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
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