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Designing for the integration of dynamic software environments in the teaching of mathematics
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.ORCID-id: 0000-0003-4553-0630
2015 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis concerns the challenge of integrating dynamic software environments into the teaching of mathematics. It investigates particular aspects of the design of tasks which employ this type of computer-based system, with a focus on improvement, both of the tasks themselves and of the design process through which they are developed and refined.

The thesis reports two research projects: a small initial one preceding a larger main project. The initial case study, involving two graduate students in mathematics, develops a task design model for geometrical locus problems. The main study constitutes the first iteration of a design-based study, conducted in collaboration with four upper-secondary school teachers and their classes. It seeks to identify task design characteristics that foster students’ mathematical reasoning and proficient use of software tools, and examines teachers’ organisation of ‘follow-up’ lessons.

The findings concern three particular aspects: features of tasks and task environment relevant to developing a specific plan of action for a lesson; orchestration of a particular task environment to support the instrumental genesis of specific dynamic software tools; how to follow up students’ work on computer-based tasks in a whole-class discussion.

sted, utgiver, år, opplag, sider
Karlstad: Karlstads universitet, 2015. , s. 107
Serie
Karlstad University Studies, ISSN 1403-8099 ; 50
Emneord [en]
design research, dynamic mathematics software, intrumental orchestration, mathematics education, task design
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-38213ISBN: 978-91-7063-669-1 (tryckt)OAI: oai:DiVA.org:kau-38213DiVA, id: diva2:861920
Disputas
2015-12-15, Eva Erikssonsalen, 21A 342, Karlstad University, Karlstad, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2015-11-24 Laget: 2015-10-19 Sist oppdatert: 2017-11-29bibliografisk kontrollert
Delarbeid
1. A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment
Åpne denne publikasjonen i ny fane eller vindu >>A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment
2014 (engelsk)Inngår i: Technology, Knowledge and Learning, ISSN 2211-1662, E-ISSN 2211-1670, Vol. 19, nr 3, s. 287-315Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The increasing availability of new technologies in schools provides new possibilities

for the integration of technology in mathematics education. However, research

has shown that there is a need for new kinds of task that utilize the affordances provided by

new technology. Numerous studies have demonstrated that dynamic geometry environments

provide opportunities for students to engage in mathematical activities such as

exploration, conjecturing, explanation, and generalization. This paper presents a model for

design of tasks that promote these kinds of mathematical activity, especially tasks that

foster students to make generalizations. This model has been primarily developed to suit

the use of dynamic environments in tackling geometrical locus problems. The model was

initially constructed in the light of previous literature. This initial model was used to design

a concrete example of such a task situation which was tested in action through a case study

with two doctoral students. Findings from this case study were used to guide revision of the

initial model.

sted, utgiver, år, opplag, sider
Springer, 2014
Emneord
Mathematics education, Task design, Dynamic geometry
HSV kategori
Identifikatorer
urn:nbn:se:kau:diva-33815 (URN)10.1007/s10758-014-9213-9 (DOI)
Tilgjengelig fra: 2014-09-24 Laget: 2014-09-24 Sist oppdatert: 2017-12-05bibliografisk kontrollert
2. Designing Prediction Tasks in a Mathematics Software Environment
Åpne denne publikasjonen i ny fane eller vindu >>Designing Prediction Tasks in a Mathematics Software Environment
2015 (engelsk)Inngår i: The International Journal for Technology in Mathematics Education, ISSN 1744-2710, E-ISSN 2045-2519, Vol. 22, nr 1, s. 3-18Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

There is a recognized need in mathematics teaching for new kinds of task which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study conducted by the authors in collaboration with four upper secondary school teachers. A task sequence was trailed with four 10th grade classes, involving a total of 85 students. The research process pinpointed key didactical variables that proved crucial in designing these tasks. As well as being useful in the task design process, the didactical variables were found to be valuable in the processes of analysis and revision. While the didactical variables identified a priori were informed by the research literature concerning reasoning and functions, those identified a posteriori deal mainly with scaffolding issues that emerged.  

sted, utgiver, år, opplag, sider
RESEARCH INFORMATION LTD, 2015
Emneord
Task design, Prediction task, Mathematics software environment
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kau:diva-35034 (URN)10.1564/tme_v22.1.01 (DOI)000382659500002 ()
Tilgjengelig fra: 2015-01-28 Laget: 2015-01-28 Sist oppdatert: 2019-12-19bibliografisk kontrollert
3. Instrumental genesis concerning scales and scaling in a dynamic mathematics software environment
Åpne denne publikasjonen i ny fane eller vindu >>Instrumental genesis concerning scales and scaling in a dynamic mathematics software environment
2015 (engelsk)Inngår i: Proceedings of the Ninth Congress of European Research in Mathematics Education / [ed] K. Krainer, N. Vondrova, Prague: European Society for Research in Mathematics Education, 2015, s. 2347-2353Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

It is recognized that the process in which an artefact becomes an instrument for a user, denoted as instrumental genesis, is a complex process. The aim of this paper is to identify elements of the process of instrumental genesis when students are dealing with scales and scaling issues in a dynamic mathematics software environment. This study involves four upper secondary school teachers and their classes. By observing the students’ instrumented techniques while working with tasks designed with a hypothetical instrumental genesis in mind, some key elements are identified.

sted, utgiver, år, opplag, sider
Prague: European Society for Research in Mathematics Education, 2015
Emneord
mathematics education, dynamic mathematics software, instrumental genesis
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kau:diva-38208 (URN)000466853903061 ()
Konferanse
CERME9 - the 9th Congress of European Research in Mathematics Education, Prague, Charles University, 4-8 Februari 2015
Tilgjengelig fra: 2015-10-19 Laget: 2015-10-19 Sist oppdatert: 2019-11-13bibliografisk kontrollert
4. Redesigning task sequences to support instrumental genesis in the use of movable points and slider bars
Åpne denne publikasjonen i ny fane eller vindu >>Redesigning task sequences to support instrumental genesis in the use of movable points and slider bars
2017 (engelsk)Inngår i: The International Journal for Technology in Mathematics Education, ISSN 1744-2710, E-ISSN 2045-2519, Vol. 24, nr 1, s. 3-15Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
Research Information Ltd, 2017
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kau:diva-38211 (URN)10.1564/tme_v24.1.01 (DOI)000424620500002 ()
Tilgjengelig fra: 2015-10-19 Laget: 2015-10-19 Sist oppdatert: 2019-12-19bibliografisk kontrollert
5. Teachers’ didactical intention and instrumental orchestrations for ‘follow-up’ lessons
Åpne denne publikasjonen i ny fane eller vindu >>Teachers’ didactical intention and instrumental orchestrations for ‘follow-up’ lessons
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
HSV kategori
Identifikatorer
urn:nbn:se:kau:diva-38212 (URN)
Tilgjengelig fra: 2015-10-19 Laget: 2015-10-19 Sist oppdatert: 2016-02-02bibliografisk kontrollert
6. Orchestration of mathematical discussions drawing on students’ computer-based work
Åpne denne publikasjonen i ny fane eller vindu >>Orchestration of mathematical discussions drawing on students’ computer-based work
2017 (engelsk)Inngår i: ICT in mathematics education: the future and the realities: Proceedings of MADIF 10 The tenth research seminar of the Swedish Society for Research in Mathematics Education / [ed] Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2017, s. 77-87Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

Research points out the importance of following up students’ work on computerbasedtasks with whole-class discussions in which students play a central role.However, at the same time, research highlights the challenge for teachers in orchestratingsuch follow-up discussions. This paper examines whether an establishedmodel developed as guidance for teachers to orchestrate mathematical whole-classdiscussions (Stein, Engle, Smith & Hughes, 2008) could be useful in this educationalsetting. Students’ written responses to two different tasks are the main data used toexamine the model. The results indicate that the model has great potential to guidethese follow-up discussions

sted, utgiver, år, opplag, sider
Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2017
Serie
Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 11
Emneord
mathematics education, dynamic software, class discussion
HSV kategori
Forskningsprogram
Pedagogik
Identifikatorer
urn:nbn:se:kau:diva-49429 (URN)978-91-984024-0-7 (ISBN)
Konferanse
MADIF10 - The tenth research seminar of the Swedish Society for Research in Mathematics Education (SMDF), Karlstad 26-27 januari 2016
Tilgjengelig fra: 2017-05-29 Laget: 2017-05-29 Sist oppdatert: 2018-11-06bibliografisk kontrollert

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