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Designing for the integration of dynamic software environments in the teaching of mathematics
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0003-4553-0630
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2015. , p. 107
Series
Karlstad University Studies, ISSN 1403-8099 ; 50
Keyword [en]
design research, dynamic mathematics software, intrumental orchestration, mathematics education, task design
National Category
Educational Sciences
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-38213ISBN: 978-91-7063-669-1 (print)OAI: oai:DiVA.org:kau-38213DiVA: diva2:861920
Public defence
2015-12-15, Eva Erikssonsalen, 21A 342, Karlstad University, Karlstad, 10:15 (English)
Opponent
Supervisors
Available from: 2015-11-24 Created: 2015-10-19 Last updated: 2017-11-29Bibliographically approved
List of papers
1. A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment
Open this publication in new window or tab >>A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment
2014 (English)In: Technology, Knowledge and Learning, ISSN 2211-1662, E-ISSN 2211-1670, Vol. 19, no 3, p. 287-315Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Springer, 2014
Keyword
Mathematics education, Task design, Dynamic geometry
National Category
Educational Sciences
Identifiers
urn:nbn:se:kau:diva-33815 (URN)10.1007/s10758-014-9213-9 (DOI)
Available from: 2014-09-24 Created: 2014-09-24 Last updated: 2017-12-05Bibliographically approved
2. Designing Prediction Tasks in a Mathematics Software Environment
Open this publication in new window or tab >>Designing Prediction Tasks in a Mathematics Software Environment
2015 (English)In: International Journal of Technology in Mathematics Education, ISSN 1744-2710, Vol. 22, no 1, p. 3-18Article in journal (Refereed) 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.  

Keyword
Task design, Prediction task, Mathematics software environment
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-35034 (URN)
Available from: 2015-01-28 Created: 2015-01-28 Last updated: 2017-08-08Bibliographically approved
3. Instrumental genesis concerning scales and scaling in a dynamic mathematics software environment
Open this publication in new window or tab >>Instrumental genesis concerning scales and scaling in a dynamic mathematics software environment
2015 (English)In: Proceedings of the Ninth Congress of European Research in Mathematics Education / [ed] K. Krainer, N. Vondrova, Prague: Charles University , 2015, p. 2347-2353Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Prague: Charles University, 2015
Keyword
mathematics education, dynamic mathematics software, instrumental genesis
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-38208 (URN)
Conference
CERME9 - the 9th Congress of European Research in Mathematics Education, Prague, Charles University, 4-8 Februari 2015
Available from: 2015-10-19 Created: 2015-10-19 Last updated: 2017-05-29Bibliographically approved
4. Redesigning task sequences to support instrumental genesis in the use of movable points and slider bars
Open this publication in new window or tab >>Redesigning task sequences to support instrumental genesis in the use of movable points and slider bars
2017 (English)In: International journal for technology in mathematics education, ISSN 1744-2710, Vol. 24, no 1, p. 3-15Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Plimuth: Research Information Ltd., 2017
National Category
Didactics
Identifiers
urn:nbn:se:kau:diva-38211 (URN)10.1564/tme_v24.1.01 (DOI)
Available from: 2015-10-19 Created: 2015-10-19 Last updated: 2017-06-15Bibliographically approved
5. Teachers’ didactical intention and instrumental orchestrations for ‘follow-up’ lessons
Open this publication in new window or tab >>Teachers’ didactical intention and instrumental orchestrations for ‘follow-up’ lessons
(English)Manuscript (preprint) (Other academic)
National Category
Didactics
Identifiers
urn:nbn:se:kau:diva-38212 (URN)
Available from: 2015-10-19 Created: 2015-10-19 Last updated: 2016-02-02Bibliographically approved
6. Orchestration of mathematical discussions drawing on students’ computer-based work
Open this publication in new window or tab >>Orchestration of mathematical discussions drawing on students’ computer-based work
2017 (English)In: 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, p. 77-87Conference paper, Published paper (Refereed)
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

Place, publisher, year, edition, pages
Göteborg: Svensk förening för matematikdidaktisk forskning (SMDF), 2017
Series
Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 11
Keyword
mathematics education, dynamic software, class discussion
National Category
Didactics
Research subject
Education
Identifiers
urn:nbn:se:kau:diva-49429 (URN)978-91-984024-0-7 (ISBN)
Conference
MADIF10 - The tenth research seminar of the Swedish Society for Research in Mathematics Education (SMDF), Karlstad 26-27 januari 2016
Available from: 2017-05-29 Created: 2017-05-29 Last updated: 2017-11-29

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