Methodological Considerations in the Analysis of Classroom Interaction in Community College Trigonometry

Abstract

We report analyses of classroom interaction in trigonometry classes taught at an American community college focusing on two dimensions: the mathematical novelty of questions that instructors and students ask and the interactional moves that the instructors use to encourage student involvement in the lesson. The analyzed lessons were particularly challenging because existing frameworks that analyze classrooms did not account for the cases in which the delivery mode was lecture. We discuss the analytical strategies we used and show data to illustrate how they help us in capturing the complexity of classroom interaction and differences between instructors when lecture is the primary mode of instructional delivery. We conclude with suggestions for further work.

Achievement Goal Orientations of Community College Mathematics Students and the Misalignment of Instructor Perceptions

“…But there is little research on how mathematics instruction is related to retention and success in community colleges (Mesa, 2007), particularly for students with an interest in pursuing a STEM major. Some studies have started to investigate this connection by looking at how students and teachers discuss mathematical content (Mesa, in press; Mesa, Lande, & Whittemore, 2011) and by analyzing how textbooks use examples to illustrate mathematically demanding work (Mesa, 2010; Mesa & John, 2009; Mesa, Suh, Blake, & Whittemore, in press). The focus of this article is on students’ achievement goal orientations and how instructors perceive those goals.…”

Teaching Approaches of Community College Mathematics Faculty

“…A related analysis could investigate how novel questions are used in the classroom. We have found that trigonometry instructors tend to answer about 30% of the novel questions they pose or to restate them in ways that reduce the complexity for the students (Mesa & Lande, in press). Although reducing the novelty of questions might be seen as an interest in showing students how to deal with unknown situations, it is not clear that students are actually given opportunities to work through the process of answering novel questions.…”

“…We define questions as novel when the answer or the procedure needed to answer it is not known (e.g., students are required to explain new and old connections between mathematical notions or to figure out something new) or to make explicit student problem-solving strategies or methods that are not routine. We made the classification taking into account the talk that preceded and followed the question (for details, see Mesa & Lande, in press).…”

“…Questions that invite students to state conjectures, propose alternative solutions, investigate mathematical reasons, and justify their own thinking are in general associated with high cognitive work and are preferred over questions that ask students to repeat known facts or to practice a procedure (Stein, Smith, Henningsen, & Silver, 2000). These questions, also called novel or authentic (Mesa & Lande, in press; Truxaw & DeFranco, 2008), play a significant role in shaping the opportunities that students have to learn authentic mathematics in the classroom.…”