Introducing the structure of proof in lower secondary school geometry: A learning progression based on flow-chart proving

Miyazaki, Mikio, Fujita, Taro and Jones, Keith (2012) Introducing the structure of proof in lower secondary school geometry: A learning progression based on flow-chart proving. In Pre-proceedings of the 12th International Congress on Mathematical Education (ICME-12). International Commission on Mathematical Instruction. pp. 3023-3032 .

Record type: Conference or Workshop Item (Paper)

Abstract

This paper reports on a learning progression based on flow-chart proving and aimed at providing a basis for introducing the structure of proof in lower secondary school geometry. The proposed learning progression has three phases: constructing flow-chart proofs in an open situation, constructing formal proofs by reference to flow-chart proofs in a closed situation, and refining formal proofs by placing them into flow-chart proof format in a closed problem situation. Through teaching this progression in three Grade 8 classrooms (students aged 14), and assessing the learning through a test administered several months later, our evidence indicates that students who studied proof and proving with this learning progression were better able to construct a proof than other students who did not follow this approach.

Text

Miyazaki-etc_ proof_learning_progression_ICME12_2012 - Accepted Manuscript

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