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PACKAGE ISBN-13: 9780132626972

By SDSU San Diego State University Research Foundation, Randolph Philipp, Candace Cabral, Bonnie Schappelle

Published by Pearson

Published Date: May 3, 2011

Components of the Package:

IMAP Integrating Mathematics and Pedagogy: Searchable Collection of Children's-Mathematical-Thinking Video Clips
By SDSU San Diego State University Research Foundation, Randolph Philipp, Candace Cabral, Bonnie Schappelle

Facilitator's Guide for IMAP Integrating Mathematics and Pedagogy: Searchable Collection of Children's Mathematical Thinking Video Clips
By SDSU San Diego State University Research Foundation, Randolph Philipp, Candace Cabral, Bonnie Schappelle


The IMAP (Integrating Mathematics and Pedagogy) Searchable DVD  and Facilitator's Guide features a unique collection of over three hundred video clips, images, and resources which capture a range of K-5 school children’s mathematical reasoning and demonstrate prominent aspects of the children’s solutions. Designed to support professional development (PD) facilitators, math coaches and their teachers, these resources, 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. Proven 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.


What makes the IMAP DVD and Facilitator's Guide an indispensable resource?


  • 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 provides philosophy and context for using the DVD materials, a detailed appendix of all clips and their descriptions, search terms, and related materials as well as guidance for staff developers, coaches and instructors to integrate the video clips (with specific examples) into a variety of teacher learning activities.

Table of Contents



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



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



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



APPENDIX A: Glossary 104

APPENDIX B: Complete List and Description of 232 IMAP Clips 107

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