Conceptualizing routines of practice that support algebraic reasoning in elementary schools: a constructivist grounded theory

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Jessie Chitsanzo Store (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Sarah Berenson

Abstract: There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research on elementary school students' algebraic reasoning, there is a scarcity of research on how elementary school teachers implement algebraic reasoning curriculum and how their practices support algebraic reasoning. The purpose of this study therefore was to discover practices that promote algebraic reasoning in elementary classrooms by studying elementary school teachers' practices and algebraic reasoning that the practices co-constructed. Specifically, the questions that guided the study included (a) what were the teachers' routines of practice, and (b) in what ways did the routines of practice support algebraic reasoning. I sampled On Track Learn Math project and worked with six teachers to explore their routines of practice and students' algebraic reasoning. As a participant observer, I analyzed video data of the classroom activities, memos, field notes, students' written transcripts and interview data using constructivist grounded theory approach and descriptive statistics. Member checking, data triangulation, and data coding by multiple raters ensured consistency and trustworthiness of the results. Descriptive analysis of students' written generalizations showed that about 74% of the generalizations were explicit and about 55% of the generalizations included names of variables indicating that students were learning how to reason algebraically. Data analysis also revealed five routines of practice. These routines are; (a) maintaining open-endedness of the tasks, (b) nurturing co-construction of ideas, (c) fostering understanding of variable, (d) creating a context for mathematical connections and (e) promoting understanding of generalizations. Teachers maintained open-endedness by giving minimal instructions when launching the tasks and providing students with workspaces. They nurtured co-construction of ideas by creating opportunities for students to collaborate, fostering collaboration, and balancing the support of discourse and content. They fostered understanding of variable as a changing quantity and as a relationship. Teachers created a context for mathematical connections between On Track tasks and students' everyday experiences, between student strategies, between different tasks, between On Track tasks and other curriculum ideas, and between different representations. Teachers promoted understanding of generalizations by encouraging students to justify their conjectures, to apply and evaluate peers' generalizations among other practices. These practices were dependent and informed each other.