A Focus on Multiplication and Division Bringing Research to the Classroom

A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K–6 mathematics educators. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers.

Preface Acknowledgments What is Multiplicative Reasoning? The OGAP Multiplication Progression The Role of Visual Models The Role of Concepts and Properties Problem Contexts Problem Structures Developing Whole Number Division Understanding Algorithms Developing Math Fact Fluency References About the Authors Index

Elizabeth T. Hulbert is an educational consultant in mathematics instruction and assessment and a co-director of OGAPMath LLC. Elizabeth provides leadership to the OGAP National Professional Development Team. Marjorie M. Petit is an educational consultant in mathematics instruction and assessment and a co-director of OGAPMath LLC. Caroline B. Ebby, Ph.D., is a senior researcher at the Consortium for Policy Research in Education (CPRE) and an adjunct associate professor at the Graduate School of Education at the University of Pennsylvania. Caroline is also a member of the OGAP National Professional Development Team. Elizabeth P. Cunningham, Ph.D., is an assistant professor at the University of Michigan-Flint. Elizabeth is also a member of the OGAP National Professional Development Team. Robert E. Laird is a research associate with the Vermont Mathematics Initiative (VMI) at the University of Vermont, co-director of OGAPMath LLC, and a member of the OGAP National Professional Development Team.