This article presents a prescriptive analysis of the kinds of knowledge and procedures leading to effective human problem solving in a quantitative science such as physics. The knowledge about such a science, explicated in the case of mechanics, specifies special descriptive concepts and relations described at various levels of abstractness, is organized hierarchically, and is accompanied by explicit guidelines specifying when and how this knowledge is to be applied. General problem-solving procedures, to be used in conjunction with such domain-specific knowledge, specify how initially to describe and analyze any problem so as to facilitate its subsequent solution; how to search for a solution by methods of constraint satisfaction used together with heuristic methods for decomposing problems and exploring decisions; and how to assess whether the resulting solution is correct and reasonably optimal. The preceding model of effective human problem solving is compared with some relevant observations and with special experiments designed to test such a prescriptive model. It also suggests methods for teaching students improved scientific problem-solving skills.