Converging evidence for the functional significance of imagery in problem solving

Two kinds of explanations have been offered for the process by which three-term series problems are solved, one in terms of linguistic principles and the other in terms of visual-spatial imagery. Two experiments are reported in which three different classes of operations are brought to bear on the problem: (1) Manipulation of stimulus attributes (characteristics of problems), (2) manipulation of variables that selectively encourage or inhibit the use of imagery (facilitating instructions; the suppression of visualization by reading), and (3) measurement of relevant individual differences (spatial-reasoning ability). All of the results indicate that imagery plays a functional but not a necessary role in the solution of three-term series problems; it is suggested that imaginal representation is functional because it reduces the load on memory. An adequate explanation of problem-solving will have to address certain general issues, such as the diversity of forms of cognitive representation and differences within and between individuals in the choice of problem-solving strategies.     

The functional equivalence of problem solving skills

The tower of Hanoi problem is used to show that, even in simple problem environments, numerous distinct solution strategies are available, and different subjects may learn different strategies. Four major classes of solution strategies are described for the problem. Different strategies have different degrees of transferability, place different burdens on short-term memory and on perception, and require different learning processes for their acquisition. The analysis underscores the importance of subject-by-subject analysis of “what is learned” in understanding human behavior in problem-solving situations, and provides a technique for describing subjects' task performance programs in detail.     

Spatial and ordinal components of form perception and literacy

We suppose that the visual nervous system possesses compensatory rectifying mechanisms by means of which it achieves “constancy” of visual recognition despite variation in physical appearance of the stimulus object. Using geometric rotations, reflections, and other transformations of text as the physical variation, we studied the recognizability of the texts and the influence that practice in reading one type of transformation exerted on the recognition of others. The mathematical structure of the training set was used as a clue to the perceptual mechanisms mediating transfer, isolating perceptual functions involving a geometric transformation and an ordinal operator. The main feature of the theory is its emphasis upon a dialogue or interaction between ongoing problem-solving processes in visual rectification and the sample being recognized. The theory developed is contrasted with other theories of pattern recognition in which concepts such as stimulus generalization, tuned detectors, and preprocessing play major roles. A relation of this theory to problems encountered among disabled readers (“dyslexics”) is also brought out.     

Leading questions and the eyewitness report

A total of 490 subjects, in four experiments, saw films of complex, fast-moving events, such as automobile accidents or classroom disruptions. The purpose of these experiments was to investigate how the wording of questions asked immediately after an event may influence responses to questions asked considerably later. It is shown that when the initial question contains either true presuppositions (e.g., it postulates the existence of an object that did exist in the scene) or false presuppositions (e.g., postulates the existence of an object that did not exist), the likelihood is increased that subjects will later report having seen the presupposed object. The results suggest that questions asked immediately after an event can introduce new—not necessarily correct—information, which is then added to the memorial representation of the event, thereby causing its reconstruction or alteration.     

Family resemblances: Studies in the internal structure of categories

Six experiments explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes in common with other categories. In probabilistic terms, the hypothesis is that prototypicality is a function of the total cue validity of the attributes of items. In Experiments 1 and 3, subjects listed attributes for members of semantic categories which had been previously rated for degree of prototypicality. High positive correlations were obtained between those ratings and the extent of distribution of an item's attributes among the other items of the category. In Experiments 2 and 4, subjects listed superordinates of category members and listed attributes of members of contrasting categories. Negative correlations were obtained between prototypicality and superordinates other than the category in question and between prototypicality and an item's possession of attributes possessed by members of contrasting categories. Experiments 5 and 6 used artificial categories and showed that family resemblance within categories and lack of overlap of elements with contrasting categories were correlated with ease of learning, reaction time in identifying an item after learning, and rating of prototypicality of an item. It is argued that family resemblance offers an alternative to criterial features in defining categories.