This paper presents the results of an experimental comparison of two competing predictions based on different theoretical models explaining the process of resolving the 9-dot problem. The first model is based on the concept of insight (the solution is found by instant transformation of the problem representation) and the second model is based on a stepwise approach and denies the existence of instant changes in the problem-solving process. Mental operators (i.e. the procedures described by Newell and Simon in their theory of problem space) were experimentally studied.

It was shown that the declarative hint of an essential operator did not lead to improved performance; on the contrary, it delayed the solution compared to the control group. Experimental manipulation of various operators could not identify any single one that, when activated, could alone speed up the solution. Apparently, a change in the holistic task representation (or at least, a change in some larger parts of the task structure, larger than those manipulated in this study) underlies the correct solution. The high efficiency of the hint consisting of four different operators provides indirect evidence of the same: in fact, in that case, the subject was presented with a unified visual pattern that was then entirely transferred from perceptual to mental space. Presumably, insight suggests the possibility to procedurally operate some earlier inaccessible parts of the problem conditions and the change in problem representation.

Thus, the present study provides evidence that the operators do not have the key to solving the problem of 9 dots and the arguments in favor of the classical understanding of insight – as a general rather than local change in the representation of the problem during the problem-solving process.