This paper describes a study of the connections between beliefs about mathematics, autonomy, and knowledge structures in mathematics. Assumptions underlying the study were (1) that students' beliefs and knowledge are constructs of the individual and play a dynamic role in the learning and doing of mathematics; and (2) that autonomy theoretically affects persistence, confidence, and mathematical growth. The study was conducted in a high school in a university town in New Hampshire. Six volunteers distributed evenly across Algebra I and II courses were interviewed after participating with their class in a unit on functions. Eight 45-minute interviews were conducted with each student to gather information on their beliefs about mathematics as conceptual versus procedural, their beliefs about their role and the teacher's role in learning mathematics, their autonomy with mathematics, and their constructed knowledge from the unit on functions. The interviews were treated as case studies and were examined individually and then cross-compared. Autonomy and beliefs were found to be integral to the students' conception of mathematics and influenced how problems were approached and mathematics learned. Further study in the formation and modification of beliefs and in the interplay between beliefs, autonomy, and learning in actual classroom contexts is suggested. Contains 71 references. (PDD)