Functions of Open Flow-Chart Proving in Introductory Lessons of Formal Proving.
Mikio Miyazaki, Taro Fujita, Keith W. Jones · ePrints Soton (University of Southampton) · 2014
Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs.With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory flow-chart proofs that use 'open problems' that have multiple possible solutions.Through an analysis of a teaching experiment in Grade 8, and by using a model of levels of understanding of proof structure, we identify the functions as enhancing the transition towards a relational understanding of the structure of formal proof, and encouraging forms of forward/backward thinking interactively that accompany such a relational understanding of the structure of proofs in mathematics.