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Representations and reasoning in 3-D geometry in lower secondary school

Representations and reasoning in 3-D geometry in lower secondary school
Representations and reasoning in 3-D geometry in lower secondary school
A key question for research in geometry education is how learners’ reasoning is influenced by the ways in which geometric objects are represented. When the geometric objects are three-dimensional, a particular issue is when the representation is two-dimensional (such as in a book or on the classroom board). This paper reports on data from lower secondary school pupils (aged 12-15) who tackled a 3-D geometry problem that used a particular representation of the cube. The analysis focuses on how the students used the representation in order to deduce information and solve the 3-D problem. This analysis shows how some students can take the cube as an abstract geometrical object and reason about it beyond reference to the representation, while others need to be offered alternative representations to help them ‘see’ the proof.
mathematics, education, 3D geometry
0771-100X
339-346
International Group for the Psychology of Mathematics Education
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Tso, Tai-Yih
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Tso, Tai-Yih

Jones, Keith, Fujita, Taro and Kunimune, Susumu (2012) Representations and reasoning in 3-D geometry in lower secondary school. Tso, Tai-Yih (ed.) In Proceedings of the 36th conference of the International Group for the Psychology of Mathematics Education (PME36). vol. 3, International Group for the Psychology of Mathematics Education. pp. 339-346 .

Record type: Conference or Workshop Item (Paper)

Abstract

A key question for research in geometry education is how learners’ reasoning is influenced by the ways in which geometric objects are represented. When the geometric objects are three-dimensional, a particular issue is when the representation is two-dimensional (such as in a book or on the classroom board). This paper reports on data from lower secondary school pupils (aged 12-15) who tackled a 3-D geometry problem that used a particular representation of the cube. The analysis focuses on how the students used the representation in order to deduce information and solve the 3-D problem. This analysis shows how some students can take the cube as an abstract geometrical object and reason about it beyond reference to the representation, while others need to be offered alternative representations to help them ‘see’ the proof.

Text
Jones-etc_represent&reason3D_PME36_2012 - Accepted Manuscript
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More information

Published date: July 2012
Venue - Dates: Conference of the International Group for the Psychology of Mathematics Education, , Taipei, Taiwan, 2012-07-18 - 2012-07-22
Keywords: mathematics, education, 3D geometry

Identifiers

Local EPrints ID: 445627
URI: http://eprints.soton.ac.uk/id/eprint/445627
ISSN: 0771-100X
PURE UUID: 6bd1678b-eaca-4f76-99a4-8e96891a728e
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

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Date deposited: 04 Jan 2021 17:32
Last modified: 16 Mar 2024 10:24

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Contributors

Author: Keith Jones ORCID iD
Author: Taro Fujita
Author: Susumu Kunimune
Editor: Tai-Yih Tso

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