2nd Edition

A Focus on Multiplication and Division Bringing Mathematics Education Research to the Classroom

    204 Pages 235 B/W Illustrations
    by Routledge

    204 Pages 235 B/W Illustrations
    by Routledge

    The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers.

    Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:

    • New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning
    • In-chapter sections on how Common Core State Standards for Math are supported by math education research
    • Case Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction
    • Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division
    • 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 to help teachers relate concepts from each chapter to their own instructional materials and programs
    • Accompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression

    A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

    1. What Is Multiplicative Reasoning?  2. The OGAP Multiplication Progression  3. Using the OGAP Multiplication Progression to Inform Instruction and Support Student Learning  4. The Role of Visual Models  5. The Role of Concepts and Properties  6. Problem Contexts  7. Structures of Problems  8. Developing Whole Number Division  9. Understanding Algorithms  10. Developing Math Fact Fluency                                                                                                   


    Elizabeth T. Hulbert is Managing Partner and Professional Development Coordinator at the Ongoing Assessment Project. 

    Marjorie M. Petit is Co-Director of OGAPMath LLC.

    Caroline B. Ebby is Senior Researcher at the Graduate School of Education, University of Pennsylvania. 

    Elizabeth P. Cunningham, PhD, is Assistant Professor at the University of Michigan-Flint. Elizabeth is also a member of the OGAP National Professional Development Team. 

    Robert E. Laird is Co-Director of Teaching, Learning and Research with the Vermont Mathematics Initiative, Co-Director of OGAPMath LLC, and a member of the OGAP National Professional Development Team.