Identifying local proof ‘modules’ during proving
Identifying local proof ‘modules’ during proving
Given that understanding a proof entails students breaking the proof into components or modules and then specifying the logical relationship between each of the modules, in this paper we focus on what proof modules can be identified during the process of learning deductive proving in school geometry. Through an analysis of observations of grade 8 geometry lessons, and corresponding to three level of understanding characterised as elemental, relational, and holistic, we identified three structure ‘modules’: 1) vague ‘chunks’ of propositions, 2) small networks with universal and singular propositions by universal instantiations, and 3) series of small networks.
proof, proving, geometry, structure, PME
246
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
Ichikawa, Daisuke
57bf048d-9f85-4f84-bcba-08587d79bb14
17 July 2017
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Ichikawa, Daisuke
57bf048d-9f85-4f84-bcba-08587d79bb14
Miyazaki, Mikio, Fujita, Taro, Jones, Keith and Ichikawa, Daisuke
(2017)
Identifying local proof ‘modules’ during proving.
Kaur, Berinderjeet, Ho, Weng Kin, Toh, Tin Lam and Choy, Ban Heng
(eds.)
In Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (PME41).
vol. 1,
International Group for the Psychology of Mathematics Education.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
Given that understanding a proof entails students breaking the proof into components or modules and then specifying the logical relationship between each of the modules, in this paper we focus on what proof modules can be identified during the process of learning deductive proving in school geometry. Through an analysis of observations of grade 8 geometry lessons, and corresponding to three level of understanding characterised as elemental, relational, and holistic, we identified three structure ‘modules’: 1) vague ‘chunks’ of propositions, 2) small networks with universal and singular propositions by universal instantiations, and 3) series of small networks.
Text
Miyazaki-etc_local_proof_modules_PME41_2017
- Accepted Manuscript
More information
Accepted/In Press date: 24 April 2017
Published date: 17 July 2017
Venue - Dates:
41st Conference of the International Group for the Psychology of Mathematics Education (PME41), National Institute of Education, Singapore, Singapore, 2017-07-17 - 2017-07-22
Keywords:
proof, proving, geometry, structure, PME
Identifiers
Local EPrints ID: 415487
URI: http://eprints.soton.ac.uk/id/eprint/415487
PURE UUID: e2c6aada-1cb7-4be0-abc2-d9879a9729ab
Catalogue record
Date deposited: 13 Nov 2017 17:30
Last modified: 15 Mar 2024 16:47
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Contributors
Author:
Mikio Miyazaki
Author:
Taro Fujita
Author:
Daisuke Ichikawa
Editor:
Berinderjeet Kaur
Editor:
Weng Kin Ho
Editor:
Tin Lam Toh
Editor:
Ban Heng Choy
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