The Young Child and Mathematics, Third Edition

Angela Chan Turrou, PhD, is senior researcher and teacher educator at the University of California, Los Angeles (UCLA) Graduate School of Education and Information Studies. Her work lives at the intersection of children’s mathematical thinking, classroom practice, and teacher learning. In her work with teachers and teacher educators across preschool and elementary settings, Angela leverages purposeful Instructional Activities driven by children’s mathematical thinking to support teacher learning, collaboration, and generative growth. She is continually inspired by teachers who, on a daily basis, create space for children to drive the mathematical work and challenge the broader discourse of who does and does not get to be “good at math.” Angela is coauthor of Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education (Heinemann, 2017) and coeditor of Choral Counting and Counting Collections: Transforming the PreK–5 Math Classroom (Stenhouse, 2018). Angela lives in Los Angeles, CA. Find her on Twitter @Angelaturrou.   Nicholas C. Johnson, PhD, is assistant professor in the School of Teacher Education at San Diego State University (SDSU). His work investigates how classrooms shape children’s opportunities to participate and learn. A former classroom teacher, instructional coach, and county office coordinator, Nick partners with new and practicing teachers to explore children’s mathematical ideas and expand what “counts” as math in school. He is a member of SDSU’s Center for Research in Mathematics and Science Education, coauthor of Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education (Heinemann, 2017), and a contributor (with Natali Gaxiola) to Choral Counting and Counting Collections: Transforming the PreK–5 Math Classroom (Stenhouse, 2018). Nick lives in San Diego, CA. Find him on Twitter @CarrythZero.   Megan L. Franke, PhD, is professor of education at UCLA. Dr. Franke’s work focuses on understanding and supporting teacher learning for both preservice and in-service teachers. She is particularly interested in how teaching mathematics with attention to students’ mathematical thinking (Cognitively Guided Instruction, or CGI) can challenge existing school structures and create opportunities for students who are often marginalized to mathematically thrive. Dr. Franke is a member of the Development and Research in Early Mathematics Education (DREME) Network at Stanford University where she is studying pre-K–2 coherence and designing resources for early childhood teacher educators. She lives in Santa Monica, CA. Find her on Twitter @meganlfranke.

Preface



            About
this Edition



            Our Theory
of Learning



 



Introduction



            Everything
a Child Does Has Mathematical Value



            Finding
and Building on the Mathematical Value



            An Overview
of this Book



            Engaging
with this Book



 



Chapter 1: Counting and Operations



Instructional Activity: Counting Collections



Exploring Children’s Thinking: Counting



Exploring Children’s Thinking: Operations



Assessing Children’s Understanding



Counting and Operations in Informal Spaces



Conclusion



 



Chapter 2: Spatial Relations



            Instructional
Activity: Describe-Draw-Describe



Exploring Children’s Thinking: Describing Spatial
Relations



Exploring Children’s Thinking: Representing Spatial
Relations



Assessing Children’s Understanding



Spatial Relations in Informal Spaces



Conclusion



 



Chapter 3: Measurement and Data



            Measurement
and Data in Informal Spaces



Instructional Activity: What Do You Notice?



Exploring Children’s Thinking: Measurement



Exploring Children’s Thinking: Data



Assessing Children’s Understanding



Conclusion



 



Chapter 4: Patterns and Algebra



            Exploring
Children’s Thinking: Creating and Extending Patterns



Assessing Children’s Understanding: Tea Party Patterns



Exploring Children’s Thinking: Patterns in Counting



Assessing Children’s Understanding: How High Can
Christopher Count?



Exploring Children’s Thinking: Patterns and Algebra in
Storybooks



Assessing Children’s Understanding: Storybook Patterns



Conclusion



 



Appendix A: A
Research Overview of What Young Children Know



            What Young
Children Know: Counting and Operations



What
Young Children Know: Spatial Relations



What Young Children Know: Measurement and Data



What Young Children Know: Patterns and Algebra



Situating What a Child Knows



 



Appendix B: Using this Book to Support Professional Learning



            Bringing
an Instructional Activity into Your Classroom



Making Connections Across Math
Content



Exploring Informal Spaces



Creating Classroom Spaces that
Support Participation



            Connecting Classroom Practice to Research



Connecting Theory to Practice



Connecting to Policy and
Standards Documents



 



References



Index



Acknowledgments



About the Authors