Highs Are to Lows as Experts Are to Novices: Individual Differences in the Representation and Solution of Standardized Figural Analogies

Two experiments compared the strategies used by high and lower scorers on standardized figural analogy tests to represent and solve problems. In Experiment 1, subjects freely sorted completed analogy (A:a::B:b) problems into categories. High scorers categorized problems largely on the basis of well-constrained spatial transformations between problem terms; Low scorers sorted according to perceptual (i.e., shape) similarities among the figures constituting the problems. Experiment 2 compared the two groups' solution strategies in terms of specific patterns of eye movements used in viewing problem and answer terms. High scorers appeared to view problem terms in a more efficient fashion than did lower scorers. The lower scorers focused on noncritical figural relations (mapping figure A onto figure B), and they devoted more resources to processing the answer alternatives than did the high scorers. The pattern of results supports the view that high scorers tend to work in a more forward, or constructive, fashion, whereas lower scorers more often work backwards, using a response-elimination approach. Taken together, these findings converge to suggest specific aptitude-related differences in the representation and solution of standardized figural analogy problems. These differences bear some similarities to expert-novice differences in a number of other problem-solving domains.     

Giving up problem solving

How do people decide to abandon a problem? Participants were presented with unsolvable water jar problems, having been accurately informed of the prior probability of solvability. Across three experiments, we discovered effects of prior probability of solvability and of problem size (number of distinct problem states) on measures of effort and confidence. If a problem is more likely to be solvable and allows more problem states, a problem solver spends longer trying to solve the problem. Giving-up decisions are informed by the same judgments of probability of success and costs of solution that inform move-choice in a rational model of problem solving.     

The Effects of a Verbal and a Figural Creativity Training on Different Facets of Creative Potential

This study investigated the effects of different types of creativity interventions on different facets of creative potential, also including more school-related creativity demands. In a sample of 77 fourth-graders in the age between 9 and 12 years, we administered a verbal and a figural creativity training, realized in two school lessons over two consecutive days each. As outcome measures, creative potential in both the verbal and the figural domain by means of two well-established divergent thinking tasks was assessed. As additional measures of creative potential, a story completion task and a picture painting task were administered to examine training effects on more school-related types of creative behavior. The verbal training was found to increase both verbal and figural divergent thinking ability, but not creative potential in the story completion and the picture painting task. The figural training yielded significant training effects only regarding the picture painting task. Findings suggest a specific training effect of the figural creativity training, and moreover indicate that the verbal creativity training, rather than stimulating “verbal” creative abilities per se, was more strongly concerned with domain-general creativity processes including ideational fluency, flexibility, and originality that are characteristics of divergent thinking tasks across different domains.     

De-confusing the THOG problem: the Pythagorean solution.

Sources of facilitation for Needham and Amado's (1995) Pythagoras version of Wason's THOG problem were systematically examined in three experiments with 174 participants. Although both the narrative structure and figural notation used in the Pythagoras problem independently led to significant facilitation (40-50% correct), pairing hypothesis generation with either factor or pairing the two factors together was found to be necessary to obtain substantial facilitation (> 50% correct). Needham and Amado's original finding for the complete Pythagoras problem was also replicated. These results are discussed in terms of the "confusion theory" explanation for performance on the standard THOG problem. The possible role of labelling as a de-confusing factor in other versions of the THOG problem and the implications of the present findings for human reasoning are also considered.     

Figural after-effects, retinal size, and apparent size

The results of earlier experiments on the question of whether figural after-effects are affected by apparent as opposed to retinal size are shown to be inconclusive. A new hypothesis is proposed namely that both factors may be responsible for producing figural aftereffects, and four experiments have been made to test it. Situations were used in which the apparent sizes of the figures were determined by the size-constancy effect. It was found that where retinal sizes of test and inspection figures are the same and apparent sizes are different, figural after-effects in the direction which would be predicted on the basis of apparent sizes are obtained. It was further shown that where retinal and apparent sizes are in conflict, whether a figural after-effect is seen or not, and the direction of the figural after-effect, depends upon the balance between these two factors.     

A comparison of human performance in figural and navigational versions of the traveling salesman problem

Performance on a typical pen-and-paper (figural) version of the Traveling Salesman Problem was compared to performance on a room-sized navigational version of the same task. Nine configurations were designed to examine the use of the nearest-neighbor (NN), cluster approach, and convex-hull strategies. Performance decreased with an increasing number of nodes internal to the hull, and improved when the NN strategy produced the optimal path. There was no overall difference in performance between figural and navigational task modalities. However, there was an interaction between modality and configuration, with evidence that participants relied more heavily on the NN strategy in the figural condition. Our results suggest that participants employed similar, but not identical, strategies when solving figural and navigational versions of the problem. Surprisingly, there was no evidence that participants favored global strategies in the figural version and local strategies in the navigational version.     

Contraries as an effective strategy in geometrical problem solving

A focused review of the literature on reasoning suggests that mechanisms based upon contraries are of fundamental importance in various abilities. At the same time, the importance of contraries in the human perceptual experience of space has been recently demonstrated in experimental studies. Solving geometry problems represents an interesting case as both reasoning abilities and the manipulation of perceptual–figural aspects are involved.

In this study we focus on perceptual changes in geometrical problem solving processes in order to understand whether a mental manipulation in terms of opposites might help. Four conditions were studied, two of which concerned the search for contraries as an implicit or explicit strategy.

Results demonstrated that contraries, when used explicitly in solution processes, constitute an effective heuristic: The number of correct solutions increased, less time was needed to find a solution and participants were oriented towards the use of perception-based solutions—not only were perceptual solutions more frequent, but also, more specifically, the number of correct perceptual solutions increased. These last results concerning perception-based solutions were found both when participants were advised about the usefulness of the strategy and when they were not advised. Differences concerning which aspects of a problem were focused on during the solution process also emerged.     

Spatial problem solving and functional relations

Three experiments investigated the role of object knowledge on participants' ability to solve a spatial arrangement problem. The task was to rearrange six real-world three-dimensional objects so that their relative locations agreed with a given set of rules. The aim of the experiments was to tease out the relative extent to which object association, orientation, and object-specific functional relations affect performance on arrangement tasks. When the problem was presented vertically (objects arranged in piles), participants solved functional canonical versions of the problem significantly quicker than functional non-canonical versions both between (Experiments 1a and 2), and within subjects (Experiment 3). When the arrangement problem was presented horizontally (objects arranged flat in two rows), no significant differences in solution times were found between conditions (Experiments 1b and 2). Overall the results provide evidence for the importance of object-specific functional relations as a predictor of the solution time of spatial arrangement problems, although some differences were noted between single and multiple presentation of problems when specific rules within problems were rotated. The importance of functional information in memory as a constraint on the building of mental models and problem spaces is discussed.     

Social problem solving among popular and unpopular children

The present study investigated two issues related to children's social status and problem solving: the content of problem-solving measures and judgments of the quality of responses to social problems. Three types of social problem situations were studied: peer entry/initiation, maintaining social interaction, and management of conflict. The quality of children's strategies for solving these problems was rated on two dimensions: effectiveness and social competence. Liked-most children obtained significantly more effective and socially competent ratings than liked-least children for only one of the social problem situations-management of conflict. Significant differences between liked-most and liked-least children were also found between the quality of their best effective and best socially competent solution and their worst socially competent solutions. Results are discussed in terms of the psychometric adequacy of social problem-solving measures and the resultant problems in interpretation.This article is based on a doctoral dissertation submitted by the first author to the Graduate School, University of North Carolina-Chapel Hill. The first author appreciates the assistance of her dissertation committee: John Brantley, Donald Bailey, Barbara Goldman, and Rune Simeonsson. We also thank Carolyn Jackson, Alex Epanchin, Joanne Edelman, and the kindergarten teachers and assistants in Durham, North Carolina, for their help with data collection, Michael Fimian for his statistical help, Joanne Gartenmayer for her help with editing, and Karen Thigpen for her help with typing.     

Differences in induced brain activity during the performance of learning and working-memory tasks related to intelligence

Thirteen high intelligent (H-IQ) and 13 low intelligent (L-IQ) individuals solved two figural working-memory (WM) tasks and two figural learning tasks while their EEG was recorded. For the WM tasks, only in the theta band group related differences in induced event-related desynchronization/synchronization (ERD/ERS) were observed. L-IQ individuals displayed greater theta synchronization in the later phases of task completion (1000-2000 ms) as compared to H-IQ individuals. For the learning tasks group related differences in the three alpha bands were observed. In the upper alpha band L-IQ individuals showed greater ERD in the frontal brain areas, whereas H-IQ individuals displayed greater ERD in the parieto-occipital brain areas.     

Figural factors and the development of pictorial inferences

The role of figural characteristics in the development of pictorial inferences was examined. Two versions of 10 three-picture story sequences were presented to kindergarten and third-grade children. One version maximized while the other minimized figural similarity among pictures. After viewing the sequences, the children were asked to discriminate old study pictures and inferentially consistent new pictures from distractors. While the kindergarteners identified significantly fewer inference pictures than the third graders in all conditions, there was less difference between the grades in the figurally similar conditions. Overall, the kindergarteners identified the fewest inference pictures in the presence of distractors that figurally matched the study pictures. These results indicate that although the pictorial inferences drawn by kindergarteners are heavily influenced by figural representations, such figural dependency cannot account for all of the observed developmental differences.     

Investigating the effect of mental set on insight problem solving

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization.     

小学生图形推理策略发展特点的研究

本研究用我们修订的瑞文推理为材料,对145名儿童图形推理策略进行研究。结果发现：小学生在解决图形推理问题时使用六种策略,它们分别是分析策略、不完全分析策略、知觉分析策略、知觉匹配策略、格式塔策略和自主想象策略;不同年龄儿童在解决不同类型题目时的策略使用表现出不同的特点,儿童在解决数量规则题中,知觉分析策略在整个小学儿童阶段占主导地位,而在解决加减规则题中,分析策略占主导地位,随年龄增长而呈上升趋势;小学二年级开始出现图形推理能力发展的飞跃,二年级儿童开始能够同时观察到两种规则,五六年级儿童更能够不受题目形式的影响．而是从本质上把握逻辑规则。     

Abusive parents' perceptions of child problem behaviors: An example of parental bias

The behavior of children in 21 child abusive and 21 nonabusive matched comparison families were compared using home observations performed by professional independent observers and parental report measures (Becker Bipolar Adjective Checklist, Child Behavior Checklist, Parent Daily Report). Parental report measures of child conduct problems differed significantly between the two groups, independent observations showed few significant differences in rates of either child or parental behaviors. Results are discussed in terms of the validity of parental perceptions and reports of child problem behaviors, the informativeness of differing reports for diagnosis and clinical treatment, and the need to gather corroboration across various sources and settings before clinical decisions are made that may irrevocably alter a child's future development.     

Bicultural Effects on the Creative Potential of Chinese and French Children

This study examined possible bicultural effects on creative potential of children in four groups of Chinese and French children in Hong Kong and Paris. An international battery of widely used divergent measures (Wallach-Kogan Creativity Tests; WKCT) and newly constructed divergent-plus-integrative measures (Evaluation of Potential Creativity; EPoC) was established for assessment. Study 1 showed that most measures of WKCT and EPoC were reasonably high in reliability and they had expected correlations with the fluency scores of some subtests of Torrance Tests of Creative Thinking. Study 2 found some interestingly mixed bicultural effects favoring verbal divergent responses for French children and graphic integrative responses for Chinese children. Compared with Paris-French children, the bicultural Hong Kong-French children had significantly higher scores in figural fluency, figural flexibility, and figural uniqueness of WKCT (requiring only verbal divergent responses) but significantly lower scores in the graphic divergent-exploratory measure of EPoC. Compared with Hong Kong-Chinese children, the bicultural Paris-Chinese children had significantly higher scores in the graphic convergent-integrative measure of EPoC, but significantly lower scores in verbal fluency, verbal flexibility, figural fluency, figural flexibility, figural uniqueness, and figural unusualness of WKCT. Implications of the mixed bicultural effects in relation to the diverse creativity measures and children groups are discussed.     

The edge complex: implicit memory for figure assignment in shape perception

Viewing a stepped edge is likely to prompt the perceptual assignment of one side of the edge as figure. This study demonstrates that even a single brief glance at a novel edge gives rise to an implicit memory regarding which side was seen as figure; this edge complex enters into the figure assignment process the next time the edge is encountered, both speeding same-different judgments when the figural side is repeated and slowing these judgments when the new figural side is identical to the former ground side (Experiments 1A and 1B). These results were obtained even when the facing direction of the repeated edge was mirror reversed (Experiment 2). This study shows that implicit measures can reveal the effects of past experience on figure assignment, following a single prior exposure to a novel shape, and supports a competitive model of figure assignment in which past experience serves as one of many figural cues.     

Mathematical problem solving and working memory in children with learning disabilities: both executive and phonological processes are important

The purpose of this investigation was to explore the relationship between working memory (WM) and mathematical problem solving in children with learning disabilities (LD). Children with LD (age 11.5 years) were compared to chronologically age-matched (CA-M) and younger comprehension/computation achievement-matched children (age 8.9 years) on measures of verbal and visual-spatial WM, phonological processing, components of problem solving, and word-problem solving accuracy. The results showed that (1) children with LD were inferior on measures of word solution accuracy, components of problem solving, phonological processing, domain-general WM, and verbal WM when compared to children who were CA-M, (2) children with LD were comparable to younger children on all processing measures, except measures of domain-general WM, visual-spatial WM, phonemic deletion, and identifying problem goals, (3) measures of verbal and visual-spatial WM contributed significant variance to solution accuracy independent of phonological processing, and (4) the influence of WM on solution accuracy was mediated by long-term memory (LTM) processes related to the knowledge of algorithms. The results support the notion that information activated from LTM, rather than phonological processing, mediates the relationship between executive processing and solution accuracy in children with LD.     

Method of presentation and sex differences when using a revised figural drawing scale to measure body size estimation and dissatisfaction

The present study examined whether a revision of the Gardner, Jappe, and Gardner (2009) BIAS-BD figural drawing scale gave more accurate estimations of body size estimation and body dissatisfaction than a prior version. It also examined whether the order of figure presentation led to differing values for body size estimation and body dissatisfaction. The revised BIAS-BD scale included a continuous line beneath 17 figural drawings ordered in either ascending or descending size. Results were compared with previous studies using the original scale in which the 17 figural drawings were presented in a random order and, additionally, with a method using an adjustable video image by which the participants estimated their perceived body size by adjusting the width of their static image. The scale was presented to 330 undergraduate university students, including 199 women and 131 men. Overall, compared to BMIs calculated from the participants' reports of their height and weight, men and women participants gave less accurate estimations of body size using the revised scale when compared to the original BIAS-BD scale and video methodology. Participants reported significantly less body dissatisfaction than with the original scale. There was no significant difference in body size estimation when the figures were presented in ascending or descending size. Body dissatisfaction was greater for women than men, and when the figures were presented in descending order. Methodological considerations for using figural drawing scales in body image research are discussed.     

Retention of problem solutions: the re-solution effect

Four experiments compared the re-solution performance of prior solvers with that of prior nonsolvers given the correct solutions. Experiments 1 and 2 challenged Weisberg and Alba's (1981) contention that solving a problem and being shown the solution yield equivalent problem knowledge. In both experiments, students who initially solved problems showed near-perfect recall of the solutions after a 1-week delay, far superior to recall by students who had been shown the correct answers. In Experiment 3, solves showed poor solution retention when the connection between the problem and the solution was not meaningful. Experiment 4 showed that with meaningful problems, solvers and those merely provided with solutions have qualitatively different problem representations. The findings can be explained in terms of differential understanding of problems and their solutions.     

When insight just won't come: The failure of visual cues in the nine-dot problem

The nine-dot problem is a classic in the field of human problem solving. Cognitive accounts of the problem's difficulty have been criticized on the grounds that the experimental methods on which they rely for support involve a qualitative change to the task requirements of the problem. The three experiments reported here utilize visual and visual-procedural hints to examine the notion that its difficulty is rooted in a mismatch between problem shape and solution shape. Experiment 1 demonstrated that a perceptual cue to the shape of the solution in the form of shading gave rise to only minimal improvements in performance; an additional hint about the relevance of the shading gave rise to modest, but not statistically significant, improvements. Experiment 2 replicated these findings against an additional control condition in which a solely verbal hint to violate the perceptual boundary of the problem shape was given. Furthermore, when both the verbal and visual hints were provided, performance improved only slightly. Experiment 3 provided participants with experience in producing the shape of the correct solution in problem variants closely related to the nine-dot problem. Performance on the transfer task, the basic nine-dot problem, remained at floor, however. These data suggest that visual constraint relaxation is unlikely to be the sole process by which the insight required to find a solution is achieved. The results are interpreted in terms of a previously proposed computational model of performance.