UC Berkeley

This dissertation lives at the intersection of two essential and under-researched domains. The first concerns the impact of new pedagogies at the university level. Although lecture is still the dominant mode of teaching in university mathematics, some mathematics faculty have been exploring the use of small-group work as a primary instructional mode. Little has been documented, at a fine-grained level, regarding the impact of small-group learning at university. The second concerns the growth and change of university students’ mathematical identities, especially at key points in their academic careers. Far more students begin their university careers intending to be mathematics majors than actually graduate as such, with much of the blame for attrition being placed on the teaching methods used. Moreover, many students who major in mathematics avoid pursuing advanced mathematical studies at the graduate level because of their struggle with proof-intensive courses at undergraduate level. A key question is how students grapple with the demands of these kinds of courses. This dissertation is situated in such a course, a one-semester course in number theory. It provides a detailed examination of the experiences of two focal students as they negotiated the challenges of group work in a mathematically demanding context. A new theoretical framework and methodological tools were created to unpack what took place, at a fine grained level of detail, over three timescales: in classroom groupwork, over the course, and in rapport to the major program.

Calls for evidence-based innovative teaching at the college level have been growing since the late 1980s, specifically in STEM (Science, Technology, Engineering, and Mathematics) fields, in large part to mitigate attrition. Inspired by the educational reform in K-12, some faculty have turned to the so-called active learning or student-centered pedagogies. As indicated by this dissertation and other research, such pedagogies have the potential to rekindle some new interests in collegiate students and to foster positive relationships with the disciplines. Nevertheless, there is a history of some student resistance to active learning pedagogies, either because students are not prepared for such pedagogies or have had negative past experiences with the same. To understand the failure and success of innovative pedagogies, research must closely attend to the voices that students develop as they interact with the new learning ecologies.

Building on psychoanalytical, socio-linguistic, and socio-cultural theories, this dissertation (Chapter 1) proposes and leverages a specific conceptualization of voice that addresses students’ past, present, and future. Such a conceptualization is needed to account for the realities of undergraduate students, who draw upon their resources, individualized in past experiences, as they engage in learning activities to prepare themselves for the future. The construct of voice is broken into three constituents: identity, position, and function; hence, the name of the VIP+function framework. The framework looks at the individualized identities that students actuate by animating positions in their ongoing activities to accomplish functions that forge their near and more distal futures. Additionally, this project (Chapter 2) enhances the investigation of identity formation and development by re-purposing an existing data collection technique, renamed as stimulated construction of narratives about interactions (SCNI). The SCNI technique attempts to generate data that can be jointly studied by two robust theoretical approaches of identity, narrative and situated approaches, which have been largely independent to this point.

The impact of pedagogies should be assessed not only by examining students’ engagement or performance in a program or course, but also by their power of transforming students’ identities. The case studies reported in this dissertation unpack the processes by which two students, Ted and Bettie, boosted their mathematical identities as they adapted to a proof-intensive course and small-group learning. Ted developed the confidence to pursue advanced mathematical studies (Chapter 3). Bettie faced events that challenged and diminished her mathematical identity, which she restored and strengthened over the course of the semester (Chapter 4). Overcoming several impediments, Bettie developed a new form of active engagement with the content, in contrast to her previous reliance on memorization and practice. (Chapter 5). The case studies of this work document some of the power of the pedagogies of small-group learning, despite their limitations. They reveal processes by which the two focal students were able to support each other’s learning development through groupwork, in ways that teaching based on lecture would not afford. They also highlight some advantages of having students work in the same group over multiple sessions: In cases similar to the ones discussed here, students needed time to build accurate understandings of each other’s behaviors and together establish a group culture that optimally supported each member’s learning processes.

In sum, this dissertation explores the impact of new pedagogies on students’ identity development by providing theoretical/methodological tools and analytic examples, which are applied to University level with the potential for application at K-12 education as well.