Selecting analogous problems: Similarity versus inclusiveness

Abstract

Students were asked to select one of two analogous problems in order to solve algebra word problems. In Experiment 1, one problem was less inclusive and the other was more inclusive than a test problem. The students judged the complexity and similarity of problems, selected analogous problems, and used the solutions to solve test problems. They performed significantly better on the test problems when given the more inclusive solutions, but used perceived similarity rather than inclusiveness to select analogous problems. The same pattern of results occurred in Experiment 2, in which isomorphic problems replaced the more inclusive problems. The results show that students are deficient in selecting good analogies, both from the same category (Experiment 1) and from a different category (Experiment 2). Students who saw the analogous solutions (Experiment 3) or were majoring in mathematics (Experiment 4) were more likely to select an isomorphic problem over a less inclusive problem, but were not more likely to select a more inclusive over a less inclusive problem.