| This is a rhetorical and genealogical examination of four undergraduate mathematics courses: Real Analysis, Advanced Geometry, Complex Analysis, and Discrete Mathematics. The framework of the study is rhetorical because I read course artifacts from the perspective of literary analysis. The framework is also genealogical because I was interested in the construction of subjectivity as performed in each of the courses. To explore these issues I observed the four courses over a semester, looking at the ways students and professors interacted, how mathematics operated in the courses, and how supporting texts and documents such as textbooks, syllabi, course web pages, and course handouts contributed to the visions of teaching and mathematics presented in each course. This research presents an analysis of the construction of the subject (where the subject is undergraduate mathematics students) in these four courses to highlight the differences in pedagogical and mathematical approaches across them.;Epistemologically, the study takes a Foucaultian discourse position in which math is what math does. The approach of this study rejects a more realist stance in which 'real' mathematics exists beyond material practices. Instead, the study allows for multiple historical and temporal instantiations of mathematics, in which the subject of mathematics (both student and discipline) is constructed differently in each of the different settings.;This dissertation is a response to common stereotypes of mathematics courses as teacher-centered lectures, sites of content knowledge delivery rather than pedagogical experiences for students. This study takes the position that there is no pedagogy without content, and there is no content without pedagogy. The study also responds critically to assumptions that conventional lecture-based mathematics courses tend to be taught in similar ways. Even though three of the four courses examined here were lecture based, there was always more than lecture present, and even the lectures constructed different possibilities for subjectivity.;To analyze the construction of the mathematical subject, I used a four-part Foucaultian framework that asked: (1) What aspect of the students needed to change (substance), (2) How did the course invite students to take on these changes (mode), (3) How did the activities (or regimen) of the courses act to initiate that change, and (4) What a model or perfect outcome of the course might look like (telos).;This study concludes with a consideration of issues of inclusion and exclusion. It suggests that mathematics is practiced differently across multiple courses and that these differences allow for varied opportunities for students to engage with mathematics and to be excluded from it. Mathematicians and teacher educators can benefit from awareness of assumptions that shape subjectivity in mathematics courses, and such awareness can help increase access to various types of mathematical thinking. |
