UBC Theses and Dissertations
Problem posing as storyline: Collective authoring of mathematics by small groups of middle school students Armstrong, Alayne Cheryl
This dissertation investigates the problem posing patterns that emerge as small groups of students work collectively on a mathematics task, and describes the characteristics of problem posing that result. This case study is a naturalistic inquiry about four small groups of Grade 8 students in the Lower Mainland of British Columbia who are working in a classroom setting, with the researcher acting as participant/observer and videographer. The concept of author/ity is used to highlight human agency in mathematics. Small groups, as learning systems, are being considered to be “authors” of their discourse, and the improvisational nature of authoring is discussed. A parallel is drawn between the storyline of a literary work and the storyline that emerges as a group poses problems in order to work its way through a mathematical task. The metaphor of a tapestry is used as a way of describing how the threads of group discourse weave together. To address the challenge of documenting collective behavior at the group level, a method of data analysis is introduced that “blurs” the data in order to capture patterns that emerge over time – transcripts are color-coded and then shrunk to create tapestries that provide visual evidence of collective problem posing patterns. This dissertation finds that collective problem posing is an emergent process. Each group poses its own set of problems, and the number of problems posed and their frequency also vary, resulting in individual tapestries for each group. The tapestry patterns are then used to compare characteristics of the groups’ discussions. Problem posing appears to be an activity that these groups are able to do without receiving formal instruction or direction. The reposing of problems helps to structure each group’s discussion, with the role that each problem plays in the conversation evolving as it reemerges. The concept of groups working as bricoleurs is also explored, with bricolage in mathematics being characterized as a creative and generative process. The dissertation concludes with a discussion of expertise in school mathematics and what implications an “aesthetic of imperfection” might have in the mathematics classroom.
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