Teachers' Navigation of Mathematical Representations in Argumentation

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 signi cant 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/o er when arguing claims of generality. Eight elementary educators participated in this study. Each completed two interviews and a classroom observation. The ndings indicate that (1) arguments are to be produced in a prose format, they help support and learn mathematical content, and allow for di ering 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 Steven LeMay, University of Connecticut, 2017 relevant ideas, and thus are unwarranted. Some implications of this research upon K16 mathematics teaching and learning are discussed. This study's ndings 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 o ered. Teachers' Navigation of Mathematical Representations in Argumentation

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