Conceptualizing mathematical authority with technology
Stanton, Susan Sexton
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The purpose of this study was to identify and understand the placement of mathematical authority of four preservice elementary teachers enrolled in a geometry content course as they engaged with concepts of the course and technology in a dynamic geometry environment. Mathematical investigations were the primary pedagogical tool used in the course as the students explored concepts from geometry, measurement, and statistics and probability. Data were collected from videorecorded class sessions consisting of the participants’ investigations and interactions throughout the course, three personal interviews that I conducted with each participant, and the responses from pre- and post-surveys on the participants’ beliefs about mathematics and mathematics teaching and learning. Data on the participants’ beliefs about technology and how those beliefs affect their allocation of mathematical authority came from the clinical portion of the interviews as they interacted with a dynamic geometry software program to explore a mathematics task. To provide an understanding of how the participants sought and used various mathematics sources and where they placed mathematical authority, I classified the participants’ work method from the framework of instrumental genesis and developed a typology of authority behaviors. Collectively, the data were used to form a case study analysis of each participant. The results of the study point to the complexity of mathematical authority and show that an individual’s allocation of mathematical authority in various sources does not necessarily happen in a hierarchal fashion. Typical markers (e.g., confidence or mathematical knowledge) that may be associated with an individual’s propensity to allocate mathematical authority in particular sources were not always evident for the participants of this study. Further, technology can be viewed as a source of mathematics and serve as an absolute authority in the face of mathematical conflict or uncertainty. The results of the study indicate a need for future research that identifies learning environments that not only create mathematical understanding but also successfully promote and sustain personal mathematical authority in all learning contexts—even those in technology-based environments.