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2009•University of Southern Queensland ePrints (University of Southern Queensland)Open access

HIGHER ORDER REASONING PRODUCED IN PROOF CONSTRUCTION: HOW WELL DO SECONDARY SCHOOL STUDENTS EXPLAIN AND WRITE MATHEMATICAL PROOFS?

Oleksiy Yevdokimov

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Abstract

The culture of mathematical explanations and writings based on conceptual understanding in proof construction is on the focus of the paper. We explore students’ attempts to explain construction of mathematical proofs after reading them and write mathematical proofs after working out their own constructions. Two examples of proofs, by induction and by contradiction, are discussed in detail to highlight students’ difficulties in proving and possible ways for their resolving.

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What this paper is about

The culture of mathematical explanations and writings based on conceptual understanding in proof construction is on the focus of the paper. We explore students’ attempts to explain construction of mathematical proofs after reading them and write mathematical proofs after working out their own constructions. Two examples of proofs, by induction and by contradiction, are discussed in detail to highlight students’ difficulties in proving and possible ways for their resolving.

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Available abstract

The culture of mathematical explanations and writings based on conceptual understanding in proof construction is on the focus of the paper. We explore students’ attempts to explain construction of mathematical proofs after reading them and write mathematical proofs after working out their own constructions. Two examples of proofs, by induction and by contradiction, are discussed in detail to highlight students’ difficulties in proving and possible ways for their resolving.

Key concepts: Mathematical proof, Contradiction, Mathematical induction, Calculus (dental), Mathematical logic, Mathematics education, Focus (optics), Reading (process)

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HIGHER ORDER REASONING PRODUCED IN PROOF CONSTRUCTION: HOW WELL DO SECONDARY SCHOOL STUDENTS EXPLAIN AND WRITE MATHEMATICAL PROOFS? — Research Paper | ScholarLens