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 Role of Syllables in Anagram Solution: A Rasch Analysis

Anagrams are frequently used by experimental psychologists interested in how the mental lexicon is organized. Until very recently, research has overlooked the importance of syllable structure in solving anagrams and assumed that solution difficulty was mainly due to frequency factors (e.g., bigram statistics). The present study uses Rasch analysis to demonstrate that the number of syllables is a very important factor influencing anagram solution difficulty for both good and poor problem solvers, with polysyllabic words being harder to solve. Furthermore, it suggests that syllable frequency may have an impact on solution times for polysyllabic words, with more frequent syllables being more difficult to solve. The study illustrates the advantages of Rasch analysis for reliable and unidimensional measurement of item difficulty.     

The role of syllables in anagram solution: a Rasch analysis

Anagrams are frequently used by experimental psychologists interested in how the mental lexicon is organized. Until very recently, research has overlooked the importance of syllable structure in solving anagrams and assumed that solution difficulty was mainly due to frequency factors (e.g., bigram statistics). The present study uses Rasch analysis to demonstrate that the number of syllables is a very important factor influencing anagram solution difficulty for both good and poor problem solvers, with polysyllabic words being harder to solve. Furthermore, it suggests that syllable frequency may have an impact on solution times for polysyllabic words, with more frequent syllables being more difficult to solve. The study illustrates the advantages of Rasch analysis for reliable and unidimensional measurement of item difficulty.     

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.     

Working memory and intrusions of irrelevant information in a group of specific poor problem solvers

An important body of evidence has shown that reading comprehension ability is related to working memory and, in particular, to the success in Daneman and Carpenter's (1980) reading and listening span test. This research tested a similar hypothesis for arithmetic word problems, since, in order to maintain and process the information, they require working memory processes. A group of children possessing average vocabulary but poor arithmetic problem-solving skills was compared with a group of good problem solvers, matched for vocabulary, age, and socioeconomic status. Poor problem solvers presented lower recall and a greater number of intrusion errors in a series of tasks testing working memory and memory for problems. The results obtained over a series of six experimental phases, conducted during a 2-school-year period, offer evidence in favor of the hypotheses that groups of poor problem solvers may have poor performance in a working memory test requiring inhibition of irrelevant information (Hypothesis 1), but not in other short-term memory tests (Hypothesis 2), that this difficulty is related to poor recall of critical information and greater recall of to-be-inhibited information (Hypothesis 3), that poor problem solvers also have difficulty in remembering only relevant information included in arithmetic word problems (Hypothesis 4) despite the fact that they are able to identify relevant information (Hypothesis 5). The results show that problem-solving ability is related to the ability of reducing the memory accessibility of nontarget and irrelevant information.     

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.     

On the nature of insight solutions: Evidence from skill differences in anagram solution

According to the Gestalt psychologists, problem solutions that pop into mind suddenly with no awareness of the process by which they were generated are objectively as well as subjectively sudden. Thus, such pop-out solutions are qualitatively different from search solutions, which are constructed incrementally. The authors tested this claim in the domain of anagram solution. Experiment 1 documented that anagrams yield pop-out solutions, especially among highly skilled solvers. The results of Experiment 2 indicated that both pop-out and search solutions depended on the gradual accumulation of partial information, contrary to the Gestalt view of problem solving. Nevertheless, some aspects of the Experiment 2 results, as well as new analyses of an anagram study reported elsewhere, suggest that there may in fact be a qualitative difference between pop-out and search solutions. In particular, pop-out solutions may result from parallel processing of the constraints on the rearranged order of the anagram letters, whereas search solutions may result from a serial hypothesis-testing procedure.     

Anticipating partners’ responses: Examining item and source memory following interactive exchanges

Within the context of an interactive anagram-solving task, the present studies tested predictions about the role of cognitive anticipation in both source and item memory. After working in pairs to solve anagram problems, participants were surprised by a source-monitoring test focused on the source of solutions (self vs. partner, Experiment 1) or a standard recognition test focused on the solutions themselves (Experiment 2). With the intention of affecting the opportunity to anticipate partners' solutions, two variables were manipulated: anagram difficulty (easy vs. hard) and the delaybetween the presentation of an anagram problem and theprompt tha t designated one member of each pair as the anagram solver. Consistent w i th predictions, asthe opportunity t oanticipate partners'solutions increased, there was a decrease in source accuracy suggesting increased confusion about whether the solution had been self- or partner-generated. Generation-effect failures were observed in item memory. However, these failures reflected increases in item memory for partners' responses rather than decreases in memory for self-generated ones. These studies suggest that when opportunities to anticipate partners' responses are available, self-generative activities may be associated with both self-and partner-generated items, influencing the expression of the generation effect.     

Type and token bigram frequencies for two-through nine-letter words and the prediction of anagram difficulty

Recent research on anagram solution has produced two original findings. First, it has shown that a new bigram frequency measure called top rank, which is based on a comparison of summed bigram frequencies, is an important predictor of anagram difficulty. Second, it has suggested that the measures from a type count are better than token measures at predicting anagram difficulty.Testing these hypotheses has been difficult because the computation of the bigram statistics is difficult. We present a program that calculates bigram measures for two-to nine-letter words. We then show how the program can be used to compare the contribution of top rank and other bigram frequency measures derived from both a token and a type count. Contrary to previous research, we report that type measures are not better at predicting anagram solution times and that top rank is not the best predictor of anagram difficulty. Lastly we use this program to show that type bigram frequencies are not as good as token bigram frequencies at predicting word identification reaction time.     

The Syllable Effect in Anagram Solution: Unrecognised Evidence from Past Studies

Six previous studies of the variables affecting anagram solution are re-examined for the evidence that number of syllables contributes to solution difficulty. It was shown that the number of syllables in a solution word was confounded with imagery for one study and with diagram frequency for another. More importantly it was shown that the number of syllables has a large effect on anagram solution difficulty in the re-analysis of the results from the other four studies. In these studies, the number of syllables was either more important than the principal variable examined in the experiment or the second most important variable. Overall the effect size for the number of syllables was large, d = 1.14. The results are discussed in the light of other research and it is suggested that anagram solution may have more in common with other word identification and reading processes than has been previously thought.     

An hypothesis approach to the solution of anagrams

The attempts of subjects to reorganize the letters of an anagram were construed as a series of hypotheses about the correct letter order. It was predicted, consequently, that variables which reduce the number of tenable hypotheses or influence the order in which hypotheses are generated will affect problem difficulty. Five such variables, plus solution word frequency, were used to predict solution probabilities in two studies. The multiple Rs obtained were .92 and .82 and the two regression equations were effectively interchangeable. The process of anagram solution was described as entailing the retrieval of words from memory storage on the basis of letter order cues generated by the subject or, less usually, present in the anagram itself.     

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 solution of anagrams: A reexamination of the effects of transition letter probabilities,letter moves,and word frequency on anagram difficulty

Word frequency (WF), number of letter moves, and solution word transition letter probabilities (TP) were related to anagram solution. The solution word TP measure was based on the relative frequencies of correct to incorrect bigrams within the pool of bigrams defined by the letters of the anagram rather than on the absolute frequencies of the correct bigrams. This bigram rank measure, which also took word length and letter position into account, was a powerful predictor of anagram difficulty (p < .001). Likewise, number of letter moves predicted anagram solution strongly (p < .001), but WF was only a marginal predictor (.05 < p < .10). In addition, there were no significant interactions among the three variables, nor wasanagram TP consistently related to anagram difficulty. The results were interpreted in terms of an approach which combined elements of an hypothesis and an S-R mediational theory.     

Error detection processes in statistical problem solving

Problem solvers' error detection processes were studied by instructing 16 subjects to think aloud when solving two statistical problems. The evaluative episodes occurring in subjects' protocols were analyzed into Affirmative evaluation, Direct error-hypotheses, Error suspicion, and Standard check episodes, the last three of which are assumed to cover all main types of error detection processes. Most errors (78%) were found to have contributed to a solution part that triggered some evaluative episode. However, only one-third of the undetected errors had contributed to such a solution part. The Standard check episodes, seen as centrally-invoked, only led to the detection of few errors in proportion to the number of times they were performed. Evidence was found for two types of spontaneous error detections, one occurring abruptly and the other as a result of a more elaborated error detection process, initiated by the solver perceiving the solution as dissatisfying or strange. The perception of a symptom was a fairly reliable source of information about errors. However, subjects often did not manage to detect the error after having noticed a symptom. The closer a relevant Error suspicion episode followed an error, the greater was the probability of detecting the error. Good problem solvers detected a higher proportion of their errors compared to poor problem solvers, probably due to differences in the processes leading up to the triggering of an evaluative episode rather than to differences after the episode had been triggered.     

The relation between problem categorization and problem solving among experts and novices

These investigations were conducted to examine the relationship between problem-solving ability and the criteria used to decide that two classical mechanics problems would be solved similarly. We began by comparing experts and novices on a similarity judgment task and found that the experts predominantly relied on the problems' deep structures in deciding on similarity of solution, although the presence of surface-feature similarity had a clear adverse effect on performance. The novices relied predominantly on surface features, but were capable of using the problems' deep structures under certain conditions. In a second experiment, we compared groups of novices, at the same level of experience, who tended to employ different types of reasoning in making similarity judgments. Compared to novices who relied predominantly on surface features, novices who made greater use of principles tended to categorize problems similarly to how experts categorized them, as well as score higher in problem solving. These results suggest that principles play a fundamental role in the organization of conceptual and procedural knowledge for good problem solvers at all levels.     

平面几何解题过程中加工水平对迁移的影响

通过实验研究,平面几何靶题难度以及解题者对靶题与源题之间存在着共性关系的加工水平对解题迁移的影响得到了验证。结果表明,解题者对具有内在联系的先后问题之间共性关系的加工水平是影响解题迁移的因素之一;靶题的难度太大或太小,将导致解题者对先后问题之间共性关系的加工作用失败而出现地板效应和天花板效应,且靶题难度与加工水平在影响解题迁移时有交互作用。     

Modification and Origin of Certain Beliefs in Superstition Among 96 College Students

An experiment was designed to study the effect of practice on anagram solving. This was accomplished through the presentation of three anagram lists to 243 subjects and a comparison made of first-list performance (early stage of practice) with last-list performance (later stage of practice). The results revealed the presence of a significantly greater number of solutions on the last, rather than the first list, clearly indicating the presence of a general practice effect in the solution of anagrams. The failure of earlier studies to demonstrate this phenomenon was attributed to the use of relatively short anagram lists in previous research.     

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.     

The use of phonemic information to solve anagrams

Two studies investigated the role of phonemic information in anagram solving. In the first study, subjects were given bigram clues to beginnings of solution words. In addition, some subjects pronounced the letters, either correctly or incorrectly with respect to their pronun-ciations in the solution words. Correct pronunciations facilitated and incorrect pronunciations inhibited anagram solving. The second study required subjects to repeat the pronunciation of the entire anagram prior to attempting solution. Again, correct pronunciations were solved more quickly than were anagrams containing incorrect phonemic units. Results of the two studies support an analysis of anagram solving in which both orthographic and phonemic information are used to search memory to retrieve possible solution words. The relationship of the present results to recent research concerning reading and other lexical access tasks is discussed.     

Is comprehension of problem solutions resistant to misleading heuristic cues?

Previous studies in the domain of metacomprehension judgments have primarily used expository texts. When these texts include illustrations, even uninformative ones, people were found to judge that they understand their content better. The present study aimed to delineate the metacognitive processes involved in understanding problem solutions — a text type often perceived as allowing reliable judgments regarding understanding, and was not previously considered from a metacognitive perspective. Undergraduate students faced difficult problems. They then studied solution explanations with or without uninformative illustrations and provided judgments of comprehension (JCOMPs). Learning was assessed by application to near-transfer problems in an open-book test format. As expected, JCOMPs were polarized — they tended to reflect good or poor understanding. Yet, JCOMPs were higher for the illustrated solutions and even high certainty did not ensure resistance to this effect. Moreover, success in the transfer problems was lower in the presence of illustrations, demonstrating a bias stronger than that found with expository texts. Previous studies have suggested that weak learners are especially prone to being misled by superficial cues. In the present study, matching the difficulty of the task to the ability of the target population revealed that even highly able participants were not immune to misleading cues. The study extends previous findings regarding potential detrimental effects of illustrations and highlights aspects of the metacomprehension process that have not been considered before.