How to teach mathematics

Cover......Page 1
Table of Contents......Page 4
PREFACE TO THE SECOND EDITION......Page 7
PREFACE TO THE FIRST EDITION......Page 13
1.0 Chapter Overview......Page 17
1.1 Respect......Page 18
1.2 More on Respect......Page 20
1.3 Prepare......Page 23
1.4 Clarity......Page 25
1.5 Speak Up......Page 26
1.6 Lectures......Page 27
1.7 Questions......Page 31
1.8 Advanced Courses......Page 35
1.9 Time......Page 36
1.10 Computers......Page 38
1.11 Applications......Page 44
1.12 The Moore Method......Page 48
2.0 Chapter Overview......Page 50
2.1 Voice......Page 51
2.2 Eye Contact......Page 53
2.3 Blackboard Technique......Page 54
2.4 Body Language......Page 57
2.5 Homework......Page 59
2.6 Office Hours......Page 60
2.7 Designing a Course......Page 63
2.8 Handouts......Page 65
2.9 Teaching Evaluations......Page 66
2.10 Exams......Page 71
2.11 Grading......Page 78
2.12 The Syllabus (and the Course Diary)......Page 81
2.13 Choosing a Textbook......Page 84
2.14 Large Lectures......Page 87
2.16 Problem Sessions, Review Sessions, and Help Sessions......Page 93
2.17 Transparencies......Page 95
2.18 Tutors......Page 97
2.19 On Being а ТА......Page 99
2.20 Advising, Letters of Recommendation, and Graduate School......Page 100
3.0 Chapter Overview......Page 102
3.1 Personal Aspects......Page 103
3.2 Attitude......Page 105
3.3 Caring......Page 109
3.4 Breaking the Ice......Page 110
3.5 Why Do We Need Mathematics Teachers?......Page 111
3.6 Math Anxiety......Page 115
3.7 How Do Students Learn?......Page 116
3.8 Inductive vs. Deductive Method......Page 120
3.9 Who Is My Audience?......Page 123
3.10 Teaching Reform......Page 125
3.11 Mentors and Neophytes......Page 130
3.12 How to Ask, How to Answer......Page 132
3.13 Teaching with the Internet......Page 137
3.14 The Art of Discourse......Page 138
3.15 What about Research?......Page 140
3.16 Do I Have to Teach Calculus Again?......Page 141
4.0 Chapter Overview......Page 143
4.1 Non-Native English Speakers......Page 144
4.2 Late Work......Page 145
4.3 Cheating......Page 146
4.4 Incompletes......Page 148
4.5 Frustration......Page 149
4.6 Annoying Questions......Page 152
4.7 Discipline......Page 153
4.8 Mistakes in Class......Page 156
4.9 Advice and Consent......Page 157
4.10 Sexism, Racism, Misogyny, and Related Problems......Page 158
4.11 Begging and Pleading......Page 161
5.0 Chapter Overview......Page 164
5.1 The Role of the University Professor......Page 165
5.2 Closing Thoughts......Page 166
APPENDICES......Page 167
George E. Andrews, The Irrelevance of Calculus Reform: Ruminations of a Sage-on-the-StSLge......Page 168
Richard Askey, Mathematical Content......Page 171
David M. Bressoud, Personal Thoughts on Mature Teaching......Page 182
William J. Davis, Remember the Students......Page 191
Ed Dubinsky, ReBections on Krantz\'s How to Teach Mathematics: A Different View......Page 204
Deborah Hughes Hallett, Are We Encouraging Our Students to Think Mathematically?......Page 221
David Klein, Big Business, Race, and Gender in Mathematics Reform......Page 227
William McCallum, Will This Be on the Exam?......Page 239
Kenneth C. Millett, Teaching or Appearing to Teach: What\'s the Difference?......Page 246
J. J. Uhl, Why (and How) I Teach without Long Lectures......Page 258
H. Wu, The Joy of Lecturing—with a Critique of the Romantic Tradition in Education Writing......Page 265
Steven Zucker, Teaching Freshmen to Learn Mathematics......Page 276
BIBLIOGRAPHY......Page 288
INDEX......Page 294