An analysis of social interaction in the context of a radical constructivist teaching experiment
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The mathematical interactions among two fourth grade children and their teacherresearcher were analysed. The children were paired with respect to their conceptual number sequences at the beginning of the teaching experiment. Both children had constructed a number sequence sufficiently powerful to enable them to construct basic fractional schemes. From the analysis of the mathematical interactions, it was found that the children’s fractional schemes served as instruments of interaction and that the schemes both constrained and enabled their interactive mathematical activity. When the children constructed schemes that they used to produce proper fractions, neither child took what the other child said or did as an occasion for acting further. The situation changed after the children constructed more complex fractional schemes during the first part of their fifth grade in school for both the children and the teacher. The children could engage in dialogue in the context of producing fractions equal to a given unit fraction and the teacher became able to interact with the children in a way that emphasized the children’s ways and means of operating. In general, the success of teacher-child interactions that had the purpose of promoting mathematical interactions among the children depended on the state of the children’s schemes and of their mathematical operations.