1st Edition

A Focus on Ratios and Proportions
Bringing Mathematics Education Research to the Classroom

ISBN 9780367374051
Published June 3, 2020 by Routledge
240 Pages

USD $44.95

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Book Description

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts.

Special features include:

  • A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding.
  • A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work.
  • Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research.
  • Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses.
  • An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions.

Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

Table of Contents




    1. Understanding Ratio, Rates, and Proportions
    2. Deepening Understanding of Ratio and Proportion Concepts
    3. Understanding the OGAP Proportionality Framework and Progression
    4. Using the OGAP Ratio and Proportion Progression to Inform Instruction and Student Learning
    5. Structures in Proportion Problems
    6. Structures in Ratio and Rate Problems
    7. More Problem Contexts
    8. Understanding the Cross Products Procedure
    9. Percents-Building Understanding, Flexibility and Fluency



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Marjorie M. Petit is an educational consultant in mathematics instruction and assessment and a co-director of OGAPMath LLC.

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

Matthew F. Wyneken is an associate professor of mathematics education at the University of Michigan-Flint.

Frances R. Huntoon is an educational consultant in mathematics instruction and a member of the OGAP National Professional Development Team.

Mary D. Abele-Austin is a middle school math coach and a member of the OGAP National Professional Development Team.

Jean D. Sequeira is a middle school math interventionist and a member of the OGAP National Professional Development Team.