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Its behavioral correlate (or rather causal effect) is sometimes identified as the critical move—the first move that goes outside the restricted search space (Jones, 2003).The fourth stage is conscious search again, but now, in the extended search space, at the end of which the problem solver finds the solution (Öllinger et al., 2014b).
Those people who do not solve the task get stuck in this state, while others overcome the self-imposed constraints.
The latter start to look for the solution in an extended search space, in which, eventually they find the solution (in the Five-Square problem, they start putting sticks to further positions, and decompose the initial cross shape).
Overcoming constraints and restructuring the task in one's mind is often accompanied by an “Aha!
” experience that is usually used as the defining feature of insight problem solving (Bowden and Beeman, 1998; Boden, 2004; Bowden et al., 2005; Kounios et al., 2006; Danek et al., 2013, 2014).
After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task.
We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times.
An example is the Five-Square problem (Katona, 1940), where problem solvers see a cross shape made of matchsticks (Figure 1) and they have to replace three matchsticks in order to get a shape of four squares of equal size instead of the given five squares in the cross shape.
According to the restructuring hypothesis, insight problem solving is different from analytic problem solving (Fleck and Weisberg, 2013): problem solvers cannot assess how far they are from the solution (Metcalfe and Wiebe, 1987), and the solution pops into the problem solvers' mind suddenly and unexpectedly, evoking an Eureka moment, or “Aha! This moment of enlightenment is usually—according to some, necessarily (Ohlsson, 1992; Knoblich et al., 1999, 2001; Jones, 2003; Öllinger et al., 2014a)—preceded by a longer period of impasse when the problem solver gets stuck and has no idea how to proceed. The initial position of sticks on the grid in the five square problem. We show a 5-by-5 grid here, but in the computerized task, the cross shape was in the middle of a 9-by-9 grid.
According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task.
The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally.