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Designing a web-based learning support system for flow-chart proving in school geometry

Designing a web-based learning support system for flow-chart proving in school geometry
Designing a web-based learning support system for flow-chart proving in school geometry
As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can ‘drag’ sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners’ proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs
Flow-chart proving, Web-based, Learning support system, Geometry, Deductive proof, Teaching, Learning, mathematics, proof
2199-3246
233-256
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Iwanaga, Yasuo
2ffb0c0a-2ada-43ed-9ad2-7153b03e9323
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Iwanaga, Yasuo
2ffb0c0a-2ada-43ed-9ad2-7153b03e9323

Miyazaki, Mikio, Fujita, Taro, Jones, Keith and Iwanaga, Yasuo (2017) Designing a web-based learning support system for flow-chart proving in school geometry. Digital Experiences in Mathematics Education, 3 (3), 233-256. (doi:10.1007/s40751-017-0034-z).

Record type: Article

Abstract

As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can ‘drag’ sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners’ proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs

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More information

Accepted/In Press date: 25 March 2017
e-pub ahead of print date: 16 June 2017
Published date: December 2017
Keywords: Flow-chart proving, Web-based, Learning support system, Geometry, Deductive proof, Teaching, Learning, mathematics, proof
Organisations: Mathematics, Science & Health Education

Identifiers

Local EPrints ID: 411618
URI: http://eprints.soton.ac.uk/id/eprint/411618
ISSN: 2199-3246
PURE UUID: 23876443-8bee-4ab9-9298-5807b4aa6b7e
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 21 Jun 2017 16:31
Last modified: 21 Nov 2021 07:09

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Contributors

Author: Mikio Miyazaki
Author: Taro Fujita
Author: Keith Jones ORCID iD
Author: Yasuo Iwanaga

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