Problem solving is viewed as an increasing area of interest that focuses on the theory, research, and teaching of general cognitive skills which are applicable to broad problem classes. This document gives an overview of some important aspects of the theory and research in order to identify what general cognitive skills ought to be taught. Modern cognitive psychology, chiefly represented by Piaget, and artificial intellitence, represented by researchers such as Allen Newell and Herbert Simon are identified and examined. Piaget's theory is reviewed in some detail, with observations from his work extended to certain results from information processes. Teaching implications are drawn from this examination and a course entitled, "Patterns of Problem Solving," taught under the Department of Philosophy, St. Louis University, is examined. (MP)