Proceedings of the Annual Meeting of the Cognitive Science Society

We present a theoretical analysis of students' implicit understanding of the concept of variables and functions, and present a cognitive model of this understanding based on the idea that reasoning involves a successful interaction between psychological agents and the things and other people in a situation. In the first part of the paper, we provide evidence that middle-and high-school students demonstrate implicit understanding of functional relations among quantities when they reason about a physical model of linear functions. Implicit understanding is knowledge of concepts or principles that enables and constrains performance, but is not articulate. In the second part of the pa^r, we describe several theoretical properties of our computational model: a.) activities are modeled as interactions between a parson and a situation; b.) reasoning is modeled as a form of activity that produces new information; and c.) understanding is modeled as attunement to the constraints of conceptual activities.