Proof validation and modification in secondary school geometry
Proof validation and modification in secondary school geometry
Proof validation is important in school mathematics because it can provide a basis upon which to critique mathematical arguments. While there has been some previous research on proof validation, the need for studies with school students is pressing. For this paper, we focus on proof validation and modification during secondary school geometry. For that purpose, we employ Lakatos’ notion of local counterexample that rejects a specific step in a proof. By using Toulmin’s framework to analyze data from a task-based questionnaire completed by 32 ninth-grade students in a class in Japan, we identify what attempts the students made in producing local counterexamples to their proofs and modifying their proofs to deal with local counterexamples. We found that student difficulties related to producing diagrams that satisfied the condition of the set proof problem and to generating acceptable warrants for claims. The classroom use of tasks that entail student discovery of local counterexamples may help to improve students’ learning of proof and proving.
proof, Proof validation, Proof modification, Local counterexample, Secondary school geometry, Proof problem with diagram, teaching and learning
1-15
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Ikeda, Takehiro
beb90e59-c937-4407-8f96-3f98a13ff88b
Narazaki, Akito
5c8ecc7e-0390-4e03-9750-b374db80b67f
1 September 2017
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Ikeda, Takehiro
beb90e59-c937-4407-8f96-3f98a13ff88b
Narazaki, Akito
5c8ecc7e-0390-4e03-9750-b374db80b67f
Komatsu, Kotaro, Jones, Keith, Ikeda, Takehiro and Narazaki, Akito
(2017)
Proof validation and modification in secondary school geometry.
Journal of Mathematical Behavior, 47, .
(doi:10.1016/j.jmathb.2017.05.002).
Abstract
Proof validation is important in school mathematics because it can provide a basis upon which to critique mathematical arguments. While there has been some previous research on proof validation, the need for studies with school students is pressing. For this paper, we focus on proof validation and modification during secondary school geometry. For that purpose, we employ Lakatos’ notion of local counterexample that rejects a specific step in a proof. By using Toulmin’s framework to analyze data from a task-based questionnaire completed by 32 ninth-grade students in a class in Japan, we identify what attempts the students made in producing local counterexamples to their proofs and modifying their proofs to deal with local counterexamples. We found that student difficulties related to producing diagrams that satisfied the condition of the set proof problem and to generating acceptable warrants for claims. The classroom use of tasks that entail student discovery of local counterexamples may help to improve students’ learning of proof and proving.
Text
Komatsu_et_al_JMB_2017
- Accepted Manuscript
More information
Accepted/In Press date: 24 May 2017
e-pub ahead of print date: 7 June 2017
Published date: 1 September 2017
Keywords:
proof, Proof validation, Proof modification, Local counterexample, Secondary school geometry, Proof problem with diagram, teaching and learning
Organisations:
Mathematics, Science & Health Education
Identifiers
Local EPrints ID: 411718
URI: http://eprints.soton.ac.uk/id/eprint/411718
ISSN: 0732-3123
PURE UUID: 49eb8d6e-3088-4373-96eb-e79a17c21055
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Date deposited: 22 Jun 2017 16:31
Last modified: 16 Mar 2024 05:28
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Contributors
Author:
Kotaro Komatsu
Author:
Takehiro Ikeda
Author:
Akito Narazaki
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