Rhoads, Kathryn E.. High school mathematics teachers’ use of beliefs and knowledge in high-quality instruction. Retrieved from https://doi.org/doi:10.7282/T3FJ2H69
DescriptionHigh-quality mathematics instruction is important for students’ learning, and teachers are a key part of instruction. As they engage in instruction, teachers draw on their beliefs and knowledge. Yet mathematics education still lacks a robust understanding of the specific ways in which beliefs and knowledge contribute to high-quality instruction, particularly at the high school level. The purpose of this dissertation is to explore the mathematical knowledge and beliefs used by high school teachers who facilitate high-quality instruction. Three main research questions guide this dissertation: (a) What is the nature of mathematical knowledge expressed in exemplary high school mathematics teachers’ reflections on teaching? (b) What teacher beliefs and knowledge support high-quality responses to students? (c) How can productive teacher beliefs about mathematics and mathematics teaching lead to instruction that is limited in mathematical richness? To investigate the first research question, I interviewed 11 high school mathematics teachers who were recognized for exemplary instruction. I used grounded analysis to explore the mathematical knowledge for teaching that was expressed through teachers’ reflections on their lessons. In response to the second research question, I observed and interviewed 12 high school teachers, five of whom were recognized for exemplary instruction. I used video-based, stimulated-recall interviews to understand the teacher beliefs and knowledge that supported or hindered high-quality responses to students’ mathematical questions, claims, and solutions. To address the third research question, I explored the case of one recognized teacher who expressed beliefs and goals aligned with mathematical meaning and sense making, yet his instruction did not exemplify these aspects. I used observations and interviews to understand the teacher’s perspectives on his instruction, and I offer explanations for why this instruction was limited in richness. The findings highlight the depth and complexity of mathematical knowledge and beliefs used in high-quality instruction and challenge the assumption that either teacher beliefs or teacher knowledge can be studied in isolation or outside of the instruction in which they are used.