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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