Move evaluationasa predictor and moderator of success in solutions to well-structured problems

This paper presents three studies concerned with the evaluation of moves in solutions to Tower of Hanoi problems and the effect that such evaluation processes have on solution success. The existing literature on problem solving suggests that verbalizing whilst solving a problemcan havea positive effect upon performance. However,such verbalization has to be directed toward an explicit evaluation of particular moves. What remains unclear is whether evaluation without verbalization has the same effects or whether some characteristic of the process of verbalization gives rise to improved performance on such tasks. For example, the act of verbalizing per se may simply mean that more processing time is directed toward the problem-solving process. The studies reported in this paper suggest that the process of evaluation may be independent of verbalization processes and that non-verbal evaluation of moves (indicated by a key press) produces the same effects as a verbal evaluation of such moves. Moreover, the process of evaluating moves appears to producea form of behaviour that is prone to disruption via the administration of secondary tasks, whereas non-evaluated solutions are not. This may suggest that problem solvers who engage in evaluation processes develop an explicit representation of the strategies used to solve the problem.     

Problem solving with a simple transformation problem with and without continuous external memory support

Problem solvers can use external memory aids to represent problem information. In this study, an external problem representation was either continuously available or available on demand of the participants. Two experiments explore the hypothesis that despite the higher working memory load without a continuous external memory support, problem solvers try to reduce the cognitive costs by implementing deliberate problem solving strategies. Problem solving with and without continuous external memory support was found to be largely equivalent with high and low operator implementation costs and in problem spaces of different sizes.     

Lasting reductions in illegal moves following an increase in their cost: evidence from river-crossing problems

The authors present 3 experiments demonstrating ways to reduce illegal moves in problem-solving tasks. They propose a 3-stage framework for the rejection of illegal moves. An illegal move must come to mind and be selected, checked for legality, and correctly rejected. Illegal move reduction can occur at any stage. Control group participants benefited from solving the same problem twice but failed to show transfer to an isomorph, replicating results from S. K. Reed, G. W. Ernst, and R. Banerji (1974). Participants who were penalized for making illegal moves showed reductions in illegal moves even when solving a novel isomorph without penalty. The authors propose that illegal move reduction occurs when solvers are cautious and check moves for legality frequently.     

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.     

知识经验与顿悟：来自认知神经科学的证据

知识经验对于顿悟问题解决是一把双刃剑,强势知识会阻碍顿悟问题解决,弱势知识才是顿悟问题解决的关键。强势知识引导的组块效应、约束效应和固着效应等心理定势现象,“帮助”问题解决者以惯用方案来理解、思考和解决问题。之所以会这样,可能是因为大脑内存在一套具有优先级差的层级加工系统,赋予惯用方案的优先级最高。不过,惯用方案不仅不能够解决顿悟问题,而且还会通过注意竞争和注意失灵方式来阻碍新异方案的探索和执行,所以,问题解决者往往都会进入思维僵局。僵局的打破和顿悟的实现,需要抑制住强势知识及其相关的惯用方案、激活弱势知识和新异方案,这违反了大脑的认知加工惯性,是很难以自发发生的。但是,可以通过激活扩散来增强弱势知识的激活水平,或者是拓宽注意范围、提高注意灵活性来增加弱势知识激活的可能性,从而促进顿悟问题解决。     

The influence of verbalization on problem-solving

The performance of subjects who were required to state reasons for moves while solving the Tower-of-Hanoi problem was compared to the performance of subjects who were not required to do so. In accordance with previous research it was found that stating reasons facilitated performance in reducing superfluous moves (errors). In addition it was found that the effect was due to a significant decrease in errors for moves close to important subgoals in a goal hierarchy of moves. The effect was explained in terms of the replacement of an automated process with controlled calculations for moves close to subgoals.     

Problem Variables that Promote Incubation Effects

Three studies sought to determine whether incubation effects could be reliably generated in a problem‐solving task. Experimental variables manipulated were the duration of the interval between two problem‐solving opportunities and the activity performed by the problem solvers during the interval. A multi‐solution anagram task was used which required problem solvers to generate five‐letter words from the letters in a ten‐letter “starter” word until they could produce no more words. After a break (the incubation period) the problem solvers returned to the anagram task anew. Some participants also engaged in an activity related to the anagram task during the break which was expected to prime potential solutions that would emerge during the second problem‐solving attempt. In all conditions problem solvers were able to generate new responses after the break, thus demonstrating a reliable incubation effect. The optimal incubation period was between 15 and 30 min long. The priming task increased the number of solutions to the anagram task on the second attempt, suggesting that exposure to solution ideas during the incubation period may facilitate an incubation effect during problem solving.     

Modeling strategy shifts in a problem-solving task

A computer simulation model was fitted to human laboratory data for the Missionaries and Cannibals task to explain (1) the effects upon problem performance of giving a hint, and (2) the effects of solving the problem a second time after one successful solution had been achieved. Most of the variance in the relative frequencies of different moves can be explained by positing that the effect of the hint, or of previous experience in solving the problem, is to cause subjects to switch more promptly from a strategy of balancing the numbers of missionaries and cannibals on both sides of the river, to a means-ends strategy.     

Information processing and insight: a process model of performance on the nine-dot and related problems

The 9-dot problem is widely regarded as a difficult insight problem. The authors present a detailed information-processing model to explain its difficulty, based on maximization and progress-monitoring heuristics with lookahead. In Experiments 1 and 2, the model predicted performance for the 9-dot and related problems. Experiment 3 supported an extension of the model that accounts for insightful moves. Experiments 4 and 5 provided a critical test of model predictions versus those of previous accounts. On the basis of these findings, the authors claim that insight problem solving can be modeled within a means-ends analysis framework. Maximization and progress-monitoring heuristics are the source of problem difficulty, but also create the conditions necessary for insightful moves to be sought. Furthermore, they promote the discovery and retention of promising states that meet the progress-monitoring criterion and attenuate the problem space.     

Probability and category redefinition in the fault tree paradigm

Fault trees have been advocated as aids for problem solvers. However, research has suggested limitations in their usefulness. Fischhoff, Slovic, and Lichtenstein (1978) found that subjects given incomplete (pruned) trees were insensitive to omissions; these authors hypothesized that Tversky and Kahneman's (1974) availability heuristic was the mediating factor. Using a within-subjects design, subjects in Experiment 1 received both full and pruned trees and estimated probabilities for various reasons why a car would fail to start. To increase the availability of omissions, some Experiment 1 subjects first generated possible causes of starting failure. The basic Fischhoff et al. findings were replicated, but several aspects of the results argued against the availability hypothesis as the mechanism for judgment. Instead, subjects appeared to idiosyncratically redefine category membership when making judgments based upon pruned trees. By employing a sorting task in Experiment 2 we corroborated the results of Experiment 1: Subjects do redefine the actual contents of the categories when faced with an omission from the fault tree. The implications of these results for the use of fault trees as a problem solving aid are discussed.     

The effects of superficial and structural information on online problem solving for good versus poor anagram solvers

The two experiments reported here tested two predictions concerning the sensitivity of good and poor problem solvers to superficial and structural information during online problem solving: (a) Superficial features have a greater effect on solution difficulty for poor problem solvers, whereas (b) structural features have a greater effect on solution difficulty for good problem solvers. The tests were conducted in the domain of anagram solution by manipulating or measuring several superficial and structural characteristics in this domain. The results supported both predictions. They also indicated that better problem solvers have access to structural information from the earliest stages of processing (within the first 2 s). The authors discuss the implications of their results for the types of solution strategies used by more and less competent anagram solvers.     

The effects of superficial and structural information on online problem solving for good versus poor anagram solvers

The two experiments reported here tested two predictions concerning the sensitivity of good and poor problem solvers to superficial and structural information during online problem solving: (a) Superficial features have a greater effect on solution difficulty for poor problem solvers, whereas (b) structural features have a greater effect on solution difficulty for good problem solvers. The tests were conducted in the domain of anagram solution by manipulating or measuring several superficial and structural characteristics in this domain. The results supported both predictions. They also indicated that better problem solvers have access to structural information from the earliest stages of processing (within the first 2 s). The authors discuss the implications of their results for the types of solution strategies used by more and less competent anagram solvers.     

代数应用题项目生成中的认知过程与任务特征分析

认知项目设计起源于理论驱动的测量模式,要求在详尽阐述测量建构理论的基础上,鉴别测验项目类型的任务特征,建立和标定与测量建构认知变量之间的对应关系,从而通过系统变换任务特征生成项目.本文以Greeno (1994)提出的代理者-情境交互作用(agent-situation interaction)的问题解决观为基础,对代数应用题解决的认知过程和任务蕴含性(affordance)进行了系统分析.具体而言,代数应用题被视为以文本形式呈现的,嵌套在现实情境中的某种量化结构.在代数应用题解决的转译、整合、计划、执行的认知过程中需要形成三种不同的表征,即文本基、情境模型和问题模型.其形成及解决过程受到个体问题图式知识的深刻影响.对应于不同表征方式,对代数应用题语法/语义结构、量化元素及结构、问题情境特征进行了系统分析和综合.该分析表明,为了保证代数应用题项目生成的科学性,当前研究的关键在于建立任务特征与问题解决认知变量之间的经验关系,并在问题领域整体水平上检验这种关系的可推广性.     

When shoes become hammers: Goal-derived categorization training enhances problem-solving performance

Problem-solving theories have not examined how solvers navigate their knowledge to interpret problem situations or to plan strategies toward goals. In this article, the author argues that success in problem solving depends on the solver's ability to construct goal-derived categories, namely categories that are formed ad hoc to serve goals during the instantiation of problem frames. Experiment 1 (N = 140) showed improved problem-solving performance after training to construct goal-derived categories. Experiment 2 (N = 80) demonstrated that effects of training in category construction can be obtained without participants being explicitly informed regarding the relevance of training to problem solving. These studies suggest that problem solving is a dynamic expression of goal-directed cognition and provide evidence for the involvement of categorization in problem-solving processes.     

Problem-Solving Appraisal,Health Complaints,and Health-Related Expectancies

The authors examined the relation of problem-solving appraisal to health complaints and health-related expectancies among 321 undergraduates. Results indicated that self-appraised effective problem solvers reported fewer current physical symptoms during the 3 weeks prior to assessment and fewer health problems on the day of assessment than did ineffective problem solvers. Self-appraised effective problem solvers also had greater internal and lower chance expectancies for health outcomes than did ineffective problem solvers. Ineffective self-appraised problem solvers reported more negative health perceptions 3 months later during the week of final examinations. Personal control over emotional experiences when engaging in problem solving was significantly predictive of health perceptions. Results are integrated with theoretical models of problem solving and behavioral health. Implications for counseling are discussed.     

Problem‐Solving Appraisal and Depression: Evidence for a Recovery Model

The purpose of this study was to examine whether problem‐solving appraisal plays a role in recovery from depression in a university population. It was predicted that self‐appraised effective problem solvers would be more likely to recover from a depressive episode than self‐appraised ineffective problem solvers. Consistent with this hypothesis, there was a significant Time 1 problem‐solving appraisal x Time 1 depression interaction in predicting Time 2 depression scores. More specifically, by Time 2 the self‐appraised effective problem solvers reported only mild levels of depressive symptoms (Beck Depression Inventory [BDI] = 12), whereas the self‐appraised ineffective problem solvers reported levels of depression that were moderate to severe (BDI = 20).     

心理定势现象的认知神经机制

问题解决活动中的心理定势,是指人们固执地沿用熟悉方案、忽略其他方案的反应倾向。它可能源于人们已经掌握的陈述性知识,也可能源于程序性知识,两类不同来源的心理定势的发生条件和影响效果都不尽相同。然而,过往的研究都没有做出严格区分。本文通过梳理相关研究,描述心理定势现象,解释心理定势是怎么发生的,分析心理定势是在什么条件下发生的、会对心理与行为活动造成什么样的影响,从而评述两种来源的心理定势的认知神经机制,指出尚未解决的科学问题。     

Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving

The relations between short-term memory, working memory, inhibitory control, and arithmetic word problem solution were studied in children who were poor in arithmetic problem solving (n = 23). The children were compared with a group of good problem solvers (n = 26), matched for vocabulary, age, and gender. The results corroborate the hypothesis of poor problem solvers' general deficit in inhibitory processes. They had lower scores and made more intrusion errors in a series of working memory tasks requiring inhibition of irrelevant information. The results showed that problem solving performance is related to the ability of reducing the accessibility of nontarget and irrelevant information in memory. Span tasks that imply passive storage of information showed that poor problem solvers were impaired when they have to retain numerical information, but they did not differ from children who did not have difficulty with mathematics when the material included words.     

Analogy Events: How Examples are Used During Problem Solving

In attempting to fit a model of analogical problem solving to protocol data of students solving physics problems, several unexpected observations were made. Analogies between examples and exercises (a form of case-based reasoning) consisted of two distinct types of events. During an initialization event, the solver retrieved an example, set up a mapping between it and the problem, and decided whether the example was useful. During a transfer event, the solver inferred something about the problem's solution. Many different types of initialization and transfer events were observed. Poor solvers tended to follow the example verbatim, copying each solution line over to the problem. Good solvers tried to solve the problem themselves, but referred to the example when they got stuck, or wanted to check a step, or wanted to avoid a detailed calculation. Rather than learn from analogies, both Good and Poor solvers tended to repeat analogies at subsequent similar situations. A revised version of the model is proposed (but not yet implemented) that appears to be consistent with all the findings observed in this and other studies of the same subjects.     

Flexible strategy use: A characteristic of gifted problem solving

The aim of the study was to investigate the relationship between flexible strategic thinking and problem solving performance. In the first experiment, gifted, average, and poor problem solvers performed a number of tasks which were designed to provoke rigidity. The results indicated that the average and poor performance groups did not differ in the number of answers indicating response and perceptual set. On the other hand, creative and intelligent students showed fewer rigid answers than the other two groups. In the second experiment, gifted and average students were asked to think aloud while solving different problems with open and closed solution situations. The thinking aloud protocols were analyzed by classifying the statements into different strategy types. Gifted students used a variety of strategies when solving problems, as well as different strategies for different problem types. No such differences were observed with the average problem solvers. The results of both experiments demonstrated consistent evidence for the role of flexible strategic thinking in gifted problem solving, as well as less direct evidence of the importance of metacognitive knowledge.