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Learning to Teach and Teaching to Learn Mathematics: Resources for Professional Development

Matt DeLong and Dale Winter
Mathematical Association of America
Publication Date: 
Number of Pages: 
MAA Notes 57
[Reviewed by
George Ashline
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According to Matt DeLong and Dale Winter, their purpose in writing this book is to "describe a set of tools and experiences for helping mathematicians to develop and enhance their instructional skills". They address the challenges encountered by every mathematics department in teaching classes, especially at the introductory level, with students of varying abilities and needs. This text is intended for departments with accomplished teachers not necessarily trained in instructor development and other teachers in need of that development (such as graduate student instructors, new/visiting faculty, or part time/adjunct faculty). In this review, I will offer some of my impressions of the abundant professional development resources that this text has to offer.

To begin, it may be helpful to mention the authors' background that frames their writing. Both DeLong and Winter were graduate student instructors trained in the professional development program of the Michigan Calculus Project, and both became instructor trainers at the end of their graduate student careers. Some details about the Michigan Mathematics Introductory Program can be found in Appendix B of this text and online at The instructor's guide for that program is also available online at

These sites give a sense of the course goals and the various teaching methods (with emphasis on an interactive and cooperative learning approach) featured in that program. Learning to Teach and Teaching to Learn Mathematics is a culmination of their seven years of collective professional development experience at the University of Michigan, Duke University, Taylor University, and Harvard University.

In the initial chapter, the authors discuss a comprehensive, integrated professional development program. They include a schematic of the five basic components of such a program, namely a pre-semester training week, an educational issues seminar, teaching portfolios, weekly in-semester development meetings, and class visits and feedback. The first three components are briefly described in the text, with the details of a much shorter pre-semester training orientation provided in Chapter 3. The last two components are the main focus of the text. Specifically, Chapters 4 through 16 offer detailed guides and sample handouts for implementing weekly development meetings, and Chapter 17 contains a wealth of information and materials for conducting classroom visits and providing instructors feedback. The heart of this text lies in its hands-on, "how to" instructions for running these sessions designed to help instructors become more effective teachers. In Appendix A, the authors provide a number of useful tips for making these meetings as successful and efficient as possible.

The pre-semester orientation information given in Chapter 3 illustrates well what this book is all about. These materials offer a thorough, step-by-step approach to prepare instructors for the classroom. As done in their meticulous descriptions of each of the professional development meetings, the authors specify for the orientation session a list of goals, a meeting agenda, an in-depth session outline with suggested times to allot to each part, meeting materials featuring a variety of pertinent handouts, and a valuable annotated bibliography containing references for more information. The orientation session is intended to acclimate and integrate instructors into a new department with its own unique courses, expectations, and instructional approaches. Since new instructors may not be familiar with some of these methods (such as a student-centered approach), then practice teaching opportunities are encouraged so that they can try out these new techniques.

Of course, departmental expectations will vary greatly according to the type of institution, and the text offers materials and advice that will better suit some departments than others. The text is especially relevant for departments with a large number of new/visiting faculty and/or graduate teaching instructors or part-time faculty/adjuncts. For instance, in several of the developmental meetings, there are suggestions for making new faculty aware of common departmental instructional strategies and consulting with course coordinators when certain issues arise. At some institutions (such as some small liberal arts colleges), this advice would not be as pertinent since there may be only one or two sections of a given course (even at the introductory level) and new instructors would have more autonomy and responsibility for the creation of a course syllabus and its implementation. Those responsible for instructor training in such a department would find a number of important considerations in this text, but would approach the professional development of a new instructor in a more individualized and less systematic fashion.

Throughout the text are many nuggets of wisdom that the authors have harvested through their extensive experience in instructor training. For example, one of the suggestions for the pre-semester orientation session is to debunk two assumptions that some instructors may hold, namely "that students can only possibly learn mathematics if it first proceeds out of the instructor's mouth", and "that students can only possibly attain a poor imitation of the mathematics that they see their instructor do". DeLong and Winter devote much of their text to illustrate ways in which instructors can actively engage their classes in doing mathematics through "student-centered" instruction. In contrast to a traditional "instructor-centered", lecture-based approach that is typical among some new instructors, the authors advocate a student-centered approach and provide a rich collection of materials throughout the text that incorporate such methodologies as collaborative learning, student presentations, interactive lectures, direct questioning, and writing.

The professional development sessions detailed in the text focus on a number of "nuts and bolts" issues faced by all instructors, especially those adopting a student-centered approach. The chapters in the text devoted to these sessions offer concrete suggestions and much practical advice on such topics as:

  • effectively running in-class groups and out-of-class homework teams, creating lesson plans which take advantage of a variety of active learning methodologies, and establishing and maintaining control in an interactive classroom.

  • engaging students to read their textbooks, with students responsible for reading prior to each class and instructors not teaching as if their students have never before encountered the material.

  • evaluating student work (ranging from written assignments to team homework to student presentations) systematically and consistently, and fulfilling such end-of-semester responsibilities as proctoring final exams and determining course grades.

  • developing insight into other aspects of the instructor-student relationship, such as helping students during office hours, developing strategies to engage both intrinsically and extrinsically motivated students, and managing disagreements that can arise from disparate instructor-student beliefs and expectations.

  • modifying the instructor training meetings of this book to meet the needs of a particular mathematics department.

  • structuring a series of classroom visits (such as observational, student feedback, and peer visits) to provide instructors with "constructive, compassionate, credible, and concrete" feedback -- the "4 c's" of good advice!

A few other aspects of the text are worth mentioning. First, the authors provide at the end of each chapter an extensive annotated bibliography. The references detailed in these "Suggested Readings" offer the reader an array of resources accessible for further information and alternate perspectives on specific professional development issues. Although the text does not offer an index, which would have been beneficial for the reader, the table of contents helps to make up for this, since it gives a detailed inventory of the topics covered in each chapter. Also, the bibliography at the end of the text offers a thorough and varied collection of references that can be used to learn more about the issues addressed in the text.

All in all, Learning to Teach and Teaching to Learn Mathematics is a useful reference for departments interested in creating or enhancing an integrated program to improve the teaching of mathematics by their new and even not so new instructors. The book is a user-friendly guide for implementing such a program through a series of meetings that address a number of important issues in teaching, especially in an interactive, student-centered setting. Such a program (as described early in the text) would "adequately equip new instructors for their first experiences teaching collegiate mathematics, continue to support instructors as they grow in their teaching philosophies and abilities, increase the value of teaching in the department, help create a community of teachers, and help unify a departmental teaching vision, if one is not already established". If you are part of mathematics department wishing to accomplish such objectives, then this book offers a treasure chest of ideas for making progress in these areas.

 George Ashline ( and is an associate professor of mathematics at St. Michael's College in Colchester, VT. He is a member of Project NeXT, a professional development program for new or recent Ph.D.s in the mathematical sciences who are interested in improving the teaching and learning of undergraduate mathematics.