Exploring students’ identities through routines of encapsulation: A case study on characteristics of narratives about struggle in mathematics

Abstract

Identity has become a hot topic in mathematics education research. It has been acknowledged as a powerful research tool for investigating learning and teaching by unifying cognition and affect (Lerman, 2009). Additionally, it has been called the “missing link” between learning and sociocultural contexts (Sfard & Prusak, 2005a), and a “nexus” of affect and discourse in mathematical learning (Heyd-Metzuyanim, 2017). Several definitions have been proposed for identity, such as: who one is (Holland, Lachicotte, Skinner, & Cain, 1998), a sense of who individuals are (Boaler, Wiliam, & Zevenbergen, 2000), a sense of belonging (Tajfel & Turner, 1986), and being a certain kind of person (Gee, 2000). However, many of these definitions have also come under scrutiny for some of their features which lead to tangibility and operational issues. The research question in this study was: What encapsulation routines may students enact when generating identifying narratives about their participation in a mathematical discourse? In this case study, I adopt the commognitive framework and its discursive approach to investigating identity. The theoretical notion of an encapsulation routine is proposed and utilized for dissecting the characteristics of students’ encapsulations as they reflect on their participation in a mathematical discourse. Two collaborative workshops were conducted with a group of three secondary school students. Fine-grained discourse analysis was utilized to focus on examining the characteristics of encapsulation of one student, Sara, who began the study as a student who had frequently talked about failing to engage in mathematical discourse in her classroom-based narratives. An analysis of Sara’s encapsulations about her classroom-based and workshop-based narratives found four characteristics: (i) encapsulations about participating in mathematical discourse can be told with a lack of mathematizing; (ii) identifying can be substantiated with dichotomous distinctions of participation, (iii) narratives about oneself can be told in first- and second-person narration, and (iv) narratives of success and struggle about oneself are shared based on the reactions of others. These characteristics provided the tools for understanding Sara’s routines for mathematizing, how she identified herself through comparison with other people, and under what circumstances did she choose to speak of success or struggle.