Making Sense of Fractions, Ratios, and Proportions (2002 NCTM Yearbook)

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Contents

Preface

Part 1: Elementary School

  1. Introduction by Judith Sowder
  2. The Development of Students' Knowledge of Fractions and Ratios by John P. Smith III
  3. Children's Development of Meaningful Fraction Algorithms: A Kid's Cookies and a Puppy's Pills by Janet M. Sharp, Joe Garofalo, and Barbara Adams
  4. Organizing Diversity in Early Fraction Thinking by Susan B. Empson
  5. Using Manipulative Models to Build Number Sense for Addition and Fractions by Kathleen Cramer and Apryl Henry
  6. Young Children's Growing Understanding of Fraction Ideas by Elena Steencken and Carolyn A. Maher
  7. Go Ask Alice About Multiplication of Fractions by Susan B. Taber
  8. Examining Dimensions of Fraction Operation Sense by DeAnn Huinker
  9. Part-Whole Comparisons with Unitizing by Sue Lamon
  10. Butterflies and Caterpillars: Multiplicative and Proportional Reasoning in the Early Grades by Patricia Ann Kenney, Mary M. Lindquist, and Cristina L. Heffernan

Classroom Challenges: Exploring Proportional Reasoning: Mr. Tall/Mr. Short; 3/5's Problem; The Part-Whole Relationship

Part 2: Middle School

  1. Introduction by Teresa Yazujian
  2. Percents and Proportion at the Center: Altering the Teaching Sequence for Rational Number by Joan Moss
  3. Making Explicit What Students Know About Representing Fractions by Barbara M. Moskal and Maria E. Magone
  4. Using Literature as a Vehicle to Explore Proportional Reasoning by Denisse R. Thompson, Richard A. Austin, and Charlene E. Beckmann
  5. Proportional Reasoning: One Problem, Many Solutions! by Suzanne Levin Weinberg
  6. Using Representational Contexts to Support Multiplicative Reasoning by Laura B. Kent, Joyce Arnosky, and Judy McMonagle
  7. Fraction Division Interpretations by Rose Sinicrope, Harold W. Mick, and John R. Kolb
  8. Developing Understanding of Ratio and Measure as a Foundation for Slope by Joanne Lobato and Eva Thanheiser
  9. Using Technology to Teach Concepts of Speed by Janet Bowers, Susan Nickerson, and Garrett Kenehan

Classroom Challenges: Number Patterns; Candy Bars and Lawns; Condo Problem

Part 3: Professional Development

  1. Introduction by David Duncan
  2. Developing Students' Proportional Reasoning: A Chinese Perspective by Jinfa Cai and Wei Sun
  3. The Development of Rational Number Sense by Irene T. Miura and Jennifer M. Yamagishi
  4. Multiplicitave Reasoning: Developing Student's Shared Meanings by Christina Gomez
  5. Fraction Instruction That Fosters Multiplicative Reasoning by Lee Vanhille and Arthur J. Baroody
  6. Profound Undersanding of Division of Fractions by Alfinio Flores
  7. Connecting Informal Thinking and Algorithms: The Case of Division of Fractions by Daniel Siebert

Classroom Challenges: Fraction Problem; Fraction Problem; A Fraction Activity

Cite

APA 7

Litwiller, B., & Bright, G. (Eds.). (2002). Making sense of fractions, ratios, and proportions. National Council of Teachers of Mathematics.

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