ABSTRACT
In recent years, the social interaction involved in the construction of the mathematics of children has been brought into the foreground in order to specify its constructive aspects (Bauersfeld, 1988; Yackel, et al., 1990). One of the basic goals in our current teaching experiment is to analyse such social interaction in the context of children working on fractions in computer microworlds. In our analyses, however, we have found that social interaction does not provide a full account of children’s mathematical interaction. Children’s mathematical interaction also includes enactment or potential enactment of their operative mathematical schemes. Therefore, we conduct our analyses of children’s social interaction in the context of their mathematical interaction in our computer microworlds.1 We interpret and contrast the children’s mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. We challenge what we believe is a common interpretation of learning in radical constructivism by those who approach learning from a social-cultural point of view. Renshaw (1992), for example, states that ‘In promulgating an active, constructive and creative view of learning,…the constructivists painted the learner in close-up as a solo-player, a lone scientist, a solitary observer, a meaning maker in a vacuum.’ In Renshaw’s interpretation, learning is viewed as being synonymous with construction in the absence of social interaction with other human beings. To those in mathematics education who use the teaching experiment methodology, this view of learning has always seemed strange because we emphasize social interaction as a primary means of engendering learning and of building models of children’s mathematical knowledge (Cobb and Steffe, 1983; Steffe, 1993).
