Academic journal article Academic Exchange Quarterly

Creating a Culture of (In)dependence

Academic journal article Academic Exchange Quarterly

Creating a Culture of (In)dependence

Article excerpt

Abstract

In this study, the interactions in one middle-school mathematics classroom are examined for potential sharing of mathematical authority that takes place via a teacher's uses of authoritative discourse. The discourse of several classes is analyzed to investigate an alignment between the teacher's intentions and practices in the context of creating a sense of independence in students. Results indicate that by not allowing students much stake in judgments of mathematical validity, teachers may unwittingly create a classroom culture of students' dependence on "other" mathematical authorities.

Introduction

This discussion begins with a brief narrative that situates the researcher in the mathematics and education community. The author's story is intended to provide readers with a notion of the potentially common struggles to align his pedagogical intentions with his practices. The author's practice began as a secondary mathematics teacher intent on bringing learning experiences to students in his classroom that were more beneficial than his own. After a short time in the classroom, the author's intentions to share mathematical authority and develop mathematical agency became moot for various reasons. He resorted to the controlling methods of teaching and knowing that he experienced as a student. He found it difficult to separate his authority over the events in the classroom and his authority as an "expert" in the field of high-school mathematics. Teaching from the mathematical pulpit became less demanding and more comfortable. On many occasions, he would encourage students to be creative with their solutions by modeling multiple ways to solve problems and encouraging multiple solution methods for a given problem. The author hoped by modeling multiple solution methods students would emulate his behavior when they were working individually or cooperatively. The author found, instead, he was trying to compel a way of thinking by forcing certain behaviors using his classroom authority to exert mathematical authority.

The author often made attempts to force, or allow, students to verify the mathematical validity of statements and solutions in class by responding to their oft asked question of "is this right?" with questions such as "what do you think?" These questions often frustrated students rather than inspired them to develop argumentative skills and share in the authority to justify and verify mathematical validity, as was intended. Students would often say that the teacher should know the answer, and, most importantly, tell them. With increased frequency, the answers were eventually revealed and judgments were made by the teacher. The author believes some reflection would have shown him that his practices of enabling students mathematically did not mirror his intentions of empowering them.

About midway through his first year of teaching, the author made the decision to leave the classroom and continue graduate studies as a fulltime doctoral student. His frustration with the inconsistency between his beliefs about the learning of mathematics and his teaching practices steered him toward the line of research in this investigation. The context of authoritative discourse and its effect on student's mathematical agency is one of many in which the author found his practices not reflecting his beliefs or intentions. As a researcher, these shortcomings as a well-intentioned teacher provide him with a critical lens by which to view teaching practices with the hope that other teachers can, through reflection, realign their practices and intentions.

Theory and Literature Review

The purpose of this study was to examine teacher's discursive practices in mathematics classrooms and offer a mechanism for teacher reflection. Specifically, the research question for this investigation was, "How do teachers' discursive practices align with their intentions of creating a sense of mathematical independence among students? …

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