Learning and Teaching Early Math: The Learning Trajectories Approach / Edition 2

by Douglas H. Clements, Julie Sarama

Overview

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.

Product Details

ISBN-13:	9780415828505
Publisher:	Taylor & Francis
Publication date:	04/14/2014
Series:	Studies in Mathematical Thinking and Learning Series
Edition description:	Revised
Pages:	394
Product dimensions:	7.00(w) x 9.80(h) x 0.90(d)

About the Author

Douglas H. Clements is Distinguished University Professor, the Kennedy Endowed Chair in Early Childhood Learning, and co-Executive Director of the Marsico Institute of Early Learning, at the University of Denver.

Julie Sarama is Distinguished University Professor, the Kennedy Endowed Chair in Innovative Learning Technologies, and co-Executive Director of the Marsico Institute of Early Learning, at the University of Denver.

Table of Contents

Preface xi

Acknowledgments xv

What is Learning and Teaching with Learning Trajectories-[LTJ²? xviii

1 Young Children and Mathematics Learning 1

2 Quantity, Number, and Subitizing 18

3 Verbal and Object Counting 36

4 Comparing, Ordering, and Estimating 67

5 Arithmetic: Early Addition and Subtraction and Counting Strategies 88

6 Arithmetic: Composition of Number, Place Value, Multidigit Addition and Subtraction, Multiplication and Division, and Fractions 114

7 Spatial Thinking 161

8 Shape 185

9 Composition and Decomposition of Shapes 223

10 Geometric Measurement: Length 246

11 Geometric Measurement: Area, Volume, and Angle 260

12 Other Content Domains: Patterns, Structure, and Algebraic Thinking: Classification and Data 279

13 Mathematical Processes and Practices 303

14 Cognition, Affect, and Equity 312

15 Early Childhood Mathematics Education: Contexts and Curricula 338

16 Instructional Practices and Pedagogical Issues 353

References 405

Index 460

Editorial Reviews

"This state-of-the art book makes an invaluable contribution to our understanding of this vital component of early childhood practice and to the children who will benefit from its publication."—Young Children (NAEYC), March 2010

"What math is most important for young learners? What concepts and skills are foundational for their reaching the next level of math understanding? And how can teachers help children grasp each new idea and remain enthusiastic about math? These are the key questions in this incredibly valuable book from Doug Clements and Julie Sarama. For each topic area, they clearly describe the developmental path, or "learning trajectory," along which children move to develop mathematical concepts and skills. And they offer evidence-based guidelines and instructional activities in an engaging, straightforward way that reflects their deep respect for and understanding of what teachers do."—Carol Copple, Director, Publications and Initiatives in Educational Practice National Association for the Education of Young Children

"Learning and Teaching Early Math: The Learning Trajectories Approach is a required text for any early mathematics educator, professional developer, early childhood teacher or researcher. The domain-specific learning trajectories that outline developmental progressions provide information that has been missing from professional development resources. In addition, the instructional tasks aligned with each level provide practical suggestions for the teacher. Clements and Sarama have given us a comprehensive, research-based, rich resource... one that will make a difference to the mathematics learning of the young child!"—Juanita Copley, Professor Emeritus, University of Houston

From the Publisher