ERIC Number: ED323084
Record Type: RIE
Publication Date: 1990
A Recursive Theory for the Mathematical Understanding--Some Elements and Implications.
Pirie, Susan; Kieren, Thomas
There has been considerable interest in mathematical understanding. Both those attempting to build, and those questioning the possibility of building intelligent artificial tutoring systems, struggle with the notions of mathematical understanding. The purpose of this essay is to show a transcendently recursive theory of mathematical understanding which is based on the consideration of understanding as a nonlinear process of growth. This theory of growth has a built-in dynamic of folding back to move out, but also shows understanding as an organizing process to entail action, perception of action, conception of percepts, conception of concepts, conception of forms (or classes) and logical explanation in an embedded manner. The theory and its elements, and the properties and applications of the theory are discussed. (CW)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Note: Paper presented at the Annual Meeting of the American Educational Research Association (Boston, MA, April 1990).