In an epistemology where mathematics teaching is viewed as goal-directed interactive communication in a consensual domain of experience, mathematics learning is viewed as reflective abstraction in the context of scheme theory. In this view, mathematical knowledge is understood as coordinated schemes of action and operation. Consequently, research methodology has to be designed as a flexible, investigative tool. The constructivist teaching experiment is a technique that was designed to investigate children’s mathematical knowledge it might be learned in the context of mathematics teaching (Cobb & Steffe, 1983; Hunting, 1983; Steffe, 1984). In a teaching experiment, the role of the researcher changes from an observer who intends to establish objective scientific facts to an actor who intends to construct models that are relative to his or her own actions.
Open peer commentary on the target article “From Objects to Processes: A Proposal to Rewrite Radical Constructivism” by Siegfried J. Schmidt. Upshot: My suggestion is that the shift from objects to processes can be seen as grounded in the processes of self-generation common to all living organisms. Specifically human cognition is a subsequent evolutionary emergence.
Excerpt: Being grateful to von Glasersfeld for having pointed out to me what I now accept, I have no desire to attack radical constructivism. There are, however, three ways in which I find it seriously, even radically, deficient, and I want in this chapter to set them out in the hope that my doing so will be some use where I, and apparently von Glasersfeld, care most about usefulness, in education. These deficiencies are a lack of due emphasis on the construction of the self, whether over against the world or as a part of it, the denial of the possibility of knowledge of the world, and von Glasersfeld’s ignoring of the massive social assistance in one’s construction of one’s notion of the world. The latter two of these deficiencies have considerable importance for education, and that is my reason for airing my criticisms in this place.
Upshot: Michael Tomasello is Director of the Department of Developmental and Comparative Psychology and Co-Director of the Max Planck Institute for Evolutionary Anthropology in Leipzig. He completed his PhD with Ernst as his supervisor in 1980. In his reminiscence essay he describes the “total enculturation” he experienced on encountering Ernst von Glasersfeld.
Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: In the light of the almost brilliant equilibrium of the author, who manages to compose a resourceful explanation, switching between the notional conditionality and the expected contextual understanding, I intend to focus on the interdisciplinary potential of some suggestions that offer new perspectives on conceiving society, which are driven by a non-analytical and holistic vision.