|Abstract:||Implementing high-quality elementary mathematics instruction is challenging and requires proficiency in a variety of classroom practices. As such, teacher educators must support preservice teachers (PSTs) in developing these teaching practices in order for them to be as effective as possible in their future classrooms. Given its central role in high-quality math instruction, recent research has addressed the practice of teacher noticing, what a teacher sees and responds to in a classroom (Jacobs & Spangler, 2017). Past research has generally focused on what elementary PSTs notice in a classroom setting, while relatively little is understood about why elementary PSTs notice what they do.
Using fraction concepts for coherence among measures, this dissertation explores how PSTs’ Mathematical Knowledge for Teaching (MKT; Ball, Thames, & Phelps, 2008), beliefs about the role of children’s thinking in math teaching, and experiences may be related to their noticing of students’ mathematical thinking. The study involves 92 PSTs in four sections of an elementary mathematics methods course, including 23 PSTs in a focal section involving additional activities designed to measure PSTs’ noticing of students’ mathematical thinking at different timepoints in the semester. Employing a mixed methods design, this study first investigates the statistical relationship among PSTs’ MKT, beliefs, and their noticing of students’ mathematical thinking using assessments at the start and end of the course. PSTs’ beliefs about the role of children’s thinking in math teaching are measured with both existing and new survey items, which are then reduced through factor analysis to four distinct factors: Teacher Telling, Students’ Thinking, Productive Struggle, and Classroom Discourse. To provide a deeper understanding of the complex relationships among PSTs’ knowledge, beliefs, experiences and their noticing of students’ mathematical thinking, this study draws on qualitative analyses of PSTs’ group discussions, interviews, and the PSTs’ responses to a qualitative measure of their beliefs.
Results show that growth in the PSTs’ MKT was predictive of growth in their attending/interpretation of students’ mathematical thinking, particularly for the PSTs who participated in the additional noticing activities over the semester. Changes in the PSTs’ conversations about students’ thinking over the semester demonstrated how groups that had larger gains in MKT had notable shifts in their discussion toward a greater focus on students’ mathematical thinking. Although some evidence pointed to a potential relationship between PSTs’ beliefs about the role of children’s thinking in math teaching, specifically the Classroom Discourse Factor, and their response to students’ thinking, this study also illuminates the challenges of accurately capturing PSTs’ beliefs. More research is required to understand how PSTs’ beliefs may be related to their noticing of students’ mathematical thinking, including continuing to refine measures to accurately capture such beliefs.
Overall, findings from this study suggest that PSTs’ interpretation of students’ math thinking is math content-specific. In other words, PSTs’ MKT of fraction concepts, not necessarily success in prior math courses, or developing their noticing through specifically designed activities, supports their interpretation of students’ thinking in a fraction problem. Consequently, in addition to developing PSTs’ noticing of students’ thinking through purposeful activities, mathematics teacher educators must also support PSTs’ development of MKT of elementary math content in order to enable PSTs to best interpret students’ thinking. Additionally, results support the use of short, video-based noticing activities as an effective way to support PSTs’ noticing, through both exposing them to students’ complex mathematical reasoning, as well as helping them develop skills in noticing.