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Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom

Solomon Friedberg et al.
American Mathematical Society/Mathematical Association of America
Publication Date: 
Number of Pages: 
CBMS Issues in Education 10
[Reviewed by
Eileen Shugart
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The use of case studies has long been a standard part of the professional training in many disciplines, for example, business and law. They expose the participant to a wide range of complex real-life situations, and allow for thoughtful analysis and discussion, free from immediacy or personal involvement. In education, a variety of brief "what would you do under these circumstances?" scenarios have been around for quite some time, but rarely do they have any breadth or depth. The book under review fills that gap.

Case Studies for Today's Classroom, Volume 10 of the CBMS Issues in Mathematics Education series, is a marvelous resource for faculty involved in the supervision and professional development of graduate teaching assistants in mathematics — and for the TAs themselves. The cases go far beyond the short, one-dimensional situations that we're all familiar with, introducing a series of fourteen multi-faceted narratives about mathematics teachers, students, and pedagogical issues.

Included are such topics as suspected cheating on an exam, managing cooperative group work effectively, motivating students, dealing with grade disputes and poor test results, and responding to a struggling student who asks for extensions and special consideration. In addition, they are mathematical in nature, which was especially appealing to me as a mathematics educator and made the scenarios quite relevant to the graduate students who used the studies with me.

The situations presented are both realistic and thought-provoking. An experienced teacher reading through one of the cases will nod and say, "Yes, that's happened to me." A novice teacher will realize that if it hasn't happen yet, it probably will.

And that's the whole point behind the book and its approach to professional development. To be able to reflect on a situation, talk about approaches and solutions, listen to ideas offered by other teachers, whether experienced or fellow neophytes, gives TAs a risk-free chance to consider, in advance, what they might do when they are faced with a particular problem, before they have a personal stake in it. The stories presented in the book give TAs a sense of what really happens in a college classroom and serve as a link between theory and practice. They identify the predicaments new teachers typically struggle with and provide a setting for lively discussion on important issues.

There are two editions available — a faculty edition and a separate edition for graduate students. Together, they provide an unbeatable combination for use in TA training workshops and seminars. Part I of the faculty edition is essentially the GTA version of the book — fourteen detailed, stand-alone case studies. The second part, included only in the faculty edition, is a comprehensive guide to using discussion and case studies in TA development programs. Each case is summarized, key points and possible pitfalls are identified, and a guide for initiating, focusing, and concluding the discussion is provided. There's helpful advice on addressing goals, fostering active participation, and effectively managing the dynamics of a small group activity.

A typical case study session would require a one- to two-hour time block, a group of GTAs, and one or more faculty (or lead GTA) facilitator. Some advance preparation is required of the discussion leader, but with the wealth of supporting materials provided in the faculty edition, that is by no means a difficult task. A GTA participant would be told in advance which of the fourteen cases in his or her edition would be discussed in the coming meeting. This gives the student an opportunity to read through the case privately, then formulate and jot down reactions and ideas before the group convenes for whatever form of facilitated discussion the leader has planned. This group meeting may include small-group brainstorming, role playing, or general discussion on specifically chosen topics related to the case.

An alternate activity using this book — depending on the logistics of a particular TA training program — would be for TAs to be assigned to read a case study and turn in a written response for feedback. This might be a good approach where scheduling constraints prevent regular group meetings.

Because identifying issues and developing independent solutions are two of the primary goals of a case study activity, it is, in my opinion, preferable not to give graduate student participants access to the faculty edition. The reflective process and the ability to analyze a challenging situation is too valuable to circumvent it with built-in short-cuts.

A well-planned program to prepare graduate teaching assistants for the classroom and provide them with on-going professional development must include a variety components, including nuts and bolts of teaching, administrative details, presentation skills, apprenticeship, and mentoring. Case Studies for Today's Classroom doesn't presume to provide a basis for a complete course or program. What it does offer is a valuable and highly-usable resource to advance graduate student teachers beyond the basics, to introduce them to the deeper principles of good teaching, wise decision-making, and successful communication skills. It provides TA development specialists with a set of well-constructed, meaningful activities that will both engage and benefit the teachers under their supervision.

In short, this book is a "must have" for anyone involved in the training, supervision, and professional development of graduate teaching assistants in mathematics.

Eileen Shugart ( is the GTA Coordinator for the Virginia Tech Department of Mathematics since 1996 and an award-winning teacher at Virginia Tech. She has been active in the Preparing Future Faculty in project and is currently serving on the new MAA Committee on Graduate Students.
  • Introduction

Fourteen case studies

  • Changing sections
  • Emily's test
  • Fundamental problems
  • Making the grade (College algebra version/Calculus I version/Multivariable calculus version)
  • Making waves
  • Order out of chaos
  • Pairing up
  • The quicksand of problem four
  • Salad days
  • Seeking points
  • Study habits
  • Studying the exam (College algebra questions/Calculus II questions/Multivariable calculus questions)
  • There's something about Ted
  • What were they thinking?