Date of Completion

8-23-2017

Embargo Period

8-23-2017

Major Advisor

Fabiana Cardetti

Associate Advisor

Álvaro Lozano-Robledo

Associate Advisor

David R. Solomon

Field of Study

Mathematics

Open Access

Open Access

Abstract

Mathematical argumentation has recently received more prominent attention in K-12 classrooms which has immediate consequences in the undergraduate mathematics classroom, including the critical intersection with representing mathematical concepts. Educators' perceptions of this intersection is important to understand as they have a significant impact on the skills undergraduates bring to their mathematics classrooms. This qualitative study investigated (1) how K-5 elementary educators conceptualized argumentation, (2) the role(s) and purpose(s) they attribute to representations within argumentation, and (3) the criteria for representations they use/offer when arguing claims of generality. Eight elementary educators participated in this study. Each completed two interviews and a classroom observation. The findings indicate that (1) arguments are to be produced in a prose format, they help support and learn mathematical content, and allow for differing perspectives; (2) there are no roles for representations within arguments but they were purposed to help navigate concepts involved in a claim statement as well as supplement arguments; and (3) representations called forth to determine the truth value of a claim of generality are relevant to the claim but are not universal instantiations of those relevant ideas, and thus are unwarranted. Some implications of this research upon K-16 mathematics teaching and learning are discussed. This study's findings contribute to the literature about mathematical argumentation in the classroom, its relationships with representing mathematical concepts, and how elementary educators perceive both. Future lines of research to strengthen this area are offered.

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