{"pk":32841,"title":"Implicit Understanding of Functions in Quantitative Reasoning","subtitle":null,"abstract":"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.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[],"section":"Paper Presentations -- Regularities and Estimation","is_remote":true,"remote_url":"https://escholarship.org/uc/item/0697n5gm","frozenauthors":[{"first_name":"Joyce","middle_name":"L.","last_name":"Moore","name_suffix":"","institution":"Stanford University","department":""},{"first_name":"James","middle_name":"G.","last_name":"Greeno","name_suffix":"","institution":"Stanford University","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"1991-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/32841/galley/23901/download/"}]}