ERIC Number: ED228045
Record Type: RIE
Publication Date: 1983-Apr
Theoretical and Pragmatic Issues in the Design of Mathematical "Problem Solving" Instruction.
Schoenfeld, Alan H.
This paper considers the nature of "understanding" in mathematics, and of instruction designed to foster it. The first part is theoretical, presenting an argument that there are (at least) three qualitatively different components to competent mathematical performance: (1) possession of the appropriate set of cognitive "resources," (2) the ability to select appropriately from the resources potentially at one's disposal, and use them with some efficiency (i.e., good "control" behavior), and (3) possession of a "mathematical perspective" that establishes the context within which resources are selected and used. Examples are given to show that the absence of any of these can cause failure in students. The second part is practical, and the focus turns to "positive" behavior. Suggestions are made for (1) solidifying resources including a focus on representations and the use of heuristic strategies, (2) inducing more efficient "control" behaviors, and (3) uncovering inappropriate (anti-mathematical) perspectives in students, and working towards replacing them with perspectives that support the development and utilization of mathematical skills. (Author)
Publication Type: Opinion Papers; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Note: Paper presented at the annual meeting of the American Educational Research Association (Montreal, Quebec, Canada, April 11-14, 1983).