Constraints on the Abstraction of Solutions.

摘要

Students in college algebra classes attempted to solve a series of three mixture problems and three distance problems and to match concepts between the first two problems in a series. The detailed comparison of two isomorphs did not result in the abstraction of a solution schema, as it was found to do by Gick and Holyoak (1983) for convergence problems. Attempts to promote abstraction by not allowing students to refer to a specific analogue (Experiment 2) and by providing information about corresponding concepts and principles (Experiment 3) were unsuccessful. These findings suggest that the bottom-up, similarity-based approaches encouraged by mapping concepts may need to be supplemented by top-down, principle-driven instruction. The abstraction of solutions is constrained by (1) the requirements to sucessfully compare two specific analogues (the bootstrapping constraint) and (2) the existence of superordinate concepts to describe the abstraction. Keywords: Performance human; Decision theory; Schema; Examples; Procedures; Analogs; Mathematics; Reprints; Categorization; Word problems; Problem solving. (KT)