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Bergman Ärlebäck, JonasORCID iD iconorcid.org/0000-0001-5013-8890
Alternative names
Publications (10 of 69) Show all publications
Stillman, G. A., Ikeda, T., Schukajow, S., de Loiola Araújo, J. & Bergman Ärlebäck, J. (2023). Survey of interdisciplinary aspects of the teaching and learning of mathematical modelling in mathematics education. In: Gilbert Greefrath, Susana Carreira, Gloria Ann Stillman (Ed.), Advancing and Consolidating Research on Applications and Modelling in Mathematics Education – Approaches from ICME 14.: (pp. 21-41). Cham: Springer
Open this publication in new window or tab >>Survey of interdisciplinary aspects of the teaching and learning of mathematical modelling in mathematics education
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2023 (English)In: Advancing and Consolidating Research on Applications and Modelling in Mathematics Education – Approaches from ICME 14. / [ed] Gilbert Greefrath, Susana Carreira, Gloria Ann Stillman, Cham: Springer, 2023, p. 21-41Chapter in book (Refereed)
Abstract [en]

This survey on interdisciplinary aspects of the teaching and learning of mathematical modelling focuses on the period 2012–2021. Based on our review of research literature published during this time, following the brief we were given to conduct the survey, we identified four major threads of contributions as these relate to schooling. These threads were: the importance of a well-understood relation between mathematics and the real world supporting interdisciplinary work in mathematics education; the contribution to knowledge about modelling of interdisciplinary research and teaching teams; issues and challenges in the relationships among mathematical modelling, mathematics, the real world and interdisciplinarity; and, mathematical modelling providing critical high leverage to ensure mathematical depth in STEM integration. Each thread is exemplified with relevant research. Future directions are offered in our final reflections.

Place, publisher, year, edition, pages
Cham: Springer, 2023
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-195266 (URN)9783031271151 (ISBN)
Available from: 2023-06-18 Created: 2023-06-18 Last updated: 2023-09-12Bibliographically approved
Bergman Ärlebäck, J. & Kawakami, T. (2023). The relationship between mathematical modelling, statistics, and statistical modelling. In: Gilbert Greefrath, Susana Carreira, Gloria Ann Stillman (Ed.), Advancing and Consolidating Research on Applications and Modelling in Mathematics Education – Approaches from ICME 14: (pp. 293-309). Springer
Open this publication in new window or tab >>The relationship between mathematical modelling, statistics, and statistical modelling
2023 (English)In: Advancing and Consolidating Research on Applications and Modelling in Mathematics Education – Approaches from ICME 14 / [ed] Gilbert Greefrath, Susana Carreira, Gloria Ann Stillman, Springer, 2023, p. 293-309Chapter in book (Refereed)
Abstract [en]

This chapter presents arguments and examples highlighting the similarities and differences between statistics, statistical modelling and mathematical modelling. Based on educational research that focuses on statistical modelling and mathematical modelling, we elaborate on the potentially productive connections for the development of, and research on, the teaching and learning of statistics, statistical modelling and mathematical modelling. We outline the development of an ongoing research agenda that pursues a framework for how to conceptualise the connection between statistics and statistical modelling on the one hand, and mathematical modelling on the other, as well as suggest how to further develop this emerging framework in order to provide a richer, more nuanced and useful picture of the relationship between statistics, statistical modelling and mathematical modelling.

Place, publisher, year, edition, pages
Springer, 2023
Series
International Perspectives on the Teaching and Learning of Mathematical Modelling, ISSN 2211-4920, E-ISSN 2211-4939
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-195267 (URN)10.1007/978-3-031-27115-1_18 (DOI)9783031271175 (ISBN)9783031271144 (ISBN)
Available from: 2023-06-18 Created: 2023-06-18 Last updated: 2023-09-12Bibliographically approved
Kawakami, T. & Bergman Ärlebäck, J. (2022). Characterising rationales for using statistical modelling in education research from a mathematical modelling perspective: A review. In: Hodgen J., Geraniou E., Bolondi G., & Ferretti, F. (Ed.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): . Paper presented at Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2 – 5 February, 2022 (pp. 1109-1116). Free University of Bozen-Bolzano, Italy and ERME
Open this publication in new window or tab >>Characterising rationales for using statistical modelling in education research from a mathematical modelling perspective: A review
2022 (English)In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) / [ed] Hodgen J., Geraniou E., Bolondi G., & Ferretti, F., Free University of Bozen-Bolzano, Italy and ERME , 2022, p. 1109-1116Conference paper, Oral presentation only (Other academic)
Abstract [en]

This study developed and discussed a framework for characterising rationales for using statistical modelling from a mathematical modelling perspective based on a systematic literature review. We used this framework to provide an overview of the distributions of these rationales in the analysed studies, focusing on statistical modelling. The results identified three categories of rationales for using statistical modelling, namely, competency, content, and socially oriented types. This work discussed how the conceptualised rationales for using statistical modelling in the teaching and learning of statistics can guide the initial step in task design and curriculum development related to statistical modelling. These rationales may also serve as a common point of departure for discussions and collaboration between the mathematics and statistics education communities on the use of models and modelling.

Place, publisher, year, edition, pages
Free University of Bozen-Bolzano, Italy and ERME, 2022
Keywords
Statistical modelling, mathematical modelling, rationale, systematic review
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-195270 (URN)
Conference
Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2 – 5 February, 2022
Available from: 2023-06-18 Created: 2023-06-18 Last updated: 2023-07-07Bibliographically approved
Bergman Ärlebäck, J. & Frejd, P. (2022). Developing and testing a framework for analysing, comparing and visualizing content matter in and across mathematics textbooks. In: Linda Mattsson, Johan Häggström, Martin Carlsen, Cecilia Kilhamn, Hanna Palmér, Miguel Perez, Kerstin Pettersson (Ed.), The relation between mathematics education research and teachers’ professional development.: Proceedings of MADIF 13The thirteenth research conference ofthe Swedish Society for Researchin Mathematics EducationVäxjö, March 29–30, 2022. Paper presented at The thirteenth research seminar of the Swedish Society for Research in Mathematics Education, Växjö, March 29–30, 2022 (pp. 105-115).
Open this publication in new window or tab >>Developing and testing a framework for analysing, comparing and visualizing content matter in and across mathematics textbooks
2022 (English)In: The relation between mathematics education research and teachers’ professional development.: Proceedings of MADIF 13The thirteenth research conference ofthe Swedish Society for Researchin Mathematics EducationVäxjö, March 29–30, 2022 / [ed] Linda Mattsson, Johan Häggström, Martin Carlsen, Cecilia Kilhamn, Hanna Palmér, Miguel Perez, Kerstin Pettersson, 2022, p. 105-115Conference paper, Published paper (Refereed)
Abstract [en]

In this methodological paper we discuss the development and testing of a framework for analysing and visualizing the overall structure of the content and tasks in mathe-matics textbooks. The aim of the framework is to provide a lens on mathematics textbooks at the secondary level that is mathematics topic- and content-area-unbiased to facilitate an as objective as possible comparisons between both (a) different contents, topics, and tasks within a textbook; and (b) contents, topics, and tasks across different series of textbooks or within a textbook series. The paper explores the results of the framework applied to four mathematical textbook chapters visualized in terms of so-called hierarchy charts. Inter-rater coding reliability with respect to a developed coding manual, and future development and applications of the framework is also discussed.

Series
Skrifter från SMDF, E-ISSN 1651-3274 ; 16
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-188388 (URN)978-91-984024-5-2 (ISBN)
Conference
The thirteenth research seminar of the Swedish Society for Research in Mathematics Education, Växjö, March 29–30, 2022
Available from: 2022-09-11 Created: 2022-09-11 Last updated: 2022-10-10Bibliographically approved
Bergman Ärlebäck, J. & Frejd, P. (2022). Developing and testing a framework for analysing, comparing and visualizing content matter in and across mathematics textbooks. In: L. Mattsson, J. Häggström, M. Carlsen, C. Kilhamn, H. Palmér, M. Perez, M. & K. Pettersson (Ed.), The relation between mathematics education research and teachers’ professional development. Proceedings of MADIF13. The thirteenth research seminar of the Swedish Society for Research in Mathematics Education, Växjö, 2022: . Paper presented at Madif13, Växjö, Sweden, March 29-30, 2022 (pp. 105-115).
Open this publication in new window or tab >>Developing and testing a framework for analysing, comparing and visualizing content matter in and across mathematics textbooks
2022 (English)In: The relation between mathematics education research and teachers’ professional development. Proceedings of MADIF13. The thirteenth research seminar of the Swedish Society for Research in Mathematics Education, Växjö, 2022 / [ed] L. Mattsson, J. Häggström, M. Carlsen, C. Kilhamn, H. Palmér, M. Perez, M. & K. Pettersson, 2022, p. 105-115Conference paper, Published paper (Refereed)
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-194779 (URN)
Conference
Madif13, Växjö, Sweden, March 29-30, 2022
Available from: 2023-06-12 Created: 2023-06-12 Last updated: 2023-06-30Bibliographically approved
Frejd, P., Bergman Ärlebäck, J. & Bergfors, M. (2022). Developing pre-service teachers’ communications skills using Socratic lectures: The audience’s perspective. In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy.: . Paper presented at Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy..
Open this publication in new window or tab >>Developing pre-service teachers’ communications skills using Socratic lectures: The audience’s perspective
2022 (English)In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy., 2022Conference paper, Published paper (Refereed)
Abstract [en]

This study investigates the potential of engaging secondary pre-service teachers in a team-teaching approach called Socratic lectures to develop their communicational skills. An intervention was designed centered around a workshop sandwiched between a pre- and a post-presentation on natural logarithmic and derivatives to an audience of undergraduate students. A quantitative and qualitative analysis of 155 pre- and 92 documented post-experiences of the undergraduate students’ shows that the pre-service teachers’ presentations and communicating skills developed positively over the course of the intervention. The accompanying statistical analysis of Likert evaluation items shows asignificant increase of multiple communicational aspects of the pre-service teachers, and the line-by-line analysis of written evaluations support this claim regarding the pre-service teachers’interactivity. Issues about generalizability and future research is also discussed.

Keywords
Interaction, pre-service teachers, socratic lectures, team teaching, questions
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-188389 (URN)
Conference
Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy.
Available from: 2022-09-11 Created: 2022-09-11 Last updated: 2022-10-10
Albarracín, L. & Bergman Ärlebäck, J. (2022). Esquemas de resolución de problemas de Fermi como herramienta de diseño y gestión para el profesor [Fermi problem activity templates as a design and managementtool for the teacher]. Educación Matemática, 34(2), 289-309
Open this publication in new window or tab >>Esquemas de resolución de problemas de Fermi como herramienta de diseño y gestión para el profesor [Fermi problem activity templates as a design and managementtool for the teacher]
2022 (Spanish)In: Educación Matemática, E-ISSN 2448-8089, Vol. 34, no 2, p. 289-309Article in journal (Refereed) Published
Abstract [es]

Se presenta una caracterización de las resoluciones posibles a unproblema de Fermi a partir de los Esquemas de Resolución de Problemas deFermi (ERPF). El artículo presenta la fundamentación teórica basada en inves-tigaciones previas sobre problemas de Fermi en Educación Matemática y otroscampos de investigación que permite identificar las cuatro actividades princi-pales que pueden utilizarse al resolverlos. Estas actividades son la estimaciónrazonada, la experimentación, la búsqueda de datos de fuentes fiables y larecogida y tratamiento estadístico de datos. A partir de estas actividades seconcretan los ERPF y se discuten sus posibilidades como herramientas parala gestión y el diseño de actividades de aula. Se incluyen ejemplos concretosde propuestas de aula para sustentar tanto el trabajo de los alumnos comolas opciones de diseño de actividades y gestión que habilitan los ERPF parafomentar la resolución de problemas y la modelización matemática.

Abstract [en]

This article presents a characterization of the possible resolutions toa Fermi problem from the Fermi problem Activity Templates (FpAT). The articlepresents the theoretical foundation based on previous research on Fermi prob-lems in Mathematics Education and other fields of research that allows theidentification of the four main activities that can be used when solving them.These activities are reasoned estimation, experimentation, searching for datafrom reliable sources, and statistical data collection and processing. From theseactivities, the FpAT are specified and their possibilities as tools for the manage-ment and design of classroom activities are discussed. Specific examples ofclassroom proposals are included to support both the work of students and theactivity design and management options enabled by the FpAT to promoteproblem solving and mathematical modelling.

Keywords
Fermi problems, mathematical modeling, task design, Problemas de Fermi, modelización matemática, diseño de tareas
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-198295 (URN)10.24844/em3402.11 (DOI)
Available from: 2023-10-03 Created: 2023-10-03 Last updated: 2023-10-20Bibliographically approved
Barquero, B., Bergman Ärlebäck, J., Carreira, S., Greefrath, G., Eyrich Jessen, B. & Vorhölter, K. (2022). Introduction to the papers of TW6: Application and modelling. In: Hodgen, J., Geraniou, E., Bolondi,G. & Ferretti, F. (Ed.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): . Paper presented at Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2 – 5 February, 2022 (pp. 999-1008). Free University of Bozen-Bolzano, Italy and ERME
Open this publication in new window or tab >>Introduction to the papers of TW6: Application and modelling
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2022 (English)In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) / [ed] Hodgen, J., Geraniou, E., Bolondi,G. & Ferretti, F., Free University of Bozen-Bolzano, Italy and ERME , 2022, p. 999-1008Conference paper, Oral presentation only (Other academic)
Place, publisher, year, edition, pages
Free University of Bozen-Bolzano, Italy and ERME, 2022
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-195268 (URN)
Conference
Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2 – 5 February, 2022
Available from: 2023-06-18 Created: 2023-06-18 Last updated: 2023-07-07Bibliographically approved
Bergman Ärlebäck, J. & Frejd, P. (2022). Towards a dual integrated modeling approach to the teaching and learning of mathematics: Challenges and tensions in implementation. In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy.: . Paper presented at Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education, Bozen-Bolzano, Italy, February, 2-6, 2022.
Open this publication in new window or tab >>Towards a dual integrated modeling approach to the teaching and learning of mathematics: Challenges and tensions in implementation
2022 (English)In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education February, 2-6, 2022. Bozen-Bolzano, Italy., 2022Conference paper, Published paper (Refereed)
Abstract [en]

This paper elaborates on the theoretical conceptualization of a so-called dual integrated modeling approach to the teaching and learning of modeling and the teaching and learning of mathematics through modeling. Departing from a sociocultural perspective on teaching, the models and modeling perspective, and using the previously developed theoretical constructs of the Teaching Triad and the Expanded Mediated Triangle, we discuss modeling in terms of (i) micro modeling in which modeling is used as a vehicle to teach and learning other curricula content; and (ii) macro modeling in which modeling is a self-standing mathematics curricula goal. We illustrate this dual integrated approach by analyzing and discussing a lower secondary teachers’ implementation of a modeling activity focusing on a simple statistical investigation and measures of central tendency in statistics.

Keywords
Dual integrated modeling approach, expanded mediational triangle, measures of central tendency, models and modeling perspective, teaching triad
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-188390 (URN)
Conference
Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education, Bozen-Bolzano, Italy, February, 2-6, 2022
Available from: 2022-09-11 Created: 2022-09-11 Last updated: 2022-10-10
Frejd, P. (2021). Connections and synergies between the teaching and learning of statistics and modelling: a pilot study. In: F. Leung, G. A. Stillman, G. Kasier, & K. L. Wong (Ed.), Mathematical modelling in education in east and west: (pp. 607-617). Cham: Springer
Open this publication in new window or tab >>Connections and synergies between the teaching and learning of statistics and modelling: a pilot study
2021 (English)In: Mathematical modelling in education in east and west / [ed] F. Leung, G. A. Stillman, G. Kasier, & K. L. Wong, Cham: Springer, 2021, p. 607-617Chapter in book (Refereed)
Abstract [en]

This chapter presents pilot study with aim to characterise the potential connections and synergies between statistics and modelling education. By developing a methodological approach of applying the software NVivo and grounded theory, we analysed the 17 ICTMA books published to date and the books from ICME-6 and the 14th ICMI study. The results show synergies in terms of the identified themes: teach and learn statistics/modelling; ICT; curriculum; and theory.  The context units analysed frequently provide suggestions for how to teach statistics using modelling approach, but seldom is the relationship between mathematical and statistical modelling from a theoretical point of view discussed.  The discussion brings forward some limitations of the methodological approach applied and suggestions for how to overcome these to develop a more robust methodology.

Place, publisher, year, edition, pages
Cham: Springer, 2021
Series
International Perspectives on the Teaching and Learning of Mathematical Modelling, ISSN 2211-4920, E-ISSN 2211-4939
Keywords
mathematics, mathematical modelling, statistics, literature review, grounded theory, statistical modelling
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-179317 (URN)10.1007/978-3-030-66996-6_51 (DOI)9783030669959 (ISBN)9783030669966 (ISBN)
Available from: 2021-09-17 Created: 2021-09-17 Last updated: 2022-04-05Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-5013-8890

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