Implementation of a problem-based mathematics curriculum, the "Interactive Mathematics Program" (IMP), at three high schools in California has been associated with more than just differences in student achievement. The outcomes that distinguished students who participated in the IMP program from students who followed a conventional algebra/geometry syllabus were the students' perceptions of the discipline of mathematics, of mathematical activity and the origins of mathematical ideas, of the mathematical nature of everyday activities, and of school mathematics and themselves as mathematicians. A coherent and consistent picture has emerged of the set of beliefs, perceptions and performances arising from such a program. Students who have participated in the IMP program appear to be more confident than their peers in conventional classes; to subscribe to a view of mathematics as having arisen to meet the needs of society, rather than as a set of arbitrary rules; to value communication in mathematics learning more highly than students in conventional classes; and to be more likely than their conventionally-taught peers to see a mathematical element in everyday activity. These outcomes occurred while the IMP students maintained performance levels on the mathematics portion of the SAT at or above those of their peers in conventional classes. If student achievement outcomes are comparable, the mathematics education community must decide whether it values these consequences of a problem-based curriculum. (Contains 1 figure and 8 tables.)