Workshop on

Excellence in Undergraduate Mathematics:
Mainstreaming in-depth mathematical experiences for students*

Loras College, Dubuque, IA

Thursday-Sunday, March 25-28, 2004

Workshop Program:

In teaching undergraduate mathematics, we would like our students to learn about and appreciate what it means to do mathematics, as well as gain mathematical content knowledge. Further, there is a tradition in the mathematics community for creating in-depth experiences in mathematics for students including programs in Research Experiences for Undergraduates and outreach programs for talented high school and middle school students. Faculty and departments that have organized and run such programs have a great deal of collective wisdom about how to develop students as mathematical thinkers. Others in the community have sought to develop courses for general math students that help students learn to think about mathematical ideas and experience mathematical insights.

The workshop is designed to:

highlight the resources and expertise within the mathematics community -- gained from running extra-curricular programs, and developing innovative courses-- for fostering students' mathematical thinking, and

challenge departments to adapt these ideas to mainstream undergraduate mathematics.

Discussions will explain the development and rationale of the pedagogy and curriculum of selected programs, the impact for faculty and departments in running these programs, and the influences on reform of standard courses and the implementation of innovative courses.

The workshop will also feature a panel of invited speakers to present their views of the critical educational issues facing, or soon to face, the mathematics community.

Time is provided throughout the workshop for informal discussions among the participants, including the invited speakers.

Plenary Speakers:
Deborah Hughes Hallett from University of Arizona:
      "ConcepTests: Active Learning in the Classroom"
ConcepTests— a powerful tool for improving student learning—were originally developed by Eric Mazur at Harvard to teach introductory physics. They were subsequently adopted in chemistry and biology. ConcepTests are now available for calculus, where they have shown the same impressive results. The pedagogy underlying Conceptests is active learning and peer-instruction. These have proved effective in many contexts, particularly for non-traditional students who do not learn as well in a passive lecture format. The research data showing the effectiveness of Conceptests in calculus will be presented.

Daniel Shapiro from Ohio State University:
      "The Ross Mathematics Program"
Students often encounter difficulties when moving to successive levels of mathematics. Typical transition points are: using variables in algebra, working with functions in calculus, dealing with abstraction in post-calculus courses, learning to write accurate and readable proofs, and understanding how to do independent research. In the summer program founded long ago by Dr. Arnold Ross, young students use ideas of elementary number theory to discover that abstraction and generalization are valuable tools. Participants learn by considering open-ended questions, making conjectures, and writing (and re-writing) abstract proofs. This program can benefit students of many different backgrounds, from bright ninth graders to beginning graduate students, but it requires student commitment and considerable instructor time.

In this plenary session I will discuss the structure of the Ross Mathematics Program, providing sample materials and suggesting ways that related programs could be implemented elsewhere.

Larry Zettel, Marlene Pinzka, Donald Marxen, and Robert Keller from Loras College:
      "What A Small Mathematics Department Can Do: A Case Study From Loras College"
Mathematics Departments at institutions across the country face many challenges. Often the pressure these cause seem greater at smaller departments due to their lack of workforce to address them. However, these smaller departments also have many opportunities for meeting these challenges. The four speakers will present steps that Loras has taken to confront issues of a revised general education program, changing needs of major programs, and increasing concern about the mathematical preparation of teachers.

Michael Starbird from University of Texas, Austin:
      "The Moore Method: Math and Beyond"
Variations on the Moore Method of instruction center on students’ proving theorems on their own and presenting their results to their peers. Expected outcomes for students include their developing theorem-proving skills and the ability to tell whether a proof is correct or flawed. But beyond those mathematical skills, the Moore Method experience frequently involves interesting consequences on students’ attitudes concerning self-reliance, independent thinking, and willingness to make mistakes.

Margaret Robinson from Mount Holyoke College:
      "The Effect of a Summer REU Program on the Faculty and Students of the Mathematics and Statistics Department at Mount Holyoke College"
The Undergraduate Mathematics Summer Research Institute at Mount Holyoke College has been funded by NSF for 14 of the last 16 summers. During that time, all department faculty except one have run a summer research group at least once; we have added a new sophomore level course in mathematical experimentation to the requirements for the mathematics major; writing has become a much bigger part of all courses; we have done away with many of the prerequisites for advanced courses; and the number of department majors has been very healthy. The summer program has become an essential part of the workings of the department. It has raised considerably the visibility of the Mathematics and Statistics Department to the college. A significant amount of collaborative faculty research has stemmed from the summer program. Our students know of our summer program and because of this and our encouragement they are more likely to apply to other summer research programs around the country. We use internal Mount Holyoke funds to allow some of our international students to either participate in our program or to apply to other REUs with their own funding. To the students the REU is evidence that there are exciting opportunities available for mathematicians.

Breakout Speakers:
Deborah Hughes Hallett, University of Arizona:
"Interdisciplinary Links: Pitfalls and Payoffs"

Dan Willis, Loras College:
      "Math for Elementary School Teachers"

Andy Long, Northern Kentucky University
      "The creation, care and feeding of an undergraduate-centered mathematical and statistical consulting center"

Jim Fulmer and Tom McMillan, University of Arkansas at Little Rock
      "Assessing the Undergraduate Major in Mathematics – A Department Model"

Dan Shapiro, Ohio State University:
      "Analyzing the Problem Sets from the Ross Mathematics Program"

Roger Waggoner, Victor Schneider, Kathleen Lopez, University of Louisiana at Lafayette:
      "Opportunities Related to Developing a Mathematics/Biology Option for Undergraduates"

Geoffrey Martin, University of Toledo:
      "Management of Developmental Mathematics at the University of Toledo"

Jeremy Teitelbaum, University of Illinois at Chicago:
      "Proofs as a unifying principle in the major"

Michael Starbird, University of Texas at Austin:
      "Abandoning Dead Ends: Presenting Mathematical Masterpieces to all students"

Margaret M. Robinson, Mount Holyoke College:
      "Opportunities Related to The operation and funding of an REU program and the Mount Holyoke"

Barbara M. Moskal and Graeme Fairweather, Colorado School of Mines:
      "The Design of a Departmental Assessment Plan"