Relations as transformations: implications for analogical reasoning

We present two experiments assessing whether the size of a transformation instantiating a relation between two states of the world (e.g., shrinks) is a performance factor affecting analogical reasoning. The first experiment finds evidence of transformation size as a significant factor in adolescent analogical problem solving while the second experiment finds a similar effect on adult analogical reasoning using a markedly different analogical completion paradigm. The results are interpreted as providing evidence for the more general framework that cognitive representations of relations are best understood as mental transformations.     

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.     

Relations as transformations: Implications for analogical reasoning

We present two experiments assessing whether the size of a transformation instantiating a relation between two states of the world (e.g., shrinks) is a performance factor affecting analogical reasoning. The first experiment finds evidence of transformation size as a significant factor in adolescent analogical problem solving while the second experiment finds a similar effect on adult analogical reasoning using a markedly different analogical completion paradigm. The results are interpreted as providing evidence for the more general framework that cognitive representations of relations are best understood as mental transformations.     

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.     

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 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.     

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.     

The effects of similarity of theme and instantiation in analogical reasoning.

The influence of 2 types of structural similarity on analogical reasoning was examined. The theme of a story is a structural component that constrains other relationships in the story. Another structural component is the way in which the theme is implemented. Participants received pairs of stories that varied in the similarity of these two components. Participants in Experiment 1 judged stories containing similar themes as more analogous than stories with dissimilar themes. Likewise, stories with similar implementations were judged as more analogous than stories with dissimilar implementations. Experiment 2 revealed a similar pattern when participants had the opportunity to transfer information from source to target stories. Greater transfer was seen for stories with similar themes than for stories with dissimilar themes. Greater transfer was also seen for stories with similar implementations of different themes than for stories with different implementations.     

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.     

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.     

Dual-process theories of reasoning: The test of development

Dual-process theories have become increasingly influential in the psychology of reasoning. Though the distinction they introduced between intuitive and reflective thinking should have strong developmental implications, the developmental approach has rarely been used to refine or test these theories. In this article, I review several contemporary dual-process accounts of conditional reasoning that theorize the distinction between the two systems of reasoning as a contrast between heuristic and analytic processes, probabilistic and mental model reasoning, or emphasize the role of metacognitive processes in reflective reasoning. These theories are evaluated in the light of the main developmental findings. It is argued that a proper account of developmental phenomena requires the integration of the main strengths of these three approaches. I propose such an integrative theory of conditional understanding and argue that the modern dual-process framework could benefit from earlier contributions that made the same distinction between intuition and reflective thinking, such as Piaget’s theory.     

Different time courses of integrative semantic processing for plural and singular nouns: implications for theories of sentence processing

The research investigated the time course of integrative semantic processing during sentence processing. Reading time was measured on sentences containing an NP composed of an adjective and a noun whose combined meaning was plausible or anomalous (Experiment 1) or was typical or atypical (Experiment 2). The noun in the NP was either plural or singular. Plural nouns were expected to be more rapidly integrated with a preceding adjective than singular nouns because plural nouns can be ruled out as the first noun in a noun compound more rapidly than singular nouns. The results confirmed this prediction, showing that the effects of semantic plausibility and typicality were observed immediately during the processing of plural nouns, but were observed at a delay following the processing of singular nouns. Implications for theories of sentence processing are discussed.     

Children's development of analogical reasoning: insights from scene analogy problems

We explored how relational complexity and featural distraction, as varied in scene analogy problems, affect children's analogical reasoning performance. Results with 3- and 4-year-olds, 6- and 7-year-olds, 9- to 11-year-olds, and 13- and 14-year-olds indicate that when children can identify the critical structural relations in a scene analogy problem, development of their ability to reason analogically interacts with both relational complexity and featural distraction. Error patterns suggest that children are more likely to select a distracting object than to make a relational error for problems that present both possibilities. This tendency decreases with age, and older children make fewer errors overall. The results suggest that changes in analogical reasoning with age depend on the interplay among increases in relational knowledge, the capacity to integrate multiple relations, and inhibitory control over featural distraction.     

Hierarchical models for relational event sequences

Interaction within small groups can often be represented as a sequence of events, each event involving a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner—we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics from 297 sessions.     

An evaluation of dual-process theories of reasoning

Current theories propose that reasoning comprises two underlying systems (Evans & Over, 1996; Sloman, 1996; Stanovich & West, 2000). The systems are identified as having functionally distinct roles, differ according to the type of information encoded, vary according to the level of expressible knowledge, and result in different responses. This article evaluates the arguments and the evidence from a select number of key tasks that have been supportive of dual-reasoning theorists' proposals. The review contrasts the dualist approach with a single-system framework that conjectures that different types of reasoning arise through the graded properties of the representations that are utilized while reasoning, and the different functional roles that consciousness has in cognition. The article concludes by arguing in favor of the alternative framework, which attempts to unify thedifferent forms of reasoning identified by dual-process theorists under a single system.     

The impact of semantic distance and induced stress on analogical reasoning: A neurocomputational account

In a study of reasoning with four-term verbal analogy problems, we explored the relationship between the effects of an acute, mild stressor and the complexity of the reasoning process. Participants judged whether analogy problems in the form A:B :: C:D were valid or invalid, on the basis of whether the relation in the A:B term matched that in the C:D term. Half of the problems contained a C:D pair semantically near the A:B pair (e.g., NOSE:SCENT :: TONGUE:TASTE), and the other half contained ones semantically far from A:B (e.g., NOSE:SCENT :: ANTENNA:SIGNAL). After an initial block without stress, participants were randomly assigned to count backward by 13?s from 1,000 while being told to go faster, or to count forward by 1?s from 0. The stress-induced participants reported a significant increase in state anxiety as compared to controls immediately after the mental arithmetic task. Stressed participants performed less accurately (as measured by d') on both near and far analogy problems, mainly due to an increase in false alarms. We were able to model the influence of semantic distance using the ??learning and inference with schemas and analogies?? (LISA) model. Our findings indicated that even mild increases in stress impair analogical reasoning. However, the decrement does not seem to directly involve the integration of relations, but rather is due to a shift in decision strategy: Under stress, people show an increased tendency to endorse analogies as valid when the terms in the individual pairs are semantically related to each other, even if the overall analogical relationship is not valid.     

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.     

Deciding between theories of how reasoning develops is hard

Although Sloutsky agrees with our interpretation of our data, he argues that the totality of the evidence supports his claim that children make inductive generalisations on the basis of similarity. Here we take issue with his characterisation of the alternative hypotheses in his informal analysis of the data, and suggest that a thorough Bayesian analysis, although practically very difficult, is likely to result in a more finely balanced outcome than he suggests.     

Introduction to the special section on the neural substrate of analogical reasoning and metaphor comprehension

The special section on the neural substrate of relational reasoning includes 4 articles that address the processes and brain regions involved in analogical reasoning (Green, Kraemer, Fugelsang, Gray, & Dunbar, 2011; Maguire, McClelland, Donovan, Tillman, & Krawczyk, 2011) and in metaphor comprehension (Chettih, Durgin, & Grodner, 2011; Prat, Mason, & Just, 2011). We see this work as an example of how neuroscience approaches to cognition can lead to increased understanding of cognitive processes. In this brief introduction, we first situate the 4 articles in the context of prior cognitive neuroscience work on relational reasoning. We then highlight the main issues explored in these articles: different sources of complexity and difficulty in relational processing, potential differences between the roles of the 2 hemispheres, and the impact of individual differences in various cognitive abilities. The 4 articles illustrate a range of methodologies, including functional magnetic resonance imaging (fMRI; Green et al., 2011; Prat et al., 2011), event-related potentials (ERPs; Maguire et al., 2011), and different types of semantic priming (Chettih et al., 2011; Prat et al., 2011). They highlight the connections between research on analogy and on metaphor comprehension and suggest, collectively, that a cognitive neuroscience approach to relational reasoning can lead to converging conclusions.