ABSTRACT

The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematics and how best to develop foundational knowledge to realize more effective teaching.

Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how learning trajectories help teachers understand children’s level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous: helping teachers understand the varying levels of knowledge exhibited by individual students, it allows them to better meet the learning needs of all children.

This thoroughly revised and contemporary third edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become confident, credible professionals. The new edition draws on numerous new research studies, offers expanded international examples, and includes updated illustrations throughout.

This new edition is closely linked with Learning and Teaching with Learning Trajectories–[LT]²–an open-access, web-based tool for early childhood educators to learn about how children think and learn about mathematics. Head to LearningTrajectories.org for ongoing updates, interactive games, and practical tools that support classroom learning.

chapter 1|17 pages

Young Children and Mathematics Learning

chapter 2|18 pages

Quantity, Number, and Subitizing

chapter 3|31 pages

Verbal and Object Counting

chapter 4|21 pages

Comparing, Ordering, and Estimating

chapter 5|26 pages

Arithmetic

Early Addition and Subtraction and Counting Strategies

chapter 6|47 pages

Arithmetic

Composition of Number, Place Value, Multidigit Addition and Subtraction, Multiplication and Division, and Fractions

chapter 7|24 pages

Spatial Thinking

chapter 8|38 pages

Shape

chapter 9|23 pages

Composition and Decomposition of Shapes

chapter 10|14 pages

Geometric Measurement

Length

chapter 11|19 pages

Geometric Measurement 1

Area, Volume, and Angle

chapter 12|24 pages

Other Content Domains

Patterns, Structure, and Algebraic Thinking: Classification and Data

chapter 13|9 pages

Mathematical Processes and Practices

chapter 14|26 pages

Cognition, Affect, and Equity

chapter 15|20 pages

Early Childhood Mathematics Education

Contexts and Curricula