Accentuation of category Differences: Revisiting a Classic Study

Problem Representation in Experts and Novices: Part 1. Differences in the Content of Representation Aaron S. Yarlas (yarlas.1@osu.edu) Center for Cognitive Science and School of Teaching & Learning, The Ohio State University 21 Page Hall, 1810 College Road, Columbus, OH 43210 USA Vladimir M. Sloutsky (sloutsky.1@osu.edu) School of Teaching & Learning and Center for Cognitive Science, The Ohio State University 21 Page Hall, 1810 College Road, Columbus, OH 43210 USA Abstract Two experiments examined the content of novice and expert representations for both surface and deep structural elements of arithmetic equations. Experiment 1, which used a forced- choice categorization task in which surface features of equa- tions (e.g., digits) competed with deep structural principles of mathematics (associativity and commutativity), found that ex- perts were more likely to focus on principles in their judg- ments than were novices, who focused more often on surface elements. Experiment 2, using a similar task, introduced trials in which only principled elements varied. Novices were able to focus on principled elements in this case, but failed to transfer these representations when surface features were re- introduced. These findings indicate that novices had knowl- edge of the principles, but that they did not attend to them when competing surface features were present. Introduction It has been well established that in various knowledge domains (e.g., physics, mathematics, or chess) experts ap- proach problems in a manner different from that of novices (Chase & Simon, 1973; Chi, Feltovich, & Glaser, 1981; Larkin, 1983; Simon & Simon, 1978; Reed, Ackinclose, & Voss, 1990). In particular, while experts are more likely to focus on hidden relational properties of a problem, novices are more likely to focus on less important surface features of a problem. However, while there is some understanding of the content of mental representation (i.e., of which aspects of information are likely to be represented and which are likely to be left out), the process of construing the represen- tation remains largely unknown. Do people attend to and encode those aspects that are left out, but then discard them, or do they fail to attend to and encode these irrelevant aspects? The current paper (Part 1) focuses both on establishing differences in content of representation for experts and nov- ices within a simple domain (arithmetic) and testing a num- ber of viable explanations that could account for these dif- ferences. A subsequent paper (Part 2) focuses on examining differences in the process of construing representations for experts and novices. There is a large body of literature indicating that in prob- lem solving, reasoning, learning and transfer, and problem categorization, novices tend to focus on surface features rather than on deep relational properties. These effects have been demonstrated in a variety of knowledge domains, in- cluding chess (Chase & Simon, 1973), mathematics (Bless- ing & Ross, 1996; Schoenfeld & Herrmann, 1982; Bassok, 1996, 1997; Novick, 1988; Reed, et al, 1990; Silver, 1981), physics (Chi, et al 1981; Simon & Simon, 1978; Larkin, 1983; Larkin, McDermott, Simon, & Simon, 1980), and computer programming (Adelson, 1984). Similar effects have been observed in a variety of knowledge-lean domains, such as deductive and inductive inference. When presented with deduction problems, untrained reasoners often tended to ignore the argument's logic (i.e., its deep structure) while relying on the argument's surface features, such as content and believability (Evans, Newstead, & Byrne, 1993; John- son-Laird & Byrne, 1991). When presented with induction and analogy problems, novices and young children also of- ten ignored deep relational structure while relying on the surface features (Gentner, 1989; Holyoak & Koh, 1987). While there is little disagreement that novices focus on surface features, it remains unclear why novices tend to fo- cus on surface features and not on deep relational properties. One possible explanation of novices' tendency to represent surface features is that novices merely have little knowledge of deep structural relations. However, while this possibility is capable of explaining expert-novice differences in ex- tremely knowledge-demanding domains, such as medical diagnostics, chess, or advanced physics, it falls short of ex- plaining these differences in fairly simple domains, such as elementary mathematics and physics. For example, re- searchers examining novices' representations in mathematics and physics often drew examples from students' textbooks, thus reasonably assuming that students should be familiar with the deep structure underlying these problems (Chi, et al, 1981; Larkin, 1983; Novick, 1988). The credibility of the lack of knowledge explanation is further undermined by findings that even those novices who receive instruction in a domain often continue to focus on surface features rather than the deep structure of a problem. These has been dem- onstrated across a variety of knowledge domains, including mathematics (Morris & Sloutsky, 1998) and physics (Kaiser, McCloskey, & Proffitt, 1986; McClosskey, 1983). Finally, the fact that findings on novices' representations in knowl- edge-lean domains are compatible with those in knowledge-