Contents

Acknowledgements xiii

Introduction 1

Part I. Fourteen Case Studies

Case 1. Changing Sections: On the first days of dass, 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 (Part I): 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: Á precalculus dass struggles with graphing

calculators 27

Case 7. Pairing Up: Managing group work 31

Case 8. The Quicksand of Problem Four: Á recitation section covering

average velocity goes awry 35

Case 9. Salad Days: Á struggling calculus Student 43

Case 10. Seeking Points: Á Student protests his exam grade, having used

prior knowledge about the derivative to solve the examination question 45

Case 11. Study Habits: Á TA seeks ways to get her dass to work harder 49