Negotiating meaning for the symbolic expressions for vectors and vector equations in a classroom community of practice

Abstract

In this study, I analyze the development of meaning for the symbolic expressions for vectors and vector equations in an introductory, inquiry-oriented linear algebra course. Linear algebra is one of the first in-depth experiences that students have with vectors and vector equations, and as such my study examines these meanings in their formative and advanced states. The analysis in this study seeks to answer two fundamental questions : 1. What are the different meanings that this classroom community develops for vectors and vector equations? 2. In what ways do individual students contribute to and take responsibility for the different meanings that this classroom community develops for vectors and vector equations? Both of these questions deal with meaning making from two different, but mutually informing perspectives: what is created and how the individual feels about what is created. Answering the first question entailed examining the collective meanings that the community develops for symbolic expressions for vectors and vector equations. For this part of the study, I used the Toulmin argumentation scheme to analyze classroom argumentation from the first six days of class. In this analysis, video and transcripts from whole class discussion were used. To answer the second question, I analyzed a series of six focus group interviews made at the beginning and end of the semester. I used a grounded theory and thematic analysis of the transcripts and videos of these focus groups in order to ascertain the kinds of responsibility and contribution that these individual students demonstrated and expressed as members of the classroom community. There are several contributions that this study makes to the field of mathematics education. First, the examination of the collective creation, use and interpretation of vectors and vector equations will add insight into the process of meaning making for these specific expressions and mathematical expressions in general. Second, my analysis examines the often overlooked affective aspects of meaning making and the notion that this process is tied to the roles that the individual feels that they occupy within the community. Third, I examine the possible and observed connections between the identity of the individual and knowledge construction during classroom discourse