COGNITIVE FACTORS AFFECTING PROBLEM SOLVING AT THE PRE-ALGEBRAIC LEVEL

The paper continues the authors ’ previous studies on algebraic solving strategies of the one comparison problem. The study focuses on arithmetic solutions of the same word problem, in an attempt to find out whether the choice of the arithmetic strategy is influenced by the same variables as in the algebraic case. In our earlier studies (Nesher, Hershkovitz, and Novotná, to be published; Hershkovitz, Nesher, and Novotná, 2002; Hershkovitz, Nesher, and Novotná, 2001), algebraic solutions1 of twelve separate formulations of the same comparison problem2 were analyzed in terms of its linguistic surface structure, its underlying propositional structure, its underlying schemes, and the symbolic modeling selected empirically by the solvers in their attempt to solve. The purpose of the studies was to find factors that affect the way solvers construct their equations to solve a simple comparison problem. The work is based on cognitive theories related to solving word problems such as that of Kintsch distinguishing between the text base and the situation model, see e.g. (Kintsch 1986), and works emphasizing the schemes approach, see e.g. (Nesher, Greeno et al. 1982; Vergnaud 1998; Fischbein 1997). In (Hershkovitz