<P>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. </P><P>Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how <I>learning trajectories</I> 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. </P><P>This thoroughly revised and contemporary third edition of <I>Learning and Teaching Early Math </I>remains the definitive, research-based resource to help teachers understand the learning trajectories of early m