Abstract
In this paper I conceptualize the relationship between the children's actively constructed argument, and the formal conventions of the culture of schooling and mathematics which the teacher introduces, in ways which move beyond the dichotomous view of reasoning as either everyday or scientific-mathematical. The analysis draws on Vygotsky's (1986) notion of spontaneous (informal) and scientific (formal, schooled) learning as well as, on Halliday (1975, 1978) and Pimm's (1987) view of register.
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