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Article: Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction

TitleTheorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction
Authors
KeywordsDynamic geometry
Justification
Proof
Visualization
Issue Date2002
PublisherSpringer-Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1382-3892
Citation
International Journal of Computers for Mathematical Learning, 2002, v. 7 n. 2, p. 145-165 How to Cite?
AbstractTheorem acquisition and deductive proof have always been core elements in the study and teaching of Euclidean geometry. The introduction of dynamic geometry environments,DGE (e.g., Cabri-Géomètre, Geometer's Sketchpad), into classrooms in the past decade has posed a challenge to this praxis. Student scan experiment through different dragging modalities on geometrical objects that they construct, and consequently infer properties(generalities, theorems) about the geometrical artefacts. Because of the inductive nature of the DGE, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical and epistemological concern. In this paper, we will describe and study a ‘Cabri proof by contradiction’ of a theorem on cyclic quadrilaterals given by a pair of 16 year-old students in a Hong Kong secondary school. We will discuss how their construction motivates a visual-cognitive scheme on `seeing' proof in DGE, and how this scheme could fit into the theoretical construct of cognitive unity of theorems proposed by Boero, Garuti and Mariotti(1996). The issue of a cognitive duality and its relation to visualization will be raised and discussed. Finally, we propose a possible perspective to bridge the experimental-theoretical gap in DGE by introducing the idea of a dynamic template as a visualizer to geometrical theorem justification and acquisition.
Persistent Identifierhttp://hdl.handle.net/10722/48565
ISSN
2013 SCImago Journal Rankings: 0.432

 

DC FieldValueLanguage
dc.contributor.authorLeung, AYLen_HK
dc.contributor.authorLopez-Real, FJen_HK
dc.date.accessioned2008-05-22T04:17:20Z-
dc.date.available2008-05-22T04:17:20Z-
dc.date.issued2002en_HK
dc.identifier.citationInternational Journal of Computers for Mathematical Learning, 2002, v. 7 n. 2, p. 145-165en_HK
dc.identifier.issn1382-3892en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48565-
dc.description.abstractTheorem acquisition and deductive proof have always been core elements in the study and teaching of Euclidean geometry. The introduction of dynamic geometry environments,DGE (e.g., Cabri-Géomètre, Geometer's Sketchpad), into classrooms in the past decade has posed a challenge to this praxis. Student scan experiment through different dragging modalities on geometrical objects that they construct, and consequently infer properties(generalities, theorems) about the geometrical artefacts. Because of the inductive nature of the DGE, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical and epistemological concern. In this paper, we will describe and study a ‘Cabri proof by contradiction’ of a theorem on cyclic quadrilaterals given by a pair of 16 year-old students in a Hong Kong secondary school. We will discuss how their construction motivates a visual-cognitive scheme on `seeing' proof in DGE, and how this scheme could fit into the theoretical construct of cognitive unity of theorems proposed by Boero, Garuti and Mariotti(1996). The issue of a cognitive duality and its relation to visualization will be raised and discussed. Finally, we propose a possible perspective to bridge the experimental-theoretical gap in DGE by introducing the idea of a dynamic template as a visualizer to geometrical theorem justification and acquisition.en_HK
dc.format.extent166318 bytes-
dc.format.extent7292240 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeimage/jpeg-
dc.languageengen_HK
dc.publisherSpringer-Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1382-3892en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsThe original publication is available at www.springerlink.comen_HK
dc.subjectDynamic geometryen_HK
dc.subjectJustificationen_HK
dc.subjectProofen_HK
dc.subjectVisualizationen_HK
dc.titleTheorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradictionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1382-3892&volume=7&issue=2&spage=145&epage=165&date=2002&atitle=Theorem+Justification+and+Acquisition+in+Dynamic+Geometry:+A+Case+of+Proof+by+Contradictionen_HK
dc.identifier.emailLeung, AYL: aylleung@hkucc.hku.hken_HK
dc.identifier.emailLopez-Real, FJ: lopezfj@hkucc.hku.hken_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1023/A:1021195015288en_HK
dc.identifier.scopuseid_2-s2.0-0036907430-
dc.identifier.hkuros77660-
dc.identifier.citeulike6375531-

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