ERIC Number: ED338642
Record Type: RIE
Publication Date: 1991-Apr
Conceptual Structures in Mathematical Problem Solving.
The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity as they attempt to resolve situations that they experience as genuinely problematic. Subjects were nine students in introductory calculus classes at the University of California (San Diego) who were interviewed as they solved a set of similar algebra word problems. Experimenters prepared videotaped and written protocols for each subject. Analyses of these protocols are reported within a case study format. Solution activities indicated a gradual construction and elaboration of conceptual knowledge as subjects solved their tasks. Generalizing across the case studies yielded four levels of solution activity: (1) structural; (2) re-presentation; (3) recognition; and (4) instrumental. These levels encompassed three broad categories of conceptual structure: recognition, re-presentation, and abstract. Findings indicate that subjects' developing ability to monitor and plan their solution activities is made possible by their cognitive advances. Two tables and two figures illustrate the discussion. A 19-item list of references is included. (SLD)
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 (Chicago, IL, April 3-7, 1991). Handwritten figures in text may not reproduce well.