When insight just won't come: The failure of visual cues in the nine-dot problem

The nine-dot problem is a classic in the field of human problem solving. Cognitive accounts of the problem's difficulty have been criticized on the grounds that the experimental methods on which they rely for support involve a qualitative change to the task requirements of the problem. The three experiments reported here utilize visual and visual-procedural hints to examine the notion that its difficulty is rooted in a mismatch between problem shape and solution shape. Experiment 1 demonstrated that a perceptual cue to the shape of the solution in the form of shading gave rise to only minimal improvements in performance; an additional hint about the relevance of the shading gave rise to modest, but not statistically significant, improvements. Experiment 2 replicated these findings against an additional control condition in which a solely verbal hint to violate the perceptual boundary of the problem shape was given. Furthermore, when both the verbal and visual hints were provided, performance improved only slightly. Experiment 3 provided participants with experience in producing the shape of the correct solution in problem variants closely related to the nine-dot problem. Performance on the transfer task, the basic nine-dot problem, remained at floor, however. These data suggest that visual constraint relaxation is unlikely to be the sole process by which the insight required to find a solution is achieved. The results are interpreted in terms of a previously proposed computational model of performance.     

儿童表征深度的微观变化:路线、速度及来源

以往研究表明,表征深度的发展是一个随年龄增长而单调上升的过程,但这些年龄尺度上的横断研究难以说明表征深度变化的发生过程及其机制.本研究采用微观发生法,以齿轮推断任务为材料,探讨了68名小学五年级儿童表征深度的变化路线、速度及来源.结果表明,在整个实验期间,儿童的表征深度发生了显著变化;其变化路线主要体现为从最基本的一级水平向更高级的二、三级水平的递增过程,但这种变化路线的个体间差异较大;变化速度体现出先快后慢的特点;上述变化特点与练习及自我解释、练习模式的特征以及任务难度等因素有关.     

Working memory and insight in the nine-dot problem

In the present article, we examine the contribution of working memory (WM) to solution of the nine-dot problem, a classic insight problem. Prior research has generally demonstrated a limited role for WM in the solution of insight problems, which are typically assumed to be solved without conscious planning. However, MacGregor, Ormerod, and Chronicle (2001) proposed an information-processing model that solves the nine-dot problem by relying on a visual WM mechanism, which they term lookahead. In the present research, we examine whether performance on the nine-dot problem is indeed predicted by WM capacity. The results indicated that spatial WM capacity predicted the tendency to draw lines outside the configuration of dots and predicted the solution on a hint-aided version of the problem. Furthermore, within those solving the problem, higher spatial WM capacity was also related to faster solutions. The results support the information-processing model and suggest a more essential role for WM and planning in insight problem solving than has previously been acknowledged.     

影响9点问题解决的关键行为

在已有研究的基础上,作者提出划出第三条线是解决9点问题关键行为的假设,并设计了三个实验来验证假设.结果表明:任意两条线的提示训练使9点问题的解决率接近或达到100%,因而,提示两条线不能被看成是解决9点问题的关键行为;而提示划出第三条线的训练使9点问题的解决率明显高于提示其它任何一条线训练的效果,可以被认为是解决9点问题的关键行为;能够引导被试划出第三条线的训练使9点问题的解决率明显提高.     

顿悟问题解决的心理机制的验证性研究

目前顿悟问题解决的心理机制主要存在两个有争议性的理论：进程监控理论和表征变化理论。现以非限制性的停车场问题为实验材料,检验顿悟问题解决的这两个心理机制。结果发现：（1）进程监控理论可解释顿悟被试的成绩优劣;（2）表征变化理论可对顿悟问题能否解决做出解释。     

认知灵活性和顿悟表征转换：练习类型的影响

以停车场问题为实验材料,以42名大学生为被试,探讨认知灵活性高和低的被试在不同练习类型下顿悟问题表征转换的差异。结果表明：1）不同的练习类型对顿悟表征转换有影响,被试在难度逐渐增加的练习类型下比在简单的练习类型下顿悟产生得更快;2）顿悟表征转换的速度因认知灵活性的不同有差异,在简单的练习类型下,认知灵活性高的被试比认知灵活性低的被试顿悟产生得更早,在难度逐渐增加的练习类型下两者无差异;3）认知灵活性高的被试比认知灵活性低的被试顿悟问题解决更快。     

Investigating the effect of mental set on insight problem solving

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization.     

Symbolic Insight and Inhibitory Control: Two Problems Facing Young Children on Symbolic Retrieval Tasks

Many recent studies have explored young children's ability to use information from physical representations of space to guide search within the real world. In one commonly used procedure, children are asked to find a hidden toy in a room after observing a smaller toy being hidden in the analogous location in a scale model of the room. Three-year-old children readily find the hidden toy, although children at 2.5 years often have difficulty with the task. This experiment examined the causes of 2.5-year-olds' difficultly with this symbol system by incorporating testing procedures previously used with chimpanzees. Results indicate that young children's poor performance primarily stems from a difficulty achieving symbolic insight (i.e., recognizing the model-room representational relationship) but is also strongly affected by deficits in inhibitory control.     

An eye movement study of insight problem solving

The representational change theory of insight claims that insight problems cause impasses because they mislead problem solvers into constructing inappropriate initial representations. Insight is attained when the initial representation is changed. In the present study (N = 24), we tested three specific implications of these hypotheses against eye movements recorded while participants solved matchstick arithmetic problems. The results were consistent with the predictions, providing converging evidence with prior findings using solution rates and solution times. Alternative theories of insight can explain individual findings, but only the representational change theory accounts for both the performance data and the eye movement data. The present study also suggests that eye movement recordings provide an important new window into processes of insight problem solving.     

关系-表征复杂性模型的检验

目前有关问题难度的观点多是不全面的,在综合前人研究的基础上提出了关系-表征复杂性模型。在该模型里,区分了问题难度和问题解决难度两个概念,二者的本质分别是关系复杂性和表征复杂性;关系复杂性包括水平复杂性和等级复杂性,表征复杂性相应地包括表征广度和表征深度。以172名小学高年级学生为被试,以长方形面积问题方面的三种测验收集的数据对该模型的内部和外部效度进行了检验,结果表明它能够有效解释问题（解决）难度,区分优、中、差三类学生所能达到的表征复杂性。这说明该模型有理论价值     

Testing two cognitive theories of insight

Insight in problem solving occurs when the problem solver fails to see how to solve a problem and then--"aha!"--there is a sudden realization how to solve it. Two contemporary theories have been proposed to explain insight. The representational change theory (e.g., G. Knoblich, S. Ohlsson, & G. E. Rainey, 2001) proposes that insight occurs through relaxing self-imposed constraints on a problem and by decomposing chunked items in the problem. The progress monitoring theory (e.g., J. N. MacGregor, T. C. Ormerod, & E. P. Chronicle, 2001) proposes that insight is only sought once it becomes apparent that the distance to the goal is unachievable in the moves remaining. These 2 theories are tested in an unlimited move problem, to which neither theory has previously been applied. The results lend support to both, but experimental manipulations to the problem suggest that the representational change theory is the better indicator of performance. The findings suggest that testable opposing predictions can be made to examine theories of insight and that the use of eye movement data is a fruitful method of both examining insight and testing theories of insight.     

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。     

Expertise as mental set: The effects of domain knowledge in creative problem solving

Experts generally solve problems in their fields more effectively than novices because their wellstructured, easily activated knowledge allows for efficient search of a solution space. But what happens when a problem requires a broad search for a solution? One concern is that subjects with a large amount of domain knowledge may actually be at a disadvantage, because their knowledge may confine them to an area of the search space in which the solution does not reside. In other words, domain knowledge may act as a mental set, promoting fixation in creative problem-solving attempts. A series of three experiments in which an adapted version of Mednick’s (1962) remote associates task was used demonstrates conditions under which domain knowledge may inhibit creative problem solving.     

Attention and inhibition in bilingual children: evidence from the dimensional change card sort task

In a previous study, a bilingual advantage for preschool children in solving the dimensional change card sort task was attributed to superiority in inhibition of attention (Bialystok, 1999). However, the task includes difficult representational demands to encode and interpret the task stimuli, and bilinguals may also have profited from superior representational abilities. This possibility is examined in three studies. In Study 1, bilinguals outperformed monolinguals on versions of the problem containing moderate representational demands but not on a more demanding condition. Studies 2 and 3 demonstrated that bilingual children were more skilled than monolinguals when the target dimensions were perceptual features of the stimulus and that the two groups were equivalent when the target dimensions were semantic features. The conclusions are that bilinguals have better inhibitory control for ignoring perceptual information than monolinguals do but are not more skilled in representation, confirming the results of the original study. The results also identify the ability to ignore an obsolete display feature as the critical difficulty in solving this task.     

顿悟与源事件中启发信息的激活

采用先学习源事件、后进行顿悟问题解决的两阶段实验范型,探讨了大学生解决九点四划问题的成功顿悟与源事件中所包含的启发信息提取之间的内在联系。结果发现,在顿悟问题解决阶段,只有激活学习阶段所获得的源事件中所包含的启发信息,才能成功解决顿悟问题。但并非所有激活源事件的被试都能成功解决九点四划问题,这取决于从源事件中所提取的启发信息的质量。研究结果还表明,内隐学习组与外显学习组正确解决九点问题的人数百分比差异并不显著,证明源事件中所包含的启发信息的激活,可能主要是自动加工的结果。     

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 Aha! moment: Is insight a different form of problem solving?

In everyday life, we mainly solve problems with a conscious solution search (non-insight). However, sometimes a perplexing problem is resolved by a quantum leap in understanding. This phenomenon is known as the Aha! experience (insight). Although insight has a distinct phenomenological and behavioral signature, its driving mechanism remains debated. Weisberg (2015) proposed an integrated theory of insight arguing that insight, like non-insight, mainly depends on conscious, cognitive operations with restructuring as a distinguishing feature of insight. However, only if those operations lead to an impasse, insight is achieved through unconscious processes. We assessed some of the premises of this theory by asking participants (N = 42) to solve 70 word puzzles (CRAT) that can either be solved with insight or non-insight. For each puzzle, participants indicated word puzzle difficulty, solution confidence, solution suddenness, and the experiences of impasse and restructuring. As expected, participants reported higher suddenness of and confidence in insight solutions than non-insightful ones. Surprisingly, we could not corroborate the otherwise consistently reported higher solution accuracy and faster solution speed for insight. Crucially, as suggested by the integrated theory of insight, impasse was not a prerequisite for insight to occur. Although restructuring, indeed, preceded insight solutions more often, it seemed a more general problem-solving skill also applied for non-insight solutions. Moreover, early on, participants reported an increased experience of problem difficulty for puzzles later solved with insight. This ability to report on the solution search of insight demonstrates that, as proposed by the theory, insight involves conscious, cognitive operations.     

Learning Problem‐Solving Rules as Search Through a Hypothesis Space

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design.     

Effects of subliminal hints on insight problem solving

Two experiments tested a total of 509 participants on insight problems (the radiation problem and the nine-dot problem). Half of the participants were first exposed to a 1-min movie that included a subliminal hint. The hint raised the solution rate of people who did not recognize it. In addition, the way they solved the problem was affected by the hint. In Experiment 3, a novel technique was introduced to address some methodological concerns raised by Experiments 1 and 2. A total of 80 participants solved the 10-coin problem, and half of them were exposed to a subliminal hint. The hint facilitated solving the problem, and it shortened the solution time. Some implications of subliminal priming for research on and theorizing about insight problem solving are discussed.     

The whole and its parts: solution logic of the 9-point problem

The ill-defined nine-dot problem is reanalysed to provide a new theoretical perspective for this old problem. In particular, the theory shows how the functional fixedness of the dots can be overcome and the correct solution obtained by a process of logic. The perspective develops ideas from holistic and gestalt psychology, and shows how an entity defines its parts by demanding particular functions and how the parts in turn define the entity by the functions they serve. One central result for problem solving is the partition of processes into processes of composition and decomposition, thus leading to a theoretical foundation for the rule-governed process of planning backwards that contains both top-down and bottom-up processes. The theory is exemplified by providing a detailed account of the solution of the problem.