The Interplay of Teacher and Student Actions in the Teaching and Learning of Geometric Proof |
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| Authors: | Tami S Martin Sharon M Soucy McCrone Michelle L Wallace Bower Jaguthsing Dindyal |
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| Institution: | (1) Illinois State University, Campus Box 4520, Normal, IL, 61790-4520, U.S.A.;(2) Mount Saint Mary University, U.S.A.;(3) National Institute of Education, Singapore |
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| Abstract: | Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage
in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results
from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify
factors that may be related to the development of proof understanding. In this paper, we identify and interpret students'
actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures,
justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested
in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities
to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are
not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on
the students, analyze student arguments, and coach students as they reason, creates an environment in which participating
students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively
participate in the classroom discourse are supported as they engage in proof development activities. By examining connections
between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students'
understanding of proof. |
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| Keywords: | classroom interaction geometry link between teaching and learning pedagogical choices proof and reasoning secondary school mathematics |
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