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

Much of expertise in problem-solving situations involves rajiidly choosinj? a tightly-constrained schema that is appropriate to the current problem. The paradigm of explanation-based learning, is being applied to investigate hou- an intelligent system can acquire these "appropriately general" schemata. While the motivations for producing these specialized schemata are computational, results reported in the psychological literature are corroborated by a fully-implemented comjjuter model. .Acquiring these special case schemata involves combining schemata from two different classes. One class contains domain-independent problem solving schemata, while the other class consists of domain-specific knowledge. By analyzing solutions to sample problems, new domain knowledge is produced that often is not easily usable by the problem-solving schemata. .Special case schemata result from constraining these general schemata so that a k n o w n problem solving technique is guaranteed to work. This significantly reduces the amount of ])lanning that the problemsolver would other>*ise need to perlorm elaborating the general schema in a n e w problem-solving situation.The model and an application of it in the domain of classical physics are presented.