Preparing new instructors to teach college mathematics courses: An objective-based teaching laboratory

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jun 2002 by Brilleslyper, Michael A

ABSTRACT: This paper discusses the teaching preparation program for new instructors of mathematics at the U. S. Air Force Academy. The program is structured into a series of five practice lessons each focused on particular aspects of effective teaching. In addition, participant feedback from the program is summarized.

KEYWORDS: Faculty development, teaching, practice lessons.

INTRODUCTION

Mathematics departments are frequently faced with the challenge of preparing new faculty to teach college mathematics courses. At the United States Air Force Academy we have implemented a faculty development program designed to get new instructors ready to teach. A typical new instructor teaching calculus or entry-level statistics has a master's degree in mathematics or engineering and little or no teaching experience. However, most of our new instructors have held other jobs in the Air Force such as pilot, scientific analyst, acquisitions officer, etc., and thus have a wealth of practical experience from which to draw upon. Teaching mathematics, however, presents unique challenges. As we all know, to be effective in the mathematics classroom requires an ill-defined set of skills encompassing knowledge, passion, humor, toughness and communication at a variety of different levels. We are fortunate at the Air Force Academy to have several weeks in the summer devoted to new instructor training. The summer program is required for all new faculty including civilians Ph.D.'s and military faculty with prior teaching experience. A large portion of the program is devoted to aspects that are unique to the service Academies (the honor system, military training, protocol, the unusual cultural climate, history of the institution, managerial organization, chain of command, etc.). The Air Force Academy's mission is to develop tomorrow's military leaders. A significant aspect of that mission is met by providing a top-notch undergraduate education. Despite the complex and multi-faceted mission of the Air Force Academy, the faculty spends the majority of their time on teaching related tasks. The purpose of this paper is to describe the portion of the new faculty summer program directly related to effectively teaching mathematics.

There is a large collection of books and papers on how to teach effectively (see [1] and the various appendices there for a broad collection of resources). Yet, as most experienced teachers know, there is no complete list of "do's and don'ts" that, if followed, result in quality teaching. The tricky part about effective teaching is that it cannot be separated from the teacher. The instructor's personality, preferences, and prejudices have an enormous impact on student success. Recognizing this fact is important. Our development program should not attempt to prescribe a uniform method of teaching. On the other hand, the program must encompass some specific tasks or else one can never get past merely discussing the philosophy of good teaching.

In developing our program, we were guided by two principles:

1. Teaching is a craft that is never mastered.

2. Students learn in a variety of ways.

The first principle emphasizes that any sort of teacher training is merely a beginning and that to improve as a teacher one must continue to reflect, experiment and make adjustments long after the training has ended. In fact, these qualities may come closest to defining the characteristics that make up a good teacher. In an information age world, teachers that approach each course with a fresh new look are more apt to benefit their students and to enjoy the course. The constant flood of new technology and teaching methodologies provides many opportunities to present old material in new ways.

The second principle may sum up the driving force behind the mathematics education reform movement of the past decade. It is important to recognize that one method of presentation may not serve all the students. Thus, instructors need to use a variety of methods and techniques to convey the material.

Despite the fact that teaching is such a complex and nebulous endeavor, there are certain skills and traits that are common to many good teachers. These include: (1) clear explanations of difficult and abstract ideas, (2) motivation of new material and placing it in a meaningful context, (3) integration of technology into the course in essential ways, (4) development of useful and interesting activities, and (5) the presentation of the subject in a holistic manner that makes clear connections between the assorted sub-topics.

The structure of our program is to have the new instructors give a series of brief practice lessons, twenty to thirty minutes in length, that focus on the five areas mentioned above. The audiences for these lessons are the training staff and the other new instructors. Each practice lesson has a particular teaching objective and several points of emphasis. Feedback is provided through written and verbal critiques (supplied both by the faculty running the program and the other new instructors). The objectives for the lessons are shown below: