Based on the premise that psychology can be an invaluable tool to mathematics educators, this book highlights how informal mathematics develops, how children construct their view of school arithmetic, and how mathematical thinking operates. The ideas offered are intended to assist teachers in making informed decisions concerning mathematics instruction. Part 1 outlines general implications that stem from cognitive theory and provides a general framework for analyzing mathematics learning, teaching practices, and learning difficulties. Parts 2 and 3 examine aspects of informal and formal mathematics and review models of how particular skills and concepts develop. These models provide a reference point for understanding mathematical learning and how learning problems develop, devising instruction, and remedying learning difficulties. Specific learning and teaching activities are detailed throughout the book and address the areas of calculational procedures, understanding of mathematical principles, mastery of number facts, and methods of problem solving. This book is recommended for use in courses in early childhood education, elementary mathematics methods, special education, and educational psychology. (ML)