Mathematical reasoning is essential to knowing and doing mathematics, and mathematical reasoning practices can be leveraged by teachers to support student voice and choice in the learning process. This dissertation explored how one elementary teacher provided opportunities for students to engage in the mathematical reasoning practice of justification and how these opportunities supported her goals for equity in a classroom of diverse students. Given that agency emerged as a prominent theme in the teacher’s equity goals, this dissertation focused analysis of findings on the relationship between mathematical justification and agency, with connections to interrelated equity constructs (such as mathematical identity) expressed by the teacher, as well. Mathematical justification can be defined as, “the process of supporting your mathematical claims and choices when solving problems or explaining why your claim or answer makes sense” (Bieda & Staples, 2020, p. 103). Case study methodology was used to examine the teacher’s curriculum materials, classroom enactment strategies, equity goals, and perceptions on the relationship between justification and equity. This study was situated in a self-contained, racially/ethnically diverse, fourth-grade classroom in an urban district in the Midwest, taught by a female Teacher of Color. Findings are reported in the form of three articles, each discussing connections between justification and equity (with a focus on agency). Each article was written for different primary audiences: the first for mathematics education researchers, the second for mathematics teacher educators, and the third for practitioners. The first article presents the broadest overview of how and why the teacher provided justification opportunities, with the second two articles focusing more in-depth on specific types of justification opportunities. This first article, which is Chapter 2 of the dissertation, was written for researchers as the primary audience and will be submitted for publication consideration to the Journal of Mathematics Teacher Education (JMTE). This article was guided by two research questions: (1) How does a teacher facilitate opportunities for students to engage in the mathematical practice of justification? (2) How does the teacher perceive mathematical justification as supporting her equity goals? Findings showed that the teacher was committed to regularly incorporating justification opportunities in her mathematics lessons. She facilitated justification opportunities through purposeful task design and enactment strategies, situated within a conducive classroom environment. These opportunities were driven by her equity goals, which included a focus on supporting student agency in the learning process and cultivating the development of positive mathematical identity in students. Given how infrequent justification is implemented in classrooms, and the limited research on the relationship between justification and equity in the literature, these findings help illuminate how justification can be leveraged by a teacher in ways relevant to their classroom context and equity goals. The second manuscript (Chapter 3) was written for mathematics teacher educators as the primary audience and is intended to be submitted for publication consideration to the Mathematics Teacher Educator (MTE). This article was guided by two research questions: (1) What are one teacher’s goals for promoting equity in the classroom? (2) How does the teacher leverage the practice of mathematical justification to meet her equity goals? Findings showed that facilitating students’ agency and supporting students in developing positive mathematical identity were the primary equity goals for the teacher. Advancing these goals involved engaging students in problem-based learning experiences that focused on discovering and justifying mathematical patterns and relationships in ways that centered the students’ ideas and reasonings. The article elaborates how and why the nature of problem-based learning experiences opened up spaces for leveraging justification to meet these equity goals. The third manuscript (Chapter 4) is a practitioner-focused piece written for the journal, Mathematics Teacher: Learning and Teaching PK-12 (MTLT). This article discusses how the beginning of curricular units can be conducive places to facilitate justification opportunities in ways that support students’ engagement with new content and agency in the learning process. The article describes how and why the teacher in this study facilitated justification opportunities at the beginning of units and offers guidance for other teachers hoping to modify their practice to provide their students with more mathematical justification opportunities.
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