The University of Southampton
University of Southampton Institutional Repository

Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry

Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry
Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry
Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners’ can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a web-based proof learning support system. Through this analysis we illustrate the various errors they made, including using circular reasoning, which were related to their understanding of hypothetical syllogism as an element of the structure of mathematical proof. We found that, by using the computer-based feedback and, for some, teacher intervention, the learners started considering possible combinations of assumptions and conclusion, and began realising when their proof fell into logical circularity. Our findings raise important issues about the nature and role of computer-based feedback such as how feedback is used by learners, and the importance of teacher intervention in computer-based learning environments.
computer-based feedback , proving, logical circularity, geometry
1863-9690
699-713
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e

Fujita, Taro, Jones, Keith and Miyazaki, Mikio (2018) Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry. ZDM: Mathematics Education, 50 (4), 699-713. (doi:10.1007/s11858-018-0950-4).

Record type: Article

Abstract

Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners’ can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a web-based proof learning support system. Through this analysis we illustrate the various errors they made, including using circular reasoning, which were related to their understanding of hypothetical syllogism as an element of the structure of mathematical proof. We found that, by using the computer-based feedback and, for some, teacher intervention, the learners started considering possible combinations of assumptions and conclusion, and began realising when their proof fell into logical circularity. Our findings raise important issues about the nature and role of computer-based feedback such as how feedback is used by learners, and the importance of teacher intervention in computer-based learning environments.

Text
Fujita_Jones_Miyazaki_ZDM_2018 - Version of Record
Available under License Creative Commons Attribution.
Download (1MB)

More information

Accepted/In Press date: 16 May 2018
e-pub ahead of print date: 5 June 2018
Published date: 9 July 2018
Keywords: computer-based feedback , proving, logical circularity, geometry

Identifiers

Local EPrints ID: 421573
URI: https://eprints.soton.ac.uk/id/eprint/421573
ISSN: 1863-9690
PURE UUID: 23024f44-f805-40ba-a73a-3097998405e6
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 15 Jun 2018 16:30
Last modified: 15 Aug 2019 00:55

Export record

Altmetrics

Contributors

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

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×