A production system model for human problem solving

Summary A new production system model was developed for a class of transformation problems, based upon the results of an experiment which evaluated the psychological validity of a noticing order in problem solving. This model specifies how general problem solving heuristics interact with domain knowledge and how possible actions are assembled from externally presented information. The production system may conceptually be divided into three groups: move generation, move evaluation, and move execution productions. The simulation model was evaluated by a second experiment. With a common set of parameter values, good fits were obtained between the predicted and observed data. The significance of individual productions was assessed by running simulations with individual productions deleted. While previous simulations have described subjects' behavior on a single problem, the present model successfully predicted human problem solving in three structurally different problems. The proposed production system thus gives a detailed account of the procedural knowledge that subjects use in transformation problems.     

A model of problem solving with incomplete constraint knowledge

The problem-solving behavior of subjects presented with a series of Tower of Hanoi problems is examined. A production system model which incorporates elements of domain-specific knowledge into a general problem-solving framework is presented. Other models developed for the task are based on understanding of complete solution strategies and are not satisfactory models of nonexpert human performance. The current model discriminates between problem-solving behavior based on constraint knowledge and behavior based on nonspecific general search strategies. A variety of move choice and latency measures are used to compare the performance of the model to human subject performance.     

A proposed universal model of problem solving for design,science and cognate fields

A modestly generic, innovative, problem solving process with roots in the study of design and scientific research problem solving is presented and motivated. It is argued to be the shared core process of all problem solving. At its heart is a recognition of five foci or nodes of change vital to the process (changes in problem and solution formulation, method, constraints, and partial solution proposals) together with a bootstrap marked by the formation of higher order knowledge about problem solving in the domain in tandem with the solving of specific problems, the essential feature of all learned improvement. None of these elements is entirely original, but the way they are made explicit and developed (rather than folded into fewer, more abstract, boxes) is argued to provide fresh understanding of the organisation and power of the process to deal with complex practical problems.     

Extended problem solving treatment for depression

Introduction: Effective brief psychological approaches for depression that can be delivered by a variety of health professionals with minimal training increase access to treatment by patients. Problem Solving Treatment (PST) was developed for primary care and was modified for this study (EPST) to better meet the needs of mental health patients. Method: A total of 92 therapists from different professional backgrounds completed EPST workshops and treated 92 patients with major depression with interval clinical and treatment process assessments. Results: EPST achieved a significant reduction in depressive symptom scores, life problem scores, and there were few treatment non‐completers. Treatment outcome was predicted by process and therapist variables. Discussion: EPST is an effective and easy to teach treatment that can be delivered by a variety of practitioners and suitable for busy primary mental health care settings.     

Memory for impasses during problem solving

Three experiments were conducted to investigate the relative memorability of solved versus unsolved problems in long-term memory. In each experiment, subjects worked on a set of potentially solvable word problems, with the time spent on each problem held constant. Problem memorability was then measured with a free-recall task. In Experiment 1, in which a majority of problems were solved, unsolved problems were better remembered. In Experiments 2 and 3, we expanded on these results by manipulating problem difficulty and thus the ratio of solved to unsolved problems. When unsolved problems were as frequent as or more frequent than solved problems, no memory differences were found. Across all three experiments, the ratio of solved to unsolved problems was found to be a significant predictor of unsolved-problem memorability, but was not significantly related to the memorability of solved problems. The results illustrate that when impasses in problem solving are infrequent, they are more available in memory than are solved problems. It is speculated that this memory phenomenon may facilitate the recognition of opportunities to return to problems that have been terminated short of solution.     

A microgenetic study of insightful problem solving

An eight-session microgenetic study of acquisition of an insightful problem-solving strategy was conducted. A total of 35 second graders who did not use this insightful strategy initially were assigned to two groups that differed in the frequency of problems likely to facilitate discovery and generalization of the strategy. Children in the facilitative problems group discovered the insightful strategy earlier, used it more often subsequently, and transferred it more often to novel problems than did those in the nonfacilitative problems group. Children generally discovered the insightful strategy on the most facilitative items and extended it progressively to items on which its advantages were smaller but still substantial. The results indicate that experience outside the experimental situation, as well as experience inside the experimental situation, influences use of new strategies.     

Analogical problem solving

The use of an analogy from a semantically distant domain to guide the problemsolving process was investigated. The representation of analogy in memory and processes involved in the use of analogies were discussed theoretically and explored in five experiments. In Experiment I oral protocols were used to examine the processes involved in solving a problem by analogy. In all experiments subjects who first read a story about a military problem and its solution tended to generate analogous solutions to a medical problem (Duncker's “radiation problem”), provided they were given a hint to use the story to help solve the problem. Transfer frequency was reduced when the problem presented in the military story was substantially disanalogous to the radiation problem, even though the solution illustrated in the story corresponded to an effective radiation solution (Experiment II). Subjects in Experiment III tended to generate analogous solutions to the radiation problem after providing their own solutions to the military problem. Subjects were able to retrieve the story from memory and use it to generate an analogous solution, even when the critical story had been memorized in the context of two distractor stories (Experiment IV). However, when no hint to consider the story was given, frequency of analogous solutions decreased markedly. This decrease in transfer occurred when the story analogy was presented in a recall task along with distractor stories (Experiment IV), when it was presented alone, and when it was presented in between two attempts to solve the problem (Experiment V). Component processes and strategic variations in analogical problem solving were discussed. Issues related to noticing analogies and accessing them in memory were also examined, as was the relationship of analogical reasoning to other cognitive tasks.     

Arithmetic word problem solving: Evidence for the construction of a mental model

In the first experiment reported here, adults were given an unexpected task of problem recognition after a resolution task. During the recognition task, participants were presented with the original problems, inconsistent problems that had never been solved, and paraphrases, which respected the relational structure of the original problems but not their exact wording. More precisely, paraphrases were constructed by inversing the terms and the linguistic expressions in the original problems. Whereas the literal form of paraphrastic problems bore the least resemblance to original problems, paraphrastic problems were associated to higher recognition rates than inconsistent problems. A second experiment ruled out the interpretation that this result was due to a mere remembering of the exact values used in the problem text. Taken together, these results provide evidence that a non-propositional representation is built by individuals to solve arithmetic word problems and suggest that a mental model is constructed (Johnson-Laird, 1983).     

Collective efficacy and vigilant problem solving in group decision making: A non-linear model

This research explores the relationship between collective efficacy and aspects of analytic or vigilant problem solving (Janis, 1989) in the context of group decision making. We hypothesized that vigilant problem solving would be most evident under conditions of relatively moderate collective efficacy, as opposed to either very high or very low collective efficacy. We investigated this hypothesis with groups of business students who participated in a complex business strategy simulation. Results show a significant curvilinear relationship between collective efficacy and vigilant problem solving, and a significant linear relationship between vigilant problem solving and decision outcomes. There is also evidence that vigilant problem solving mediates the relationship between collective efficacy and decision outcomes. Implications for theory, managerial practice, and directions for future research are discussed.     

Developing a plan for solving a problem: A representational shift

Research analyzing transitions from lower to higher levels of problem solving has focused either on quantitative increments in processing demands (Case, 1984; Klahr & Robinson, 1981) or on qualitative shifts in the organization of representations (Fischer & Pipp, 1984; Piaget, 1976). This study is concerned with distinguishing the value of these two approaches to problem solving through a microgenetic analysis of children's initial attempts to solve the Tower of Hanoi problem. As suggested by Siegler and Crowley (1991), a microgenetic approach is particularly useful in determining the process of cognitive change. One-hundred and thirty-six children, ages 6 through 8 years, were presented with the standard three-disc problem and allowed 3 minutes to complete it. The quality of the children's performance was analyzed by noting the positioning of the first move, the number and location of illegal moves, and the frequency and location of optimal moves. The results indicate that qualitative shifts in children's representation of the problem space are a crucial aspect of successful performance.     

Automated problem solving for the behavioral sciences

In view of the obvious advantages of computers for the behavioral sciences, the question is raised as to how to make more effective use of computing capabilities. One idea is to require that fledgling behavioral scientists receive brief training in flowcharting and algorithm generation rather than a full course in computing skills. Such training would be an important adjunct for those who would go on for further instruction, especially in view of current deficiencies in many computer courses. One recurrent deficiency lies in the lack of specific guidelines for conceptualizing problems for computer implementation. Such guidelines are developed here, along with other suggestions designed to attenuate the difficulty in conceptualization.     

Interactive insight problem solving

Insight problem solving was investigated with the matchstick algebra problems developed by Knoblich, Ohlsson, Haider, and Rhenius (1999 Knoblich, G., Ohlsson, S., Haider, H. and Rhenius, D. 1999. Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory and Cognition, 25: 1534–1555. [Crossref], [Web of Science ®] , [Google Scholar]). These problems are false equations expressed with Roman numerals that can be made true bymoving one matchstick. In a first group participants examined a static two-dimensional representation of the false algebraic expression and told the experimenter which matchstick should be moved. In a second group, participants interacted with a three-dimensional representation of the false equation. Success rates in the static group for different problem types replicated the pattern of data reported in Knoblich et al. (1999 Knoblich, G., Ohlsson, S., Haider, H. and Rhenius, D. 1999. Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory and Cognition, 25: 1534–1555. [Crossref], [Web of Science ®] , [Google Scholar]). However, participants in the interactive group were significantly more likely to achieve insight. Problem-solving success in the static group was best predicted by performance on a test of numeracy, whereas in the interactive group it was best predicted by performance on a test of visuo-spatial reasoning. Implications for process models of problem solving are discussed.     

Giving up problem solving

How do people decide to abandon a problem? Participants were presented with unsolvable water jar problems, having been accurately informed of the prior probability of solvability. Across three experiments, we discovered effects of prior probability of solvability and of problem size (number of distinct problem states) on measures of effort and confidence. If a problem is more likely to be solvable and allows more problem states, a problem solver spends longer trying to solve the problem. Giving-up decisions are informed by the same judgments of probability of success and costs of solution that inform move-choice in a rational model of problem solving.