Two main classes of theory have been proposed to account forinsight problem-solving performance; those that invoke theovercoming of constraints arising from prior knowledge as thesource of insight, and those that propose strategic search formoves that make progress towards a hypothesized goal state.An experiment using matchstick algebra problems assessed thecontributions of each source. Results indicate that, while priorknowledge creates the conditions under which matchstickalgebra problems are more or less difficult to solve, search formoves that make the most apparent progress towards ahypothesized goal provides the key to eventual solution.

Despite progress in understanding the sources of difficulty in solving insight problems, how new ideas are discovered, implemented, and learned is poorly understood. We report an experiment testing a theory of how individuals use failed attempts to discover new ideas. We compared performance on the nine-dot problem with a variant requiring solution using three lines rather than four. Results supported predictions that the three-line variant is easier than the four-line, and that transfer of solution knowledge from the three- to the four-line version is facilitative, but not vice-versa. Additionally, varying the spacing between dots facilitated discovery and transfer of solutions in both variants. Our theory specifies a priority order for seeking new ideas that offers a partial solution to the frame problem. Individuals first seek ideas from the problem statement and attempts they make. Only when these sources fail do they resort to searching memory or the external task environment.