Effects of principle explanation and superficial similarity on analogical mapping in problem solving.

When solving a problem, people often make use of an earlier problem by mapping the objects from the earlier problem to the current one. Three experiments varied the superficial similarity between study and test problems to discriminate 2 views of the mapping process: direct mapping and near miss. Subjects studied 4 probability principles and study problems and solved test problems. The mapping of earlier problems on the basis of superficial similarity would lead to incorrect answers. In Experiment 1, evidence was found for the direct mapping view: Test problems with more similar objects to the study problems were more likely to be (inappropriately) mapped. However, in Experiment 2, in which the principle explanation was embedded in the study problem, this effect was reversed. In Experiment 3, 2 explanations for the differences in effect were contrasted. The discussion focuses on how principle explanation may affect analogical problem solving. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Schema induction in children's analogical problem solving.

Three experiments were conducted to explore the ability of school-age children to transfer solutions to analogous problems. This research addressed the issue of how the variability of procedural features in source examples facilitates the induction of a general problem schema and, thus, promotes subsequent transfer. Children were asked to solve a series of problems analogous to A. S. Luchins's (1942) classic waterjar problems. All the problems shared a common isomorphic structure and a general solution but required either similar or different specific procedures. Children who experienced problems with variant procedural features were more likely than those who experienced problems with invariant procedural features to construct a general problem schema and to solve novel problems requiring unfamiliar procedures. This research sheds light on the cognitive mechanisms involved in strategy generalization and analogical problem solving. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive load, schema acquisition, and procedural adaptation in nonisomorphic analogical transfer.

Cognitive load theory was explored in 3 conditions among 96 3rd graders in nonisomorphic transfer. In 1 condition, both goal attainment and problem-space exploration were emphasized on each acquisition trial. In a 2nd condition, problem-space exploration was emphasized, whereas goal attainment was not. In a 3rd condition, goal attainment was emphasized, but the problem-space was explored only until an error occurred on each trial. All children solved 2 analogs of the missionaries/cannibals problem and transferred to an analog of the jealous husbands problem. Children in the 2nd condition made fewer errors and required less time than the other groups on the 1st move in transfer, which is taken to reflect the quality of the base attained during acquisition. On later moves, children in Conditions 1 and 2 outperformed those in Condition 3. Thus, children in the 1st 2 conditions were better able to adjust the base to the target. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Training and transfer in combinatorial problem solving: The development of formal reasoning during early adolescence.

Studied training and transfer effects in combinatorial problem solving to explore the emergence of combinatorial competence as an aspect of the development of formal reasoning and to examine the effectiveness of a training procedure based on principles of "programmed discovery." 80 12-14 yr olds participated in a pretest, 2 training or placebo sessions, an immediate posttest, and a delayed posttest 2 mo later. Significant increases in combinatorial skill with age were shown, and the expression of this skill was significantly facilitated if problems involved "concrete" material of low complexity. With the oldest Ss, training produced significant improvements in performance on combinatorial tasks that were markedly different from the training items in both content and modality. Significant improvements over time and with practice were also evident with the older Ss. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Inductive problem solving: Schema inducement and memory-based transfer.

Studies of delayed transfer have been infrequent in contemporary work (M. L. Gick and K. J. Holyoak, 1987). Studies of immediate transfer by G. D. Phye (1986, 1987; see also PA, Vol 77:3557) have identified a general schema and a procedural schema as the basis for the transfer of analogical reasoning skills. This study addresses the question of memory-based processing when transfer is delayed. Ss were 183 college students. The training-for-transfer paradigm used to study immediate transfer was employed. Results indicate the use of both a general and a specific schema for retrieval when memory-based processing is required in order to demonstrate transfer within a problem domain. These data replicate and extend Phye's previous findings identifying induced schemata as a part of the architectural basis for cognitive transfer. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of solving related proofs on memory and transfer in geometry problem solving.

Three experiments investigate the relationship between memory and problem solving in the domain of geometry theorem proving. In Exp 1, Ss' memories for an original problem-solving episode were interfered with retroactively by solving a 2nd problem that had the same diagram, but no memory effects were observed that depended on the 2nd problem's logical similarity to the original. Results suggest that the diagram is the basis for geometry problem-solving memories. Exps 2 and 3 investigated problem-solving memories in use by examining Ss' transfer to a 3rd (test) problem. As with the memory results, transfer was reduced when the 1st 2 problems had the same diagram relative to when they had 2 different diagrams. Transfer was reduced most in the condition with the greatest proportion of memory-interfering steps. Results suggest that the structure and quality of problem-solving memories affect problem-solving transfer. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

From beyond to within their grasp: The rudiments of analogical problem solving in 10- and 13-month-olds.

Four experiments were conducted to assess infants' ability to solve isomorphic problems and to explore the nature of early representations. Ten- and 13-month-olds attempted to solve problems that required combining 2 subgoals to bring a toy (goal object) within reach. A problem-series paradigm was used in which 3 tasks differing in surface features but sharing common goal structures and similar solutions were presented. The results indicate that 13-month-olds transferred a modeled solution strategy across isomorphic problems, whereas 10-month-olds did so only after experiencing either multiple source problems or high perceptual similarity between problems. Comprehension of the relations between solution actions and outcome, and between tools and target object, appeared critical to transfer. The results suggest that 1-year-olds can construct relatively abstract and flexible mental representations and that analogical problem solving may be 1 of the major accomplishments during the 1st year of life. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Meta-analogical transfer: Transfer between episodes of analogical reasoning.

Meta-analogical transfer (i.e., transfer due to forming an analogy between analogies) was demonstrated in 4 experiments. Results suggest that the basis of meta-analogical transfer was transfer of predicate mappings (mappings of the concepts used to represent analogies) between separate episodes of analogical reasoning. Episodes of letter-string analogy problem solving of the form "If abc were changed into abd, how would you change kji in the same way?" were used. In Experiment 1 participants generated solutions in 2 separate analogical reasoning episodes. Order of presentation effects provided evidence of transfer of predicate mappings. Experiments 2a and 2b reinforced these findings, demonstrating transfer when mappings for the 1st analogy were directly manipulated by having participants justify an answer to the 1st analogy. Experiment 3 demonstrated that a mapping of nonidentical predicates (successor to predecessor) can also be transferred. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Role of analogical reasoning in the induction of problem categories.

In 3 experiments, novices were required to answer questions while reading a series of problems. The questions required them either to analyze individual problem structures (intraproblem processing) or compare problem structures (analogical comparison processing) to derive answers. Ss who engaged in problem comparison processing were found to categorize and describe problems on the basis of problem structure, whereas those who engaged in intraproblem processing, or simply read the problems, categorized and described them on the basis of surface features. Analogical comparisons also facilitated selection and construction of equations relative to intraproblem processing. These results suggest that analogical comparison is an important component in the induction of problem categories. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Learning and transfer: A general role for analogical encoding.

Teaching by examples and cases is widely used to promote learning, but it varies widely in its effectiveness. The authors test an adaptation to case-based learning that facilitates abstracting problem-solving schemas from examples and using them to solve further problems: analogical encoding, or learning by drawing a comparison across examples. In 3 studies, the authors examined schema abstraction and transfer among novices learning negotiation strategies. Experiment 1 showed a benefit for analogical learning relative to no case study. Experiment 2 showed a marked advantage for comparing two cases over studying the 2 cases separately. Experiment 3 showed that increasing the degree of comparison support increased the rate of transfer in a face-to-face dynamic negotiation exercise. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Learning from mistakes: Inducing analogous solution failures to a source problem produces later successes in analogical transfer.

In 4 experiments the use of analogical problem solving to facilitate the solution to a problem that usually results in persistent solution failures without hints was investigated. The results of Exps 1–3 indicate that spontaneous transfer was facilitated by a manipulation of the surface form of the source problem that tends to induce initial solution failures analogous to those produced to the target problem. Surface similarity of content words and diagrams had no effect on transfer in Exps 1–3. In Exp 4, facilitation of spontaneous transfer was not obtained when source solution failures were prevented. The importance of failed solutions in problem representation and the relationship between problem representation and surface similarity are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Explicitly teaching for transfer: Effects on third-grade students' mathematical problem solving.

The purpose of this study was to assess the effects of explicitly teaching for transfer by (a) broadening the categories by which students group problems requiring the same solution methods and (b) prompting students to search novel problems for these broad categories. This transfer treatment was combined with instruction on solution methods. The effectiveness of a combined treatment (transfer-plus-solution instruction) was contrasted to solution instruction alone and to teacher-designed instruction. Twenty-four 3rd-grade teachers, with 375 students, were assigned randomly to conditions. Treatments were conducted for 16 weeks. Improvement on immediate- and near-transfer measures supported the utility of solution instruction. Improvement on near- and far-transfer measures revealed the added contribution of explicitly teaching for transfer. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The role of content and abstract information in analogical transfer.

Analogical transfer in problem solving is one example of analogical cognition, which also includes metaphors, similes, and case-based reasoning. The dominant theories in this area posit that abstract schemata mediate transfer (K. J. Holyoak; 1984, 1985) or that problem solving by means of analogy is accomplished through application of the formal or deep structural characteristics of one problem to another (D. Gentner; see PA, Vol 71:14564, see also 1989). More recently, exemplar-based accounts (D. L. Medin and B. H. Ross, 1989; B. H. Ross; see record 1988-03388-001) have emphasized problem content and exemplar-specific details in the various stages of transfer. The present article reviews research on analogical transfer and analyzes the theoretical models in light of this evidence. An adequate theory of analogical transfer must account not only for the use of schematic knowledge but also for the importance of surface information in all stages of transfer (L. M. Reeves and R. W. Weisberg; see record 1993-20325-001). As such, it will be a hybrid of the various models presented, with exemplar-based models such as that of B. H. Ross as a base. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conformity and problem solving.

Tests of problem solving, conformity, and intelligence were given to 77 women and 64 men introductory psychology students to investigate the possibility that conformity, a nonintellectual variable, contributes to the variability in achievement in problem solving. The results show a negative correlation between tendency to conform and achievement in problem solving when the influence of intelligence is statistically removed. 17 references. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Content effects in problem categorization and problem solving.

In many domains, the content of a problem (i.e., its surface cover story) provides useful clues as to the type of problem it is and to its solution. Five experiments examined this role of problem content on the problem solution and categorization of algebra word problems with experienced participants. In the first experiment, when problem content was atypical for the the problem's deep structure, people were worse at solving the problem. Differences were also detected in the problem solution where the problem's content was highly correlated with its deep structure versus problems where content was neutral to their deep structure. In the other experiments, problem categorization and determination of information relevance depended on how closely the problem's content matched its deep structure. These results suggest that content may be influential even for experienced problem solvers. The discussion examines the implications for problem schema access and application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Role of analogical reasoning in the induction of problem categories": Correction.

Reports an error in the original article by D. D. Cummins (Journal of Experimental Psychology: Learning, Memory, and Cognition, 1992[Sep], Vol 18[5], 1103–2124). On page 1111, there are labeling errors in 2 figures. In Figure 1c, problem 11 should have a "V' in the topic column; that line should read "11 V Fl.' In Figure 1d, problems 2 and 4 should have "CU' in the structure column; those lines should read "2 T CU' and "4 T CU,' respectively. Also in that figure, problems number 8 and 13 should have "Fl' in the structure column; those lines should read "8 V Fl' and "13 W Fl.' (The following abstract of this article originally appeared in record 1993-04297-001.) In 3 experiments, novices were required to answer questions while reading a series of problems. The questions required them either to analyze individual problem structures (intraproblem processing) or compare problem structures (analogical comparison processing) to derive answers … (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Organization and creative problem solving.

"Groups from four populations differing in their amount of experience and identification with industrial vocation, were compared in their performances on the Change of Work Procedure problem." Arranged from most to least identified, there were 179 groups. "The results are interpreted as providing support for the proposition that the formal authority relations in organizations inhibit creative problem solving. They also suggest that business may be attracting people who can work comfortably, but not creatively, in such formal authority systems." (12 ref.) From Psyc Abstracts 36:04:4LI77M. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Depression and social problem solving.

20 depressed patients with major depressive disorder, 20 nondepressed matched control Ss, and 17 patients with anxiety disorders were compared in different measures of social problem solving. Problem solving was assessed with the Means-Ends Problem-Solving Test (Study 1), the solution of personal problems, and a problem-solving questionnaire (Study 2). Results showed that, as predicted, depressed Ss suffered from a deficit in problem solving in all 3 measures. The majority of these deficits were also displayed by the clinical control group rather than being specific to a diagnosis of depression. However, depressed Ss produced less effective solutions than did normal and clinical control Ss. The results suggest that depressed and anxious patients may have difficulties at different stages of the problem-solving process. (PsycINFO Database Record (c) 2010 APA, all rights reserved)