Enabling spontaneous analogy through heuristic change

Despite analogy playing a central role in theories of problem solving, learning and education, demonstrations of spontaneous analogical transfer are rare. Here, we present a theory of heuristic change for spontaneous analogical transfer, tested in four experiments that manipulated the experience of failure to solve a source problem prior to attempting a target problem. In Experiment 1, participants solved more source problems that contained an additional financial constraint designed to signal the inappropriateness of moves that maximized progress towards the goal. This constraint also led to higher rates of spontaneous analogical transfer to a superficially similar problem. Experiments 2 and 3 showed that the effects of this constraint extend to superficially and structurally different analogs. Experiment 4 generalized the finding to a non-analogous target problem that also benefitted from inhibiting maximizing moves. The results indicate that spontaneous transfer can arise through experience during the solution of a source problem that alters the heuristic chosen for solving both analogical and non-analogical target problems.     

The testing effect and analogical problem-solving

Researchers generally agree that retrieval practice of previously learned material facilitates subsequent recall of same material, a phenomenon known as the testing effect. There is debate, however, about when such benefits transfer to related (though not identical) material. The current study examines the phenomenon of transfer in the domain of analogical problem-solving. In Experiments 1 and 2, learners were presented a source text describing a problem and solution to read which was subsequently either restudied or recalled. Following a short (Experiment 1) or long (Experiment 2) delay, learners were given a new target text and asked to solve a problem. The two texts shared a common structure such that the provided solution for the source text could be applied to solve the problem in the target text. In a combined analysis of both experiments, learners in the retrieval practice condition were more successful at solving the problem than those in the restudy condition. Experiment 3 explored the degree to which retrieval practice promotes cued versus spontaneous transfer by manipulating whether participants were provided with an explicit hint that the source and target texts were related. Results revealed no effect of retrieval practice.     

Intention and outcome: key components of causal structure facilitating mapping in children's analogical transfer.

The consequences of two key features of causal structure in source stories, intention and positive outcome, for analogical transfer were examined in kindergarten and second graders. In Experiment 1, children received either structure-complete, structure-incomplete, or irrelevant source stories. Structure-incomplete stories lacked either the intention to solve a problem (a goal-directed component), evidence of a successful consequence (an outcome-related component), or both as part of the solution activity described in source stories. Evidence for transfer was obtained for second graders when a goal-directed component, and to a lesser extent, an outcome-related component were connected to the solution action in source stories. Differences among conditions for kindergartners were less evident, although they revealed a pattern of performance similar to the second graders. A second experiment was conducted to determine whether memory and an orientation to use the source story information might account for these findings. Efforts to ensure memory for and hints to use information in the source stories, however, did not benefit solution transfer when intention and positive outcome were absent. These results suggest that a complete causal structure, including goal and outcome, in source stories augments transfer in young children by promoting mapping of the analogical relationship between source stories and the target problem.     

Analogical transfer in the THOG task

The influences of surface and structural similarity on analogical transfer were examined with 318 undergraduate participants in four experiments using Needham and Amado's (1995) Pythagoras THOG problem as the source problem and Wason's standard abstract THOG task as the target problem. In Experiments 1-3, systematic changes in surface similarity between the source and target problems were introduced by changing the named exemplar, the dimensional values, and the dimensions, respectively, in the target problem. Significant transfer was obtained in all three experiments. In Experiment 4, we explored the basis of this transfer by examining three versions of the Pythagoras THOG problem, factorially combining its facilitating features as source problems. Results indicated that the inclusion of a hypothesis generation request was necessary for significant transfer. The implications of our findings for using transfer versus facilitation as the performance criterion for deductive reasoning are considered.     

Reducing structural-element salience on a source problem produces later success in analogical transfer: What role does source difficulty play?

Two experiments in reasoning by analogy were conducted to study the role of inducing source difficulty by reducing the salience of the source's structural elements. Three nonexclusive hypotheses were tested. According to the first, a difficult source problem improves analogical transfer because it increases the probability that the subject will notice the similarity between the source and the target. For example, errors made on both the source and the target can enhance the subject's awareness of the similarity between the two problems. According to the second hypothesis, a source that is difficult to solve is memorized better than an easier source. According to the third, source-problem difficulty affects the degree of abstractness in the representation of the solution elaborated by subjects. Experiment 1 showed that the higher frequency of spontaneous transfer between the source and the target when the source problem was difficult (Gick & McGarry, 1992) could be replicated in a cued-transfer situation. Experiment 2 showed that subjects given a difficult source, one in which the important element was not very salient, were better at categorizing isomorphic problems on the basis of structural features than were subjects given an easy source. The discussion deals with the implications of these results for the hypotheses tested and, more generally, for reasoning by analogy and education in general.     

Les erreurs commises lors de la résolution du problème source favorisent-elles le transfert analogique ? Un réexamen de la recherche de Gick et McGarry (1992)

Gick and McGarry (1992) show that inducing source problem difficulty by reducing the salience of its structural elements improves analogical transfer. According to them, this result is explained by similarities between mistakes made when solving the difficult source and target mistakes. In this study, we replicate Gick and McGarry study in order to do an analysis, not made by the authors, in the aim of testing the role of mistakes in analogical transfer. Our results replicate the effects Gick and McGarry observed, but show that theses effects are not explained by mistakes made on the source problem.     

Analogical problem solving

The use of an analogy from a semantically distant domain to guide the problemsolving process was investigated. The representation of analogy in memory and processes involved in the use of analogies were discussed theoretically and explored in five experiments. In Experiment I oral protocols were used to examine the processes involved in solving a problem by analogy. In all experiments subjects who first read a story about a military problem and its solution tended to generate analogous solutions to a medical problem (Duncker's “radiation problem”), provided they were given a hint to use the story to help solve the problem. Transfer frequency was reduced when the problem presented in the military story was substantially disanalogous to the radiation problem, even though the solution illustrated in the story corresponded to an effective radiation solution (Experiment II). Subjects in Experiment III tended to generate analogous solutions to the radiation problem after providing their own solutions to the military problem. Subjects were able to retrieve the story from memory and use it to generate an analogous solution, even when the critical story had been memorized in the context of two distractor stories (Experiment IV). However, when no hint to consider the story was given, frequency of analogous solutions decreased markedly. This decrease in transfer occurred when the story analogy was presented in a recall task along with distractor stories (Experiment IV), when it was presented alone, and when it was presented in between two attempts to solve the problem (Experiment V). Component processes and strategic variations in analogical problem solving were discussed. Issues related to noticing analogies and accessing them in memory were also examined, as was the relationship of analogical reasoning to other cognitive tasks.     

Accessing source information in analogical problem-solving

Several studies showed that people presented with source information fail to apply it to an analogous target problem unless they are instructed to use the source. Seven experiments were carried out to assess whether such a lack of spontaneous transfer occurs because individuals do not activate the source during the target task or because they do not realize the source-target relationship. Experiment 1 compared a condition in which the source was activated with no cue about the source-target connection to conditions in which subjects were informed about this connection. Results suggested that the lack of spontaneous transfer does not depend on failure in activating source information. Experiments 2, 3, and 4 were devised to falsify this finding by activating the source closer and closer to the target and by focusing participants' attention toward the relevant aspects of the source. Experiments 5, 6, and 7 were aimed at stressing source-target correspondences by introducing surface similarities. All experiments showed that the mere activation of the source does not facilitate analogical transfer. Results suggested that two processes should be distinguished in the access phase of analogical problem-solving: Source retrieval and identification of the source-target connection.     

Finding faults: analogical comparison supports spatial concept learning in geoscience

A central issue in education is how to support the spatial thinking involved in learning science, technology, engineering, and mathematics (STEM). We investigated whether and how the cognitive process of analogical comparison supports learning of a basic spatial concept in geoscience, fault. Because of the high variability in the appearance of faults, it may be difficult for students to learn the category-relevant spatial structure. There is abundant evidence that comparing analogous examples can help students gain insight into important category-defining features (Gentner in Cogn Sci 34(5):752–775, 2010). Further, comparing high-similarity pairs can be especially effective at revealing key differences (Sagi et al. 2012). Across three experiments, we tested whether comparison of visually similar contrasting examples would help students learn the fault concept. Our main findings were that participants performed better at identifying faults when they (1) compared contrasting (fault/no fault) cases versus viewing each case separately (Experiment 1), (2) compared similar as opposed to dissimilar contrasting cases early in learning (Experiment 2), and (3) viewed a contrasting pair of schematic block diagrams as opposed to a single block diagram of a fault as part of an instructional text (Experiment 3). These results suggest that comparison of visually similar contrasting cases helped distinguish category-relevant from category-irrelevant features for participants. When such comparisons occurred early in learning, participants were more likely to form an accurate conceptual representation. Thus, analogical comparison of images may provide one powerful way to enhance spatial learning in geoscience and other STEM disciplines.     

Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving

Background. High school and college students demonstrate a verbal, or textual, advantage whereby beginning algebra problems in story format are easier to solve than matched equations ( Koedinger & Nathan, 2004 ). Adding diagrams to the stories may further facilitate solution ( Hembree, 1992 ; Koedinger & Terao, 2002 ). However, diagrams may not be universally beneficial ( Ainsworth, 2006 ; Larkin & Simon, 1987 ). Aims. To identify developmental and individual differences in the use of diagrams, story, and equation representations in problem solving. When do diagrams begin to aid problem‐solving performance? Does the verbal advantage replicate for younger students? Sample. Three hundred and seventy‐three students (121 sixth, 117 seventh, 135 eighth grade) from an ethnically diverse middle school in the American Midwest participated in Experiment 1. In Experiment 2, 84 sixth graders who had participated in Experiment 1 were followed up in seventh and eighth grades. Method. In both experiments, students solved algebra problems in three matched presentation formats (equation, story, story + diagram). Results. The textual advantage was replicated for all groups. While diagrams enhance performance of older and higher ability students, younger and lower‐ability students do not benefit, and may even be hindered by a diagram's presence. Conclusions. The textual advantage is in place by sixth grade. Diagrams are not inherently helpful aids to student understanding and should be used cautiously in the middle school years, as students are developing competency for diagram comprehension during this time.     

The role of causal models in analogical inference

Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs and in particular on shared higher order relations. In contrast, work in philosophy of science suggests that analogical inference is also guided by causal models of the source and target. In 3 experiments, the authors explored the possibility that people may use causal models to assess the strength of analogical inferences. Experiments 1-2 showed that reducing analogical overlap by eliminating a shared causal relation (a preventive cause present in the source) from the target increased inductive strength even though it decreased similarity of the analogs. These findings were extended in Experiment 3 to cross-domain analogical inferences based on correspondences between higher order causal relations. Analogical inference appears to be mediated by building and then running a causal model. The implications of the present findings for theories of both analogy and causal inference are discussed.     

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 perceptually represented structure in analogical problem solving

Current models of analogical reasoning assume that representations of source examples and target problems occur in an amodal format--that is, a representation whose construction and processing are independent of activity in the perceptual and motor cortices of the brain. We examined the possible use of kinesthetic information--perceptual structures associated with the sensation of space and force--in the representation of source examples and target problems. Participants who recreated a source story while acting out the key elements were more likely to access the story when later working on the target problem than were participants who only verbally recreated the story or who verbally recreated it as well as sketched it. We argue that enactment made kinesthetic and spatial features more salient in participants' source story representations and that this aided performance. These results suggest that current models of analogical reasoning might be improved by including perceptual information as part of their representational schemes.     

An eye movement analysis of the spatial contiguity effect in multimedia learning

In three studies, eye movements of participants were recorded while they viewed a single-slide multimedia presentation about how car brakes work. Some of the participants saw an integrated presentation in which each segment of words was presented near its corresponding area of the diagram (integrated group, Experiments 1 and 3) or an integrated presentation that also included additional labels identifying each part (integrated-with-labels group, Experiment 2), whereas others saw a separated presentation in which the words were presented as a paragraph below the diagrams (separated group, Experiments 1 and 2) or as a legend below the diagrams (legend group, Experiment 3). On measures of cognitive processing during learning, the integrated groups made significantly more eye-movements from text to diagram and vice versa (integrative transitions; d = 1.65 in Experiment 1, d = 0.85 in Experiment 2, and d = 1.44 in Experiment 3) and significantly more eye-movements from the text to the corresponding part of the diagram (corresponding transitions; d = 2.02 in Experiment 1 and d = 1.35 in Experiment 3) than the separated groups. On measures of learning outcome the integrated groups significantly outperformed the separated groups on transfer test score in Experiment 1(d = .80) and Experiment 2 (d = .73) but not in Experiment 3 (d = .35). Spatial contiguity encourages more attempts to integrate words and pictures and enables more successful integration of words and pictures during learning, which can result in meaningful learning outcomes.     

Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.     

Analogical problem solving: a hierarchical analysis of procedural similarity

Similarity between source analogues and target problems is a central theme in the research on analogical transfer. Much of the theorizing and research has focused on the effects of superficial and structural similarity on transfer. The present research is an attempt to analyze systematically another critical type of similarity, namely, procedural similarity, and to examine its effects on the executing process. Participants viewed a schematic picture as a source model, interpreted its conceptual meaning, and then attempted to solve a problem to which the conceptual information from the source model could be applied. The results indicate that the ease with which a source solution was implemented was largely determined by the abstraction level at which a solution was shared by a source analogue and the target problem. The degree of procedural similarity was also found to influence the executing process in analogical transfer. A conceptual model concerning the function of procedural similarity as a utilizational constraint in analogical problem solving is proposed.     

Analogical reasoning in 2-year-olds: The development of access and relational inference

Eighty-four 24- and 30-month-old children were tested with two analogy tasks: formal and problem solving. Experiment 1 included three Groups: relations specified, relations unspecified, and associative control (no exposure to base relations). In Experiment 2 the relation that linked that a- and b-terms in formal problems was explicitly shown in order to reduce relational inference demands. In Experiment 1, children responded systematically to the formal problems when given two chances to answer each question. In Experiment 2, children were systematic on their first responses. In the problem-solving task the rates of spontaneous analogies produced were similar to those seen in older children. However, unlike older children, 2-year-olds benefited minimally from prompts. We believe this may indicate that 2-year-olds have difficulty explicitly controlling their analogical activity. We conclude early analogical abilities may be limited by weak relational inference abilities and difficulty intentionally initiating access.     

The effect of body and part-based motion on the recognition of unfamiliar objects

We investigated the role of global (body) and local (parts) motion on the recognition of unfamiliar objects. Participants were trained to categorise moving objects and were then tested on their recognition of static images of these targets using a priming paradigm. Each static target shape was primed by a moving object that comprised either the same body and parts motion; same body, different parts motion; different body, same part motion as the learned target or was non-moving. Only the same body but not the same part motion facilitated shape recognition (Experiment 1), even when either motion was diagnostic of object identity (Experiment 2). When parts motion was more related to the object's body motion then it facilitated the recognition of the static target (Experiment 3). Our results suggest that global and local motions are independently accessed during object recognition and have important implications for how objects are represented in memory.