Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving that occurred during 49 video-recorded lessons taught by six renowned artist teachers. When a solution to a problem came about as the result of both teacher and student involvement, I identified the problem-solving behaviors that were differentiable as performed by teacher or student. Five components, synonymous with problem-solving behaviors observed in other fields, emerged as identifiable behaviors that contributed to problem solution: establish goals, evaluate, conceive and consider options, apply principles, and decide and act. To confirm this model, I coded every observable behavior within 18 full-length lessons. Almost every on-task behavior was describable in terms of the proposed problem-solving framework.