TEACHER GRAPHING PRACTICES FOR LINEAR FUNCTIONS IN A COVARIATION-BASED COLLEGE ALGEBRA CLASSROOM

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TEACHER GRAPHING PRACTICES FOR LINEAR FUNCTIONS IN A COVARIATION-BASED COLLEGE ALGEBRA CLASSROOM

Abstract

Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this study are three levels of empirically proven practices associated with the conception of one advanced level of covariational reasoning, chunky continuous covariation. This study not only describes how practices may be described at different levels of complexity, but also demonstrates how smaller practices may be combined to form larger, more complex practices. These practices can be used to guide instruction of those who want to participate in and become practitioners in the community of teachers of function-based covariation-focused algebra curricula.

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