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, UCL
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
December 1995
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Jones, Keith
(1995)
Dynamic geometry contexts for proof as explanation.
In,
Healy, Lulu and Hoyles, Celia
(eds.)
Justifying and Proving in School Mathematics.
London, GB.
Institute of Education, UCL, .
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.
Text
Jones_DGS_proof_as_explanation_1995
- Accepted Manuscript
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
Catalogue record
Date deposited: 11 Aug 2006
Last modified: 15 Mar 2024 08:25
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Contributors
Editor:
Lulu Healy
Editor:
Celia Hoyles
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