Includes bibliographical references (p. 156-160) and indexes.
ch. 1. Subtraction with regrouping: approaches to teaching a topic -- ch. 2. Multidigit number multiplication: dealing with students' mistakes -- ch. 3. Generating representations: division by fractions -- ch. 4. Exploring new knowledge: the relationship between perimeter and area -- ch. 5. Teachers' subject matter knowledge: profound understanding of fundamental mathematics -- ch. 6. Profound understanding of fundamental mathematics: when and how is it attained.