PRESERVICE TEACHERS’ MATHEMATICAL KNOWLEDGE FOR TEACHING: FOCUS ON LESSON PLANNING, PEER TEACHING, AND REFLECTION
Creators: name: Sapkota, Bima K
Publisher: name: Purdue University Graduate School
Year: 2022
Subjects: classificationCode: 399999
subject: Other education not elsewhere classified
classificationCode: 499999
subject: Other mathematical sciences not elsewhere classified

description: Mathematics teacher educators have suggested that approximations of practice provide preservice mathematics teachers (PMTs) with opportunities to engage with, develop, and demonstrate subdomains of Mathematical Knowledge for Teaching ([MKT], Ball et al., 2008) because MKT provides a way for PMTs to understand how to contextualize their discipline-specific content knowledge for effective mathematics teaching and learning. However, the affordances and limitations of commonly used forms of approximations of practice (i.e., lesson planning and peer teaching) coupled with reflective practices to engage PMTs in subdomains of MKT are still being explored. In this study, I investigated how lesson planning, peer teaching, and associated reflections individually and collectively afforded opportunities for PMTs to demonstrate and develop the MKT subdomains. Eleven PMTs enrolled in a secondary mathematics methods course at a large Midwestern University participated in the study. My dissertation comprises three sub-studies (Sub-study “1”, “2”, and “3”), and I produced three manuscripts to individually report findings from those sub-studies. I investigated how lesson planning, peer teaching, and reflections afforded opportunities for PMTs to demonstrate and describe MKT subdomains in Sub-studies 1, 2, and 3, respectively. The findings across the sub-studies suggested that several MKT subdomains (e.g., Knowledge of Content and Teaching, Knowledge of Content and Students) were evidenced in the PMTs’ planned teacher and student actions (e.g., selecting mathematical tasks, formulating and sequencing questions), and in-the-moment actions and decisions (e.g., mathematically representing students’ responses, implementing mathematical tasks). Several aspects of MKT subdomains (e.g., evaluate the diagnostic potential of tasks) were strongly evidenced only in the PMTs’ lesson plans whereas other aspects (e.g., modifying tasks based on students’ responses) were evidenced only in peer teaching. These findings suggested that various forms of approximations of practice (planned and enacted actions) created unique opportunities for the PMTs to engage with and demonstrate MKT. I also found that the PMTs reflected on some subdomains of MKT that were not evidenced in their approximated practices, indicating that how PMTs describe the MKT subdomains is not entirely a result of what subdomains they engage in during approximations of practice. My findings also revealed limitations of using approximations of practice to engage PMTs with MKT subdomains. The MKT subdomains that required the PMTs to think about students’ alternative mathematical concepts, big mathematical ideas, and non-standard mathematics problem-solving strategies were least evidenced across the approximations of practice and reflections. These findings have two primary implications for mathematics teacher educators. First, I invite mathematics teacher educators to engage PMTs in multiple forms of approximations of practice to optimize their opportunities to engage with, demonstrate, and develop the MKT subdomains. Second, I suggest potential instructional activities (e.g., inviting PMTs to reflect on their roles as students and teachers during peer teaching) that could be incorporated into approximations of practice to address the existing limitations. Broadly, I invite mathematics teacher educators to design instructional activities at the intersection of mathematics content and pedagogy, collaborating with colleagues to enhance these opportunities across programs.