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: Constructivism is a postmodern theory of knowledge with the potential to transform educational theory. Its present popularity in science and mathematics education, however, is no assurance of its enduring influence on education in general or social studies in particular. One need only recall how Piaget’s work has been previously misunderstood and effectively misused to bolster narrow curricular ends (Egan, 1983). Constructivism could meet a similar fate in our contemporary educational and political climate. The historical tendency of educational psychology in the United States to decontextualize educational theories of their cultural and political basis could trivialize the profoundness of a constructivist theory of knowledge, especially for social studies education. This thesis is further strengthened by the significant and mutually supportive roles played by science and social studies education in supporting a positivist theory of objective realism as the basis of social knowledge. The significance of this analysis lies in the potential that constructivism has for revitalizing education for a democracy. The failure of social studies educators to seize this opportunity would be unfortunate.

Extract: For constructivists, the rationality of scientific debates is based on a usually implicit kind of contract which, however, is consensually agreed upon in the context of scientific conferences or academic practice. By means of this contract, scientists establish an agreement as to the assumptions as well as to the principles and practices underlying research. Taken as a whole, these underlying principles and assumptions are generally termed a “paradigm” or “the matrix of a discipline.” It serves as a basis upon which to work out an agreement over what, in a scientific discussion, will be considered relevant as opposed to irrelevant. Thus, scientific observation can only undergo closure on the condition that a whole series of elements are ignored which, were they taken up for consideration, would lead to observations without end. The notion of paradigm refers to these agreements between practitioners of the same discipline by which they are able to develop similar protocols of observation, come to an understanding of what they are doing, and define a particular area of objectivity. In other words, scientific paradigms are what make it possible for scientific debates to take place in accordance with socially instituted forms of rationality. A fertile approach for the study of how science is constructed, this perspective may also be put to use in the study of ethics, beginning with the notion of paradigm.

Excerpt: Constructivism must be careful not to confine itself to the purely cognitive domain of human experience. Educators must strive to include the body, its actions, and its passions more prominently in the curriculum. The pragmatic social constructivism of George Herbert Mead and John Dewey allows us to do so. Mead and Dewey maintained a lifelong friendship and were colleagues for many years during which they visited each other nearly every day. So intermeshed was their influence on each other that it is often impossible to determine who originated what. Such entwinement is typical of socially constructive contexts and illustrates a central thesis of pragmatic social constructivism – it decenters the locus of mind and self.