The University of Southampton
University of Southampton Institutional Repository

Interplay between paper-and-pencil activities and dynamic-geometry-environment use during generalisation and proving

Interplay between paper-and-pencil activities and dynamic-geometry-environment use during generalisation and proving
Interplay between paper-and-pencil activities and dynamic-geometry-environment use during generalisation and proving
Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of inter-related roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students’ paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14–15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-and-pencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students’ work, and point to the need for further research into the back-and-forth use of digital and physical tools.
Digital tool, Physical tool, dynamic geometry environments, Paper-and-pencil activity, Generalisation and proof, Teacher role
2199-3246
123-143
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f

Komatsu, Kotaro and Jones, Keith (2020) Interplay between paper-and-pencil activities and dynamic-geometry-environment use during generalisation and proving. Digital Experiences in Mathematics Education, 6 (2), 123-143. (doi:10.1007/s40751-020-00067-3).

Record type: Article

Abstract

Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of inter-related roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students’ paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14–15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-and-pencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students’ work, and point to the need for further research into the back-and-forth use of digital and physical tools.

Text
Komatsu&Jones_Interplay_PaperPencil&DGE_2020 - Version of Record
Available under License Creative Commons Attribution.
Download (636kB)

More information

e-pub ahead of print date: 19 May 2020
Published date: 11 July 2020
Additional Information: This paper is part of a journal Special Issue titled "n the intertwined contributions of physical and digital tools for the teaching and learning of mathematics"
Keywords: Digital tool, Physical tool, dynamic geometry environments, Paper-and-pencil activity, Generalisation and proof, Teacher role

Identifiers

Local EPrints ID: 441617
URI: http://eprints.soton.ac.uk/id/eprint/441617
ISSN: 2199-3246
PURE UUID: 9da49e8d-2a60-4931-b892-39ca8689573c
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 19 Jun 2020 16:38
Last modified: 12 Dec 2021 09:59

Export record

Altmetrics

Contributors

Author: Kotaro Komatsu
Author: Keith Jones ORCID iD

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 http://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.

×