# Teaching Mathematics in Colleges and Universities: Case Studies for Today’s Classroom: Faculty Edition

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*Solomon Friedberg*

A co-publication of the AMS and CBMS

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 professional mathematician. 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 to
afford 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. Teaching notes for such a facilitator are included
for each Case in the Faculty Edition.

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.

See the graduate edition at
Teaching Mathematics in Colleges and Universities: Case Studies for Today's
Classroom: Graduate Student Edition

This series is published in cooperation with the Mathematical Association of America.

#### Table of Contents

# Table of Contents

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

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Acknowledgements xiii14 free
- Introduction 118 free
- Part I. Fourteen Case Studies 320
- Case 1. Changing Sections: On the first days of class, different instructors in a multisection calculus course grapple with weak Student knowledge of prerequisites 522
- Case 2. Emily's Test: Possible cheating in a proctored exam 1128
- Case 3. Fundamental Problems (Part I): Explaining the fundamental theorem of calculus 1330
- Case 4. Making the Grade: Grading Student work 1532
- Case 5. Making Waves: Motivating Fourier series through physics 2138
- Case 6. Order Out of Chaos: A precalculus class struggles with graphing calculators 2744
- Case 7. Pairing Up: Managing group work 3148
- Case 8. The Quicksand of Problem Four: A recitation section covering average velocity goes awry 3552
- Case 9. Salad Days: A struggling calculus Student 4360
- Case 10. Seeking Points: A Student protests his exam grade, having used prior knowledge about the derivative to solve the examination question 4562
- Case 11. Study Habits: A TA seeks ways to get her dass to work harder 4966
- Case 12. Studying the Exam: Constructing an effective, appropriate examination 5572
- Case 13. There's Something about Ted (Part I): Moving to a large State university as an instructor 6380
- Case 14. What Were They Thinking?: Coping with poor exam results 6582

- Part II. Supporting Materials for Faculty 6986
- Developing Effective Mathematics Teaching Assistants Using Case Studies: An Introduction for Faculty 7188
- Using Case Studies in a TA-Development Program 7794
- Types of Cases 83100
- Summaries of Cases 85102
- How These Cases Were Created 91108
- Case 1. Changing Sections, Teaching Guide 93110
- Case 2. Emily's Test, Teaching Guide 95112
- Case 3. Fundamental Problems, Part II 97114
- Case 4. Making the Grade, Teaching Guide 103120
- Case 5. Making Waves, Part II 109126
- Case 6. Order Out of Chaos, Teaching Guide 115132
- Case 7. Pairing Up, Teaching Guide 121138
- Case 8. The Quicksand of Problem Four, Teaching Guide 125142
- Case 9. Salad Days, Teaching Guide 133150
- Case 10. Seeking Points, Teaching Guide 135152
- Case 11. Study Habits, Teaching Guide 141158
- Case 12. Studying the Exam, Teaching Guide 145162
- Case 13. There's Something about Ted, Part II 153170
- Case 14. What Were They Thinking?, Teaching Guide 157174

- Back Cover Back Cover1176