Contents: Foreword. Acknowledgments. Introduction. Subtraction With Regrouping: Approaches to Teaching a Topic. Multidigit Number Multiplication: Dealing With Students' Mistakes. Generating Representations: Division by Fractions. Exploring New Knowledge: The Relationship Between Perimeter and Area. Teachers' Subject Matter Knowledge: Profound Understanding of Fundamental Mathematics. Profound Understanding of Fundamental Mathematics: When and How Is It Attained. Conclusion.