Representation Strength Influences Strategy Use and Strategy Discovery

Abstract

Representation Strength Influences Strategy Use and Strategy Discovery Martha W. Alibali (mwalibali@facstaff.wisc.edu) Department of Psychology University of Wisconsin—Madison 1202 W. Johnson Street Madison, WI 53706 USA Tara L. Booth (boothtara@hotmail.com) Department of Psychology University of Wisconsin—Madison 1202 W. Johnson Street Madison, WI 53706 USA Abstract When attempting to solve a problem, individuals may activate multiple potential representations for that problem. Further, different representations may be activated more or less strongly. This study investigated how strength of problem representations is related to patterns of strategy use and strategy discovery. We hypothesized that the more strongly a particular representation is cued, the more likely participants should be to use a strategy that corresponds with that representation. Further, for individuals who do not initially have a corresponding strategy in their repertoires, the more strongly a particular representation is cued, the more likely participants should be to discover a strategy that corresponds with that representation. These hypotheses were investigated among adults solving word problems about constant change. The problems could be represented in terms of discrete change or continuous change. We varied two types of cues to discrete and continuous problem representations: linguistic cues and graphical cues. Both linguistic and graphical cues influenced strategy use, and the effects of the two cue types were additive. Among participants who did not use a continuous strategy at the outset of the study, discovery of a continuous strategy was relatively rare, and only participants who received a continuous graph tended to discover a continuous strategy. The findings suggest that it may be fruitful to consider problem representations as graded and variable rather than all-or-none. Introduction One step in the process of solving a problem is forming a mental representation of important features of that problem. Problem representations have been invoked to explain many aspects of people’s problem-solving behavior, including success, solution times, strategies, and errors (e.g., Kotovsky, Hayes, & Simon, 1985; Lovett & Schunn, 1998). In the present study, we investigate links between problem representations and patterns of strategy use and strategy discovery. Problem representations are sometimes conceptualized as integrated wholes, such that a particular representation is retrieved in its entirety from memory, and applied to the problem at hand (e.g., Larkin, 1983). Although this characterization may apply in some cases (e.g., for well- practiced problems), we suggest that in most cases, problem representations are constructed at the moment of solving, based on both perceivable features of the problem and on knowledge retrieved from memory about problem content or about particular problem-solving strategies (McNeil & Alibali, 2000). We further suggest that the knowledge activated in constructing a problem representation may be more or less strongly activated, and thus, aspects of the representation may be graded rather than all-or-none (see Munakata, McClelland, Johnson, & Siegler, 1997, for discussion). There is some support in the literature for the notion that problem representations may be graded. Kaplan and Simon (1990) studied this issue in the context of the mutilated checkerboard problem. In this problem, the squares from two diagonally opposite corners of a checkerboard are removed, and the solver’s task is to cover the remainder of the checkerboard with dominoes, each of which covers exactly two squares, or to prove that such a covering is impossible. Because the two diagonally opposite corners of a checkerboard are the same color (both black or both white), the covering task is indeed impossible; however, this fact is notoriously difficult for solvers to discover. In their experiment, Kaplan and Simon varied the strength of various cues to the paired-ness, or parity, of the squares. Solvers were quicker to discover that the covering was impossible when adjacent squares were labeled bread and butter than when the squares were not labeled, or when they were labeled with terms that did not form a strongly associated pair ( black and pink ). The bread-and-butter cue to parity facilitated a stronger representation of this crucial problem feature, and this led to faster discovery of the problem solution. The purpose of the present study was to investigate whether variations in the strength of problem representations can account for variations across solvers in patterns of strategy use. Several past studies have investigated the links between problem representation and strategy use (e.g., Alibali, Bassok, Solomon, Syc, & Goldin- Meadow, 1999; Morales, Shute, & Pellegrino, 1985; Siegler, 1976). However, to date, little research has examined how the strength of representations relates to patterns of strategy use. We hypothesized that the more