Boundary Transitions Within, Across, and Beyond a Set of Digital Resources: Brokering in College Algebra

Abstract

We address a problem of promoting instructional transformation in early undergraduate mathematics courses, via an intervention incorporating novel digital resources (“techtivities”), in conjunction with a faculty learning community (FLC). The techtivities can serve as boundary objects, in order to bridge different communities to which instructors belong. Appealing to Etienne Wenger’s Communities of Practice theory, we theorise a role of the instructor as a broker, facilitating “boundary transitions” within, across, and beyond a set of digital resources. By “boundary transition”, we mean a transition that is also a brokering move; instructors connect different communities as they draw links between items in their instruction. To ground our argument, we provide empirical evidence from an instructor, Rachel, whose boundary transitions served three functions: (1) to position the techtivities as something that count in the classroom community and connect to topics valued by the broader mathematics community; (2) to communicate to students that their reasoning matters more than whether they provide a correct answer, a practice promoted in the FLC; (3) to connect students’ responses to mathematical ideas discussed in the FLC, in which graphs represent a relationship between variables. Instructors’ boundary transitions can serve to legitimise novel digital resources within an existing course and thereby challenge the status quo in courses where skills and procedures may take precedence over reasoning and sense-making.