Positioning During Group Work on a Novel Task in Algebra II

Abstract

Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.

Productive Disruptions: Rethinking the Role of Off-Task Interactions in Collaborative Mathematics Learning

“…The influence framework resonates with findings from Bishop, who found that positional identities affect who talks and initiates sequences (similar to interactions around the conversational floor) and whose ideas are taken up and publicly recognized (similar to influence) [13]. DeJarnette and González likewise found that students' positioning moves related to the ways they engaged in the task, including the construction of its final product [21]. Langer-Osuna applied the Influence Framework to a case of two students, Ana and Jerome, who collaboratively solved an open-ended mathematics problem [39].…”

“…Within mathematics education research, this interactional and negotiated approach to examining identity has been applied to understand several aspects of learning and doing mathematics together in classrooms [13,14,[20][21][22][23][24][25][26] (See Figure 3). Studies have traced how particular student identities become possible and enacted through participation in classroom activities.…”

“…Positioning theory brings a lens of relational power to bear on the uptake and spread of mathematics ideas [13,16,21,39]. This becomes clearer through a focus on the social construction of influence during collaborative work.…”

Middle School Boys’ and Girls’ Own Expressions of Aspirations for Their Mathematics Learning

“…The Year 7/8 cohort made more references to wanting to work in small groups, perhaps because they had experienced fewer opportunities in secondary school (Banilower et al, 2013). A recent study found that secondary teachers were able to broaden students' learning opportunities by using collaborative learning (DeJarnette & González, 2015); this study suggests that it might also be motivating for some students. More Year 7/8 students referred explicitly to teacher support (both socioemotional and instructional aspects) than those in Year 5/6, resonating with studies that found teacher support more strongly related to affective outcomes for older middle school students (Rolland, 2012).…”

What affordances do open-ended real-life tasks offer for sharing student agency in collaborative problem-solving?

“…Civil and Hunter (2015) reminded that real-life contexts might better enable non-dominant mathematics students to "be themselves, that is, they could bring in their cultural ways of being and acting, including their home language(s), their ways of speaking, their use of humor, and values not necessarily encountered in other areas of their schooling" (p. 308). Heterogeneous student groups and novel task designs have been shown to enable reimagining agentic positions for students who are traditionally seen as underachievers (Esmonde & Langer-Osuna, 2013;DeJarnette & González, 2015). Focusing on students' authority in mathematics, Langer-Osuna et al (2020) found out that while students were able to share both social and intellectual authority in mathematics, it was social authority that was more malleable and dynamic.…”