8: Teachers’ Knowledge and Its Impact

We would like to thank Thomas Cooney, University of Georgia, and Deborah Ball, Michigan State University, for their thoughtful comments on an earlier draft of this chapter and the National Science Foundation and the Office of Education Research and Improvement of the Department of Education for partial support while writing it. The opinions expressed are those of the authors and not necessarily those of the reviewers, NSF, or OERI.

No one questions the idea that what a teacher knows is one of the most important influences on what is done in classrooms and ultimately on what students learn. However, there is no consensus on what critical knowledge is necessary to ensure that students learn mathematics. Many components of teachers’ knowledge have been identified. Some scholars suggest that since one cannot teach what one does not know, teachers must have in-depth knowledge not only of the specific mathematics they teach, but also of the mathematics that their students are to learn in the future. Only with this intensive knowledge of mathematics can a teacher know how to structure her or his own mathematics teaching so that students continue to learn. Others suggest that knowledge of cultural and ethnic diversity is essential for effective teaching. Since the United States is becoming increasingly multicultural, and since a student’s culture is a major determinant of how the student learns, before a teacher can be effective, he or she must understand the cultural diversity of the students. Still other scholars suggest that knowledge of how students think and learn is vital knowledge for teachers, while others believe that knowledge of general pedagogical principles is a necessary component of teachers’ knowledge.