Generative Adolescent Mathematical Learners: The Fabrication of Knowledge

This dissertation is embedded in a deconstruction of the field of Mathematics Education in order to reconstitute the mathematics student as a generative mathematical learner. The purpose of the dissertation is to understand how generative adolescent mathematical learners (GAMLs) maneuver through their mathematics courses while maintaining such a disposition. As a result, an initial model of constitutive characteristics of the GAML emerged. A generative disposition is meant to characterize the learner as someone who operates mathematically in ways that reflect an internal sense of authority for knowing and a constructive orientation to the knowledge they come to know. Drawing upon the radical constructivist teaching experiment methodology, I conducted a poststructural qualitative inquiry of students' experiences that may have informed a generative disposition, their orientation toward mathematical knowledge, and the role of schooling in the interactions of these students. I co-taught the mathematics classes of the studies' three students during April 2005 and interacted with the students as both teacher and classroom researcher. Field notes served as a primary data source, with some classroom episodes and student interviews videotaped in order to aid in the retrospective analysis that followed. Case studies were first developed, and then used to enrich an initial definition of the GAML. The GAMLs of this study relied on their own thinking to come to know. Confirmation of their teachers' judgments that they were competent thinkers was strongly evident. The three GAMLs demonstrated confidence in what they knew and in their potential to come to know. They considered that mathematics is a human activity and were mathematically interactive among their classroom peers. Further, they enjoyed a high social and academic status among their classroom peers. A disconnection was observed in the three GAMLs between observed classroom behavior and their observed generativity. In particular, they rejected schooling in various ways and engaged in deviant classroom behavior. Appendixes include: (1) Student Identification Request; (2) Subject Survey; (3) Subject Mathography; (4) Subject Interview 1 Protocol; (5) Subject Interview 2 Protocol; (6) Subject Video Mathography; (7) Subject Interview 3 Protocol; and (8) Former Teacher Interview Protocol. (Contains 101 footnotes, 5 tables, and 7 figures.)