Three different articles analyze aspects of Schoenfeld's undergraduate problem-solving instruction. Those articles provide new detail and insight on a well-known and widely discussed course taught by Schoenfeld for many years. The articles on understanding concepts feature a variety of methods used to examine students' understanding of the concept of a function, selected concepts from calculus, and conceptual understanding. The conclusions presented offer unique and interesting perspectives on how students learn concepts. The section on understanding proofs provides insight on student understanding from a distinctly psychological framework.
Researchers examine how existing practices can foster certain weaknesses.
They offer ways to recognize and interpret students' proof behaviors and suggest alternative practices and curricula to build more powerful schemes. The section concludes with a focused look at using diagrams in the course of proving a statement. The present book is the result of the reflection of many individuals in mathematics education on this and related questions. In the book, the reader will find a range of possible answers to these questions, a variety of analyses of the actual directions of research in different countries, and a number of visions for the future of research in mathematics education. The authors address researchers in mathematics education and all those who are concerned with problems related to defining this domain.