The Potential of Hybridity to Support Epistemic Diversity In Mathematics

• In Event: Approaches to Fostering Young People’s Mathematical Identities: Theory, Design, and Student Uptake

Abstract

This presentation describes a program of design-based research (DBR collective, 2003) that has spanned multiple learning environments focused on middle-grades students’ mathematics identity (6th-8th grade), defined as one’s participation in and across activities and the sense one makes of oneself in relation to these activities (Author). Across these projects, the design goal is to support students to exercise mathematical agency (Pickering, 1995). Such a learning environment necessarily invites multiple perspectives and ideas in the same classroom, called epistemic diversity (Agarwal & Sengupta-Irving, 2019). A classroom which fosters epistemic diversity looks different from many experiences children have in schools, which typically limit the range of ways that students are invited to think about an idea. This is a knowledge loss in general, but lands differently on particular students, who are told to change the way they think (Louie, 2017), or that they must engage in a set of practices that operate to exclude or oppress them (Martin, 2019).
Although there are obvious advantages to designing spaces that foster epistemic agency, it has proven difficult to foster, because by middle school students have been convinced that mathematics is about listening and practicing, and rarely about inventing, exploring, and justifying. Thus, efforts to get students to share their own thinking or connect what they do in school to the mathematics of their everyday lives has been especially tricky. The work in this presentation explores the potential of hybrid learning environments as a potential inroad to supporting epistemic diversity.
This presentation will share examples from two design-based research projects (DBR collective, 2003) that integrate the practices of mathematics from other domains. The first developed a hybrid learning space with video games and mathematics (Author). It focused on ideas of ratio and problem solving along with practices of videogames such as exploration, storytelling, and failure. The second project combined the practices of computer science with mathematics (Author). This involved students developing expressive artistic projects using the platform NetLogo (Wilensky, 1999) and concepts about coordinate planes.
As we will share, analyses of video of student work demonstrate first that designing for epistemic diversity is challenging, and requires repeated work reflecting on the ways that the practices of each domain are put into conversation with each other (Lehrer & Schauble, 2021). However, repeated revisions and implementations also led to promising examples of learning environments that legitimately supported epistemic diversity. As an example, in the gaming environment, the narrative of the game invited students to consider and contrast multiple ways to approach the problem and the possible solutions to those problems, which we called consequential engagement with mathematics (Author). As we will discuss, the methods of design-based research served as a crucial guide in exploring our assumptions about student identity, the design decisions that we made, and how we came to understand and draw conclusions about student outcomes.

Authors

• Melissa Sommerfeld Gresalfi, Vanderbilt University

• Panchompoo Wisittanawat, Vanderbilt University

• Madison Knowe, Vanderbilt University