@Article{OrmerodChronicleMacGregor2006,
author = {Ormerod, Thomas C. and Chronicle, Edward P. and MacGregor, James N.},
title = {Asymmetrical analogical transfer in insight problem solving},
journal = {Proceedings of the 28th Annual Conference of the Cognitive Science Society},
year = {2006},
pages = {1899--1904}
}
Research examining general problem-solving has shown that having experience on a practice problem may have a beneficial or detrimental effect on subjects’ performances on a subsequent target problem. However, this analogical transfer is asymmetrical in the sense that it is more evident when (a) the practice problem is more challenging than the target, and (b) the practice and target problems have common surface and structural characteristics.
In their study, Ormerod, Chronicle, and MacGregor (2006) investigated if this asymmetric analogical transfer extended to insight problem-solving. If insight problem-solving relied on the same processes as general problem-solving, then evidence of this asymmetry should be present. If, however, insight problem-solving was fundamentally different from general problem-solving, then this asymmetry should not manifest.
In order to maximize the power of their study, Ormerod et al (2006) chose two insight problems - the Four-Trees problem and the Four-Coins problem – that best took into consideration previous research findings, in that they (a) were of varying difficulty levels, but (b) possessed similar surface and structural aspects.
The Four-Trees problem (the harder of the two) posed the following dilemma: How can four trees be planted such that they are equal distances from each other? Similarly, the Four-Coins problems asked: What configuration will result in each of the four coins touching the other three? An answer to the former problem was to plant three trees around a mound and the fourth on top, whereas an answer to the latter problem was to arrange three coins flat and touching, with the fourth on top.
According to Ormerod et al (2006), these problem shared superficial similarities given that they both required that a set of four objects be arranged such that they meet certain constraints. The Four-Trees and Four-Coins problem were also structurally comparable in that the solution comprised of a triangular configuration of three objects with the fourth one above them.
Experiment 1 [p. 1900]
Experiment 1 was designed to test if the hypothesized asymmetry existed in insight problem-solving, 18 student volunteers were randomly assigned to receive either the Four-Trees or the Four-Coins problem first, with the expectation that if the effect did exist, then practice on the Four-Trees problem would facilitate problem-solving of the Four-Coins problem but not vice versa. During group testing, participants were provided a booklet in which they completed the practice problem, were given the correct solution, then continued with some filler questions, and the target problem. Performance was measured by solve rate and time taken.
Results showed the following:
Experiment 2 [p. 1901]
Experiment 1 was limited in that the sample size was small, and that analogical similarities between the two problems were not obvious to participants. Hence, a replication was conducted in Experiment 2, but using a larger sample (n = 127) and including instructions for participants to generalize the solution in the practice problem to the target.
Results showed the following:
Experiment 3 [p. 1901-1902]
In order to confirm that the ineffectiveness of the explicit instructions was not an artifact of a floor effect and that there was indeed no analogical transfer taking place, Ormerod et al (2006) sought to increase the solve rate of the Four-Trees problem by modifying the environment to make it more conducive for insight problem-solving.
Forty-one student volunteers were randomly assigned to solve either the Four-Trees or the Four-Coins problem first, with filler problems in-between. Unlike Experiments 1 and 2, these participants were individually tested to minimize distractions, and were provided physical props to manipulate. In the Four-Trees problem, participants were given bamboo rods (“trees”), and a sandbox/miniature shovel for “planting”. In the Four-Coins problem, participants were given four hexagonal metal tiles.
Results showed the following:
Taken as a whole, the presence of an asymmetrical analogical transfer effect in Experiments 1-3 suggested that insight problem-solving was not systematically different from general problem-solving. In both types of problem-solving, transfer was facilitated if the practice problem possessed a higher degree of difficulty than the target problem.
Ormerod et al (2006) postulated that root of the asymmetrical analogical transfer could be attributed to variations in the size of the problem space between the Four-Trees and Four-Coins problems. The contextual elaborateness of the Four-Trees problem created a higher level of difficulty, which in turn, generated an initial problem space of alternatives that may have been too inclusive. Progress was also hindered by false strategies, which were more readily available but did not yield solutions.
In contrast, the Four-Coins problem was not as complex and allowed for criterion failure (i.e., the inability to locate promising alternatives) much sooner. As a result, individuals expanded or restructured the problem space to allow for less obvious possibilities, leading to the discovery of novel solutions.
Based on this theoretical perspective, Ormerod et al (2006) argued that successful analogical transfer from the Four-Trees problem to the Four-Coins problem occurred because the earlier criterion failure acted as a cue for strategy modification and as a prompt to use previous relevant experience to expand/restructure the target problem space.
However, analogical transfer from the Four-Coins problem to the Four-Trees problem failed because the larger initial problem space of the Four-Trees problem discouraged criterion failure, which consequently failed to trigger the solver’s internal cues, and diminished the ability to recognize that the practice problem’s solution may have been relevant.
This asymmetry could suggest that features of analogs are accessed differentially, which may impact computational models of analogical problem-solving.