Relationships between community, interactions, and ways of knowing in college precalculus classes

National standards for learning mathematics increasingly emphasize learning mathematics with understanding and students as agents of their own and others' understanding. However, students may have limited experiences as agents of their own and others' understanding, while classroom community and interactions may either foster or constrain roles and behaviors that could contribute to more connected, independent, and contextual knowing. This study examined the relationship between students' ways of knowing in college precalculus classes and factors related to classroom social norms, instructor and student roles, and interactions related to mathematical activity. A qualitative two-case study approach was used to describe and analyze the development and nature of classroom community and interactions in two small community college classes during an eight-week summer quarter. Using Baxter Magolda's (1992) framework for development of students' ways of knowing in college, factors that were found to maintain students as absolute knowers included students' expectations of their roles, their entering perceptions of mathematics and learning mathematics, and the maintenance of instructor and student roles that placed mathematical and intermediate authority with the instructors. Factors that showed evidence of challenging students' absolute ways of knowing included instructors' explicit emphasis on understanding concepts, inclusion of real-life uses of mathematics, and portrayal of mathematics as uncertain. In addition, students' ways of knowing appeared to affect their perception of what they meant when they claimed a mathematical idea made sense. The discussion includes a framework classifying evidence of students' ways of knowing and evidence of constraints and affordances in instruction. When instructors and students are at the same level, students' ways of knowing are maintained. However, when instruction is provided at levels higher than students evidence, it confirms and challenges students' ways of knowing. Suggestions for supporting and challenging students' growth as learners are included