The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematicsand 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 internationalexamples,and includes updated illustrations throughout. This new edition is closely linked with Learning and Teaching with Learning Trajectories-[LT]-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.