IMAP Integrating Mathematics and Pedagogy: Searchable Collection of Children's-Mathematical-Thinking Video Clips

An invaluable tool that significantly enriches mathematics sustained professional development experiences, the IMAP (Integrating Mathematics and Pedagogy) Searchable DVD’sunique collection of 232 video clips and over 160 JPEG screen shots, which capture a range of K-5 school children’s mathematical reasoning and demonstrate salient aspects of the children’s solutions, includes Word documents containing the problem posed in each video and supporting questions. Designed to support PD facilitators and math coaches, these materials, when used in PD settings, give teachers the opportunity to consider the mathematics and grapple with issues of mathematics teaching and learning as they arise in the context of children’s thinking.  Having been shown to enhance teacher reflection and promote growth in teachers’ content knowledge of mathematics, these videos foster better understanding of the ways students approach problem-solving; illustrate the unique and creative ways children think mathematically; and underscore the importance of precise language and questioning in the teaching of mathematics.

The video medium provides opportunities for us as teachers to be critically reflective–we can see our actions in others; enables us to watch many examples of instruction in non-threatening ways; provides us opportunities to see that children’s approaches to mathematics and mathematical thinking differ from adults’ approaches; raises expectations of what students can do; and enables us to model questioning techniques in a safe way.

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

• Contains 232 high-quality video clips that illustrate elementary children's mathematical thinking and approaches to problem-solving, each with an introduction
• Provides easy-to-use, searchable video that is categorized by math content covered, math solution strategy used by students, teaching/interviewing issues, and other miscellaneous topics (technology used, Spanish speaker, wrong answer, etc.)
• Features transcripts with every video clip
• Features Clip Info descriptions with every video clip and references to related clips.
• Includes Problems and  Video Preparation and Discussion questions with every video clip
• Provides over 160 screen captures (in JPG format) of student work
• Offers a variety of additional resources including Interview Guides and glossary of terms
• Created so it’s easy to use with any other kind of professional development approach
• Perfect for professional development workshops, the accompanying Facilitator's Guide includes handouts and guidance for coaches and trainers to integrate the video clips into a variety of workshop activities

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.