Induction of Relational Schemas: Common Processes in Reasoning and Complex Learning

Five experiments were performed to test whether participants induced a coherent representation of the structure of a task, called a relational schema, from specific instances. Properties of a relational schema include: An explicit symbol for a relation, a binding that preserves the truth of a relation, potential for higher-order relations, omnidirectional access, potential for transfer between isomorphs, and ability to predict unseen items in isomorphic problems. However relational schemas are not necessarily coded in abstract form. Predictions from relational schema theory were contrasted with predictions from configural learning and other nonstructural theories in five experiments in which participants were taught a structure comprised of a set of initial-state,operator → end-state instances. The initial-state,operator pairs were presented and participants had to predict the correct end-state. Induction of a relational schema was achieved efficiently by adult participants as indicated by ability to predict items of a new isomorphic problem. The relational schemas induced showed the omnidirectional access property, there was efficient transfer to isomorphs, and structural coherence had a powerful effect on learning. The “learning to learn” effect traditionally associated with the learning set literature was observed, and the long-standing enigma of learning set acquisition is explained by a model composed of relational schema induction and structure mapping. Performance was better after reversal of operators than after shift to an alternate structure, even though the latter entailed more overlap with previously learned tasks in terms of the number of configural associations that were preserved. An explanation for the reversal shift phenomenon in terms of induction and mapping of a relational schema is proposed. The five experiments provided evidence supporting predictions from relational schema theory, and no evidence was found for configural or nonstructural learning theories.     

Schema induction in problem solving: a multidimensional analysis

The present research examined the processes of schema formation in problem solving. In 4 experiments, participants experienced a series of tasks analogous to A. S. Luchins' (1942) water jar problems before attempting to solve isomorphic target problems. Juxtaposing illustrative source instances varying in procedural features along multiple dimensions promoted the construction of a general schema that facilitated solving an isomorphic problem requiring a novel procedure. Exposure to less variant problems led to faster initial learning, but narrower and fixed schemas (mental set), whereas exposure to variant procedures led to slower initial learning, but broader and more flexible schemas. The findings support the dimensional specificity hypothesis: Generalization along 1 dimension facilitates transfer to a target problem differing from the source problems in that dimension.     

Schema induction and analogical transfer

An analysis of the process of analogical thinking predicts that analogies will be noticed on the basis of semantic retrieval cues and that the induction of a general schema from concrete analogs will facilitate analogical transfer. These predictions were tested in experiments in which subjects first read one or more stories illustrating problems and their solutions and then attempted to solve a disparate but analogous transfer problem. The studies in Part I attempted to foster the abstraction of a problem schema from a single story analog by means of summarization instructions, a verbal statement of the underlying principle, or a diagrammatic representation of it. None of these devices achieved a notable degree of sucess. In contrast, the experiments in Part II demonstrated that if two prior analogs were given, subjects often derived a problem schema as an incidental product of describing the similarities of the analogs. The quality of the induced schema was highly predictive of subsequent transfer performance. Furthermore, the verbal statements and diagrams that had failed to facilitate transfer from one analog proved highly beneficial when paired with two. The function of examples in learning was discussed in light of the present study.     

Cue redundancy and extra logical inferences in a deductive reasoning task

This study investigated the influence of extraexperimental knowledge on deductive reasoning. Two groups of subjects solved modified abstract or concrete versions of Wason’s (1966) four-card selection problem in which the “if-then” implication rule provided the sole cue to underlying logical structure. Six other groups solved abstract or concrete comparison problems in which additional information was supplied by varying the relationship between antecedents and consequents in a manner consistent with logical structure. Selection responses and subjects’ explanations were analyzed using log-linear models of data arrayed in multiway contingency tables. Results showed improved performance for concrete over abstract problems and for both abstract and concrete problems that included relational information. Subjects capitalized upon the redundancy between the implication rule and the relational cues to reason effectively with either abstract or concrete stimuli.     

Timing of schema activation and memory: Inhibited access to inconsistent information

In the present experiment, recognition of consistent and inconsistent information was measured as a function of time of schema activation. A schema was either activated before or after encoding, or not at all. Schema activation after encoding reduced recognition of inconsistent information while schema activation before encoding enhanced it (in comparison to the no schema control condition). Recognition of consistent information appeared to be unaffected by time of schema activation. It is argued that an a posteriori activated schema inhibits access to inconsistent information. In the Discussion a tentative theoretical explanation is provided.     

不同概化的问题原型对问题归类和解决的影响

探讨原理学习过程中形成不同概化程度／问题原型对解决不同适宜程度问题的影响。实验1探讨个体形成不同概化程度问题原型对解决表面内容不同适宜程度的问题的效果;实验2探讨形成不同概化程度问题原型的被试解决问题的信息加工方式与机制;实验3进一步探讨形成不同概化程度问题原型的个体解决复杂问题的效果与机制。结果表明：(1)形成概化程度较高的问题原型有利于个体对表面内容不适宜题目的解答;(2)形成概化程度较高问题原型的被试在解答适宜或不适宜问题时均能迅速激活问题原型而通达原理图式,因此,更多地采用图式的方法解决问题;(3)形成概化程度较高的问题原型会有助于被试排除题目的无关信息,正确进行解答。     

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.     

Pragmatic reasoning schemas

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.     

The belief-bias effect in the production and evaluation of logical conclusions

In this study, we examined whether adult subjects' beliefs regarding the empirical truth of a conclusion affected their production as well as their evaluation of a logical conclusion in a reasoning task. In addition, the relation between the ability to resolve an abstract reasoning problem correctly and the effect of belief-bias was examined. The subjects were given one of four paper-and-pencil reasoning tasks, two of them using an evaluation paradigm, and two of them using a production paradigm. Each paradigm comprised either neutral problems or belief problems. The neutral problems were constructed to be as similar as possible to the belief problems, in order to control for extraneous factors. All four tasks also included an abstract reasoning problem. The results indicate a significant belief-bias effect for both the evaluation and the production tasks. Qualitative analysis indicated that the belief-bias effect was more pervasive in the production condition. In addition, the belief-bias effect was found to exist independently of the subjects' abstract reasoning ability. The results are discussed with reference to a two-stage model, in which belief is used to resolve uncertainties in inferentially produced conclusions.     

Explaining away the negative effects of evaluation on analogical transfer: the perils of premature evaluation

Four experiments explored effects on analogical transfer of evaluating solutions to base problems. In contrast to reports of positive effects of explanation, evaluation consistently reduced transfer rates and impaired mental representations of base material. This effect was not ameliorated by encoding for a later memory test, summarizing, or engaging in similar processes at encoding and recall. However, providing a prior explanation task removed the inhibitory effect of evaluation. It appears that evaluation leads to encoding of extraneous material that interferes with access to solution-critical analogous information. Prior explanation inoculates against negative effects on transfer by ensuring that new information introduced via evaluation is organized around existing representations of relevant information of the base problem. The results suggest that the source of difficulty in analogical transfer may reside not only in retrieval and mapping but also in the initial encoding of problems.     

Permission schemas and the selection task

Cheng and Holyoak's abstract permission schema version of Wason's selection task and the standard abstract version of the task were examined in two experiments, each a factorial design with type of problem (permission vs. standard), presence or absence of a checking context, explicit or implicit negatives on the not-p and not-q cards, and presence or absence of a rule clarification statement as factors. The original permission problem violation-type instruction was employed in Experiment 1, and Margolis's not-p and not-q violation instruction (Griggs & Jackson, 1990) was used in Experiment 2. Subjects were 640 university undergraduates, with each subject solving only one problem. The major findings for permission tasks were: (1) facilitation for the abstract permission version was replicated but found to be dependent upon the presence of explicit negatives on the not-p and not-q cards; and (2) this facilitation was enhanced by the Margolis not-p and not-q instruction. Per Girotto, Mazzocco, and Cherubini (1992), these findings and the observed error patterns are consistent with pragmatic schema theory. The major findings for the standard version of the task were: (1) none of the factors significantly impacted proportion correct [performance was poor, ≦10% correct in 15 of 16 conditions] and (2) the number of not-p & not-q incorrect selections was increased significantly for the not-p and not-q instruction. These results are discussed in terms of Manktelow and Over's argument that the standard abstract task and the permission schema version are actually different problems.     

Learning Strategies and Transfer in the Domain of Programming

We report two studies involving an intelligent tutoring system for Lisp (the Camegie Mellon University Lisp Tutor). In Experiment 1, we developed a model, based on production system theories of transfer and analogical problem solving, that accounts for effects of instructional examples, the transfer of cognitive skills across programming problems, and practice effects. In Experiment 2, we analyzed protocols collected from subjects as they processed instructional texts and examples before working with the Lisp Tutor and protocols collected after subjects solved each programming problem. The results suggest that the acquisition of cognitive skills is facilitated by high degrees of metacognition, which includes higher degrees of monitoring states of knowledge, more self-generated explanation goals and strategies, and greater attention to the instructional structure. Improvement in skill acquisition is also strongly related to the generation of explanations connecting the example material to the abstract terms introduced in the text, the generation of explanations that focus on the novel concepts, and spending more time in planning diminishing returns. Finally, reflection on problem solutions that focus on understanding the abstractions underlying programs or that focus on understanding how programs work seems to be related to improved learning.     

样例的编码方式对问题解决迁移的影响及心理机制

以概率原理为材料,通过两个实验考察了样例的编码方式对问题解决迁移的影响及其心理机制。实验1探讨了样例的变异性与不同的自我解释模式结合对被试解决不同程度迁移问题的影响;实验2运用大声思维技术,进一步探讨不同样例的变异性和不同自我解释模式编码样例的条件下学习者的学习活动和问题解决的特点。结果表明:样例的变异性和诱发自我解释模式结合能有效地促进原理图式的获得和迁移;自我解释对理解原理和获得原理的概化图式有着重要作用。不同的学习者自我解释的特征并不一致,存在着个体差异。     

Organizational factors in picture recognition memory

Since humans have been shown to have a large capacity for dealing with pictures but not for more abstract forms of visual information, it follows that humans must rely on existing mental structures in picture recognition tasks. A series of experiments were designed to examine some characteristics of that structure. The results indicate that something analogous to categories exists for pictures and that when subjects view pictures they tag these categories. The decision in a recognition task that they have or have not seen a picture appears to be based on whether or not an existing category has been tagged. For example, the results indicate subjects can detect a new picture as new with a high degree of certainty. Further, the results show that subjects use information contained in or associated with the new member of the pair in a forced-choice procedure for deciding which member of the pair is old. Since other research has shown that figure-ground ratings made by one group of subjects is a reliable predictor of errors for subjects ranging in age from five to adult, there is evidence that whatever the exact nature of these categories they are not only common between individuals but are established at a very early age.     

Concept learning,memory and transfer of dot pattern categories

In the first experiment, subjects rated the similarity of a sample of pairs of random dot patterns generated from 3 prototypes consisting of either 4, 6, or 9 dots. The results of the experiment tended to confirm the structure imposed on the patterns by the construction method. In the second experiment, subjects learned to classify random patterns generated from 2 prototypes with either short or long interprototype distance and consisting of either 4, 6, or 9 dots in a traditional concept identification task. After acquisition, memory for old and new distortions and the prototype, which was not presented during learning, was assessed. The tendency to call a pattern “new” increased with the distance between the pattern and its prototype. In a subsequent transfer test, all subjects saw patterns of either 4, 6, or 9 dots. Performance was above chance and the transfer from larger to smaller patterns tended to be greater than the transfer from smaller to larger patterns. This is consistent with a process of schema formation based on features common to most exemplars of the category. The results are discussed in relation to several theories of concept learning and schema abstraction.     

To What Extent Do Pragmatic Reasoning Schemas Affect Performance on Wason's Selection Task?

Cheng and Holyoak's (1985) most persuasive evidence for pragmatic reasoning schema theory has been the finding that an abstract permission version of Wason's selection task yields higher rates of solution than a nonpragmatic control. Experiment 1 presented two problem sets, one modelled after Cheng and Holyoak's abstract permission problem, which is relativley rich in extraneous features, and one after Wason's, relatively impoverished, standard problem. Each problem set varied type of rule (permission, obligation, or nonpragmatic) and task type (to reason from or about a rule). Results revealed that enriched problems were solved more often than impoverished ones, that reasoning-from problems were solved more often than reasoning-about problems, and that there was a beneficial interaction between enriching features and the permission rule. Experiment 2 demonstrated that although explicit negatives were crucial for solution of reasoning-from permission problems, they played no role in solution of enriched nonpragmatic-rule problems. Experiment 3 provided a replication of the enriched reasoning-from permission problem, again revealed no beneficial effect for obligation-rule problems, and further revealed no influence of instructions to provide brief written justifications. We argue that the results show that the scope of pragmatic reasoning schema theory needs to be narrowed, that although a permission rule does have an effect, an obligation rule does not, and that some beneficial task features are independent of anything explained by pragmatic reasoning schema theory.     

Evidence for abstract, schematic knowledge of three spatial diagram representations

Spatial diagram representations such as hierarchies, matrices, and networks are important tools for thinking. Our data suggest that college students possess abstract schemas for these representations that include at least rudimentary information about their applicability conditions. In Experiment 1, subjects were better able to select the appropriate spatial diagram representation for a problem when cued to use general category information in memory about those representations than when cued to use specific example problems given during the experiment. The results of Experiment 2 showed that the superior performance in the general category condition was not based on a comparison of the test problems with examples in memory. The results of Experiment 3 showed that the superior performance was not due to learning that occurred during the experiment or to transfer appropriate processing. The General Discussion section considers the nature of students' representation schemas and the question of why college students have only rudimentary schemas for common and widely applicable diagrammatic representations.     

Justification effects on the judgment of analogy

Many of us share a strong intuition that justification forces us to better understand the situations we face. And there is substantial evidence indicating that this is often the case. However, there is a growing body of research showing that, under certain circumstances, explanation and justification can impair performance on a variety of cognitive tasks. In the present research, the effects of justification on judgment of the soundness of analogies were examined. Subjects judged the quality of the match between pairs of stories with varying degrees of superficial and analogical similarity. Experimental subjects either provided reasons for their judgments or wrote recollections of the target stimuli. These subjects rated the match between stimulus pairs as more sound than did control subjects. Also, providing reasons led to poorer discrimination between superficially similar aspects of the stimuli and analogous aspects. Explanations of these findings are proposed, and implications for problem solving and confidence judgment are discussed.     

Antimnemonic effects of schemas in young and older adults

Schema-consistent material that is aligned with an individual’s knowledge and experience is typically more memorable than abstract material. This effect is often more extreme in older adults and schema use can alleviate age deficits in memory. In three experiments, young and older adults completed memory tasks where the availability of schematic information was manipulated. Specifying nonobvious relations between to-be-remembered word pairs paradoxically hindered memory (Experiment 1). Highlighting relations within mixed lists of related and unrelated word pairs had no effect on memory for those pairs (Experiment 2). This occurred even though related word pairs were recalled better than unrelated word pairs, particularly for older adults. Revealing a schematic context in a memory task with abstract image segments also hindered memory performance, particularly for older adults (Experiment 3). The data show that processing schematic information can come with costs that offset mnemonic benefits associated with schema-consistent stimuli.