initial success, it was apparent that nearly all students had to learn how to learn in groups. The authors conclude that student empowerment is a requirement for learning with understanding. In their discussion of the teacher's learning and change, attention is drawn to the dialectical nature of the relationship between the number of perturbations and commitment to change. The authors highlight the importance to change of constructing a vision, the components of which are presented from a constructivist perspective and include the customs and taboos which apply to the vision.
Taylor deals with the pedagogical change of a mathematics teacher who is teaching out of field. Chapter 17 describes changes that occurred over a period of more than a year and critiques the change process. Some of the obstacles encountered by the teacher include his desire to cling to positivist beliefs of teaching and learning, a view of constructivism that largely ignores the social implications of knowledge construction, and a tendency to retain an objectivist view of knowledge as truth. As the study progressed, Taylor was able to learn about the role of constraints in making significant changes within the culture of schools and the significance of power relationships between the teacher and students.
In chapter 18 Confrey discusses the need for a fresh approach to teacher education within a context of the many calls for reform in mathematics education. In so doing, she examines the roles of others in assisting teachers to implement reform. A vignette presented by Confrey underlines the significance of involving parents in attempts at reform of the curriculum. Unless parents are educated to understand the nature of the reform they might inadvertently subvert the endeavors of teachers to make the changes advocated in a plethora of reports. At the classroom level Confrey raises the interesting question of how purposeful listening and talking can lead to useful knowledge. To respond to this question she turns to constructivism. Confrey then discusses the teacher's role in mathematics classrooms as recognizing students' productive ideas, being a good listener, and using multiple representations of mathematics knowledge. Confrey's thesis is that teachers are not presently educated to do these things, the implication being that reform in teacher education will be a necessary co-requisite for improving the quality of the mathematics curriculum in elementary, middle, and high schools.
The final section of the book consists of chapter 19, written by Dana and Davis, a synthesis of the earlier 18 chapters of the book organized around five themes: knowledge and knowing, teaching and learning, educating teachers, educational research, and future directions.
Constructivism should not be regarded as a new truth to replace objectivism. On the contrary, constructivism is a way of thinking about knowing, a referent for building models for learning, teaching, and curriculum. These models are hypothetical and they can be put to the test in classrooms. Von Glasersfeld has repeatedly cautioned that constructivism does not tell us what to do, only what not to do. The test for any model, or knowledge construction, is the extent to which it provides an adequate basis for accomplishing goals. Viability, the test of knowledge against experience, is the critical test of models built from constructivism or from any other referent. From a