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Bergman Ärlebäck, Jonas
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Publications (10 of 41) Show all publications
Albarracín, L., Bergman Ärlebäck, J., Civil, E. & Gorgorió, N. (2019). Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes. The Montana Mathematics Enthusiast, 16(1-2), Article ID 10.
Open this publication in new window or tab >>Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes
2019 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 16, no 1-2, article id 10Article in journal (Refereed) Accepted
Abstract [en]

In this paper, we present a qualitative study in which we analyse the video-recordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students’ problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible.

Place, publisher, year, edition, pages
Missoula, United States: Montana Council of Teachers of Mathematics, 2019
Keywords
Mathematical modelling, Modelling Activity Diagrams, Fermi problems, Secondary School
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150892 (URN)
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-09-12Bibliographically approved
Bergman Ärlebäck, J. & Doerr, H. M. (2018). Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence. ZDM - the International Journal on Mathematics Education, 50(1-2), 187-200
Open this publication in new window or tab >>Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence
2018 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 50, no 1-2, p. 187-200Article in journal (Refereed) Published
Abstract [en]

In this article, we examine how a sequence of modeling activities supported the development of students’ interpretations and reasoning about phenomena with nega- tive average rates of change in different physical phenomena. Research has shown that creating and interpreting models of changing physical phenomena is difficult, even for university level students. Furthermore, students’ reasoning about mod- els of phenomena with negative rates of change has received little attention in the research literature. In this study, 35 students preparing to study engineering participated in a 6-week instructional unit on average rate of change that used a sequence of modeling activities. Using an analysis of the students’ work, our results show that the sequence of mod- eling activities was effective for nearly all students in reason- ing about motion with negative rates along a straight path. Almost all students were successful in constructing graphs of changing phenomena and their associated rate graphs in the contexts of motion, light dispersion and a discharging capacitor. Some students encountered new difficulties in interpreting and reasoning with negative rates in the con- texts of light dispersion, and new graphical representations emerged in students’ work in the context of the discharg- ing capacitor with its underlying exponential structure. The results suggest that sequences of modeling activities offer a structured approach for the instruction of advanced math- ematical content.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Model development sequences, Modeling, Negative rates of change, Physical phenomena
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150893 (URN)10.1007/s11858-017-0881-5 (DOI)000430868400015 ()2-s2.0-85046545659 (Scopus ID)
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-09-12Bibliographically approved
Jiménez, L. & Bergman Ärlebäck, J. (2018). Using the Mathematical Working Space model as a lens on geometry in the Swedish mathematics upper secondary curriculum. In: J. Häggström, J. B. Ärlebäck, M. Fahlgren, M. Johansson, O. Olande, & Y. Liljekvist (Ed.), Perspectives on Professional development of mathematics teachers: Proceedings of MDIF11: The 11thSwedish Mathematics Education Research Seminar. Paper presented at MDIF11, The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, Sweden, January 23–24, 2018 (pp. 1-10).
Open this publication in new window or tab >>Using the Mathematical Working Space model as a lens on geometry in the Swedish mathematics upper secondary curriculum
2018 (English)In: Perspectives on Professional development of mathematics teachers: Proceedings of MDIF11: The 11thSwedish Mathematics Education Research Seminar / [ed] J. Häggström, J. B. Ärlebäck, M. Fahlgren, M. Johansson, O. Olande, & Y. Liljekvist, 2018, p. 1-10Conference paper, Published paper (Refereed)
Abstract [en]

This paper uses the model of Mathematical Working Spaces to analyse the area of geometry in the Swedish upper secondary mathematics curriculum. By applying this framework, we describe how one can understand the mathematical work advocated in the curriculum in terms three geometrical paradigms as well as in terms of different emphasis on a set of three ways of working connecting epistemological and cognitive aspects of geometrical work.

National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150894 (URN)
Conference
MDIF11, The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, Sweden, January 23–24, 2018
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-09-17Bibliographically approved
Bergman Ärlebäck, J. & Albarracín, L. (2017). Developing a classification scheme of definitions of Fermi problems in education from a modelling perspective. In: T. Dooley, & G. Gueudet (Ed.), Proceedings of the Tenth Congress of European Research in Mathematics Education : . Paper presented at CERME10, Dublin, Ireland, 1-5 February, 2017 (pp. 884-891). Ireland, Dublin
Open this publication in new window or tab >>Developing a classification scheme of definitions of Fermi problems in education from a modelling perspective
2017 (English)In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017, p. 884-891Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we use a modelling perspective to analyse three descriptions and definitions of so- called Fermi problems found in the literature. We discuss how the three definitions align with, and what they potentially have to offer to, realistic or applied modelling, contextual modelling,educational modelling (either a didactical or conceptual), socio-critical modelling, epistemological or theoretical modelling, and cognitive modelling. Our findings show that the definitions share some similarities, but for the most part are formulated in lose terms. From a modelling perspective, we found that the conceptualisation of Fermi problem we studied foremost and directly align with contextual modelling and both strands of educational modelling. We also discuss the seemly incompatibility between Fermi problems and the other modelling perspectives, and suggest new lines of research on Fermi problems in particular, and on conceptualizing modelling in general.

Place, publisher, year, edition, pages
Ireland, Dublin: , 2017
Keywords
Fermi problem, modelling, modelling perspectives
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150897 (URN)978-1-873769-73-7 (ISBN)
Conference
CERME10, Dublin, Ireland, 1-5 February, 2017
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-11-28Bibliographically approved
Jankvist, U. T., Sánchez Aguilar, M., Bergman Ärlebäck, J. & Wæge, K. (2017). Introduction to the papers of TWG23:Implementation of research findings in mathematics education. In: T. Dooley, & G. Gueudet (Ed.), Proceedings of the Tenth Congress of European Research in Mathematics Education : . Paper presented at CERME10, Dublin, Ireland, 1-5 February, 2017 (pp. 3769-3775). Ireland, Dublin
Open this publication in new window or tab >>Introduction to the papers of TWG23:Implementation of research findings in mathematics education
2017 (English)In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017, p. 3769-3775Conference paper, Published paper (Refereed)
Abstract [en]

In this introduction, we briefly present selected theoretical constructs relevant for the Thematic Working Group 23 (TWG23). We first address the topic of “implementation research” by lookinginto other research fields and domains where this topic is well-developed. Drawing on a taxonomy of so-called “implementation science” in health-care, we attempt to categorize the papers and posters of TWG23 according to their “implementation research aim” (Nilsen, 2015). Using this taxonomy, we elaborate on future perspectives for the TWG by relating to ongoing discussions in mathematics education research.

Place, publisher, year, edition, pages
Ireland, Dublin: , 2017
Keywords
Research findings, research results, theory to practice, implementation research
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150895 (URN)978-1-873769-73-7 (ISBN)
Conference
CERME10, Dublin, Ireland, 1-5 February, 2017
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-11-28Bibliographically approved
Bergman Ärlebäck, J., Claesson, M., Hällgren, M., Lindh, S., Lundell, M. & Nordling, M. (2017). IPAs - ihopparningsaktiviteter: aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>IPAs - ihopparningsaktiviteter: aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga
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2017 (Swedish)Report (Other academic)
Abstract [sv]

Syftet med denna rapport är att på ett beskrivande sätt delge hur arbetet i projektet om IPAs som genomförts HT2014 – VT2015 gått till och vilka erfarenheter och slutsatser som arbetet resulterat i. Den tänkte läsaren är framför allt kommunernas matematiklärare, men vi tror även att andra lärare och skolpersonal kan finna innehållet intressant och användbart. Det är vår förhoppning att rapporten med tillhörande aktiviteter kan inspirera till reflektion och en mer varierad undervisning. När pronomen som vi och oss används i rapporten åsyftats alla som aktivt ingått i IPAprojektets forskande grupp, vilken har bestått av såväl deltagande lärare som forskare:

Marcus Claesson (Kungsgårdsgymnasiet, Norrköping), Malin Hällgren (Birgittaskolans vuxenutbildning, Linköping), Sofia Lindh (Hagagymnasiet, Norrköping), Mia Lundell (Djäkneparksskolan, Norrköping), Mattias Nordling (Anders Ljungstedska gymnasiet, Linköping) och Jonas Bergman Ärlebäck (LiU). Huvudansvaret för författandet av rapporten har Jonas haft som medverkande forskare i projektet. De medforskande lärarna har bidragit med analyser, erfarenheter och exempel från sina klassrum, utvecklat, testat och formulerat aktiviteterna som utgjort navet i projektet, samt läst och kommenterat rapporten under dess framställning.

Rapporten följer samma logik och uppbyggnad som de rapporter skrivna inom det övergripande samarbetsprojektet Matematikdidaktik för bättre matematikkunskaper av det arbete och den forskning som bedrivits av Lisa Björklund Boistrup (Björklund Boistrup et al. 2013a; 2013b; 2013c; 2014a; 2014b). Vissa delar av texten använder därför, eller bygger till viss del på, Lisas texter, och när så är fallet tydliggörs detta med fotnoter. Andra delar av texten, så som exempelvis beskrivningen av de teoretiska utgångspunkterna, är i stort identiskt i samtliga delprojektsrapporter för de projekt som Jonas medverkat i som forskare (Ärlebäck et. al. 2017a, 2017b, 2017c, 2017d). Rapporten är dock skriven för att kunna läsas helt fristående från de andra rapporterna författade i projektet och förutsätter med andra ord ingen tidigare kunskap eller kännedom om projektet och de perspektiv som används. De läsare som redan tagit del av arbetet inom samarbetsprojektet Matematikdidaktik för bättre matematikkunskaper på olika sätt kommer här och var att känna igen sig, men vi hoppas att de delar som är unikt specifika för just detta delprojekt ska vara intressant och inspirerande.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 53
Keywords
Matematikundervisning, Gymnasieskolan
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:liu:diva-141605 (URN)
Projects
Matematik för bättre matematikkunskaper
Available from: 2017-10-02 Created: 2017-10-02 Last updated: 2017-12-14Bibliographically approved
Bergman Ärlebäck, J. (2017). Using a Models and Modeling Perspective (MMP) to frame and combine research, practice- and teachers’ professional development. In: T. Dooley, & G. Gueudet (Ed.), Proceedings of the Tenth Congress of European Research in Mathematics Education : . Paper presented at CERME10, Dublin, Ireland, 1-5 February, 2017. Ireland, Dublin
Open this publication in new window or tab >>Using a Models and Modeling Perspective (MMP) to frame and combine research, practice- and teachers’ professional development
2017 (English)In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017Conference paper, Published paper (Refereed)
Abstract [en]

This paper describes and discusses the framing of, and experiences from, a project that combine research, practice- and teachers’ professional development based on the tenets of the Models andModeling Perspective on teaching and learning (MMP). Besides providing a general description of the methodological considerations in the project design, the paper describes how the accumulated results and experiences in the research literature on so-called model eliciting activities are used to inform the design, implementation and evaluation of activities aiming at introducing functions to grade 8 students. The focus of the paper is on the implantation and aim to showcase how the teacher in question realized the offered perspective and tools in practice.

Place, publisher, year, edition, pages
Ireland, Dublin: , 2017
Keywords
Practice development, teachers’ professional development, models and modeling perspective, model eliciting activities
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-150896 (URN)978-1-873769-73-7 (ISBN)
Conference
CERME10, Dublin, Ireland, 1-5 February, 2017
Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2018-11-28Bibliographically approved
Geiger, V., Bergman Ärlebäck, J. & Frejd, P. (2016). Interpreting curricula to find opportunities for modeling: case studies from Australia and Sweden. In: Christian R. Hirsch, Amy Roth McDuffie (Ed.), Annual Perspectives in Mathematics Education (APME) 2016: Mathematical modeling and modeling mathematics (pp. 207-215). Reston, VA: National Council of Teachers of Mathematics
Open this publication in new window or tab >>Interpreting curricula to find opportunities for modeling: case studies from Australia and Sweden
2016 (English)In: Annual Perspectives in Mathematics Education (APME) 2016: Mathematical modeling and modeling mathematics / [ed] Christian R. Hirsch, Amy Roth McDuffie, Reston, VA: National Council of Teachers of Mathematics , 2016, p. 207-215Chapter in book (Refereed)
Place, publisher, year, edition, pages
Reston, VA: National Council of Teachers of Mathematics, 2016
Series
Annual Perspectives in Mathematics Education, ISSN 2332-6336
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-128821 (URN)9780873539739 (ISBN)9780873539913 (ISBN)
Available from: 2016-05-31 Created: 2016-05-31 Last updated: 2016-11-29Bibliographically approved
English, L. D., Bergman Ärlebäck, J. & Mousolides, N. (2016). Reflections on progress in mathematical modelling research. In: Ángel Gutiérrez, Gilah C. Leder, Paolo Boero (Ed.), The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues (pp. 383-413). Rotterdam: Sense Publishers
Open this publication in new window or tab >>Reflections on progress in mathematical modelling research
2016 (English)In: The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues / [ed] Ángel Gutiérrez, Gilah C. Leder, Paolo Boero, Rotterdam: Sense Publishers, 2016, p. 383-413Chapter in book (Other academic)
Place, publisher, year, edition, pages
Rotterdam: Sense Publishers, 2016
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-128172 (URN)9789463005593 (ISBN)9789463005609 (ISBN)9789463005616 (ISBN)
Available from: 2016-05-19 Created: 2016-05-19 Last updated: 2016-08-16Bibliographically approved
Bergman Ärlebäck, J., Blomberg, P. & Nilsson, P. (2015). An instructional design perspective on data-modelling for learning statistics and modelling. In: Development of mathematics teaching: Design, Scale, Effects : Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar: . Paper presented at MADIF9 (pp. 37-46). Umeå
Open this publication in new window or tab >>An instructional design perspective on data-modelling for learning statistics and modelling
2015 (English)In: Development of mathematics teaching: Design, Scale, Effects : Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar, Umeå, 2015, p. 37-46Conference paper, Published paper (Refereed)
Abstract [en]

This theoretical and methodological paper discusses the emerging theoretical framing and methodological considerations in our efforts to develop a theoretical approach supporting instructional design for teaching and learning statistics and mathematical modelling. From an instructional design point of view aligned with the goals in governing curricula documents and real classroom constraints, we argue for the integration of the models and modelling perspective on teaching and learning mathematics with a data-modelling approach to facilitate students’ learning statistics and mathematical modelling. An application of the framework is given and future research discussed.

Place, publisher, year, edition, pages
Umeå: , 2015
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-126927 (URN)
Conference
MADIF9
Available from: 2016-04-07 Created: 2016-04-07 Last updated: 2016-04-25
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