Construction and Interaction: Children's Fractional Schemes

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The goal of this project is to study children's construction of fractional schemes in the context of the children interacting in computer environments in pairs under the guidance of a teacher-researcher. Using a videotaped data of approximately 630 teaching episodes with six pairs of children over a period of three years, a retrospective analysis will be conducted for each pair of children. The child-child and adult-child social interactions will be analyzed along with the interaction in the computer environments and correlated with an analysis of the children's mathematical activity both individual and social. The case study of each pair of children will be subjected to a scientific analysis in which the children's fractional schemes and construction of those schemes are abstracted and organized into a coherent structure. Piaget's hypothesis that mathematics is contributed by the individual to the interactions and Vygotsky's hypothesis that the source of mathematics resides in the internalization of social interaction will be continually tested through both kinds of analysis (retrospective and scientific). To the extent that these hypotheses are falsified, a model of learning that supersedes both Piaget's and Vygotsky's models also will be continually tested in which subject environment interactions and within subject interactions are co-implicated.