Teaching Mathematics in Colleges and Universities

by Friedberg, Solomon; Ash, Avner; Brown, Elizabeth; Hallett, Deborah Hughes; Kasman, Reva; Kenney, Margaret

• ISBN13: 9780821828236
• ISBN10: 0821828231
• Edition: Student
• Format: Paperback
• Copyright: 2001-06-01
• Publisher: Amer Mathematical Society

Summary

Progress in mathematics frequently occurs first by studying particular examples and then by generalizing the patterns that have been observed into far-reaching theorems. Similarly, in teaching mathematics one often employs examples to motivate a general principle or to illustrate its use. This volume uses the same idea in the context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professionalmathematician. These teaching situations are the Case Studies of the title. Just as a good mathematician seeks both to understand the details of a particular problem and to put it in a broader context, the examples presented here are chosen to offer a serious set of detailed teaching issues and toafford analysis from a broad perspective. Each case raises a variety of pedagogical and communication issues that may be explored either individually or in a group facilitated by a faculty member. The methodology of Case Studies is widely used in areas such as business and law. The consideration of the mathematics cases presented here will help readers to develop teaching skills for their own classrooms.

Table of Contents

Acknowledgements	xi
Introduction	1	(4)
Fourteen Case Studies
Changing Sections: On the first days of class, different instructors in a multisection calculus course grapple with weak student knowledge of prerequisites	5	(6)
Emily's Test: Possible cheating in a proctored exam	11	(2)
Fundamental Problems: Explaining the Fundamental theorem of calculus	13	(2)
Making the Grade: Grading student work	15	(6)
College algebra version	15	(2)
Calculus I version	17	(2)
Multivariable calculus version	19	(2)
Making Waves: Motivating Fourier series through physics	21	(6)
Order Out of Chaos: A precaluculus class struggles with graphing calculators	27	(4)
Pairing Up: Managing group work	31	(4)
The Quicksand of Problem Four: A recitation section covering average velocity goes awry	35	(8)
Salad Days: A struggling calculus student	43	(2)
Seeking Points: A student protests his exam grade, having used prior knowledge about the derivative to solve the examination question	45	(4)
Study Habits: A TA seeks ways to get her class to work harder	49	(6)
Studying the Exam: Constructing an effective, appropriate examination	55	(8)
College algebra questions	56	(2)
Calculus II questions	58	(2)
Multivariable calculus questions	60	(3)
There's Something about Ted: Moving to a large state university as an instructor	63	(2)
What Were They Thinking?: Coping with poor exam results	65