Functions of open flow-chart proving in introductory lessons of formal proving
Functions of open flow-chart proving in introductory lessons of formal proving
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.
mathematics, education, proof
226-233
International Group for the Psychology of Mathematics Education
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
July 2014
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio, Fujita, Taro and Jones, Keith
(2014)
Functions of open flow-chart proving in introductory lessons of formal proving.
Liljedahl, Peter, Oesterle, Susan, Nicol, Cynthia and Allan, Darien
(eds.)
In Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (PME38 & PME-NA36).
vol. 4,
International Group for the Psychology of Mathematics Education.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
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.
Text
Miyazaki-etc_functions_of_flow-chart_proving_PME38_2014
- Accepted Manuscript
More information
Published date: July 2014
Venue - Dates:
38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, University of British Columbia, Vancouver, Canada, 2014-07-15 - 2014-07-20
Keywords:
mathematics, education, proof
Identifiers
Local EPrints ID: 445743
URI: http://eprints.soton.ac.uk/id/eprint/445743
ISSN: 0771-100X
PURE UUID: 8c135a14-994c-4771-b59c-50fa73ab7b02
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Date deposited: 06 Jan 2021 17:47
Last modified: 16 Mar 2024 10:29
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Contributors
Author:
Mikio Miyazaki
Author:
Taro Fujita
Editor:
Peter Liljedahl
Editor:
Susan Oesterle
Editor:
Cynthia Nicol
Editor:
Darien Allan
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