Deductive reasoning in Euclidean geometry : an intermediate level unit

Hogan, Joanne (1999) Deductive reasoning in Euclidean geometry : an intermediate level unit. Masters thesis, Memorial University of Newfoundland.

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Abstract

Proof has traditionally been the touchstone of mathematics. It is at the heart of mathematics as students explore, make conjectures, and try to convince themselves and others about the truth or falsity of such conjectures. Reasoning is a necessary component if proving is seen as explaining deductively. By its nature, proof should promote understanding and as such can be a valuable part of the curriculum. Yet students and teachers often find the study of proof difficult, and a debate within mathematics education is currently underway about the extent to which proof should play a role in mathematics. A reexamination of the role and nature of proof in the curriculum is needed. -- This project is designed with the purpose of creating occasions for deductive reasoning while following the provincial curriculum objectives as outlined for intermediate mathematics students in Newfoundland and Labrador. It builds upon the two documents produced by the National Council of Teachers of Mathematics (NCTM): the Curriculum and Evaluation Standards for School Mathematics (1989) and the Professional Standards for Teaching Mathematics (1991). -- The project consists of a unit plan for Euclidean Geometry at the intermediate level. It stresses a method of teaching deductive reasoning that highlights student involvement and teacher facilitation. A case has been made for establishing a classroom atmosphere that encourages students to explore and investigate geometry problems, to ask questions, to engage in divergent thinking, and to use logical reasoning to develop convincing arguments (NCTM, 1992). This project capitalizes on the opportunities such topics provide to bring deductive reasoning into the intermediate mathematics class. The aim is to offer teachers a resource that supports the instruction of deductive reasoning in their own classrooms.

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