Abstract

This thesis presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I have modeled these perceptions using a theoretical framework, which combines elements of the Anthropological Theory of Didactics, developed in mathematics education, with a framework for the study of institutions - the Institutional Analysis and Development framework - developed in political science. I describe the models and illustrate them with examples from the empirical data, on which they have been built: final examinations from the past six years (2001-2007), used in the studied College institution, and specially designed interviews with 28 students. While a model of the instructors' perceptions could be formulated mostly in mathematical terms, a model of the students' perceptions had to include an eclectic mixture of mathematical, social, cognitive and didactic norms . The analysis that I carry out shows that these students' perceptions have their source in the institutional emphasis on routine tasks and on the norms that regulate the institutional practices. Finally, I describe students' thinking about various tasks on limits from the perspective of Vygotsky's theory of concept development. Based on the 28 interviews that I have carried out, I will discuss the role of institutional practices on students' conceptual development.