| dc.description.abstract | Within this dissertation, I use design-based research along with discourse and interaction analysis to study classroom groups of mathematical learners to better understand and design for group structures and cultures that support students’ learning mathematics and becoming mathematical communities. Specifically, I focus on the phenomenon of groups of students learning mathematics together. I take the stance that groups learning math together is fundamentally different from students learning math on their own, requiring new metaphors and conceptualizations of learning. Additionally, understanding the group as a unit is important because only through groups do identity and learning happen (Lave & Wenger, 1991), the production of cultural practices (Fine, 2012), and mathematics is rehumanizing (Gutiérrez, 2018). Collectively, the three papers create a map of the different structures within classroom systems as classroom groups learn mathematics together. Each paper focuses on a specific structure while understanding it in relation to the others. Taken together, we begin to find some principles which we can use to tweak and iterate classroom design. Classroom networks and technology can jumpstart ways of learning mathematics together. Representation systems solve locally constituted problems, and researchers and teachers can better identify when the classroom group is learning strategic symbolic navigation. Finally, cultural production can reveal how important long-term social processes are, and it pushes researchers and teachers to design for conceptual neighborhood living. We need future work to better understand how these ideas fully interact and integrate. These three papers form a foundation for my research trajectory to better understand how classroom groups learn mathematics together. In future studies, I will further explore how we can design and support classroom groups to engage in conceptual neighborhood living, strategic symbolic navigation, and conceptual agency. Through long-term classroom studies and design-based research methods, I will further understand how groups create conceptual-cultural materials within classrooms and how this material supports their engagement in mathematics. My goal is to build a sense of these structures’ interaction and the mathematics that results from them. | |
