Essays on Teacher Judgements and Decisions in Ambitious Mathematics Teaching

Abstract

Ambitious mathematics teaching involves closely attending to student sensemaking while maintaining the cognitive demand as dictated in high-level mathematics tasks. This instructional domain has been linked to the construction of deep, conceptually based subject matter knowledge. Yet classrooms serving racially minoritized students often exhibit reduced cognitive challenge and inadequate opportunities to learn. Moreover, due to its emphasis on student-generated inputs and ideas, some of which may be mathematically incorrect, teachers may be inclined to reduce the cognitive demand of high-level mathematics tasks. In this set of dissertation studies, I investigate racial-ethnic biases in teacher responsiveness to students’ non-standard and innovative mathematical ideas, teachers’ causal attributions for and instructional responses to student struggles on a high-level math task, and finally how teachers preserve the connectedness of the mathematics and student accountability for high-level processes and products when responding to a student misconception on a fractions task. I characterize teacher judgements and instructional preferences using vignettes to approximate practice. I first investigate teacher biases in a) expectations and judgments about student capabilities in math and b) teacher responsiveness to students’ mathematical thinking. I find teachers expected greater task difficulty in both the Latinx/e and Black classroom conditions relative to the White, and they may have been more likely to support student sense-making and provide more positive, substantive affirmations to Black students relative to White students for the same mathematical solution. In the next study, I found teachers’ internal—but not their external—causal attributions for a student’s struggle predicted their preferences to modify the cognitive demand of high-level math tasks. Importantly, this attribution-instruction relationship was equitable across student groups, and teachers did not show racial-ethnic biases in their causal attributions nor instructional preferences. In the final paper, I qualified teacher responses to a student misconception on a high-level fractions task in terms of the connectedness of the mathematics and student accountability for high-level processes and products. I found that teachers forged connections between mathematical ideas only part of the time, and they often took over the problem solving, diminishing the cognitive demand of the task as intended. The results of this project can inform teacher education and professional development, intervention research, and teacher evaluation to support educator capacity for delivering rigorous and just mathematics learning experiences in response to students’ varied ways of thinking about mathematics.