"Mathematical Knowledge for Teaching and Instructional Quality: Lesson Reflections Explain Cases of Alignment and Misalignment"
AERA 2018 Annual Meeting: “The Dreams, Possibilities, and Necessity of Public Education”
April 13-17, 2018
Title: "Mathematical Knowledge for Teaching and Instructional Quality: Lesson Reflections Explain Cases of Alignment and Misalignment"
Author: Jiwon Lee
Prior research has examined the relationship between teacher knowledge and practice. Hill and colleagues, for example, have demonstrated a strong relationship between teachers’ knowledge, as measured by the Mathematical Knowledge for Teaching (MKT) survey (Hill, Schilling, & Ball, 2004), and their quality of instruction (Hill et al., 2008; Hill, Sleep, Lewis, & Ball, 2007). However, little is known about this relationship in beginning teachers. What is known is that novice elementary school teachers often lack teaching skills in mathematics. (Gordon, Kane, & Staiger, 2006). A plausible explanation is that even teachers who enter the teaching profession with sufficient level of knowledge encounter other challenges that influence the activation of this knowledge while teaching. The purpose of this study is to examine the relationship between knowledge and quality of instruction in a sample of beginning elementary teachers. Teachers’ lesson reflections are used to expand our understanding of teachers’ mathematical knowledge for teaching and its translation into instructional decisions.
Data are drawn from a larger five-year project that studied teacher preparation longitudinally. In this paper, I focus on four K-2nd grade teachers, who were selected based on differing levels of alignment between their knowledge and the quality of their instruction. The participants completed the MKT survey. Additionally, three mathematics lessons from their first year of teaching were videotaped and scored using the Mathematical Quality of Instruction instrument (Hill et al., 2008). After each lesson, teachers completed interviews that asked them to reflect on the lesson they had just taught by focusing on what worked and did not work and on ways they could improve their lesson. Reflections were analyzed qualitatively, first through an inductive, thematic approach that highlighted frequent themes, then through a deductive approach to examine the extent to which their MKT was evident in their reflections.
In the case of two of the participants, knowledge and quality of instruction were aligned. In the other two cases, they were misaligned: one teacher exhibited high knowledge with lower instructional quality, while the other exhibited relatively low knowledge, but relatively high quality of instruction. When knowledge and instructional quality were aligned, reflections confirmed this alignment. In case of misalignment, reflections helped to understand the relationship between knowledge and practice. When the quality of instruction was higher than expected given the teacher’s knowledge, the reflections indicated an emphasis placed on students’ mathematical thinking and understanding that contributed to relatively high scores on the instructional quality instrument. When the instructional quality was lower than expected given the teacher’s relatively high knowledge, reflections confirmed a high level of knowledge related to mathematics content, but less sophisticated understanding of ways instruction can be adapted to respond to students’ difficulties and differing levels of understanding.
These findings expand our conceptualization of knowledge and how this is typically measured by highlighting aspects that relate to instructional decisions and specifically to instruction that is responsive to students’ specific needs. Implications for teacher preparation include developing knowledge in the context of making sense of teaching.