Situated Intuition And Activity Theory Fill The Gap

Abstract

We report here an instructional method designed to address the cognitive gaps in children’s mathematical development where operational conceptions give rise to structural conceptions, such as when the subtraction process leads to the negative number concept. The method involves the linking of process and object conceptions through semiotic activity with models which first record intuitive processes on objects in situations outside school mathematics — invoking situated intuition — and subsequently mediate new mathematical activity, with mathematical signs, in the mathematical voice. We ground this in teaching experiments focused on (i) the negative integers and (ii) algorithms for two-digit subtraction. We conceptualise modelling as the transformation of outside-school knowledge into school mathematics, and discuss the opportunities and difficulties involved.