The importance of understanding: Model space moderates goal specificity effects

The three-space theory of problem solving predicts that the quality of a learner's model and the goal specificity of a task interact on knowledge acquisition. In Experiment 1 participants used a computer simulation of a lever system to learn about torques. They either had to test hypotheses (nonspecific goal), or to produce given values for variables (specific goal). In the good- but not in the poor-model condition they saw torque depicted as an area. Results revealed the predicted interaction. A nonspecific goal only resulted in better learning when a good model of torques was provided. In Experiment 2 participants learned to manipulate the inputs of a system to control its outputs. A nonspecific goal to explore the system helped performance when compared to a specific goal to reach certain values when participants were given a good model, but not when given a poor model that suggested the wrong hypothesis space. Our findings support the three-space theory. They emphasize the importance of understanding for problem solving and stress the need to study underlying processes.     

Goal specificity effects on hypothesis testing in problem solving

Previous research has found that having a nonspecific goal (NSG) leads to better problem solving and transfer than having a specific goal (SG). To distinguish between the various explanations of this effect requires direct evidence showing how a NSG affects a participant's behaviour. Therefore we collected verbal protocols from participants learning to control a linear system consisting of 3 outputs by manipulating 3 inputs. This system was simpler than the one we had used previously, so in Exp. 1 we generalized our earlier goal specificity findings to this system. In Exp. 2 protocol analysis confirmed our prediction (based on dual-space theories of problem solving) that NSG participants focused on hypothesis testing whereas SG participants focused on the goal. However, this difference only emerged over time. We also replicated the goal specificity effect on performance and showed that giving participants a hypothesis to test improved performance.     

Goal Specificity as a Determinant of Goal Commitment and Goal Change

Two hundred twenty-three subjects worked on an anagram solving task under one of two assigned goal conditions and then self-set goals on a brainstorming task. Both tasks were performed while under one of four specificity conditions. Results revealed that goal specificity raised goal commitment under assigned goal conditions and was related to goal change under self-set goal conditions. In addition, goal specificity was related to individuals′ variability in performance across trials under assigned goal conditions. The implications of these results for understanding the goal setting process are discussed.     

A generalization of the representational change theory from insight to non-insight problems: the case of arithmetic word problems

This paper provides evidence for a possible generalization of Knoblich and colleagues’ representational change theory [Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 1534-1555; Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem. Memory and Cognition, 29, 1000-1009] outside its original scope of application. While this theory has been proposed to explain insight problem solving, we demonstrate here that its main concepts, namely, constraint relaxation and chunk decomposition, are applicable to incremental problem solving. In a first experiment, we confirm, as already shown by problem solving and reasoning researchers, that individuals avoid the construction of alternative representations of the problems when possible. In the second and third experiments, we show that alternative representations of arithmetic problems are easier to construct and maintain when they violate constraints of narrow rather than wide scope. The specificity of insight problem solving is discussed in the light of these new findings.     

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.     

Autobiographical memory specificity and the persistence of depressive symptoms in HIV-positive patients: Rumination and social problem-solving skills as mediators

Individuals infected with human immunodeficiency virus (HIV) are at elevated risk for depressive conditions, which in turn can negatively impact health-related behaviours and the course of illness. The present study tested the role of autobiographical memory specificity and its interaction with perceived stress in the persistence of depressive symptoms among dysphoric HIV-positive individuals. Additionally, we examined whether rumination and social problem solving mediated these effects. Results indicated that memory specificity moderated the impact of perceived stress, such that perceived stress was more strongly associated with follow-up depressive symptoms among those with greater memory specificity. Rumination, but not social problem solving, mediated this effect. Implications of these findings are discussed.     

Reduced autobiographical memory specificity as a mediating factor between general anxiety symptoms and performance on problem‐solving tasks

This study sought to further explain the association between general anxiety symptoms and impaired problem‐solving by testing whether this occurs, in part, through a reduced ability to retrieve event‐level, specific autobiographical memory (AM). Participants (N = 301; M age = 28.2 SD = 7.7, 55.8% female) completed assessments of the retrieval of specific AM, anxiety symptoms, depressive symptoms, and rumination. They then completed the Means‐End Problem Solving Task, which assessed their ability to produce relevant problem‐solving steps. Participants who were higher in anxiety reported a lesser number of relevant problem‐solving steps, and this association was, in part, related to anxiety being associated with reduced AM specificity (after controlling for depressive symptoms). Rumination did not mediate anxiety and problem‐solving, nor anxiety and AM specificity. These findings provide further evidence that elevated anxiety is associated with reduced ability to retrieve specific AM, and a specific cognitive pathway through which anxiety may affect problem‐solving performance.     

Task Specificity in the Use of Words in Mathematics: Evidence from Bilingual Problem Solvers

Mathematics is often said to be a different language in itself. Three experiments were conducted to show some evidence for this common notion. It was hypothesized that in math word problem solving, people interpret words like “more” and “less” in specialized ways that are specific to the task of math word problem solving. Subjects were given texts with quantitative information, but the texts were framed either as math problems or as stories, and were written either in English or Filipino. Subjects were then asked to verify statements that describe quantitative relations given in the text; these relations either stated an exact or an inexact quantitative difference. The verification responses and verification times in three experiments show that subjects more often accepted the inexact difference as true when the text was framed as a story compared to when framed as a problem. These results support the hypothesis that the use of the specialized meaning is specific to the task of solving word problems in math. The data were equivocal about the role of the language used in the operation of this knowledge. The results were discussed in terms of the implications of specificity of knowledge, context sensitivity, and the possible role of language use in the process of learning and developing mathematical knowledge.     

Goal specificity and learning with a hypermedia program

Problem solving research has found that a nonspecific goal (NSG) leads to better learning than a specific goal (SG). This effect can be understood in terms of dual-space search theories of problem solving. To apply the theory, we studied goal specificity effects with a hypermedia program in which participants had to learn about the outbreak of World War 1, either with the goal to find twenty dates (i.e., SG) or with the goal to explain the reasons for the war (i.e., NSG). As expected, compared to the SG-group, the NSG-group correctly answered more factual questions about the text during the task, spent more time on average per page, and more often looked for extra information. In a final questionnaire with factual and inferential questions, the NSG-group still performed better than the SG-group. The NSG-group may also show better transfer of what they had learnt to a new situation.     

Improving insight and non‐insight problem solving with brief interventions

Developing brief training interventions that benefit different forms of problem solving is challenging. In earlier research, Chrysikou (2006) showed that engaging in a task requiring generation of alternative uses of common objects improved subsequent insight problem solving. These benefits were attributed to a form of implicit transfer of processing involving enhanced construction of impromptu, on‐the‐spot or ‘ad hoc’ goal‐directed categorizations of the problem elements. Following this, it is predicted that the alternative uses exercise should benefit abilities that govern goal‐directed behaviour, such as fluid intelligence and executive functions. Similarly, an indirect intervention – self‐affirmation (SA) – that has been shown to enhance cognitive and executive performance after self‐regulation challenge and when under stereotype threat, may also increase adaptive goal‐directed thinking and likewise should bolster problem‐solving performance. In Experiment 1, brief single‐session interventions, involving either alternative uses generation or SA, significantly enhanced both subsequent insight and visual–spatial fluid reasoning problem solving. In Experiment 2, we replicated the finding of benefits of both alternative uses generation and SA on subsequent insight problem‐solving performance, and demonstrated that the underlying mechanism likely involves improved executive functioning. Even brief cognitive– and social–psychological interventions may substantially bolster different types of problem solving and may exert largely similar facilitatory effects on goal‐directed behaviours.     

Goal specificity and knowledge acquisition in statistics problem solving: Evidence for attentional focus

Solving training problems with nonspecific goals (NG; i.e., solving for all possible unknown values) often results in better transfer than solving training problems with standard goals (SG; i.e., solving for one particular unknown value). In this study, we evaluated an attentional focus explanation of the goal specificity effect. According to the attentional focus view, solving NG problems causes attention to be directed to local relations among successive problem states, whereas solving SG problems causes attention to be directed to relations between the various problem states and the goal state. Attention to the former is thought to enhance structural knowledge about the problem domain and thus promote transfer. Results supported this view because structurally different transfer problems were solved faster following NG training than following SG training. Moreover, structural knowledge representations revealed more links depicting local relations following NG training and more links to the training goal following SG training. As predicted, these effects were obtained only by domain novices.     

The influence of open goals on the acquisition of problem-relevant information

There have been a number of recent findings indicating that unsolved problems, or open goals more generally, influence cognition even when the current task has no relation to the task in which the goal was originally set. It was hypothesized that open goals would influence what information entered the problem-solving process. Three studies were conducted to establish the effect of open goals on the acquisition of problem-relevant information. It was found that problem-relevant information, or hints, presented implicitly in a 2nd task in between attempts at solving problems aided problem solving. This effect cannot be attributed to strategic behavior after participants caught on to the manipulation, as most participants were not aware of the relationship. The implications of this research are discussed, including potential contributions to our understanding of insight, incubation, transfer, and creativity.     

Imitation and Creativity: Beneficial Effects of Propulsion Strategies and Specificity

Prior studies examining imitation of exemplar solutions have produced a mixed pattern of findings with some studies indicating that exemplar imitation contributes to creative problem‐solving and other studies indicating that it may inhibit creative problem‐solving. In the present effort, it is argued that the effects of exemplar imitation on creative problem‐solving depend on the strategies people use when working with exemplars. In the present study, people were asked to provide advertising campaigns in response to a marketing problem. Prior to starting work on this problem, manipulations were made in exemplar content. Imitation strategies used in problem‐solving, for example, forward incrementation, and redefinition, were assessed. It was found that imitation strategies were strongly related to the production of higher quality, more original, and more elegant advertising campaigns. Moreover, use of these strategies was facilitated when more specific information was presented in exemplar solutions. The implications of these findings for understanding the role of imitation in creative problem‐solving are discussed.     

Cues to solution, restructuring patterns, and reports of insight in creative problem solving

While the subjective experience of insight during problem solving is a common occurrence, an understanding of the processes leading to solution remains relatively uncertain. The goal of this study was to investigate the restructuring patterns underlying solution of a creative problem, and how providing cues to solution may alter the process. Results show that both providing cues to solution and analyzing problem solving performance on an aggregate level may result in restructuring patterns that appear incremental. Analysis of performance on an individual level provides evidence for insight-like solution patterns. However, no evidence is found for a relationship between an individual's restructuring pattern and their subjective experience of insight during problem solving.     

Enhancing Digital Fluency through a Training Program for Creative Problem Solving Using Computer Programming

The purpose of this paper is to propose a training program for creative problem solving based on computer programming. The proposed program will encourage students to solve real‐life problems through a creative thinking spiral related to cognitive skills with computer programming. With the goal of enhancing digital fluency through this proposed training program, we investigated its effects. Two sets of experiments were performed in which 119 typical students and 30 younger, gifted students participated. Two synthetic creative problem solving tests, which had a high correlation with logical ability, scientific problem solving ability and divergent thinking ability, were developed to measure creative problem solving ability. We provided the treatment group with a paper‐based booklet with relevant problems developed specifically for that group. ANCOVA statistical procedures were used to analyze the pre‐ and post‐synthetic creative problem solving tests. The findings of our study are as follows: with typical students, the originality of the treatment group outperformed the control group, a result that was compatible with previous research. With gifted students, the fluency of the treatment group outperformed the control group, and overall creative problem solving ability was enhanced. Remarkably, fluency increased significantly, a notable difference from the results of prior studies. In conclusion, we inferred that, given the definition of digital fluency, if creative problem solving ability is enhanced by a training program for creative problem solving based on computer programming, digital fluency will ultimately be improved. In this paper, we discuss the result of fluency enhancement that contradicts prior research. We suggest that this training program could be a new learning environment for the students who have grown up with digital media.     

Restructuring revisited

The central concept of the information processing theory of problem solving is search. In contrast, the central concept of the Gestalt theory of problem solving is restructuring. Both concepts express important aspects of human thinking. A theory is presented which interprets restructuring and the related concept of insight in information processing terms. It is hypothesised that restructuring is a change in mental representation which affects the applicability of problem solving operators. Insight is hypothesized to occur when restructuring of the search space brings the goal state within the horizon of mental look-ahead.     

Reasoning as simulation

The theory that human cognition proceeds through mental simulations, if true, would provide a parsimonious explanation of how the mechanisms of reasoning and problem solving integrate with and develop from mechanisms underlying forms of cognition that occur earlier in evolution and development. However, questions remain about whether simulation mechanisms are powerful enough to exhibit human-level reasoning and inference. In order to investigate this issue, we show that it is possible to characterize some of the most powerful modern artificial intelligence algorithms for logical and probabilistic inference as methods of simulating alternate states of the world. We show that a set of specific human perceptual mechanisms, even if not implemented using mechanisms described in artificial intelligence, can nevertheless perform the same operations as those algorithms. Although this result does not demonstrate that simulation theory is true, it does show that whatever mechanisms underlie perception have at least as much power to explain non-perceptual human reasoning and problem solving as some of the most powerful known algorithms.     

Can dogs defy gravity? A comparison with the human infant and a non-human primate

We conducted four experiments with 56 adult dogs (Canis lupus familiaris) involving tasks where food was dropped through an opaque tube connected either vertically or diagonally to one of two or three goal boxes. In the first experiment, modelled after studies with children and primates, the dogs first searched significantly more often in the location directly beneath the drop-off point (a gravity bias), although this box was not connected with the tube. These results are comparable to those of human infants and cotton-top tamarins. Experiments 2–4 tested which problem solving strategy the dogs applied to find the food. Results show that they do not understand the physical mechanism of the tube itself, and they apply one of three search strategies: search the gravity box (the one below the drop-off box); search the box in the middle; learn the correct location of the goal box. When the goal box was in the same location the dogs learned to search there over trials, that is, they learned to ‘defy gravity’, but when the location of the goal box changed over trials they showed no learning. These findings are compared with those from human infants and cotton-top tamarins: like these species, the dogs can learn to overcome a gravity bias, but only when the reward is to be found in a consistent location.     

Schema Creation in Programming

The creation of plan schemes is examined in a naturalistic, longitudinal study of problem solving. Ten novice programmers each wrote eight Pascal programs to solve a series of problems. Their protocols were analyzed to determine how declarative programming knowledge was used to create simple procedural program plans, and how the simple plans were used to create complex plans. Plan creation showed a process of backward development, from the goal to the plan focus, that port of the plan that directly implements the goal. Once defined; it is expanded to create the complete plan, showing backward development of plan parts from the focus. Once the plan is complete, it may be stored as a plan schema and retrieved in subsequent problem solving. The plan will then show forward development as it is implemented in schema order, the order in which plan pieces occur in the finished program. The change from backward development during creation to forward development after retrieval was strongly evident in the statistical analysis of the protocol data. Previous studies of novice programming, which showed only forward development, ore explained as special cases of this more general model, cases in which schema knowledge was available to the problem solver.     

Multiple points of entry into a circular enclosure prevent place learning despite normal vestibular orientation and cue arrays: evidence for map resetting

This study identified sources of map orientation critical for successful spatial problem solving by rats of a plus maze embedded in water. Disorientation slowed, but it did not prevent acquisition of goal location. Use of a circular enclosure with multiple points of entry prevented reliable goal location. A single entry point enabled the rats to locate a fixed goal. A cue array within the enclosure was ineffective in providing orientation. These data suggest that stable map orientation can be derived from entry location when enclosure geometry is uniformative, but is not readily taken from cue arrays. They further suggest that map orientation is reset when rats enter an enclosure.