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Publications (10 of 10) Show all publications
Fahlgren, M. & Brunström, M. (2019). Geometriska begrepp och metoder i historien: Exemplen area och klassiska konstruktioner. Karlstad: Karlstads universitet
Open this publication in new window or tab >>Geometriska begrepp och metoder i historien: Exemplen area och klassiska konstruktioner
2019 (Swedish)Report (Refereed)
Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2019. p. 34
Series
Working Papers in Mathematics Education ; 2019:2
National Category
Didactics
Identifiers
urn:nbn:se:kau:diva-75897 (URN)978-91-7867-085-7 (ISBN)
Available from: 2019-12-09 Created: 2019-12-09 Last updated: 2020-02-24
Fahlgren, M. & Brunström, M. (2018). How the word 'mathematical' influences students’ responses to explanation tasks in a dynamic mathematics software environment. In: Hans-Georg Weigand, Alison Clark-Wilson, Ana Donevska-Todorova, Eleonora Faggiano, Niels Grønbæk, Jana Trgalova (Ed.), Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA): . Paper presented at The Fifth ERME Topic Conference Mathematics Education in the Digital Age (pp. 83-90). Copenhagen, Denmark: University of Copenhagen
Open this publication in new window or tab >>How the word 'mathematical' influences students’ responses to explanation tasks in a dynamic mathematics software environment
2018 (English)In: Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA) / [ed] Hans-Georg Weigand, Alison Clark-Wilson, Ana Donevska-Todorova, Eleonora Faggiano, Niels Grønbæk, Jana Trgalova, Copenhagen, Denmark: University of Copenhagen , 2018, p. 83-90Conference paper, Published paper (Refereed)
Abstract [en]

Task design is a central issue in mathematics education, not least in relation to digital technology. This paper reports how a smal lbut significant change in wording affects students’ explanatory responses. The study is comparative and involves 229 10th grade students working on tasks designed for a dynamic mathematics software environment. The findings indicate that inclusion of the word ‘mathematical’ prompted students to use algebraic symbols and algebraic arguments, to a higher degree.

Place, publisher, year, edition, pages
Copenhagen, Denmark: University of Copenhagen, 2018
Keywords
task design, dynamic mathematics software, explanation task
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-69215 (URN)978-87-7078-798-7 (ISBN)
Conference
The Fifth ERME Topic Conference Mathematics Education in the Digital Age
Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2019-10-21Bibliographically approved
Brunström, M. & Fahlgren, M. (2017). Orchestration of mathematical discussions drawing on students’ computer-based work. In: Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist (Ed.), 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. Paper presented at MADIF10 - The tenth research seminar of the Swedish Society for Research in Mathematics Education (SMDF), Karlstad 26-27 januari 2016 (pp. 77-87). Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF
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
Keywords
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: 2018-11-06Bibliographically approved
Brunström, M., Mossberg, E. & Vinerean-Bernhoff, M. (2016). An exploratory approach to engineering mathematics using GeoGebra. In: : . Paper presented at The 18th SEFI Mathematics Working Group seminar, Göteborg, 27-29 juni, 2016.
Open this publication in new window or tab >>An exploratory approach to engineering mathematics using GeoGebra
2016 (English)Conference paper, Poster (with or without abstract) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-48211 (URN)
Conference
The 18th SEFI Mathematics Working Group seminar, Göteborg, 27-29 juni, 2016
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2019-10-14Bibliographically approved
Brunström, M. & Fahlgren, M. (2015). Designing Prediction Tasks in a Mathematics Software Environment. The International Journal for Technology in Mathematics Education, 22(1), 3-18
Open this publication in new window or tab >>Designing Prediction Tasks in a Mathematics Software Environment
2015 (English)In: The International Journal for Technology in Mathematics Education, ISSN 1744-2710, E-ISSN 2045-2519, 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.  

Place, publisher, year, edition, pages
RESEARCH INFORMATION LTD, 2015
Keywords
Task design, Prediction task, Mathematics software environment
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-35034 (URN)10.1564/tme_v22.1.01 (DOI)000382659500002 ()
Available from: 2015-01-28 Created: 2015-01-28 Last updated: 2019-12-19Bibliographically approved
Brunström, M. (2015). Matematiska resonemang i en lärandemiljö med dynamiska matematikprogram. (Doctoral dissertation). Karlstad: Karlstads universitet
Open this publication in new window or tab >>Matematiska resonemang i en lärandemiljö med dynamiska matematikprogram
2015 (Swedish)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[en]
Mathematical Reasoning in a Dynamic Software Environment
Abstract [en]

The overall problem that formed the basis for this thesis is that students get limited opportunity to develop their mathematical reasoning ability while, at the same time, there are dynamic mathematics software available which can be used to foster this ability. The aim of this thesis is to contribute to knowledge in this area by focusing on task design in a dynamic software environment and by studying the reasoning that emerges when students work on tasks in such an environment. To analyze students’ mathematical reasoning, a new analytical tool was developed in the form of an expanded version of Toulmin’s model.

Results from one of the studies in this thesis show that exploratory tasks in a dynamic software environment can promote mathematical reasoning in which claims are formulated, examined and refined in a cyclic process. However, this reasoning often displayed a lack of the more conceptual, analytic and explanatory reasoning normally associated with mathematics. This result was partly confirmed by another of the studies. Hence, one key question in the thesis has been how to design tasks that promote conceptual and explanatory reasoning. Two articles in the thesis deal with task design. One of them suggests a model for task design with a focus on exploration, explanation, and generalization. This model aims, first, to promote semantic proof production and then, after the proof has been constructed, to encourage further generalizations. The other article dealing with task design concerns the design of prediction tasks to foster student reasoning about exponential functions. The research process pinpointed key didactical variables that proved crucial in designing these tasks.

Abstract [sv]

Baksidestext

Det övergripande problem som legat till grund för denna avhandling är att elever får begränsad möjlighet att utveckla sin resonemangsförmåga samtidigt som det finns dynamiska matematikprogram som kan utnyttjas för att stimulera denna förmåga. Syftet med avhandlingen är att bidra till den samlade kunskapen inom detta problemområde, dels genom att fokusera på design av uppgifter i en lärandemiljö med dynamiska matematikprogram och dels genom att studera och karakterisera de resonemang som utvecklas när elever jobbar med olika uppgifter i denna miljö. För att analysera elevernas resonemang utvecklades ett nytt analysverktyg i form av en utökad version av Toulmins modell.

Resultat från en av studierna i avhandlingen visar att dynamiska matematikprogram i kombination med utforskande uppgifter kan stimulera till matematiska resonemang där hypoteser formuleras, undersöks och förfinas i en cyklisk process. Samtidigt visar samma studie att de resonemang som utvecklas i stor utsträckning saknar matematiskt grundade förklaringar. Detta resultat bekräftas till viss del av ytterligare en studie.  Frågan hur uppgifter bör designas för att främja matematiskt grundade resonemang har därför varit central i avhandlingen. Två av artiklarna behandlar uppgiftsdesign, men utifrån olika utgångspunkter.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2015. p. 77
Series
Karlstad University Studies, ISSN 1403-8099 ; 2015:12
Keywords
Mathematical reasoning, Task design, Dynamic mathematics software, matematiska resonemang, uppgiftsdesign, dynamiska matematikprogram
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-35037 (URN)978-91-7063-623-3 (ISBN)
Public defence
2015-03-18, 21A 342 (Eva Erikssonsalen), Karlstad, 10:15 (Swedish)
Opponent
Supervisors
Available from: 2015-03-04 Created: 2015-01-28 Last updated: 2015-03-04Bibliographically approved
Fahlgren, M. & Brunström, M. (2015). Using slider tools to explore and validate. In: CERME9 Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education: . Paper presented at The Ninth Congress of European Research in Mathematics Education 4-8 feb Prague.
Open this publication in new window or tab >>Using slider tools to explore and validate
2015 (English)In: CERME9 Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, 2015Conference paper, Poster (with or without abstract) (Refereed)
Keywords
Slider tools, Parameters, dynamic mathematics software
National Category
Humanities Mathematics
Research subject
Education
Identifiers
urn:nbn:se:kau:diva-39211 (URN)978-80-7290-844-8 (ISBN)
Conference
The Ninth Congress of European Research in Mathematics Education 4-8 feb Prague
Available from: 2016-02-02 Created: 2016-02-02 Last updated: 2016-02-10Bibliographically approved
Fahlgren, M. & Brunström, M. (2014). A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment. Technology, Knowledge and Learning, 19(3), 287-315
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
Keywords
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
Brunström, M. & Fahlgren, M. (2009). GeoGebra - A Tool to Create Favorable Learning Situations with Emphasize on Logical Reasoning and Communication. In: : . Paper presented at First International GeoGebra Conference - RISC, Castle of Hagenberg near Linz, Austria, July 14-15, 2009.
Open this publication in new window or tab >>GeoGebra - A Tool to Create Favorable Learning Situations with Emphasize on Logical Reasoning and Communication
2009 (English)Conference paper, Published paper (Other (popular science, discussion, etc.))
Abstract [en]

Logic reasoning and communication are general competencies, important in all areas of mathematics. We think that one of the major advantages of GeoGebra is the possibility to create favorable learning situations for these competencies. We would like to investigate these possibilities. Our main interest is to find out how students use logic reasoning and how they communicate when they work in pairs with GeoGebra. We think that investigating the validity of certain geometrical statements is a kind of task appropriate for this purpose

Keywords
Subject Didactics
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-9903 (URN)
Conference
First International GeoGebra Conference - RISC, Castle of Hagenberg near Linz, Austria, July 14-15, 2009
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2016-02-02Bibliographically approved
Brunström, M. Students’ Mathematical Reasoning in a Dynamic Software Environment.
Open this publication in new window or tab >>Students’ Mathematical Reasoning in a Dynamic Software Environment
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Mathematical reasoning has been identified as one of the key competencies needed to master mathematics. It is also well documented that dynamic mathematics software can be utilized to provide students with opportunities to practice different aspects of mathematical reasoning. In this study an expanded version of Toulmin’s model of argumentation was used to analyze the reasoning that emerged when three student pairs used GeoGebra to explore how the different parameters influence the graph of the function y = A sin (Bx + C) + D. Several characteristic features, both promising and cautionary, were discerned in the students’ reasoning.

Keywords
Mathematical reasoning, Dynamic mathematics software, Toulmin's model
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-35035 (URN)
Available from: 2015-01-28 Created: 2015-01-28 Last updated: 2017-03-30Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-2897-9188

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