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

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