Theory of constructions and set in problem solving

Hierarchically organized knowledge about actions has been postulated to explain planning in problem solving. Perdix, a simulation of problem solving in geometry with schematic planning knowledge, is described. Perdix’s planning knowledge enables it to augment the problem space it is given by constructing auxiliary lines. The planning system also provides a mechanism that can result in problem solving set. Results of three experiments involving set and constructions seem consistent with the kinds of knowledge structures hypothesized in the model. Protocols given during solution of 11 geometry problems showed general agreement with the explanation of constructions and set based on planning knowledge, but they also indicated processes of human problem solving not represented in the model. Finally, the explanation of constructions is discussed in relation to the general question of ill-structured problems and creativity, and the explanation of set is discussed in relation to other phenomena in the problem solving literature, including functional fixedness.