Many tasks (e.g., solving algebraic equations and running errands) require the execution of several component processes in an unconstrained order. The research reported here uses the geometric analogy task as a paradigm case for studying the ordering of component processes in this type of task. In solving geometric analogies by applying mental transformations such as rotate, change size, and add a pan, the order of performing the transformations is unconstrained and does not in principle affect solution accuracy. Nevertheless, solvers may bring cognitive constraints with them to the analogy task that influence the ordering of the transformations. First, we demonstrate that solvers have a preferred order for performing mental transformations during analogy solution. We then investigate three classes of explanations for the preferred order, one based on general information processing considerations, another based on task-specific considerations, and a third based on individual differences in analogy ability. In the first and third experiments, college students solved geometric analogies requiring two or three transformations and indicated the order in which they performed the transformations. There was close agreement on nearly the same order for both types of analogies. In the second experiment, subjects were directed to perform pairs of transformations in the preferred or unpreierred order. Both speed and accuracy were greater for the preferred orders, thus validating subjects' reported orders. Ability differences were observed for only the more difficult three-transformation problems: High-and middle-ability subjects agreed on an overall performance order, but the highs were more consistent in their use of this order. Low-ability subjects did not consistently order the transformations for these difficult problems. The general information processing factor examined was working-memory toad. A number of task factors have been shown to affect working-memory load during the solution of inductive reasoning problems. Of these, we chose to examine process difficulty. Because analogies are solved in working memory, performing more difficult transformations earlier may reduce working-memory load and facilitate problem solution. However, the observed performance order was not correlated with transformation difficulty. The first task-specific factor considered was that some transformations may be identified earlier, possibly because of perceptual salience, and that the performance order follows the identification order. Howcvet; the order of transformation identification also did not account for the order of transformation application in either experiment. Solving geometric analogies is an imagery task in which the solution is constructed mentally by performing the inferred transformations on the given figure. Performance on geometric analogy tests is moderately to highly correlated with a variety of spatial visualization tests that involve image generation, transformation, and retention. The second task-specific factor considered was that the order of transformation application would resemble the order of using the corresponding information in an analogous physical task, the planning and execution of a drawing. Thus, in the fourth experiment, subjects were asked to indicate the order in which they would need specific types of information, each corresponding to a transformation, in order to draw a simple picture. This drawing order paralleled the order of performing mental transformations during analogy solution. Perceptual processing during object identification is also shown to proceed in a similar order These results suggest that in solving geometric analogies, subjects tap into procedures and constraints common to the domains of imagery, drawing, and object identification. In sum, we have shown that a logically unconstrained ordering of component processes 50
Furthermore, common drawing theories consider the order of strokes in a painting as a reflection of the mental organization of a scene and its hierarchical relationships REF .
Cognitive Constraints on Ordering Operations: The Case of Geometric Analogies
Journal of experimental psychology. General
Journal of experimental psychology. General
Psychology Medicine