Non-traditional socio-mathematical norms in undergraduate real analysis
This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative investigation of classroom instruction and interactions, student and instructor interviews, and class exams. The study explores the roles of each norm as the students constructed understanding of advanced mathematics and transitioned to advanced mathematical thinking. I define "non-traditional" according to research accounts of traditional instruction in proof-based mathematics courses and considerations on the culture of the mathematics community. Evidence from this study indicates that classrooms in which students participate in constructing mathematics and act as mathematical validators strongly facilitates the transition to advanced modes of mathematical thinking and promotes students' mathematical autonomy. Students moved toward mathematical mindsets common to mathematicians by practicing the creative and constructive processes similar to research mathematicians. These norms led the classes to operate as microcosms of the greater mathematical community and institutionalize meaning as a classroom community (Cobb, 1989).