In this study, I investigated 27 university calculus students' mathematical beliefs and connections between those beliefs and their understandings of limit. Participants were selected on the basis of questionnaire and interview responses to real-number, infinity, function, and sourcesof- conviction items. Data obtained in a subsequent limit interview suggest a relationship between sources of conviction and understanding of limit; students with external sources of conviction gave more incoherent or inappropriate definitions of limit, held more misconceptions of limit as bound or unreachable, and were less able to justify limit calculations than those with internal sources of conviction. The influence of content beliefs on understanding of limit is less evident.
Jennifer E. Szydlik, Assistant Professor, Mathematics Department, University of Wisconsin Oshkosh, 800 Algoma Boulevard, Oshkosh, WI 54901; email@example.com