Randolph Philipp is Professor of Mathematics Education in the School of Teacher Education at San Diego State University and a member of CRMSE, the Center for Research in Mathematics and Science Education. His research interests include studying the effects of integrating mathematics content and students' mathematical thinking. Randy started his educational career as a secondary school mathematics teacher in Los Angeles, California, and as a teacher in the Peace Corps in Liberia, West Africa.
Bonnie Schappelle is a Research Associate at San Diego State University's Center for Research in Mathematics and Science Education. Her research interests include studying the effects of integrating mathematics content and students' mathematical thinking. She also serves as a professional editor. Earlier in her career, Bonnie taught secondary school.
PART I VIDEO OF CHILDREN'S MATHEMATICAL THINKING:
AN OVERVIEW 1
About Children's Thinking and Linking to IMAP 1
What Is Children's Mathematical Thinking? Why Focus on It? 2
Children's Mathematical Thinking 2
Connections to Cognitively Guided Instruction 4
A Stance Toward Teaching Mathematics 4
Teaching as Learning (An Inquiry Stance) 5
Children's Mathematical Thinking: The Teacher's Path Through the Mathematical Terrain on an Inquiry Journey 5
Learning to Notice Differently 7
How Do Teachers Benefit From Using Video of Children's Mathematical Thinking? 9
PART II USING THIS PRODUCT 11
An Important Note About Professionalism and Respect 11
Four Emergent Principles From the Video 11
Using Video and Written Student Work: A Conjectured Sequence 16
Step 1 : Teachers Consider the Mathematics 17
Step 2: Teachers Consider Students' Thinking 17
Step 3: View and Discuss the Video 17
Finding and Using Video Clips 18
General Content Information 18
Using the Search Functionality 18
Resources Listed on the Resource Tab 23
Appendix: Instructor Interview Guide 24
PART Ill THEMATIC STORIES 27
Introduction to Stories 27
Story 1: Students' Answers Are Only Part of the Story 28
Story 2: Understanding Is Not an All or Nothing Enterprise 36
Story 3: Procedural and Conceptual Understanding 48
Story 4: Developing Fraction Understanding 55
Story 5: Mathematical Proficiency 76
Story 6: Introduction to Interviewing 87
REFERENCES CITED AND OTHER SOURCES 101
APPENDIX A: Glossary 104
APPENDIX B: Complete List and Description of 232 IMAP Clips 107
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