Introduction Who We Are Funding Acknowledgments Case Studies 
The Boston College Mathematics Case Studies Project

Welcome to the Boston College Mathematics Case Studies Project.  This website is devoted to the materials we have developed for math graduate students who are serving as TAs or instructors.  It includes information for faculty who are considering using these materials with their students.  The materials we have created have been published jointly by the AMS and the MAA in the CMBS series Issues in Mathematics Education.  Though the project has been completed, a community of case study users is available to provide information to you on using the BC Case materials.

The title: Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom.  (Available in graduate student and faculty editions.)
To order copies of the books go to the AMS website  and search for "friedberg".

Reviews of our book are available at:
(a) MAA  Online  (b) Zentralblatt fur Mathematik

Some papers by Solomon Friedberg on the Case Study method:

Teaching mathematics graduate students to teach:  an international perspective, in:  Enhanncing University Mathematics,  Proceedings of the First KAIST International Symposium on Teaching (eds. Ko, Arganbright),  Issues in Mathematics Education Volume 14, American Mathematical Society, Providence RI, 2007, 51--55.

Teaching mathematics graduate students how to teach, Notices of the American Mathematical Society 52 (2005), 842--847.  For a .pdf file, click here.

An Introduction to BCCase:
The Boston College Mathematics Case Studies Project, BCCase, was a four year project to develop new training materials - Case Studies - for use in TA-training programs for mathematics graduate students.  Graduate student teaching assistants and instructors are an important part of undergraduate mathematics education in universities in the United States.  These graduate students also go on to become the next generation of university faculty.  The Case Studies enable institutions to better prepare their mathematics graduate students for their roles as teaching assistants and instructors.  A more complete description of the project is given below.  For a description of the cases click on the following link:  Summaries of Completed Cases (9/12/2000)

The BCCase case studies have been used at the following universities (among others): Boston College, Boston University, Brown,  Cornell, Dartmouth, Harvard, Michigan Tech. University, Oklahoma State University, Pennsylvania State University, Stanford University, South Dakota State University, Texas Tech. University, The University of Arizona,  The University of California at Santa Barbara, The University of Chicago, The University of Illinois at Chicago, The University of Massachusetts, The University of Memphis, The University of Michigan, The University of Oklahoma at Norman, The University of Oregon, The University of New Hampshire, The University of Washington, and Virginia Tech.  Our evaluation suggests that the cases have the potential to be a significant component of your mathematics TA-development program.  For more information please contact us!!

Development Team
Principal Investigator:  Solomon Friedberg
Development Team Members:  Elizabeth Brown, Solomon Friedberg, Deborah Hughes Hallett, Reva Kasman, Margaret Kenney, Lisa Mantini, William McCallum, Jeremy Teitelbaum, Lee Zia, and Avner Ash
Project Evaluator:  Mary Sullivan
Project Administrator (1999-2001):  David Foster

The Boston College Case Studies Project was supported by FIPSE grant number P116B980015 from the Fund for the Improvement of Post-Secondary Education, FIPSE, administered by the United States Department of Education.  Matching funds were provided by the Boston College Office of the Associate Vice President for Research and the Boston College Department of Mathematics.  Special thanks to Michael A. Smyer, Dean and Associate Vice President for Research, and Richard A. Jenson, former Chair of the Mathematics Department at Boston College for their support.

We would like to thank the many people who have aided us in the development of the case studies.  Special thanks go to our technical advisors, Katherine Merseth of Harvard University and Dorothy Wallace of Dartmouth College, whose sage advice helped get the project off the ground.  We also benefited greatly at that stage from advice by Jim Leitzel of the University of New Hampshire.  Jim's untimely death saddened us; his memory inspires us still.  We express our appreciation to the Boston College administrators who gave us the green light and ultimately committed extensive resources to support this project:  Fr. Robert Barth, former Dean of the College of Arts and Sciences, Michael Smyer, Vice President for Research, and Richard Jenson, former Chair of the Mathematics Department. We would also like to thank John Neuhauser who, both as Dean of the School of Management and later as Academic Vice President and Dean of the Faculty at Boston College, shared with us and with our colleagues his extensive experience with the use of case studies.

Once the project got underway, we depended upon the feedback and insightful comments of mathematics graduate students from around the country who used and evaluated the case studies as we wrote and revised them. We would like to sincerely thank them all. We would like to especially mention the small group of graduate students whose initial use often led to the early demise or major revision of a case.  The group included: Lynette Kelley, Sarah Lehan, Carolyn Pointek, Steven Rattendi, Ben Brubaker, Allison Pacelli, Brian Munson, Craig Friedland, Mark Evans, Jay Douglas Wright, Randy Sesto,  Todd Grundmeier, Sarah James,  and Amy Lehan. Parallel to the contributions of the mathematics graduate student community has been the contribution from mathematics faculty. We would like to thank the small army of faculty from around the country who have tested and evaluated the case studies.  Among the faculty who provided sage council and advice were Judith Arms of The University of Washington, Margaret Balachowski of Michigan Technology University, Tina Garn of The University of Arizona, Thomas Goodwillie of Brown University, Daniel L. Goroff of Harvard University, Tim Gutmann of The University of New Hampshire, Gary Harris of Texas Tech University, Diane Herrmann of The University of Chicago, Teri Jo Murphy of The University of Oklahoma, Emma Previato of Boston University, Karen Rhea of The University of Michigan, David Rohrlich of Boston University, Ned Rosen of Boston College, Eileen T. Shugart of Virginia Tech., Glenn Stevens of Boston University, Maria Terrell of Cornell University, Steve Wheaton of The University of Arizona, and Dale Winter of Harvard University.

Finally, we would like to thank those involved with the administration of the project, including our first year project administrator, Elin Norberg, our second and third year project administrator David Foster, the mathematics department secretary Marilyn Adams, Susan Hoban of the BC research office, Jay Donahue of FIPSE, and Gwen Sneedon and Tom Seidenberg of the Phillips Exeter Academy, who were instrumental in our summer workshops on using the case studies.

Training Mathematics TA's Using Case Studies

Solomon Friedberg

Department of Mathematics, Boston College
Chestnut Hill, MA 02467-3806

It is important for mathematics graduate students to develop good teaching skills.  Many institutions address this by offer TA-training programs in a great variety of formats.  The Boston College Mathematics Case Studies Project, BCCase, is developing new kinds of materials---Case Studies--- to be used as components of TA-training programs for mathematics graduate students, supplementing such traditional training techniques as practicing explaining problems and videotaping.

Case Studies are narratives of realistic situations which require analysis.  The use of Case Studies as a teaching tool is common in certain disciplines, such as law and business.  They have been used for over 30 years in the training of university faculty, primarily in the liberal arts, and have recently become popular as a tool for training pre-collegiate teachers.  Our project seeks to use this methodology at the level of graduate students in mathematics.

A Case Study is an excerpt from a teaching situation that focuses on and describes one or more of the following:  the teacher's behavior, student responses, student learning or mislearning, classroom management, instructional content or practice, the relation between teacher, students, and the TA.  Our Case Studies are narratives of university mathematics teaching scenarios, typically a compendium of actual situations, described from the perspectives of various students and of the instructor.  Each Case raises a variety of pedagogical and communication issues, to be explored through group discussion and analysis.

Case Studies give your graduate students the chance to:

Our work to date suggests that the Case Studies methodology can be adapted to mathematics graduate students, and that Case Studies can add a useful additional dimension to a mathematics graduate student TA-training program.  In particular, we have found that graduate students who have some teaching experience can successfully discuss complicated Case  scenarios, and that many foreign students do well in such discussions.

For more information on our project, please contact us directly.  We greatly value all feedback from the mathematics community.

Last Updated: 09/02/2009
The Boston College Mathematics Case Studies Project
Copyright © 2009 by Solomon Friedberg. All Rights Reserved.