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.     

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.     

Both attentional control and the ability to make remote associations aid spontaneous analogical transfer

Given the widespread belief that analogical processing is an important mechanism for creative problem solving, despite the rarity of spontaneous transfer in laboratory studies, a critical direction for future research is to address which abilities may allow for the spontaneous analogizing between distant (superficially dissimilar) sources and targets. This study explores the role of individual differences in attentional control and the ability to make remote associations and their possible combined effects on spontaneous analogical transfer. Participants attempted to solve Duncker's radiation problem after having been exposed to a distant source as part of an earlier task. Results indicated that both measures of attentional control and the ability to make remote associations uniquely predicted spontaneous transfer between a superficially dissimilar source and target. Further, a critical role was seen for the quality of the representation of the source analog on the likelihood of transfer. The present results affirm that the likelihood of spontaneous transfer depends critically on the quality of the representation for the source, but also suggest that individual differences in the ability to make remote associations may be more conducive to constructing a broader representation of that source than individual differences in attentional control.     

Having the memory of an elephant: long-term retrieval and the use of analogues in problem solving

The authors report 4 experiments exploring long-term analogical transfer from problem solutions in folk tales participants heard during childhood, many years before encountering the target problems. Substantial culture-specific analogical transfer was found when American and Chinese participants' performance was compared on isomorphs of problems solved in European versus Chinese folk tales. There was evidence of transfer even among participants who did not report being reminded of the source tale while solving the target problem. Comparisons of different versions of a target problem indicated that similarity of solution tool affected accessing, mapping, and executing components of problem solving, whereas similarity of goal object had only a moderate effect on accessing. High school students also evidenced greater transfer than did middle school students.     

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.     

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.     

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.     

Analogical transfer, problem similarity, and expertise

When we encounter a new problem, we are often reminded of similar problems solved earlier and may use the solution procedure from an old problem to solve a new one. Such analogical transfer, however, has been difficult to demonstrate empirically, even within a single experimental session. This article proposes a framework for conceptualizing analogical problem solving that can account for the conflicting findings in the literature. In addition, the framework leads to two predictions concerning the transfer behavior of experts and novices. These predictions concern both positive and negative transfer and are based on the different types of features included in the problem representations of experts and novices. First, when two problems share structural features but not surface features, spontaneous positive transfer should be more likely in experts than in novices. Second, when two problems share surface but not structural features, spontaneous negative transfer should be stronger for novices than for experts. These predictions were supported by the results of three experiments involving college students solving a complex arithmetic word problem.     

儿童问题解决中的类比迁移

儿童问题解决中的类比迁移是儿童认知发展中的一个基本问题,但在儿童发展研究中却一直没有得到足够的重视。在对儿童问题解决中的类比迁移研究进行回顾和总结的基础上,特别是仔细分析最近十年里的类比迁移研究,该文总结出了儿童问题解决中类比迁移研究的发展趋势,主要包括从探讨迁移是否存在到验证迁移是一种早期能力、从关注迁移的年龄差异到关注促进迁移的有关因素、从关注迁移是否是基本能力到关注迁移的加工机制、从描述迁移技能到领域概化、从关注近迁移到关注远迁移。最后,该文对未来儿童问题解决中的类比迁移研究进行了展望     

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.     

Using dual-process theory and analogical transfer to explain facilitation on a hypothetico-deductive reasoning task

Using the analogical transfer paradigm, the present study investigated the competing explanations of Girotto and Legrenzi (Psychological Research 51: 129–135, 1993) and Griggs, Platt, Newstead, and Jackson (Thinking and Reasoning 4: 1–14, 1998) for facilitation on the SARS version of the THOG problem, a hypothetico-deductive reasoning task. Girotto and Legrenzi argue that facilitation is based on logical analysis of the task [System 2 reasoning in Evans’s (Trends in Cognitive Sciences 7: 454–459, 2003) dual-process account of reasoning] while Griggs et al. maintain that facilitation is due to an attentional heuristic produced by the wording of the problem (System 1 reasoning). If Girotto and Legrenzi are correct, then System 2 reasoning, which is volitional and responsible for deductive reasoning, should be elicited, and participants should comprehend the solution principle of the THOG task and exhibit analogical transfer. However, if Griggs et al. are correct, then System 1 reasoning, which is responsible for heuristic problem solving strategies such as an attentional heuristic, should occur, and participants should not abstract the solution principle and transfer should not occur. Significant facilitation (68 and 82% correct) was only observed for the two SARS source problems, but significant analogical transfer did not occur. This lack of transfer suggests that System 1 reasoning was responsible for the facilitation observed in the SARS problem, supporting Griggs et al.’s attentional heuristic explanation. The present results also underscore the explanatory value of using analogical transfer rather than facilitation as the criterion for problem understanding.     

The unique contributions of the facilitation of procedural memory and working memory to individual differences in intelligence

Individual differences in working memory account for a substantial portion of individual differences in complex cognitive processes (e.g., comprehension) and fluid intelligence. However, a large portion of the variance in fluid intelligence and comprehension is unexplained. The current investigation was conducted to evaluate whether individual differences in the facilitation of procedural memory accounts for unique variance in intelligence not accounted for by working memory. To measure variability in the facilitation of procedural memory, we used a task that required participants to first classify exemplars of two categories; facilitation was then operationalized by subsequent improvements in the speed of classifying new exemplars from those categories (i.e., an operation-specific memory procedure). Three measures of each focal construct (facilitation in procedural memory, working memory, comprehension and fluid intelligence) were administered to 256 participants. We used structural equation modeling to examine the relationships among these latent variables. Working memory did account for variance in fluid intelligence and comprehension, but most important, individual differences in facilitation of procedural memory accounted for unique variance in fluid intelligence and comprehension.     

The use of diagrams in analogical problem solving

In four experiments, we examined the impact of perceptual properties on the effectiveness of diagrams in analogical problem solving, using variants of convergence diagrams as source analogues for the radiation problem. Static diagrams representing the initial problematic state (one large line directed at a target) and the final state for a convergence solution (multiple converging lines) were not accessed spontaneously but were often used successfully once a hint to consider the diagram had been provided. The inaccessibility of static diagrams was not alleviated by adding additional diagrams to represent intermediate states (Experiment 1), but spontaneous access was improved by augmenting static diagrams with a verbal statement of the convergence principle (Experiment 3). Spontaneous retrieval and noticing were increased markedly by animating displays representing converging forces and thereby encouraging encoding of the lines as indicating motion toward a target (Experiments 3 and 4). However, neither static nor animated diagrams were effective when the arrows were reversed to imply divergence rather than convergence (Experiment 2). The results indicate that when animation encourages the interpretation of a diagram as a helpful source analogue, it can greatly enhance analogical transfer.     

Analogical priming via semantic relations

Research on semantic memory has often tacitly treated semantic relations as simple conduits for spreading activation between associated object concepts, rather than as integral components of semantic organization. Yet conceptual relations, and the role bindings they impose on the objects they relate, are central to such cognitive tasks as discourse comprehension, inference, problem solving, and analogical reasoning. The present study addresses the question of whether semantic relations and their bindings can influence access to semantic memory. The experiments investigated whether, and under what conditions, presenting a prime pair of words linked by 1 of 10 common semantic relations would facilitate processing of a target pair of words linked by the same relation. No effect was observed when participants merely read the prime; however, relational priming was observed under instructions to note and use the semantic relations. Participants were faster at making a lexical decision or naming a word on a related pair of target words when that pair was primed with an analogously related pair of words than when the prime pair consisted of either two unrelated words or two words linked by some other relation. This evidence of analogical priming suggests that under an appropriate strategic set, lexical decisions and naming latencies can be influenced by a process akin to analogical mapping.     

大学生学科问题类比迁移的实验研究

考察了单个和两个源问题条件下大学生学科问题类比迁移的情况。实验1考察表面特性对学科问题迁移成绩的影响,以及个体的时间控制、解题策略。实验2考察两个源问题表面相似关系和思路归纳关系对迁移成绩的影响。结果表明：1)表面相似性对迁移成绩影响显著,同领域学科问题之间更容易迁移;2)依据表面和依据结构来激活源问题都是有效策略．源问题学习时间与迁移效果之间不存在显著关系;3)思路归纳对迁移成绩影响显著。     

Spontaneous analogical transfer in 4-year-olds: a microgenetic study

The purpose of the current microgenetic study was to examine children's spontaneous application of analogical problem solving from story problems to physical tasks. Thirty-six 4-year-olds (M=54.7 months), randomly assigned to an experimental or a control condition, participated. The results indicate that 4-year-old children did, with varying success, spontaneously apply analogical solutions to physical problems across sessions. A positive effect over time on children's spontaneous analogical problem solving was found. Additionally, a few children even gave an analogical strategy-related explanation for their own physical behavior. There was much inter- and intra-individual variability, which may indicate that 4 years of age is a period of change in the development of analogical reasoning.     

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.     

基于问题解决式的类比推理的老化：表面相似性和结构相似性的作用

采用2年龄(老年/年轻)×2表面相似性(高/低)×2结构相似性(高/低)三因素混合设计, 考察表面信息和结构信息在基于问题解决范式的类比推理老化中的作用。结果发现, 老年人的类比推理成绩显著差于年轻人。源问题和靶问题的表面相似性和结构相似性的提高, 会促进个体检索源问题, 并提高推理质量。对于老年人而言, 表面相似性更重要; 对于年轻人而言, 结构相似性更重要。     

Facilitation and analogical transfer in the THOG task

This study was concerned with Wason's THOG task, a hypothetico-deductive reasoning problem for which performance is typically very poor (<20% correct). Recently, however, Needham and Amado (1995) and Koenig and Griggs (2004) have observed both facilitation and spontaneous analogical transfer effects for the Pythagoras version of this task. Based on their findings, Koenig and Griggs concluded that in addition to the separation of the data (the properties of the designated THOG) from the hypotheses that need to be generated (the possible combinations of properties written down), an explicit request to generate these hypotheses is necessary to obtain significant analogical transfer. In the present study we extended the generalisability of this conclusion in three experiments with 214 undergraduate participants using O'Brien et al.'s (1990) Blackboard version of the task. We discuss the relationship of the results to dual process theories of reasoning and propose that analogical transfer may be a better criterion than task facilitation for judging participants' task understanding.     

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.