Proceedings of the Annual Meeting of the Cognitive Science Society

We propose that three qualitatively different strategies help focus attention during problem solving.The first strategy is to apply operators that will lead to definite progress toward the goal. Attention will befocussed by this strategy as long as some operator in this class is applicable, Whe n clear progress can not beachieved, the problem solver must decide how best to proceed. It then invokes the second strategy to selectoperators that preserve important characteristics of the current problem. These operators are likely to keepthe problem solver from diverging sharply from the goal while possibly enabling the application of operatorsby the first strategy. Whe n the problem solver can follow neither of the first two strategies, it invokes thethird strategy of arbitrarily applying legal operators. W e see the second strategy as an essential differencebetween novice and expert problem solvers. It is easy to recognize definite progress to^*'ard a goal and it iseasy to recall which operators can be legally applied. Expertise involves knowing which characteristics of asituation should be preserved (or created) when no way to definitely progress toward the goal is known. Thisthree-strategy theory has been implemented and tested in a system that performs mathematical calculationsin the course of solving physics problems. W e describe a number of mathematical calculation operators usedunder each strategy