The development of analogical reasoning processes.

Two experiments were conducted to test the generalizability to children of a theory of analogical reasoning processes originally proposed for adults (R. J. Sternberg, Psychological Review, 1977a, 84, 353–378; R. J. Sternberg, Intelligence, information processing, and analogical reasoning: The componential analysis of human abilities, Hillsdale, N.J.: Lawrence Erlbaum Associates, 1977b) and to examine the development of analogical reasoning processes in terms of five proposed sources of cognitive development: (a) availability of component operations; (b) strategy for combining multiple component operation; (c) strategy for combining multiple executions of the same component operation; (d) consistency in use of strategy; (e) component-operation latency and difficulty. Between 15 and 21 subjects in each of grades 2, 4, 6, and adulthood (ages 8, 10, 12, and 19 years, respectively) were tested in their ability to solve analogies of systematically varied difficulty. Performance was measured in terms of latencies for items solved correctly, latencies for all items solved, and error rates. A slightly modified version of the Stenberg, 1977(a), Stenberg, 1977(b) theory was found to be applicable to the data for each of the age levels tested. In analogies with perceptually separable attributes, change over age was found in sources (d) and (e) noted above. In analogies with perceptually integral attributes, change over age was found in sources (a), (c), (d), and (e). Developmental trends were discussed in terms of past theory and findings, and possible reasons for differences in developmental patterns between the two kinds of analogies were suggested.     

Automatic activation of categorical and abstract analogical relations in analogical reasoning

We examined activation of concepts during analogical reasoning. Subjects made either analogical judgments or categorical judgments about four-word sets. After each four-word set, they named the ink color of a single word in a modified Stroop task. Words that referred to category relations were primed (as indicated by longer response times on Stroop color naming) subsequent to analogical judgments and categorical judgments. This finding suggests that activation of category concepts plays a fundamental role in analogical thinking. When colored words referred to analogical relations, priming occurred subsequent to analogical judgments, but not to categorical judgments, even though identical four-word stimuli were used for both types of judgments. This finding lends empirical support to the hypothesis that, when people comprehend the analogy between two items, they activate an abstract analogical relation that is distinct from the specific content items that compose the analogy.     

Surface and structural similarity in analogical transfer

Two experiments investigated factors that influence the retrieval and use of analogies in problem solving, Experiment 1 demonstrated substantial spontaneous analogical transfer with a delay of several days between presentation of the source and target analogues. Experiment 2 examined the influence of different types of similarity between the analogues. A mechanism for retrieval of source analogues is proposed, based on summation of activation from features shared with a target problem. The results of Experiment 2 indicated that both structural features, which play a causal role in determining possible problem solutions, and salient surface features, which do not have a causal role, influence spontaneous selection of an analogue. Structural features, however, have a greater impact than do surface features on a problem solver’s ability to use an analogue once its relevance has been pointed out.     

The role of representations in age differences in analogical reasoning

Age-related declines in the efficiency of a number of cognitive tasks have been postulated to be attributable to decreases with age in the quality of internal representations used to mediate performance on those tasks. This proposal was investigated in a geometric analogies task by manipulating variables (i.e., the number of elements per term and the temporal delay between presentation of pairs of terms) assumed to affect the quality or stability of internal representations. As expected, the performance of older adults was impaired more than that of young adults by these manipulations. Further analyses revealed that these representational deficits may be due to a reduction of approximately 40% in the quantity of some type of processing resource between, approximately, 20 and 70 years of age.     

Neural correlates of creativity in analogical reasoning

Brain-based evidence has implicated the frontal pole of the brain as important for analogical mapping. Separately, cognitive research has identified semantic distance as a key determinant of the creativity of analogical mapping (i.e., more distant analogies are generally more creative). Here, we used functional magnetic resonance imaging to assess brain activity during an analogy generation task in which we varied the semantic distance of analogical mapping (as derived quantitatively from a latent semantic analysis). Data indicated that activity within an a priori region of interest in left frontopolar cortex covaried parametrically with increasing semantic distance, even after removing effects of task difficulty. Results implicate increased recruitment of frontopolar cortex as a mechanism for integrating semantically distant information to generate solutions in creative analogical reasoning.     

The implications of processing event sequences for theories of analogical reasoning

Sternberg (1977a, 1977b) has proposed a componential theory of information processing on analogies. The current study attempts convergent validation of the basic findings in verbal analogies by a method that is based on different underlying assumptions. Although the data were generally consistent with Sternberg’s theory, the data indicated thatapplication is better described by two separate events. Furthermore, the extent of individual differences in strategy models was so substantial that a higher level processing operation, such as control strategies, should be postulated, rather than to support a single-strategy model as characterizing Analogy solving.     

Structural constraints and object similarity in analogical mapping and inference

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent.     

Tracking cognitive phases in analogical reasoning with event-related potentials

Analogical reasoning consists of multiple phases. Four-term analogies (A:B::C:D) have an encoding period in which the A:B pair is evaluated prior to a mapping phase. The electrophysiological timing associated with analogical reasoning has remained unclear. We used event-related potentials to identify neural timing related to analogical reasoning relative to perceptual and semantic control conditions. Spatiotemporal principal-components analyses revealed differences primarily in left frontal electrodes during encoding and mapping phases of analogies relative to the other conditions. The timing of the activity differed depending upon the phase of the problem. During the encoding of A:B terms, analogies elicited a positive deflection compared to the control conditions between 400 and 1,200 ms, but for the mapping phase analogical processing elicited a negative deflection that occurred earlier and for a shorter time period, between 350 and 625 ms. These results provide neural and behavioral evidence that 4-term analogy problems involve a highly active evaluation phase of the A:B pair.     

Components of analogical reasoning in a mildly head injured population

This study sought to investigate the effects of mild head injury on a particular type of cognitive ability, verbal analogical reasoning. The performance of 19 individuals with head injuries was compared to a group of 30 control subjects matched for age, education, and gender on 100 verbal analogies. Solution times and error rates were modeled. Unstandardized regression weights for individual subjects were correlated with subjects’ performance on a number of standardized ability tests. Results showed that compared to the control subjects, the head injured subjects: (a) were significantly slower to solve the analogies, and were particularly slow to perform certain processes: encoding/inference and comparison; (b) tended to show greater variability in performance; and (c) had data that had a poorer componential model fit. The data suggest that analogical reasoning is affected by a head injury, and that certain information processes may be responsible for performance deficits.     

Relational integration, inhibition, and analogical reasoning in older adults

The difficulty of reasoning tasks depends on their relational complexity, which increases with the number of relations that must be considered simultaneously to make an inference, and on the number of irrelevant items that must be inhibited. The authors examined the ability of younger and older adults to integrate multiple relations and inhibit irrelevant stimuli. Young adults performed well at all but the highest level of relational complexity, whereas older adults performed poorly even at a medium level of relational complexity, especially when irrelevant information was presented. Simulations based on a neurocomputational model of analogical reasoning, Learning and Inference with Schemas and Analogies (LISA), suggest that the observed decline in reasoning performance may be explained by a decline in attention and inhibitory functions in older adults.     

The ABCs of analogical abilities: Evidence for formal analogical reasoning abilities in 24‐month‐olds

Solving formal analogy problems requires the identification of an initial term and the transformation that occurs between the initial two terms as well as the determination of the final term. Experiment 1 tested 24‐month‐olds' ability to determine final terms when they were shown the initial term and told the transformation that was to occur. Children selected their responses from an array of two principled distracters. The children were able to determine the correct final term when they were given information about the initial term and transformation. Experiment 2 tested 24‐month‐olds' ability to solve final‐term problems, partial analogies, and complete analogies. The children solved all the three types of problems.     

Object encoding, goal similarity, and analogical transfer

Although the importance of goal similarity and similarity of encoding are well known in analogical transfer literature, there has never been a study in which one of these factors was maintained constant and the other manipulated. This point was studied in our first experiment. The results show that the interaction between the two factors is not significant. However, the width of the credibility intervals suggests that it is difficult to conclude that there is either a presence or an absence of an interaction. The second experiment concerned more directly the impact of the encoding process on recognition of analogy. The results show that analogical transfer can be highly dependent on the way subjects interpret problems and that the encoding process can be influenced by the visual characteristics of the problems. These results can be related to a recent body of research on the importance of interpretive effects on analogy, as well as to the categorization literature.     

Melting chocolate and melting snowmen: analogical reasoning and causal relations

Children's performance in the classical a:b::c:d analogy task is traditionally very poor prior to the Piagetian stage of formal operations. The interpretation has been that the ability to reason about higher-order relations (the relations between the a:b and c:d parts of the analogy) is late-developing. However, an alternative possibility is that the relations used to date in the analogies are too difficult for younger children. Two experiments presented children aged 3, 4 and 6 years with a:b::c:d analogies which were based on relations of physical causality such as melting and cutting, for example chocolate bar:melted chocolate::snowman:melted snowman. Understanding of these particular causal relations is known to develop between the ages of 3 and 4 years. It was found that even 3-year-olds could solve the classical analogies if they understood the causal relations on which they were based.     

Using analogical mapping to simulate time-course phenomena in perceptual similarity

We present a computational model of visual similarity. The model is based upon the idea that perceptual comparisons may utilize the same mapping processes as are used in analogy. We use the Structure Mapping Engine (SME), a model of Gentner’s structure-mapping theory of analogy, to perform comparison on representations that are automatically generated from visual input. By encoding visual scenes incrementally and sampling the output of SME at multiple stages in its processing, we are able to model not only the output of similarity judgments, but the time course of the comparison process. We demonstrate the model’s effectiveness by replicating the results from three psychological studies that bear on the time course of comparison.     

The facilitatory effect of negative feedback on the emergence of analogical reasoning abilities

This paper focuses on the development of analogical reasoning abilities in 5‐ and 6‐year‐old children. Our particular interest relates to the way in which analogizing is influenced by the provision of task‐based feedback coupled with a self‐explanation requirement. Both feedback and self‐explanation provide children with opportunities to engage in self‐reflective thinking about the process of analogical reasoning. To examine the role of such metacognitive factors in analogical strategy development the reported study combined a proportional analogy paradigm with a small‐scale microgenetic approach involving multiple testing sessions over a restricted time period. The key manipulation involved exposing participants either to the correct or incorrect analogy completions of another reasoner that they were then asked to explain. The data revealed that the development of an effective analogizing strategy embodying a ‘relational shift’ from superficial to relational responding was modulated by the feedback condition that the child was placed in, with a negative feedback intervention providing the greatest developmental benefit. We suggest that the value of negative feedback for the acquisition of analogical reasoning abilities derives from the way in which a self‐reflective analysis of the reasons for erroneous responses sensitizes the child to a deeper understanding of how to make effective relational mappings.     

Higher-order structure and relational reasoning: contrasting analogical and thematic relations

A popular explanation of younger children's success in analogy tasks is that lower-level associative reasoning strategies are used. Younger children are said to have a primarily associative understanding of analogy, with the ability to coordinate sets of relations largely emerging later in development (Goldman, Pellegrino, Parseghian, & Sallis, 1982; Sternberg & Nigro, 1980). One way of testing the associative claim is to pit young children's emergent analogical abilities against thematic (associative) relations, which are known to play an important role in the knowledge structures of young children. The present experiments presented 4-, 5- and 9-year-old children with a:b::c:d analogies in a picture choice format, offering a choice between Analogy and Thematic responses. Only the Analogy responses were correct in terms of the higher-order structure of the analogies. The results showed that the Analogy responses were consistently preferred to the Thematic responses by children of all ages. It is concluded that analogy is an important building block for learning from an early age.     

The effects of relational structure on analogical learning

Relational structure is important for various cognitive tasks, such as analogical transfer, but its role in learning of new relational concepts is poorly understood. This article reports two experiments testing people’s ability to learn new relational categories as a function of their relational structure. In Experiment 1, each stimulus consisted of 4 objects varying on 2 dimensions. Each category was defined by two binary relations between pairs of objects. The manner in which the relations were linked (i.e., by operating on shared objects) varied between subjects, producing 3 logically different conditions. In Experiment 2, each stimulus consisted of 4 objects varying on 3 dimensions. Categories were defined by three binary relations, leading to six logically different conditions. Various learning models were compared to the behavioral data, based on the theory of schema refinement. The results highlight several shortcomings of schema refinement as a model of relational learning: (1) it can make unreasonable demands on working memory, (2) it does not allow schemas to grow in complexity, and (3) it incorrectly predicts learning is insensitive to relational structure. We propose schema elaboration as an additional mechanism that provides a more complete account, and we relate this mechanism to previous proposals regarding interactions between analogy and representation construction. The current findings may advance understanding of the cognitive mechanisms involved in learning and representing relational concepts.     

Interpretation of instructions: A source of individual differences in analogical reasoning

Two studies were conducted to identify individual differences in the effect of instruction on strategies used to solve figural/numerical analogies. In Study 1, students aged 9, 11, 13, and 19 years were given incomplete instructions and then were assessed for (a) consistent use of an appropriate rule for solving analogies and (b) the type and number of stimulus attributes that are incorporated in those analogical rules. Use of an analogical rule increased with age and corresponded to higher scores on a psychometric test of reasoning within each age group. In Study 2, analysis of verbal protocols was used to identify the strategies of some 9- and 11-year-olds who showed a peculiar pattern of responding in Study 1. These children attended to relevant attributes but used systematic nonanalogical rules to solve problems. When provided with more specific instructions, most of these children adopted an analogical rule but failed to incorporate relevant attributes. Results indicate that selection or construction of task-relevant solution strategies from incomplete instructions may partially account for differential performance on tests of analogical reasoning.