Contents Acknowledgements xi Introduction 1 Fourteen Case Studies Case 1. Changing Sections: On the first days of class, different instructors in a multisection calculus course grapple with weak student knowledge of prerequisites 5 Case 2. Emily’s Test: Possible cheating in a proctored exam 11 Case 3. Fundamental Problems: Explaining the fundamental theorem of calculus 13 Case 4. Making the Grade: Grading student work 15 College algebra version 15 Calculus I version 17 Multivariable calculus version 19 Case 5. Making Waves: Motivating Fourier series through physics 21 Case 6. Order Out of Chaos: A precalculus class struggles with graphing calculators 27 Case 7. Pairing Up: Managing group work 31 Case 8. The Quicksand of Problem Four: A recitation section covering average velocity goes awry 35 Case 9. Salad Days: A struggling calculus student 43 Case 10. Seeking Points: A student protests his exam grade, having used prior knowledge about the derivative to solve the examination question 45 Case 11. Study Habits: A TA seeks ways to get her class to work harder 49 Case 12. Studying the Exam: Constructing an effective, appropriate examination 55 College algebra questions 56 vii

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2001 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.