Proceedings of the Annual Meeting of the Cognitive Science Society

Given that the single most important mathematical skill for students who wish to study beyond arithmetic is the ability to take a problem situation (usually stated in words) and formulate a mathematical model (usually an equation), we are working on a cognitive developmental model of this skill to be used in an intelligent tutoring system. We call this skill symbolization. High school students do it poorly and improve slowly. We are using a Difficulty Factors Assessment as an efficient methodology for identifying the critical cognitive factors that distinguish competent from less competent symbolizers. We present a developmental model identifying three major transitions through which a student must pass. Underlying the developmental model are empirical results which suggest, contrary to prior research and common belief, the difficulty in algebra word problem solving is less about the difficulties of comprehending the word problems, and more about the difficulty of speaking in the foreign language of algebra. Many of students' errors are analogous to the errors people make when learning to speak in a new language. While it may be that mathematically algebra symbolization is a generalization of arithmetic, cognitively it is more accurate to say algebra symbolization is the articulation of arithmetic.