Being a mathematician: An ethnographic account of the cultural production of a mathematician at a university

By investigating the nature of mathematical knowledge communicated in university level mathematics classes, this ethnography of the practice of mathematics describes and analyzes the social transformation of a mathematics learner. This research shows that the mathematics department at a large metropolitan university is a community of practice with an indigenous epistemology, and that learning is a process of participating in the practice of mathematics in a sociocultural context by which a learner becomes socially transformed into a certain kind of practitioner according to the cultural norms and values developed in a mathematics community.; However, social transformation is not a passive process of acculturation. As a practicing mathematician, a learner renegotiates not only his/her logicomathematical cognitive schema but also the meaning of lived experience. More importantly, this negotiation of meaning is based on a learner's worldview, which is developed through his/her experience outside of the mathematics community as well as through the indigenous epistemology of the mathematics community. Specifically, the analysis of metaphor in mathematical communication reveals the dialectical relation between a learner's mathematical subjectivity and the objective system of mathematics.; More generally, this research traces the trajectory of social transformation of a mathematics learner as a coordination between what is communal and what is personal and, as an interaction between the cultural epistemological standpoint developed by a mathematics community and those by outside communities. From this perspective, educational implications for learning mathematics in school are drawn. First, the notion of indigenous epistemology in mathematics class implies that the kind of competence developed there is cultural competence, which includes a cultural way of seeing, reasoning, knowing, speaking and being in the world. Second, the cultural notion of mathematical competence suggests that learning is culturally constructed. In particular, it provides a perspective on a mathematical deficit as a cultural mismatch between school mathematics and the mathematical culture that the learner has been socialized into outside school. This implies that a mathematics teacher should be aware of and respect cultural differences in order to help a learner overcome difficulties in mathematics caused by a cultural mismatch.