Several central ideas emerging from a systematic approach to teaching problem-solving in the quantitative sciences (chemistry, physics, engineering) are discussed. Areas addressed include: differences between teaching and performance, between naturalistic and effective functioning, and between detailed observations and gross statistical data; insights derived from naturalistic studies, focusing on preexisting knowledge of students, tacit knowledge of experts, and significant differences between problem-solving behaviors of students and of experts; and kinds of procedures and knowledge essential for good human problem-solving performance, pointing out general issues addressed by any theoretical model of good problem-solving and discussing characteristics of the knowledge base containing knowledge about a specific domain. Problem-solving procedures considered include initial problem description, synthesis of the problem, and assessment/improvement of the solution. Current problem-solving activities in science teaching (focusing on student behaviors and instructional practices) are addressed, followed by a discussion of improved methods for teaching problem-solving. These methods include teaching explicitly and separately the various kinds of knowledge essential for good problem-solving performance (including knowledge of how to describe problem effectively), procedures useful for making judicious decisions in search for solutions, procedures for assessing solutions for correctness/optimality, and methods for organizing large amounts of knowledge so information can be easily recalled/remembered. (JN)