The Journal of Problem Solving

The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

Damian G. Stephen — Fri, 01 May 2009 06:50:26 PDT

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive science in terms of symbolic representation. Cognition may be better described in terms of an open, nonlinear dynamical system. By this reasoning, insight would be the self-organization of novel structure. Self-organization is a well-studied phenomenon of dynamical systems theory, associated with specific trends in entropy and power-law behavior. We present work using nonlinear dynamics to capture these trends in entropy and power-law behavior and thus to predict the self-organization of novel cognitive structure in a problem-solving task. Future explorations of problem solving will benefit from considerations of the continuous nonlinear interactions among action, cognition, and the environment.

Human Problem Solving in 2008

Zygmunt Pizlo — Fri, 01 May 2009 06:46:50 PDT

This paper presents a bibliography of more than 200 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo database. Journal papers, book chapters, books and dissertations are included. The topics include human development, education, neuroscience, research in applied settings, as well as animal studies.

Individual Differences in Optimization Problem Solving: Reconciling Conflicting Results

Edward P. Chronicle — Thu, 24 Jul 2008 06:25:58 PDT

Results on human performance on the Traveling Salesman Problem (TSP) from different laboratories show high consistency. However, one exception is in the area of individual differences. While one research group has consistently failed to find systematic individual differences across instances of TSPs (Chronicle, MacGregor and Ormerod), another group (Vickers, Lee and associates) has found individual differences both within TSP performance and between TSP performance and other cognitive tasks. Among possible reasons for the conflicting results are differences in procedure and differences in the problem instances used. To try to resolve the discrepancy, we collected data on TSP performance by combining the procedure used by one group with problem instances used by the other. The comparison involved nine 30-node and nine 40-node TSP problems previously used by the Vickers group, using computer presentation. Here, we had the same problems completed by 112 participants using a paper-and-pencil mode of presentation. We examined the results in the form of distributions of correlations across individuals for each pair of problems of the same size. The distributions for the computer and paper forms of presentation were very similar, and centered between correlations of 0.20 and 0.30. The results indicated the presence of individual differences at a level that fell between those previously reported by the two laboratories. The pattern of results indicated that previous discrepancies did not arise because of differences in procedure. Instead, individual differences appeared to become more prevalent as the difficulty of problems increased. The results are consistent with an explanation that performance on simpler instances is dominated by lower-level processes, but that as instance difficulty increases, higher-level functions become increasingly involved.

Seeing is as Good as Doing

Magda Osman — Thu, 24 Jul 2008 06:25:55 PDT

Given the privileged status claimed for active learning in a variety of domains (visuomotor learning, causal induction, problem solving, education, skill learning), the present study examines whether action-based learning is a necessary, or a suffi cient, means of acquiring the relevant skills needed to perform a task typically described as requiring active learning. To achieve this, the present study compares the effects of action-based and observation-based learning when controlling a complex dynamic task environment (N = 96). Both action- and observation-based individuals learn either by describing the changes in the environment in the form of a conditional statement, or not. The study reveals that for both active and observational learners, advantages in performance (p < .05), accuracy in knowledge of the task (p < .05), and self-insight (p < .05) are found when learning is based on inducing rules from the task environment. Moreover, the study provides evidence suggesting that, given task instructions that encourage rule-based knowledge, both active and observation-based learning can lead to high levels of problem solving skills in a complex dynamic environment.

Some Tours are More Equal than Others: The Convex-Hull Model Revisited with Lessons for Testing Models of the Traveling Salesperson Problem

Susanne Tak — Thu, 24 Jul 2008 06:25:32 PDT

To explain human performance on the Traveling Salesperson problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors claimed empirical support for their model. In this paper we argue that the empirical tests performed by MacGregor et al. do not constitute support for the model, because they instantiate what Meehl (1997) coined "weak tests" (i.e., tests with a high probability of yielding confi rmation even if the model is false). To perform "strong" tests of the model, we implemented the algorithm in a computer program and compared its performance to that of humans on six point sets. The comparison reveals substantial and systematic differences in the shapes of the tours produced by the algorithm and human participants, for fi ve of the six point sets. The methodological lesson for testing TSP models is twofold: (1) Include qualitative measures (such as tour shape) as a dependent variable, and (2) use point sets for which the model makes "risky" predictions.

Volume 2 Issue 1 — Thu, 24 Jul 2008 06:25:29 PDT

Group Decision-Making on an Optimal Stopping Problem

Michael D. Lee — Fri, 29 Jun 2007 09:05:35 PDT

We consider group decision-making on an optimal stopping problem, for which large and stable individual differences have previously been established. In the problem, people are presented with a sequence of five random numbers between 0 and 100, one at a time, and are required to choose the maximum of the sequence, without being allowed to return to earlier values in the sequence. We examine group decision-making on these problems in an experimental setting where group members are isolated from one another, and interact solely via networked computers. The group members register their initial accept or reject decision for each value in the sequence, and then providing a potentially revised decision having viewed the recommendations of the other group members. Group decisions are made according to one of three conditions, requiring either consensus to accept from all group members, a majority of accept decisions from the group, or the acceptance of an appointed group leader. We compare individual decision-making to group decision-making under these three conditions, and find that, under some conditions, groups often significantly outperform even their best members. Using a signal detection analysis we provide an account of how the group decision-making conditions differ from one another, and from individual decision-making. Key findings are that people do not often revise their decisions, but, in the consensus and leadership conditions, are more conservative in their initial decisions. This conservatism removes the individual bias towards choosing values too early in the sequence, allowing the groups to perform better than their individual members. In the majority condition, however, people continue to behave as they did individually, and the group shows the same bias in decision-making.

Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities

Michael Brusco — Wed, 13 Jun 2007 11:09:34 PDT

The study of human performance on discrete optimization problems has a considerable history that spans various disciplines. The two most widely studied problems are the Euclidean traveling salesperson problem and the quadratic assignment problem. The purpose of this paper is to outline a program of study for the measurement of human performance on discrete optimization problems related to clustering of points in the two-dimensional plane. I describe possible objective criteria for clustering problems, the measurement of agreement of solutions produced by subjects, and categories of experiments for investigating human performance on clustering problems.

Theory Driven Hints in the Cheap Necklace Problem: A Preliminary Investigation

Yun Chu — Wed, 13 Jun 2007 11:07:13 PDT

Three experiments investigated the effects of two hints derived from the Criterion for Satisfactory Progress theory (CSP) and Representational Change Theory (RCT) on the cheap necklace problem (insight problem). In Experiment 1, fewer participants given the CSP hint used an incorrect (maximizing) first move than participants given the RCT hint or control participants given no hint on a single attempt at the problem. Experiment 2 found the number of trials to solution was fewer in the CSP condition than in the control over ten trials, and there were fewer incorrect first moves in the CSP. The results appear to support the CSP theory. However, in Experiment 3, the CSP and RCT hints were combined yielding a 75% solution rate over 34.88% in the control. Perhaps aspects from both theories are employed during the problem solving process.

Human Problem Solving in 2006

Zygmunt Pizlo — Mon, 14 May 2007 13:25:09 PDT

This paper presents a bibliography of a little more than 100 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Compendex databases. Only journal papers, books and dissertations are included. The topics include human development, education, neuroscience, research in applied settings, as well as animal studies. A few references from artificial intelligence are also given.