Interdomain Transfer Between Isomorphic Topics in Algebra and Physics

Three experiments examined transfer between two isomorphic subdomains of algebra and physics. The two areas were arithmetic-progression problems in algebra and constant-acceleration problems in physics. High school and college students who had learned one of these subtopics were presented with word problems that used either content from the domain they had originally studied or content based on the unfamiliar but analogous domain. Students who had learned arithmetic progressions were very likely to spontaneously recognize that physics problems involving velocity and distance can be addressed using the same equations. Analysis of problemsolving protocols revealed that the recognition was immediate and that the solutions were a straightforward application of the algebraic method. Such recognition occurred even when the algebraic procedures were taught using example word problems all of which were drawn from a single content area (e.g., "money" problems). In contrast, students who had learned the physics topic almost never exhibited any detectable transfer to the isomorphic algebra problems. In the only case of transfer from physics to algebra, the process was analogical in nature. In addition, transfer from algebra to physics word problems was impaired if the physics transfer problems were embedded in a discussion of motion concepts. The results were interpreted in terms of content-free versus content-specific applicability conditions for mathematical procedures.