Teaching Mathematics in Colleges and Universities: Case Studies for Today’s Classroom: Graduate student edition
About this Title
Solomon Friedberg, Boston College, Chestnut Hill, MA
Publication: CBMS Issues in Mathematics Education
Publication Year 2001: Volume 10
ISBNs: 978-0-8218-2823-6 (print); 978-1-4704-1756-7 (online)
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.
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 faculty edition at Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom: Faculty Edition
Advanced undergraduates, graduate students, research mathematicians and mathematics teachers.
Table of Contents
Fourteen case studies
- Case 1. Changing sections
- Case 2. Emily’s test
- Case 3. Fundamental problems (Part I). Explaining the fundamental theorem of calculus
- Case 4. Making the grade: Grading student work
- Case 5. Making waves: Motivating Fourier series through physics
- Case 6. Order out of chaos: A precalculus class struggles with graphing calculators
- Case 7. Pairing up: Managing group work
- Case 8. The quicksand of problem four: A recitation section covering average velocity goes awry
- Case 9. Salad days: A struggling calculus student
- Case 10. Seeking points: A Student protests his exam grade, having used prior knowledge about the derivative to solve the examination question
- Case 11. Study habits: A TA seeks ways to get her class to work harder
- Case 12. Studying the exam: Constructing an effective, appropriate examination
- Case 13. There’s something about Ted (Part I): Moving to a large state university as an instructor
- Case 14. What were they thinking? Coping with poor exam results