Learning and Teaching Early Math

The Learning Trajectories Approach

Douglas H. Clements, Julie Sarama

• Publisher: Routledge
• Year: 2026
• Print ISBN:
  9781032949758
  9781032949765
• eBook ISBN:
  9781040663967
• Edition: 4
• Topic: Education
• Subtopic: Early Childhood Education

This definitive fourth edition synthesizes the research and wisdom of expert teachers on how young children learn mathematics and how effective teachers support their development with learning trajectories. The learning trajectories approach builds on what children know and can do, using activities tailored to develop the next level of thinking. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning, learning trajectories make teaching more joyful. Through helping teachers understand the varying levels of children's thinking and learning, this approach allows teachers to better meet the learning needs of all children. This thoroughly revised edition builds on the comprehensive research base of past volumes while drawing on numerous new research studies, expanded international examples, and updated illustrations. Chapters are also more closely linked with Learning and Teaching with Learning Trajectories [LT]²–an open-access, web-based tool that includes videos, interactive games, and practical classroom resources to help early childhood educators understand how children think and learn about mathematics. Ideal as a curriculum planning resource for mathematics administrators and leaders, as a professional development resource for early math teachers, and as a resource for math methods courses, this book brings the authors' nationally recognized learning trajectories approach directly into your classroom.

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• Acknowledgments
• 1 Young Children and Mathematics
• 2 Quantity, Number, and Subitizing
• 3 Verbal and Object Counting
• 4 Comparing, Ordering, and Estimating
• 5 Arithmetic: Early Addition and Subtraction and Counting Strategies
• 6 Arithmetic: Composition of Number, Place Value, Multidigit Addition and Subtraction, Multiplication and Division, and Fractions
• 7 Spatial Thinking
• 8 Shape
• 9 Composition and Decomposition of Shapes
• 10 Geometric Measurement: Length
• 11 Geometric Measurement: Area, Volume, and Angle
• 12 Other Content Domains: Patterns, Structure, and Algebraic Thinking; Classification and Data
• 13 Mathematical Processes and Practices
• 14 Cognition and Affect
• 15 Early Childhood Mathematics Education for All: Contexts, Curricula, and Cultures
• 16 Instructional Practices and Pedagogical Issues
• References
• Index