How Do Secondary Mathematics Teachers Manage Students' Responses In-The Moment?

Abstract

A ubiquitous and complex challenge for mathematics teachers is managing students' responses in-the-moment during whole-class instruction. In-the-moment, managing students' responses involves a variety of internal resources---including specialized content knowledge for teaching, productive beliefs about teaching and learning mathematics, and the ability to self-regulate ones' own emotional state and anxiety---in addition to skill in perceiving and interpreting important aspects of students' answers. Beyond these specialized internal resources and skills which make this complex work, managing students responses becomes more salient to research when one considers that the public nature of this interaction means that how a teacher handles these situations can have important implications for the learning of all students in the class.

In this three-paper dissertation, I explore the complexities of managing students' responses in-the-moment. In the first paper, I explore a special case of managing students' responses when a student response is perceived by a teacher as incorrect. Here, I outline the important consequences of managing students' responses for students and explore why this might be difficult and challenging work for teachers. For the second and third papers, I used an interactive-video based teaching simulation to first explore how teachers responded to students (in paper 2) and then to consider what factors (such as various internal resources a teacher might have) might be related to various features teachers' responses (paper 3).

In paper 2, I describe the ways in which teachers responded to apparently correct and incorrect student answers. In general regardless of whether the student answer is apparently correct or incorrect, teacher responses tend to go back to the student who provided the answer. However, the ways in which the same student was asked to think about particular mathematics depended on whether the student answer was apparently correct or incorrect. When a student answer was apparently incorrect, teacher responses predominantly asked questions to get the student to correct or fix their response. In contrast, when a student answer was apparently correct, the majority of teacher responses would ask the student to elaborate on some aspect of his/her response. A small subset of teachers in this sample did not exhibit these same, clear evaluative patterns and I discuss trends in their responses that could inform ways in which teacher education supports teachers in responding to students.

In paper 3, I quantitatively investigate how teachers’ responses to students relate to teachers' individual characteristics, including their anxiety, teaching experience, beliefs and mathematical knowledge for teaching, as well as their self-reported emotional reaction to student responses. The analyses showed that teachers' self-reported emotional reactions, with the exception of sense of control, had almost no significant correlations to any aspects of their responses to students. Additionally, teachers' anxiety was generally negatively correlated with aspects of teacher responses while years of experience was positively correlated with features of teachers' responses. Findings indicate that exploring teachers' anxiety is a promising avenue for understanding teaching performance and that important methodological considerations arise when attempting to assess an action-related competence such as managing students' responses.