The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem solving heuristics and representational change to explain problem difficulty

Insight and search in Katona’s five-square problem

Insights are often productive outcomes of human thinking. We provide a cognitive model that explains insight problem solving by the interplay of problem space search and representational change, whereby the problem space is constrained or relaxed based on the problem representation. By introducing different experimental conditions that either constrained the initial search space or helped solvers to initiate a representational change, we investigated the interplay of problem space search and representational change in Katona’s five-square problem. Testing 168 participants, we demonstrated that independent hints relating to the initial search space and to representational change had little effect on solution rates. However, providing both hints caused a significant increase in solution rates. Our results show the interplay between problem space search and representational change in insight problem solving: The initial problem space can be so large that people fail to encounter impasse, but even when representational change is achieved the resulting problem space can still provide a major obstacle to finding the solution

Software scaffolds to promote regulation during scientific inquiry learning

This research addresses issues in the design of online scaffolds for regulation within inquiry learning environments. The learning environment in this study included a physics simulation, data analysis tools, and a model editor for students to create runnable models. A regulative support tool called the Process Coordinator (PC) was designed to assist students in planning, monitoring, and evaluating their investigative efforts within this environment. In an empirical evaluation, 20 dyads received a “full” version of the PC with regulative assistance; dyads in the control group (n = 15) worked with an “empty” PC which contained minimal structures for regulative support. Results showed that both the frequency and duration of regulative tool use differed in favor of the PC+ dyads, who also wrote better lab reports. PC− dyads viewed the content helpfiles more often and produced better domain models. Implications of these differential effects are discussed and suggestions for future research are advanced