Rules and problem solving: another look

College students were trained on problems similar to the water jar problems developed by Luchins (1942). Some students were instructed that a particular rule would solve all the problems, others had the same problems but were not instructed about the rule, and a third set of students had a series of novel problems in which no single rule operated throughout. In two experiments students in the instructed rule group not only performed best in training but also performed best when transferred to a condition in which a single novel rule was appropriate. Although results from the set of conditions most similar to those of Luchins suggested that students sometimes inappropriately persisted in rule usage, the overall results suggest that rigidity is not a necessary outcome of instructed problem solving. Indeed, many of the results were consistent with the notion that instructed problem solving is flexible problem solving.     

A developmental and cross-cultural study of the influences of rule structure and problem composition on the learning of conceptual classifications

Five experiments were conducted permitting direct comparisons in the way Ss of different ages and cultures solved conceptual problems. One group of problems (Traditional) could be solved using a reference rule of conjunction or disjunction. Another group of problems (Intradimensional) could be solved either by one of the reference rules, or by a structurally simpler rule. Analysis of American performance confirmed that older Ss not only solved using the simpler rule more often than younger Ss, but when they did so they solved faster. For both American age groups, solution using the simpler rule led to no difference in performance between conjunctive and disjunctive Intradimensional problems. Conjunction proved easier than disjunction only for the Traditional problems. Unlike Americans, the Kpelle of Liberia did not solve using the simpler rule, and found conjunction easier than disjunction for both Traditional and Intradimensional problems. When a memory aid was provided the Kpelle showed a pattern of performance exactly like Americans.     

From poor performance to success under stress: working memory, strategy selection, and mathematical problem solving under pressure

Two experiments demonstrate how individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies. Under low-pressure conditions, the higher individuals' WM, the more likely they were to use computationally demanding algorithms (vs. simpler shortcuts) to solve the problems, and the more accurate their math performance. Under high-pressure conditions, higher WM individuals used simpler (and less efficacious) problem-solving strategies, and their performance accuracy suffered. Experiment 2 turned the tables by using a math task for which a simpler strategy was optimal (produced accurate performance in few problem steps). Now, under low-pressure conditions, the lower individuals' WM, the better their performance (the more likely they relied on a simple, but accurate, problem strategy). And, under pressure, higher WM individuals performed optimally by using the simpler strategies lower WM individuals employed. WM availability influences how individuals approach math problems, with the nature of the task performed and the performance environment dictating skill success or failure.     

Effect of multiple images on associative learning

The present research investigated the effects of multiple images on associative learning. In Experiment 1, subjects formed either a noninteractive image of two words, a single interactive image, a multiple interactive image consisting of multiple copies of the same image, or a multiple interactive image consisting of different images. In Experiment 2, the different multiple images were formed across trials instead of simultaneously during the same trial. Both experiments showed that, although interactive images are superior to noninteractive images, there is no reliable facilitation from multiple images as compared with single images. The results were discussed in terms of the variable-encoding hypothesis and previous findings that multiple retrieval paths facilitate verbal learning.     

Getting the Right Idea: Semantic Activation in the Right HemisphereMay Help Solve Insight Problems

Two experiments examined hemispheric differences in information processing that may contribute to solving insight problems. We propose that right-hemisphere (RH) coarse semantic coding is more likely than left-hemisphere (LH) fine semantic coding to activate distantly related information or unusual interpretations of words, and thus more likely to activate solution-relevant information for insight problems. In Experiment 1, after trying to solve insight problems, participants read aloud solution or unrelated target words presented to the left visual field (lvf) or right visual field (rvf). Participants showed greater lvf-RH than rvf-LH priming for solutions for solved problems and priming only in the lvf-RH for unsolved problems. In Experiment 2, participants showed an lvf-RH advantage for recognizing solutions to unsolved problems. These results demonstrate that in a problem-solving context, there was greater activation of solution-relevant information in the RH than in the LH. This activation is useful for recognizing, and perhaps producing, solutions to insight problems.     

Memory for Brand-Product Information in Pictorial Advertising

In two experiments, we investigated whether the type of picture that accompanies a brand-product pair has an effect on memory in an advertising context. Subjects were students in introductory psychology classes who received course credit for participation. We formed 24 fictitious brand-product pairs and illustrated them using pictorial presentation and letter accentuation in both interactive and noninter-active relationships. In Experiment 1, subjects in the interactive pictorial presentation group recalled more brands in a paired-associate task than did the interactive letter accentuation group or the control group. In a paired-associate task in Experiment 2, we examined relative effectiveness of interactive and noninteractive presentation relationships and revealed two main effects: (a) Interactive was superior to noninteractive, and (b) pictorial presentation was superior to letter accentuation in aiding recall. Results are discussed in terms of implications for advertising.     

Spontaneous gestures influence strategy choices in problem solving

Do gestures merely reflect problem-solving processes, or do they play a functional role in problem solving? We hypothesized that gestures highlight and structure perceptual-motor information, and thereby make such information more likely to be used in problem solving. Participants in two experiments solved problems requiring the prediction of gear movement, either with gesture allowed or with gesture prohibited. Such problems can be correctly solved using either a perceptual-motor strategy (simulation of gear movements) or an abstract strategy (the parity strategy). Participants in the gesture-allowed condition were more likely to use perceptual-motor strategies than were participants in the gesture-prohibited condition. Gesture promoted use of perceptual-motor strategies both for participants who talked aloud while solving the problems (Experiment 1) and for participants who solved the problems silently (Experiment 2). Thus, spontaneous gestures influence strategy choices in problem solving.     

Probability Biases in Genetic Problem Solving: A Comparison of Undergraduates, Genetic Counseling Graduate Students, and Genetic Counselors

Heuristics are mental shortcuts that aid people in everyday problem-solving and decision-making. Although numerous studies have demonstrated their use in contexts ranging from consumers’ shopping decisions to experts’ estimations of experimental validity, virtually no published research has addressed heuristics use in problems involving genetic conditions and associated risk probabilities. The present research consists of two studies. In the first study, 220 undergraduates attempted to solve four genetic problems—two common heuristic problems modified to focus on genetic likelihood, and two created to study heuristics and probability rule application. Results revealed that the vast majority of undergraduates used heuristics and also demonstrated a complete misuse of probability rules. In the second study, 156 practicing genetic counselors and 89 genetic counseling students solved slightly modified versions of the genetic problems used in Study 1. Results indicated that a large percentage of both genetic counselors and students used heuristics, but the counselors demonstrated superior problem-solving performance compared to both the genetic counseling students and the undergraduates from Study 1. Research, training, and practice recommendations are presented.     

Hypothesis testing in a rule discovery problem: when a focused procedure is effective.

We investigated individuals' ability to use negative evidence in hypothesis testing. We compared performance in two versions of Wason's (1960) rule discovery problem. In the original version, a triple of numbers--(2, 4, 6)--was presented as an example of a rule that the experimenter had in mind (i.e., "increasing numbers"). Participants had to discover the rule by proposing new triples. In the other version, the same triple was presented as a counter-example to the experimenter's rule (i.e., "decreasing numbers"). We predicted that, in both conditions, participants would form hypotheses based on the features of the triple, and test only instances of the hypothesized rule. However, in the counter-example condition, such focused testing would invariably produce negative evidence. As a consequence, participants would be forced to revise their hypotheses. The reported results corroborated our predictions: Participants solved the counter-example version significantly better than the original problem.     

The effects of cumulative practice on mathematics problem solving

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.     

Effects of problem format on division and multiplication performance: division facts are mediated via multiplication-based representations

In 2 experiments participants solved division problems presented in multiplication-based formats (e.g., 8 x _ = 72) more quickly than division problems presented in division-based formats (e.g., 72 / 8 = _). In contrast, participants solved multiplication problems presented in a division-based format (e.g., _ / 8 = 9) slowly and made many errors. In both experiments, the advantage for multiplication-based formats on division problems was found only for large problems (i.e., those with products or dividends greater than 25). These findings provide support for the view that large single-digit division facts are mediated via multiplication-based representations and that multiplication is the primary mode of representation for both division and multiplication facts.     

系列项目时间和空间信息学习的分组效应研究

运用顺序回忆方法考察分组对系列项目时间和空间信息学习的影响。包括两个实验,实验一考察简化时间上的分组,或事先告知被试分组规则的情况下,分组是否会有助于时间顺序信息的学习。结果发现,这两个操作对时间顺序信息学习的促进作用不显著。实验二考察了垂直维度上不同形式的分组对空间位置信息学习的影响。结果发现,不同的分组方式对空间位置信息学习所起的作用不同。本研究支持了时间和空间两类顺序信息学习的内在过程不同,不应该用同一理论机制进行解释。     

Comparing online and lab methods in a problem-solving experiment

Online experiments have recently become very popular, and--in comparison with traditional lab experiments--they may have several advantages, such as reduced demand characteristics, automation, and generalizability of results to wider populations (Birnbaum, 2004; Reips, 2000, 2002a, 2002b). We replicated Dandurand, Bowen, and Shultz's (2004) lab-based problem-solving experiment as an Internet experiment. Consistent with previous results, we found that participants who watched demonstrations of successful problem-solving sessions or who read instructions outperformed those who were told only that they solved problems correctly or not. Online participants were less accurate than lab participants, but there was no interaction with learning condition. Thus, we conclude that online and Internet results are consistent. Disadvantages included high dropout rate for online participants; however, combining the online experiment with the department subject pool worked well.     

On the adaptive function of children's and adults’ false memories

Recent research has shown that memory illusions can successfully prime both children's and adults' performance on complex, insight-based problems (compound remote associates tasks or CRATs). The current research aimed to clarify the locus of these priming effects. Like before, Deese–Roediger–McDermott (DRM) lists were selected to prime subsequent CRATs such that the critical lures were also the solution words to a subset of the CRATs participants attempted to solve. Unique to the present research, recognition memory tests were used and participants were either primed during the list study phase, during the memory test phase, or both. Across two experiments, primed problems were solved more frequently and significantly faster than unprimed problems. Moreover, when participants were primed during the list study phase, subsequent solution times and rates were considerably superior to those produced by those participants who were simply primed at test. Together, these are the first results to show that false-memory priming during encoding facilitates problem-solving in both children and adults.     

The politics of insight

Previous studies showed that liberals and conservatives differ in cognitive style. Liberals are more flexible, and tolerant of complexity and novelty, whereas conservatives are more rigid, are more resistant to change, and prefer clear answers. We administered a set of compound remote associate problems, a task extensively used to differentiate problem-solving styles (via insight or analysis). Using this task, several researches have proven that self-reports, which differentiate between insight and analytic problem-solving, are reliable and are associated with two different neural circuits. In our research we found that participants self-identifying with distinct political orientations demonstrated differences in problem-solving strategy. Liberals solved significantly more problems via insight instead of in a step-by-step analytic fashion. Our findings extend previous observations that self-identified political orientations reflect differences in cognitive styles. More specifically, we show that type of political orientation is associated with problem-solving strategy. The data converge with previous neurobehavioural and cognitive studies indicating a link between cognitive style and the psychological mechanisms that mediate political beliefs.     

Constraints on spontaneous transfer in problem-solving tasks

In three experiments, we investigated the conditions under which relevant knowledge is spontaneously transferred to problem-solving tasks. Subjects were presented with key concepts that could help them solve problems presented at a later time in the experiment. The key concepts were embedded in statements that had surface structures similar or dissimilar to those of the problems and that emphasized relevant or irrelevant properties of the key concepts for the problemsolving task (contextual relevance). The results indicated that the spontaneous transfer of clue information to subsequent problem-solving tasks is affected by the contextual relevance and the surface-structure similarity of the clue statements to the problems. The findings also suggested that the surface-structure similarity and the contextual relevance of clue statements differentially affect the accessibility and appropriate application of key concepts in problem-solving tasks. The implications of these results for understanding the transfer of knowledge in problem-solving tasks are discussed.     

Cognitive components of troubleshooting strategies

This study investigated the kinds of knowledge necessary to learn an important troubleshooting strategy, elimination. A total of 50 college-level students searched for the source of failures in simple digital networks. Production system modelling suggested that students using a common but simpler backtracking strategy would learn the more advanced elimination strategy if they applied certain domain-specific knowledge and the general-purpose problem-solving strategy of reductio ad absurdum. In an experiment, students solved network troubleshooting problems after being trained with either the domain-specific knowledge, the reductio ad absurdum strategy, both types of knowledge, or neither. Students needed both the domain-specific and general knowledge identified by the models in order to significantly increase their elimination use.     

Schema induction in problem solving: a multidimensional analysis

The present research examined the processes of schema formation in problem solving. In 4 experiments, participants experienced a series of tasks analogous to A. S. Luchins' (1942) water jar problems before attempting to solve isomorphic target problems. Juxtaposing illustrative source instances varying in procedural features along multiple dimensions promoted the construction of a general schema that facilitated solving an isomorphic problem requiring a novel procedure. Exposure to less variant problems led to faster initial learning, but narrower and fixed schemas (mental set), whereas exposure to variant procedures led to slower initial learning, but broader and more flexible schemas. The findings support the dimensional specificity hypothesis: Generalization along 1 dimension facilitates transfer to a target problem differing from the source problems in that dimension.     

A “misrepresentation” of method as theory : Reply

Previous studies on the development of problem-solving skills in compensation tasks suggest that sequential decision theory more accurately describes the earlier phases of development than information integration theory. Compared to information integration theory, sequential decision theory appears to provide a more valid representation of children's and adults' processing of simpler compensation problems. On more developmentally advanced compensation problems, adults appear to use a variety of strategies. Information integration is capable of describing many of these patterns accurately. However, detailed analyses of performances by children and adults indicate that processing compensation problems by algebraic integration is the exception, rather than the general rule.     

Automatic vigilance for task-related information: Perseverance after failure and inhibition after success

In three experiments, the influence of failure and success on persistent automatic vigilance task-related information was investigated. Participants first had to work on a series of synonym selection problems for which negative and positive feedback was given independently of their performance. In the second part of the experiments, words from the synonym selection problems were presented as distractors in a dual task with speeded responses. Interference effects of the distractors served as a measure of automatic vigilance for the previous synonym selection problems that was unbiased by strategic processes. Interference effects were stronger for words from failure tasks than for words from success tasks. Comparing the success and failure conditions against a neutral baseline suggested that this difference was due to both a perseverance of automatic vigilance for failure tasks and an inhibition of cognitive accessibility after success.