Carving Curriculum out of Chaos: Exploring Teacher Interventions and the Patterning of Small Groups in Mathematics Class
Small group work is becoming an increasingly popular structure for promoting communication, sense-making, and reasoning in the mathematics class. This increased sense of student autonomy must co-exist with the curriculum, the expectation to provide opportunities for students to master certain mathematical ideas. This study is an exploration into the patterns that emerge when a teacher of mathematics establishes small groups in their classroom and attempts to balance the inherent complexity of
... udent interaction with the ultimate goal of affecting action toward curricular outcomes. The analytical framework of complexity theory and the epistemology of enactivism are used to frame the mathematics curriculum as a landscape, and the process of learning mathematics as one of emergence with the mathematical environment while operating in certain curriculum spaces. The image of the curriculum space is introduced as an interpretive tool to visualize the dynamic, drifting nature of the problem deemed relevant to a group, and their movement as they work at varying levels of sophistication with targeted outcomes. Through this lens, I offer illustrative episodes of group action and an analysis of patterns of teacher action to provide a language to observe small groups as complex systems, inform the work of teachers by presenting viable images of complex systems of learners making sense of their experience, and explore the tendencies of teacher actions when consciously balancing complexity and curriculum. My research suggests that the complex action of small groups can generate curriculum, and that a teacher of mathematics can both prompt action with curricular outcomes and honour the complexity of small groups if they attune themselves to the dynamic movement of a group's problem drift. iii PREFACE This thesis is an original work by Nathaniel J. A. Banting. The research project, of which this thesis is a part, received research ethics approval from the University of Alberta Research Ethics Board 1, Study Title: "Carving Curriculum out of Chaos", Study ID: Pro00064660, June 2, 2016. iv "Enjoy thinking sideways" -The Big Show v ACKNOWLEDGEMENTS Things like this don't happen but for the support of others. Most glaringly that of my wife, Andra. Your steadying presence and support during this process was always exactly what I needed. This degree has subsumed many long nights, countless moments of indecision, and two complete pregnancies. You are nothing short of spectacular.