Exploring the Episodic Structure of Algebra Story Problem Solving. Revision.
Abstract
This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of 'model-based reasoning' to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of thes findings for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1989
- Accession Number
- ADA206403
Entities
People
- Chris Truxaw
- Dennis Kibler
- Etienne Wenger
- Rogers Hall
Organizations
- University of California, Irvine