Figure 1412

Two of the matchstick problems used by Knoblich et al. (1999), and the cumulative solution rates produced to these types of problems in their study. Copyright © 1999 by the American Psychological Association. Reprinted with permission.

modifiable. Furthermore, they proposed that people should find some of these constraints were easier to relax than others, depending to how radically a constraint changed the representation of the equation. For example, removing a stick from a value just changes the value in the equation, but removing a stick in the equality sign changes the whole equation. Based on these assumptions they defined sets of problems that they expected to be harder or easier to solve based on the different constraints that had to be relaxed in them. So, the "VI=VII+I" problem was predicted to be easier than the "IV=III - I" problem, because the former can be solved by relaxing the value of the equation whereas the latter involves relaxing constraints on the function and equality sign. Figure 14.12 shows a plots of the cumulative solution times produced to problems of these two different types, showing a marked difference in the difficulty of the two. Knoblich et al. found substantial evidence to support a detailed analysis of the impact of different constraints on the solution of these insight problems.

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