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.     

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.     

Production of negative transfer in a problem-solving task

72 students solved two problems using a source problem designed to inhibit performance on the target problem relative to baseline performance when the target problem was solved alone. Both source and target problems shared surface similarity but were structurally dissimilar. Negative transfer was found for three different source and target combinations. The decreased performance below baseline for three of the source-target programs provides a reliable context to demonstrate negative transfer and facilitate continued investigation of this phenomenon.     

Facilitation and transfer with narrative thematic versions of the THOG task

This article reports two experiments investigating the use of narrative form in the presentation of thematic versions of Wason's (1977) THOG problem. Experiment 1 demonstrated that narrative thematic versions that use actions of characters to present the elements of the problem are easier to solve than the classic version. This result was found both for a problem that used thematic examples and for a problem that used the same geometric figures as the classic THOG. Results also suggested that the presence of a character who creates the comparison properties to be used in applying the disjunction rule was useful in separating those properties from the properties of the positive example. Experiment 2 demonstrated that the solution of a narrative thematic version of the THOG could lead to improved performance on the classic abstract THOG, but only when the examples in the narrative version were the geometric figures. Issues of transfer with the THOG problem are discussed.     

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.     

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。     

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.     

How analogies are generated: The roles of structural and superficial similarity

Laboratory studies of analogical reasoning have shown that subjects are mostly influenced by superficial similarity in the retrieval of source analogs. However, real-world investigations have demonstrated that people generate analogies using deep structural features. We conducted three experiments to determine why laboratory and real-world studies have yielded different results. In the first two experiments, we used a "production paradigm" in which subjects were asked to generate sources for a given target. Results show that the majority of the analogies that were generated displayed low levels of superficial similarity with the target problem. Moreover, most of the analogies were based on complex underlying structures. The third experiment used a "reception paradigm" methodology. The subjects had to retrieve predetermined sources instead of generate their own. In this case, retrieval was largely constrained by surface similarity. We conclude that people can use structural relations when given an appropriate task and that this ability has been underestimated in previous research on analogy.     

相似性、相似性组合及元认知监控对问题类比推理的影响研究

以改编Holyoak等设计的“汇聚问题”为实验材料,同时自编元认知监控问卷测试被试的元认知监控水平,考察相似性的不同水平,源问题个数,两个源问题情境下源问题的组合方式以及被试的元认知监控水平对类比迁移的影响。结果表明,一个源问题呈现情境下,源、靶问题不同的相似性水平差异显著,表面相似性显著促进类比迁移;两个源问题呈现情境下,源问题的不同组合方式差异显著;无论是呈现一个源问题,还是呈现两个源问题,元认知监控差异均显著,类比迁移主要是控制性加工;源问题个数差异显著。     

Analogical transfer: From schematic pictures to problem solving

A series of experiments was conducted to explore whether individuals can solve problems by transferring conceptual information gained from schematic pictures and to examine the mechanisms involved in this transfer process. Subjects viewed a schematic picture and then attempted to solve an insight problem to which the conceptual information from the picture could be applied. The results indicate that the degree of similarity—specifically, superficial and procedural similarity—between a source schematic picture and the target problem determined transfer performance. Discussion focuses on the relationship between these two types of similarity and the two key cognitive components involved in transferring pictorial analogies to solve problems: accessing the pictorial analogues and executing the solutions. Portions of this research were presented at the 33rd meeting of the Psychonomic Society in St. Louis, November 1992.     

Transfer of conditional reasoning: Effects explanations and initial problem types

Transfer of reasoning on Wason's (1966) selection task was explored in three experiments. Experiment 1 tested the effects of problem explanations and verbalization instructions on transfer from abstract or thematic problems to abstract problems. Explanations facilitated transfer only when the initial problems were abstract; verbalization did not produce transfer between problems. Experiment 2 explored the effects of problem similarity and explanations on transfer between problems. Although transfer occurred following explanations, no effect of similarity was found for thematic problems. In both of these experiments, the thematic effect (Wason & Shapiro, 1971) was observed. Experiment 3 examined the effects of explanations to abstract or thematic problems on transfer to subsequent abstract or thematic problems. Transfer of reasoning occurred from both initial problem types, particularly to problems of the same type; however, transfer occurred to a greater extent from abstract problems than from thematic problems. The results are discussed in terms of problem similarity and Cheng and Holyoak's (1985) pragmatic reasoning schema hypothesis.     

Reducing cognitive complexity in a hypothetico-deductive reasoning task

The confusion/non-consequential thinking explanation proposed by Newstead, Girotto, and Legrenzi (1995) for poor performance on Wason's THOG problem (a hypothetico-deductive reasoning task) was examined in three experiments with 300 participants. In general, as the cognitive complexity of the problem and the possibility of non-consequential thinking were reduced, correct performance increased. Significant but weak facilitation (33-40% correct) was found in Experiment 1 for THOG classification instructions that did not include the indeterminate response option. Substantial facilitation (up to 75% correct) was obtained in Experiment 2 with O'Brien et al.'s (1990) one-other-THOG classification instruction. In Experiment 3, a revised version of O'Brien et al.'s pre-test problem format also led to substantial facilitation, even with the use of the standard three-choice THOG classification instruction. These findings are discussed in terms of Newstead et al.'s theoretical proposal and possible attentional factors.     

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.     

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.     

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.     

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.     

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.     

Naming the parents of the THOG: Mental representation and reasoning

It was hypothesized that subjects misrepresent the THOG problem by confusing data and hypotheses. An abstract version of the problem in which the given exemplars and the hypothetical ones were designated by two different labels was used in three experiments. Experiment 1 showed that this version elicits a better performance than the standard version of the problem. Experiments 2 and 3 confirmed these results, by ruling out a possible alternative account of the facilitatory effect obtained in Experiment 1. The present results are discussed in relationship to the general issues of content effects and non-consequentialism in reasoning.     

阅读保持的类比结构映射效应研究

探讨文章阅读过程中类比结构映射效应与共同元素效应对阅读信息保持的迁移作用,包括两个实验,实验Ｉ探讨前阅读的源文章与目标文章在结构上与命题上的共同性对目标文章信息保持的迁移效果,结果表明,前后阅读文献的结构共同目标文章的保持有显著的促进作用,命题共同的促进作用不显著,实验２进一步探讨在源文章与目标文章结构或命题有共同性的情况下,提示与否对目标文章的信息保持效果的影响作用,结果证明,有两种情况下,提示     

THOG问题的演译结构及其非Wason-Brooks判定方法

本文探讨THOG问题的演绎结构及其非Wason-Brooks判断方法,据于Wason-Brooks判断程序和THOG问题逻辑结构的分析导致如下结论：1．Wason-BrooksTHOG判定方法并非判定THOG的唯一方法;2、被试选择那一种演绎判定模式取决于被试如何对原问题进行等效表征转换;3．判断失败可能意味着被试存在短时记忆容量障碍或者等效表征转换障碍。