RUME 14 (Volume 4)
2011
Portland, Oregon
NAVIGATING THE IMPLEMENTATION OF AN INQUIRY-ORIENTED TASK IN A COMMUNITY COLLEGE
Page: 108
Teachers implementing inquiry-oriented, discourse-promoting tasks can face a number of challenges (Speer & Wagner, 2009; Ball, 1993). In this study we will examine the challenges faced by two community college instructors as they implement such a task in a "transition to proof" course. In this task students initially use their informal ideas of symmetry to develop a criteria to quantify the symmetry of six figures (see Larsen & Bartlo, 2009), these criteria are then formalized into definitions for symmetry and equivalent symmetries. During this task a number of conflicts arise, and to resolve these conflicts the students engage in rich mathematical discourse. While this task and ensuing discourse offer opportunities for learning mathematics, they also offer significant challenges for effective implementation. We aim to identifying these challenges and the ways in which these challenges were navigated as the class worked towards formal definitions of symmetry and equivalent symmetries. While working on a project aimed to develop a community college "transition to proof" course, bases on an inquiry-oriented abstract algebra curriculum, we began to wonder what sort of challenges the community college instructors would face as they navigated the curriculum. In order to begin looking at this question we decided to focus our attention on an inquiry-oriented task in which the students reinvent and define the concepts of symmetry and equivalent symmetries. In this task students are initially given six shapes (see figure below) and are asked to arrange the figures from least to most symmetric. The students work on this task individually and then in small groups prior to a whole class discussion. The groups share how they ordered the figures and how they came to that decision. The students are then asked to determine a way to quantify the symmetry of each figure and, using their quantification criteria, the groups rank the figures and present both their criteria and their ranking to the whole class. Following these presentations the groups work to develop both a definition of what a symmetry is and what makes two symmetries equivalent (see Larsen & Bartlo, 2009). bis Bae your an Fig. 1 Symmetry Task Launch