国外关于问题解决的研究及其教学意义

提高学生解决问题能力已经成为现代教育的一个重要目标。问题解决就是由一定情境引起的,按照一定的目标,应用各种认知活动、技能等,经过一系列思维操作,使问题得以解决的过程。本文综述了问题解决的过程模型,影响问题解决的心理因素,并寻找其教学意义,以期给当前我国教育与教学改革提供参考。     

Working in Dyads and Alone: Examining Process Variables in Solving Insight Problems

This study investigated the effects of working in dyads and their associated gender composition on performance (solution rate and time) and process variables (number of impasses, number of passed solutions, and number of problem solving suggestions and interactions) in a set of classic insight problem solving tasks. Two types of insight problems were used: multiple moves available (MMA) and few moves available (FMA) problems. The results showed no effects on number of problems solved or solving time, but group and gender composition effects emerged when looking at process variables such as number of impasses, time to impasse, number of passed solutions, number of problem solving suggestions, and number of interactions between dyad members. Results support prior evidence that process loss in creative problem solving may be due to differences in interpersonal interactions during group problem solving that do not necessarily affect overall problem solving success.     

问题表征过程的一项研究

问题表征是解决问题时理解问题的方式．本研究选用智力数学题为实验作业,通过详细分析３４名大学生被试的问题表征环节及他们问题解决的结果,探讨问题表征中的信息加工过程及其对问题解决结果的影响．实验结果表明：（１）正确的问题表征是解决问题的必要前提,在错误的或者不完整的问题空间中进行搜索不可能求得问题的正确解．（２）问题表征是对问题信息的提取和理解的过程,问题规则在问题表征中起重要作用．（３）在问题表征过程中,导致建构出错误的或者不完整的问题空间的因素包括：信息遗漏（未能将问题的有关信息全部提取出来）,信息误解（对某些问题信息做了错误的分析和理解）,隐喻干扰（问题信息中潜在的歧义性使被试困惑或误导被试的解题思路）等．     

Mental arithmetic: effects of calculation procedure and problem difficulty on solution latency

In this chronometric study of mental arithmetic, problems with sums greater than 20 and less than 100 were presented to third-grade subjects (age 8-9). It is argued that such problems are calculated by using procedures in which the problem is broken down into subproblems for which solutions are retrieved from a declarative knowledge base. Important bottlenecks in this process are the processing capacity (since only one subproblem can be handled at a time) and the storage capacity of working memory (since the original problem and all outcomes of subproblems have to be retained). Therefore it can be hypothesized that arithmetic procedures and types of problems that necessitate more subproblems will lead to longer solution times. Both hypotheses were confirmed. Significant interactions between types of problems and arithmetic procedures show an increasing difference in solution time between the procedures with increasing problem difficulty. It can be concluded that for the type of problems studied, arithmetic procedures requiring a smaller number of subproblems lead to better performance.     

What makes an insight problem? The roles of heuristics, goal conception, and solution recoding in knowledge-lean problems

Four experiments investigated transformation problems with insight characteristics. In Experiment 1, performance on a version of the 6-coin problem that had a concrete and visualizable solution followed a hill-climbing heuristic. Experiment 2 demonstrated that the difficulty of a version of the problem that potentially required insight for solution stems from the same hill-climbing heuristic, which creates an implicit conceptual block. Experiment 3 confirmed that the difficulty of the potential insight solution is conceptual, not procedural. Experiment 4 demonstrated the same principles of move selection on the 6-coin problem and the 10-coin (triangle) problem. It is argued that hill-climbing heuristics provide a common framework for understanding transformation and insight problem solving. Postsolution receding may account for part of the phenomenology of insight.     

No Role of Initial Problem Representation in Insight Problem Solving

The literature on insight problems—problems that supposedly can only be solved by rejection of an initial faulty problem representation and sudden comprehension of another, nonobvious representation (restructuring)—suggests that the size of initial representations affects the very process of problem solving. Large initial representations impose systematic, analytical search, whereas only small representations promote intuitive, associative processes assumed by some theorists to underpin insight. In a group of 353 young healthy participants, 6 previously validated insight problems were applied in either a small or large initial representation variant. Results demonstrated no reliable difference in performance between the problem variants with regard to (a) solution accuracy, (b) self-reported insight accompanying solutions, (c) effects of fatigue, (d) correlations with another 6 small representation-size problems, and (e) correlations with working memory capacity (which were notable). This outcome suggests that the size of initial faulty representation plays no role in insight problem solving process, supporting the account assuming its strong similarity to systematic, analytical problem solving.     

Solving Everyday Problems Creatively: The Role of Problem Construction and Personality Type

Problem construction has been determined to be an important process contributing to creative problem solving. The purpose of this study was to investigate whether problem construction plays a role in how individuals interpret ambiguous, ill-defined problems in a way that fits with their personality. We also hypothesized that solution quality and originality would be related not only to problem construction ability but also to the degree to which the solution fits the personality of the individual. Students who participated in this study (N = 195) were asked to complete measures to identify personality types, a measure of problem construction ability, and a problem-solving exercise. Solutions were rated for fit of the solution to the personality, quality, and originality. Results suggest that problem construction ability is positively related to the fit of the solution to the personality type, and that solution quality and originality are related to both problem construction and solution fit. Implications of the role of problem construction in solving everyday problems are discussed.     

THE EFFECTS OF VIDEO MODELING ON STAFF IMPLEMENTATION OF A PROBLEM‐SOLVING INTERVENTION WITH ADULTS WITH DEVELOPMENTAL DISABILITIES

We investigated the effects of video modeling on the percentage of correctly implemented problem‐solving steps by staff in a group home for adults with developmental disabilities, using a nonconcurrent multiple baseline design across participants. The treatment consisted of staff watching a video model demonstrating the correct implementation of a problem‐solving intervention (i.e., teaching clients to identify problems, possible solutions, and consequences to each solution, and to choose the best solution). The percentage of correctly implemented problem‐solving steps increased for all participants, and the effect was maintained over time, generalized to novel problems, and generalized from role play with a researcher to actual clients.     

The contributions of convergent thinking,divergent thinking,and schizotypy to solving insight and non-insight problems

The ability to generate diverse ideas (divergent thinking) is valuable in solving creative problems (e.g., insight problems); yet, however advantageous, this ability is insufficient to solve the problem alone and requires the ability to logically deduce an assessment of correctness of each solution (convergent thinking). Positive schizotypy may help isolate the aspects of divergent thinking prevalent in insight problem solving. Participants were presented with a measure of schizotypy (Oxford-Liverpool Inventory of Feelings and Experiences), divergent and convergent thinking tasks, insight problems, and non-insight problems. We found no evidence for a relationship between schizotypy and insight problem solving. Relationships between divergent thinking and insight problem solving were also surprisingly weak; however, measures of convergent thinking had a stronger relationship with problem solving. These results suggest that convergent thinking is more important than divergent thinking in problem solving.     

Discovering the Sequential Structure of Thought

Multi‐voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel mathematical problems. We identify four states in the solution of these problems: Encoding, Planning, Solving, and Respond. The method allows us to interpret what participants are doing on individual problem‐solving trials. The duration of the planning state varies on a trial‐to‐trial basis with novelty of the problem. The duration of solution stage similarly varies with the amount of computation needed to produce a solution once a plan is devised. The response stage similarly varies with the complexity of the answer produced. In addition, we identified a number of effects that ran counter to a prior model of the task. Thus, we were able to decompose the overall problem‐solving time into estimates of its components and in way that serves to guide theory.     

Depression and social problem solving.

Twenty depressed patients with major depressive disorder, 20 nondepressed matched control subjects, 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 subjects suffered from a deficit in problem solving in all three 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 subjects produced less effective solutions than did normal and clinical control subjects. The results suggest that depressed and anxious patients may have difficulties at different stages of the problem-solving process.     

小学生数学应用题解决的认知机制研究

研究的目的是探讨影响小学生应用题解决的认知因素及其作用机制。采用自编的应用题解决问卷对183名小学生进行了测量和统计分析。结果表明：情境理解、问题表征、问题归类、解题计划和自我评价是影响小学生应用题解决的主要认知因素。其中,情境理解首先影响问题表征、问题归类、解题计划和自我评价,后四个因素又进一步影响解题成绩。     

Promoting Insightful Problem Solving

This work assessed whether insightful problem solving could be trained. Specifically, we tested whether solutions to a heterogeneous set of verbal insight problems could be promoted. A training scheme was developed to promote the application of mechanisms that underlie the process of restructuring. Training across the five experiments consisted of different combinations of the following training techniques: advance strategic instructions, varying amounts of practice, practice with different types of feedback, and problem comparison. Results from all five experiments showed that training can promote solutions to verbal insight problems. Facilitation effects ranged from a 14%–24% gain in overall solution rates relative to no‐treatment controls. This work demonstrated that insightful problem solving could be trained at a relatively high level of generality.     

Deconstructing the tower: Parameters and predictors of problem difficulty on the Tower of London task

The Tower of London (TOL) task has been widely used in both clinical and research realms. In the current study, 104 healthy participants attempted all possible moderate- to high-difficulty TOL problems in order to determine: (1) optimal measures of problem solving performance, (2) problem characteristics, other than the minimum moves necessary to solve the problem, that determine participants’ difficulty in solving problems successfully, quickly, and efficiently, and (3) effects of increased task experience on which problem characteristics determine problem difficulty. A factor analysis of six performance measures found that, regardless of task experience, problem difficulty could be captured well either by a single factor corresponding to general quality of solution or possibly by three subordinate factors corresponding to solution efficiency, solution speed, and initial planning speed. Regression analyses predicting these performance factors revealed that in addition to a problem’s minimum moves three problem parameters were critical in determining the problem difficulty: goal position hierarchy, start position hierarchy, and number of solution paths available. The relative contributions of each of the characteristics strongly depended on which performance factor defined performance. We conclude that TOL problem performance is multifaceted, and that classifying problem difficulty using only the minimum moves necessary to solve the problem is inadequate.     

Mental models in word problem-solving: A comparison between American and Korean sixth-grade students

Mental model analysis was conducted in word problem solving using American (n = 42) and Korean (n = 44) sixth-graders. Two levels of mental models–the problem model and the mathematical model–constructed in the process of word problem solving were investigated. Categories for correct and incorrect models were developed to be used in think-aloud protocol analysis. The majority of students who constructed correct problem models classified the problems rapidly according to solution procedures as they read the problems, or restated the problems focusing on the specific words relating them to other statements in the problems. However, significant differences were found between American and Korean sixth-graders' in some categories of problem and mathematical models. While many Korean sixth-graders' problem-solving process steps were proceduralized, this was not the case for American sixth-graders, even for those who had a readily accessible knowledge base of basic mathematical facts.     

顿悟:是进程监控还是表征转换

当前解释顿悟问题解决机制的理论主要有表征转换理论和进程监控理论。进程监控理论主要解释了顿悟问题为什么困难,但事实上它并没有说明顿悟问题为什么会解决,只回答了在什么情况下被试才会寻求其他的方法,而且它把顿悟问题解决的一般过程看成是同常规问题解决方法相同的过程。而表征转换理论主要解释了顿悟是如何获得的——顿悟的获得是由于问题解决者对问题的表征实现了正确的转变,但它并没有解释表征什么时候、怎么样才能转变?顿悟问题的解决经历了三个认知加工阶段,顿悟问题的解决需要在消除定势情况下激活正确的启发信息(线索),并验证了顿悟问题的原型激活和关键启发信息理论假说。     

From Walls to Windows: Using Barriers as Pathways to Insightful Solutions

The purpose of this study was to explore and develop a conceptual model for how individuals unlock insight. The concept of insight — the ‘out of the box’ or ‘aha!’ solution to a problem — offers a framework for exploring and understanding how best to enhance problem solving skills due to the cognitive shift insight requires. Creative problem solving (CPS) is inherent to a variety of performance realms including effective decision making, innovation, and organizational development; however, related processes of insight, innovation and creativity remain intangible. The model, based on a review of the problem solving literature, proposes that insight involves a five stage, cyclical process emerging as: primary appraisal of the problem, secondary appraisal based on prior knowledge, initial focus, problem representation, and solution generation when, if no solution is found, the cycle begins again. The research has implications for individual, team and organizational settings suggesting that performance on a wide variety of problems may be improved by utilizing an integrated focus rather than a barrier or goal focus alone.     

Children's Reasoning in Solving Relational Problems of Deduction

This article reports on a study of children's deductive reasoning in solving novel relational problems. Detailed protocols were obtained from 264 children (aged 9- 12 years) who verbalised their thinking as they solved the problems. The study included the development of a three-phase theory based on Johnson-Laird and Byrne's mental models perspective, but with some distinct modifications. These include a focus on the relational complexity entailed in model construction and in premise integration, and the advancement of four reasoning principles that are applied throughout problem solution (in contrast to Johnson-Laird's falsification processes as the hallmark of deductive reasoning). The reported case studies and the results of statistical analyses supported predictions arising from the proposed theory, including the key role of the reasoning principles. The results also showed that problem difficulty is a function of relational complexity, not of the number of models to be constructed, as argued by Johnson-Laird and Byrne.     

Insight versus analysis: Evidence for diverse methods in problem solving

Since the Gestalt psychologists made the distinction approximately 100 years ago, psychologists have differentiated between solving problems through analysis versus insight. The present paper presents evidence to support the idea that, rather than conceptualising insight versus analysis as distinct modes of solving problems, it is more useful to conceive of insight and analysis as two approaches within a set of possible solving methods. In the present research, 60 participants solved insight problems while thinking aloud, which provided evidence concerning the processes underlying problem solution. Comparison with performance of a nonverbalisation control group (n = 35) indicated no negative effects of thinking aloud on insight in problem solving. The results supported the idea that various methods are utilised in solving insight problems. The “classic” impasse–restructuring–insight sequence occurred in only a small minority of solutions. A number of other solution methods were found, ranging from relatively direct applications of knowledge, to various heuristic methods, to restructuring arising from new information gleaned from a failed solution. It is concluded that there is not a sharp distinction between solving a problem through analysis versus insight, and implications of that conclusion are discussed.     

Incubation and the persistence of fixation in problem solving

Extra work on unsolved problems may lead to more improvement if the new work is delayed rather than undertaken immediately after initial solution attempts. Such a result constitutes incubation in problem solving. "Unconscious work" on a problem, commonly assumed to be responsible for incubation effects, may not be necessary to observe the phenomenon. We hypothesize that fixation, a block to successful problem solving, may develop during initial solution attempts and persist, interfering with immediate extra work more than with delayed extra work. Five experiments are reported in which fixation was induced to prevent optimal performance on the initial test of Remote Associates Test (RAT) problems (e.g., Mednick, 1962). After the fixation manipulation in three of the experiments, the effects of incubation intervals were examined by retesting the fixated problems. Both fixation (poorer initial problem-solving performance) and incubation (more improvement after a delayed retest than an immediate retest) were found in all the experiments which tested for the effects. In Experiments 1, 2, and 3, misleading distractors were presented alongside the RAT problems during the initial test of the problems to cause fixation. In Experiment 4, a block of paired associates--pairing the RAT words with the misleading distractors prior to problem solving--successfully induced fixation, indicating that the distractors affected memory retrieval. In Experiment 5, a trial-by-trial technique allowed fixation and incubation to be induced and tested separately for each item. All of our findings of incubation effects appear to have depended upon the initial induction of fixation. Although the experiments may not be representative of all naturally occurring cases of incubation, they provide a methodology for the study of fixation and incubation effects in problem solving in the laboratory.