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Dynamic geometry contexts for proof as explanation

Dynamic geometry contexts for proof as explanation
Dynamic geometry contexts for proof as explanation
Providing a mathematics curriculum that makes proof accessible to school students appears to be difficult. This paper describes work carried out in a secondary school mathematics class in which students worked on tasks designed to enable them to experience the necessity of certain geometrical facts that are true in Euclidean geometry. In these tasks, the students were asked to construct figures using the dynamic geometry package Cabri-Géomètre such that each figure was invariant when any basic object used in the construction was dragged. It is argued that working on these tasks provided the students with suitable experiences to enable them to explain why these geometrical facts are necessarily true. The changing quality of the students' mathematical analysis suggests that working on suitable tasks with a dynamic geometry package may allow some students to develop an appreciation of proof as explanation.
teaching, learning, pedagogy, curriculum, appropriation, computer environments, deductive reasoning, proof, proving, dynamic geometry software, geometry, mathematical explanation, mediation of learning, quadrilaterals, secondary school
142-154
Institute of Education
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f

Jones, Keith (1995) Dynamic geometry contexts for proof as explanation. In, Justifying and Proving in School Mathematics. London, GB. Institute of Education, pp. 142-154.

Record type: Book Section

Abstract

Providing a mathematics curriculum that makes proof accessible to school students appears to be difficult. This paper describes work carried out in a secondary school mathematics class in which students worked on tasks designed to enable them to experience the necessity of certain geometrical facts that are true in Euclidean geometry. In these tasks, the students were asked to construct figures using the dynamic geometry package Cabri-Géomètre such that each figure was invariant when any basic object used in the construction was dragged. It is argued that working on these tasks provided the students with suitable experiences to enable them to explain why these geometrical facts are necessarily true. The changing quality of the students' mathematical analysis suggests that working on suitable tasks with a dynamic geometry package may allow some students to develop an appreciation of proof as explanation.

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More information

Published date: December 1995
Keywords: teaching, learning, pedagogy, curriculum, appropriation, computer environments, deductive reasoning, proof, proving, dynamic geometry software, geometry, mathematical explanation, mediation of learning, quadrilaterals, secondary school
Organisations: Mathematics, Science & Health Education

Identifiers

Local EPrints ID: 41243
URI: http://eprints.soton.ac.uk/id/eprint/41243
PURE UUID: e164e006-41f4-4760-9e51-7e1ce563b472
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

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Date deposited: 11 Aug 2006
Last modified: 07 Oct 2020 01:40

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Author: Keith Jones ORCID iD

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