The purpose of this study was to discover what teachers believe about problem solving in mathematics and to what extent their beliefs are reflected in the beliefs of students. Ten 5th-grade teachers in a large rural school district volunteered to participate. Each teacher identified one student perceived as successful and one perceived as unsuccessful in problem solving in mathematics. Interviews were conducted with teachers and their students. Interview questions were designed to elicit beliefs about the nature of mathematical problem solving, attributions about the causes of students' performance in problem solving, and beliefs about the teaching and learning of problem solving in mathematics. Major conclusions were: (1) students and teachers believe that problem solving is primarily an application of computational skills; (2) students and teachers reported that their judgments about successful problem solving were based on right answers; (3) students' and teachers' attributions about the causes of success and failure affect learning in problem solving; (4) teachers focused on right answers and strongly discouraged the use of calculators for problem solving; and (5) teachers tended to overestimate students' ability to do problems involving computation and underestimate students' ability to do reasoning problems. (YP)