Excerpt: The main thesis of this chapter is that the culture of teacher education must share the core characteristics of the desired mathematics classroom culture. In particular, this relationship must hold if teacher education is to exercise a reforming influence on in-service teachers and create a break in the circle of reproduction by which the weaknesses of the existing school system are perpetuated. It follows that more attention should be devoted to the relation between alternative classroom experiences and theoretical instruction, to the fundamental role of everyday language for the understanding of mathematics, the balance of self-directed work and the negotiation of meanings in seminars and tutorials, and to the development of reflection and self-monitoring.

Excerpt: Since World War II, mathematics and science education have been high on the educational reform agenda in many countries, including the United States. […] In this chapter, I wish to suggest some ways to reframe this conception of reform in science education. These ways are at one time theoretical and empirical – that is, rooted in the constructivist perspective and in The Professional Practice Community (PPC), a grassroots model for collaboration that may be a constructivist medium to foster educational reform even in the present era of national standards. This model may offer effective structures not only for “valuing questions and ideas” in relation to the usual beliefs on cognition, learning, and teaching, but also for providing a network to support risk taking and change. But before that, some comments on the current U. S. reform project.

Excerpt: For the past six years we, together with Erna Yackel and Terry Wood, have conducted a classroom-based research and development project in elementary school mathematics.’ In this paper, we draw on our experiences of collaborating with teachers and of analyzing what might be happening in their classrooms to consider three interrelated issues. First, we argue that the teacher and students together create a classroom mathematics tradition or microculture and that this profoundly influences students’ mathematical activity and learning. Sample episodes are used to clarify the distinction between the school mathematics tradition in which the teacher acts as the sole mathe-matical authority and the inquiry mathematics tradition in which the teacher and students together constitute a community of validators. Second, we consider the theoretical and pragmatic tensions inherent in the view that mathematical learning is both a process of individual cognitive construction and a process of acculturation into the mathematical practices of wider society. In the course of the discussion, we contrast constructivist attempts to cope with this tension with approaches proposed by sociocultural theorists. Finally, we use the preceding issues as a backdrop against which to consider the development of instructional activities that might be appropriate for inquiry mathematics classrooms.

Excerpt: In this chapter, I have argued that radical constructivist interpretations of constructivism differ from other interpretations in that radical constructivism is an epistemological theory based in viability. It is suggested that viability commits one to the expectation of and support for diversity in the classroom. Moreover, it obliges the radical constructivist to also reinterpret the mathematical meaning of concepts in light of the students’ inventions. To do this effectively, the radical constructivist must learn techniques of close listening and follow these by the articulation of student voice and the examination of the changes in his or her own perspective. It is the “voice-perspective” relationship which makes radical constructivism capable of deep reform in mathematics instruction.

Excerpt: In this chapter we would like to stress the contingency of the socially constructed world along with the social and political consequences of reifying and decontextualizing knowledge so as to make it appear necessary, indubitable, and unalterable. We want to develop a critical-constructivist stance toward the production and ownership of knowledge, in particular scientific knowledge, in society at large. We will examine some of the issues of power and social regulation involved in the social production of knowledge.

Excerpt: I use the pre-Socratics’ contrast of the one and the many as my organizing theme. It fits well with the aim of this chapter: to offer both an analysis and synthesis of half of the preceding contributions. Synthesis constructs unity (the one), whereas analysis turns out to suggest diversity (the many). Starting with “the one,” I consider what different positions in constructivism have in common. Then I consider “the many” – analyzing some salient differences between different constructivist positions (and a few others). Finally, I offer a synthesis, “the one” again, identifying what seem to be deeply shared themes, problems and points of growth for constructivism, and alternative epistemologies in education.