Ah-Ha, I Knew It All Along: Differences in Hindsight Bias Between Insight and Algebra Problems

Abstract

Ah-Ha, I Knew It All Along: Differences in Hindsight Bias Between Insight and Algebra Problems Ivan K. Ash (iash1@uic.edu) Jennifer Wiley (jwiley@uic.edu) Department of Psychology The University of Illinois at Chicago 1007 West Harrison Street (M/C 285) Chicago, IL 60607, U.S.A. Abstract The present study investigated the role of restructuring in the solution of insight and incremental problems. Participants were presented with a series of insight and algebra word problems in a hindsight bias paradigm (Fischoff, 1975). Those who solved the insightful problems correctly showed increases in importance ratings on the key problem components. However, no increases in importance ratings were detected for the key problem components of algebra problems. These results are consistent with theories that propose that representational restructuring plays a fundamental role in the insightful problem solving process (Davidson & Sternberg, 1984; Ohlsson, 1992). Restructuring and Insightful Problem Solving A number of researchers have suggested that insight problems may be solved in a qualitatively different manner from incremental or analytic problems (Duncker, 1945, Davidson & Sternberg, 1984, Metcalfe & Wiebe, 1987, Ohlsson, 1992). For example, when Metcalfe and Wiebe (1987) had subjects make feeling of warmth ratings while solving algebra and insight problems, they found that while solving algebra problems, subjects’ warmth ratings steadily increased towards the time of solution; whereas during the solution of insight problems subjects’ warmth ratings remained low and suddenly increased right before they solved the problem. These results suggest the processes for solving insight problems are different from the systematic or analytical processes used for incremental problems. However, this only represents the suddenness of the insightful process and does not shed light on the causes of the solution patterns. It has been suggested that insight problems differ from incremental problems in that the nature of the solvers’ experience causes them to construct a representation of the problem that cannot lead to the correct solution (Duncker, 1945, Davidson & Sternberg, 1984, Ohlsson, 1992). In order to come to the correct solution, solvers must restructure their original conception of the problem. Proposed evidence for restructuring in insight problem solving has come from a wide range of empirical findings. For example, Dominowski and Buyer (2000) found decreases in re-solution time for those who correctly solve insight problems but not for those who were simply shown the answer. Knoblich, Ohlsson, and Raney (2001) analyzed eye movements during the solution of matchstick arithmetic problems and found evidence for impasses followed by increased fixations on components of the problems that were key to solution. Durso, Cornelia, and Dayton (1994) attempted to find an independent measure of restructuring by statistically modeling successful and unsuccessful problem representations after the problem solving session. They found that successful solvers representations centered on concepts key to the nature of the solution, whereas non- solvers representations centered on the principle characters in the story problem, which were not relevant to the solution. These empirical studies suggest an insight problem solving process that involves the restructuring of the mental problem representation. However, these studies fall short of proving the existence of a restructuring process because they fail to directly measure representational change before and after solving across an individual and fail to compare problems that involve incremental solutions to the problems proposed to elicit insightful solutions. What is needed is an independent measure of restructuring in order to test theories that predict an insight process involving restructuring against theories which do not predict restructuring in any problem solving process (such as Weisberg’s nothing special view, 1986). Furthermore, this method must be able to directly test whether more restructuring is involved in insightful than incremental problem solving. The present study uses a hindsight bias paradigm to produce an independent measure of the amount of restructuring involved in solving different types of problems. Hindsight Bias Hindsight bias is the observation that people with outcome knowledge of a situation falsely believe that they would have predicted the correct outcome (Hawkins & Hastie, 1990). Fischoff (1975) originally developed the basic paradigm. He had people read a narrative of a situation with or without receiving the outcome and then had them rate the probability of alternate outcomes as if they had no knowledge of the outcome. The general finding is that people with outcome knowledge unknowingly rate the outcome they were told as more probable than alternatives, as if they “knew it all along.” Individuals who receive outcome knowledge also rate the sentences in the narrative that support the given outcome