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Students’ geometrical constructions and proving activities: A case of cognitive unity?

Students’ geometrical constructions and proving activities: A case of cognitive unity?
Students’ geometrical constructions and proving activities: A case of cognitive unity?
Geometrical constructions (whether with paper and pencil or with appropriate software) are widely considered to be a suitable vehicle for secondary school students to gain experience of proof and proving. It is also recognised, however, that there can be a tension between the practical aspect of physically carrying out a geometrical construction and the theoretical aspect of constructing the related proof. This paper reports on data from a teaching experiment in which Grade 9 students worked on a series of challenging geometrical construction problems. Analysing the data through the lens of cognitive unity, we report on whether, or to what extent, geometrical constructions in particular encourage the uniting of student conjecture production and proof construction. Our analysis suggests that this is not automatic.
mathematics, education, proof
0771-100X
9-16
International Group for the Psychology of Mathematics Education
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Pinto, Márcia M. F.
Kawasaki, Teresinha F.
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Pinto, Márcia M. F.
Kawasaki, Teresinha F.

Fujita, Taro, Jones, Keith and Kunimune, Susumu (2010) Students’ geometrical constructions and proving activities: A case of cognitive unity? Pinto, Márcia M. F. and Kawasaki, Teresinha F. (eds.) In Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (PME34). vol. 3, International Group for the Psychology of Mathematics Education. pp. 9-16 .

Record type: Conference or Workshop Item (Paper)

Abstract

Geometrical constructions (whether with paper and pencil or with appropriate software) are widely considered to be a suitable vehicle for secondary school students to gain experience of proof and proving. It is also recognised, however, that there can be a tension between the practical aspect of physically carrying out a geometrical construction and the theoretical aspect of constructing the related proof. This paper reports on data from a teaching experiment in which Grade 9 students worked on a series of challenging geometrical construction problems. Analysing the data through the lens of cognitive unity, we report on whether, or to what extent, geometrical constructions in particular encourage the uniting of student conjecture production and proof construction. Our analysis suggests that this is not automatic.

Text
Fujita-etc_geom_constructions_unity_PME34_2010 - Accepted Manuscript
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More information

Published date: July 2010
Venue - Dates: 34th Conference of the International Group for the Psychology of Mathematics Education, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil, 2010-07-18 - 2010-07-23
Keywords: mathematics, education, proof

Identifiers

Local EPrints ID: 445833
URI: http://eprints.soton.ac.uk/id/eprint/445833
ISSN: 0771-100X
PURE UUID: cf08b912-5880-4822-883d-dc77fbfd1b6e
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 08 Jan 2021 17:31
Last modified: 27 Feb 2024 18:24

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Contributors

Author: Taro Fujita
Author: Keith Jones ORCID iD
Author: Susumu Kunimune
Editor: Márcia M. F. Pinto
Editor: Teresinha F. Kawasaki

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