| 1. |
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| 2. |
- Albarracín, Lluís, et al.
(författare)
-
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
-
Ingår i: Educación Matemática. - : Sociedad Mexicana de Investigacion y Divulgacion de la Educacion Matematica A. C.. - 2448-8089. ; 34:2, s. 289-309
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Albarracín, Lluís, et al.
(författare)
-
Exploring the use of Fermi problems and the FRAT-framework with pre-service primary teachers to bring real-life contexts into classrooms
- 2021
-
Ingår i: 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. - Göteborg, Sweden : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402452 ; , s. 81-91
-
Konferensbidrag (refereegranskat)abstract
- In this paper we analyse 11 pairs of pre-service primary teachers’ solutions to twoFermi problems. The solutions were expressed using the descriptive and analytic FPATframework (Fermi problem Activity Template), and our analysis focus on characterizingthe FPAT representations produced by the pre-service teachers. The results show thatalmost half of the produced FPATs in principle solved the problems but that only threesolutions provided enough detail to be practically implementable. Multiple keyconstructs were used to structure the solutions in the first problem, but not so in thesecond problem. The variation of different activities and ways of working suggested insolving the sub-problems in the two problems also differ in a significant way.
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| 4. |
- Albarracín, Lluís, et al.
(författare)
-
Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes
- 2019
-
Ingår i: The Mathematics Enthusiast. - Missoula, United States : Montana Council of Teachers of Mathematics. - 1551-3440. ; 16:1
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 5. |
- Albarracín, Lluís, et al.
(författare)
-
REPENSANDO LOS PROBLEMAS DE FERMI PARA LA ENSEÑANZA Y APRENDIZAJE DE LAS CIENCIAS [Rethinking Fermi problems for science teaching and learning]
- 2021
-
Ingår i: Investigações em Ensino de Ciências. - Brazil : Universidade Federal do Rio Grande do Sul. - 1518-8795. ; 26:3, s. 56-56
-
Tidskriftsartikel (refereegranskat)abstract
- In this article we present a compilation of research results on the educational use of Fermi problems. While working on these problems, the key aspect is identifying the most relevant variables of a phenomenon and estimating them in order to obtain a solution to the problem. Fermi problems come from a long tradition, they have been used at all educational levels, but they have not yet established as a common activity in the classroom, especially in science classrooms. Given the broad didactic potential of Fermi problems identified in the literature, our contribution in this article is the connections with areas of interest for science teaching. We propose four didactic axes to which Fermi problems can make a relevant contribution in the science classroom: (a) To better understand what science is like, (b) To better participate in school science, (c) To better construct scientific ideas, (d) To better raise awareness of socio-scientific problems. To make the proposal more concrete, we show an example of a concrete solution with a problem of estimation of energy values, which allows us to exemplify classroom work and allows discussion with students on the relevance of science in social problems.
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| 6. |
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| 7. |
- Barquero, Berta, et al.
(författare)
-
Introduction to the papers of TW6: Application and modelling
- 2022
-
Ingår i: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). - : Free University of Bozen-Bolzano, Italy and ERME. ; , s. 999-1008
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Barquero, Berta, et al.
(författare)
-
Introduction to the papers of TWG6 : Applications and modelling
- 2019
-
Ingår i: <em>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education</em>. - Utrecht, the Netherlands : Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. ; , s. 1104-1111
-
Konferensbidrag (refereegranskat)
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| 9. |
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| 10. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
A case study of tensions and challenges arising as a Swedish upper secondary teacher designs and implements a Model Development Sequence on statistics
- 2020
-
Ingår i: Mathematical modelling education and sense-making. - Cham : Springer. - 9783030376727 - 9783030376734 ; , s. 139-150
-
Bokkapitel (refereegranskat)abstract
- A study of an upper secondary teacher trying to transform her teaching by designing and implementing a model development sequence on statistics in a grade 11 mathematics class in Sweden is presented. Cultural-historical activity theory (CHAT) is used to analyse lesson plans, reflection notes, recordings from planning meetings, and student data to identify tensions and challenges arising as she tried to adopt this new perspective on teaching and learning mathematics. The results illustrate the need to renegotiate appropriate classroom norms and facilitate shifts in power, ownership, and responsibilities in the mathematics classroom if a modelling approach is to effectively impact and change the teaching and learning of mathematics using mathematical modelling.
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| 11. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
A framework for exploring the use of Fermi problems to elicit students’ and pre-service teachers’ intercultural awareness in mathematics classrooms.
- 2023
-
Ingår i: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). - Budapest. ; , s. 1127-1134
-
Konferensbidrag (refereegranskat)abstract
- This theoretical paper outlines and discusses our first attempt to formulate the foundation and selected components of an emerging framework for using novel modelling problems (Fermi problem) as a tool in the teaching and learning of mathematics to make different cultural aspects of the world visible and accessible for students. We present (i) an argument relating mathematical modelling, aspects of culture and intercultural awareness; and (ii) an analysis investigating to what extent the six design principles of models eliciting activates aligns with, or need to be developed and modified in order to align with, the three levels of intercultural awareness discussed by Will Baker in a paper from 2011. The focus of the analysis is to evaluate the potential of the (potentially modified) six design principles of model eliciting activities to effectively also be applicable for designing Fermi problems that make different cultural aspects of the world visible and accessible for students.
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| 12. |
- Bergman Ärlebäck, Jonas, et al.
(författare)
-
A Modeling Perspective on Interpreting Rates of Change in Context
- 2013
-
Ingår i: Mathematical Thinking and Learning. - : Routledge. - 1098-6065 .- 1532-7833. ; 15:4, s. 314-336
-
Tidskriftsartikel (refereegranskat)abstract
- Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students abilities to describe and interpret rates of change in the context of exponential decay. In this article, we elaborate the characteristics of the model development sequence and we examine how students interpreted and described non-constant rates of change in context. We provide evidence for how a focus on the context made visible students reasoning about rates of change, including difficulties related to the use of language when describing changes in the negative direction. We argue that context and the use of language, forefronted in a modeling approach, should play an important role in supporting the development of students reasoning about changing phenomena.
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| 13. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
An extension of the MAD framework and its possible implications for research
- 2019
-
Ingår i: <em>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education </em>. - Utrecht, the Netherlands : Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. ; , s. 1128-1135
-
Konferensbidrag (refereegranskat)abstract
- In this paper we investigate the potential in extending Model Activity Diagrams (MADs) as an analytical tool for studying the activities students engage in when working on modelling problems. By including a sub-division of the task students work on in the MAD framework, we are able to make a more nuanced analysis that in a more explicit way reveals the structure of the students’ modelling process. The framework is applied to groups of students engaged in solving a Fermi problem using a two-level analysis, and the result is contrasted and discussed by comparing the outcome of the analysis with the corresponding analysis made using the modelling cycle. In addition, possible applications of the extended MAD framework in research and the training of teachers are discussed.
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| 14. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
An instructional design perspective on data-modelling for learning statistics and modelling
- 2015
-
Ingår i: Development of mathematics teaching: Design, Scale, Effects. - Umeå : Svensk förening för MatematikDidaktisk Forskning - SMDF. ; , s. 37-46, s. 37-46
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 15. |
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| 16. |
- Bergman Ärlebäck, Jonas, et al.
(författare)
-
An instructional design perspective on datamodelling for learning statistics and modelling
- 2014
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 17. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
At the core of modelling: Connecting, coordinating and integrating models
- 2015
-
Ingår i: <em>Proceedings of the 9th Congress of European Research in Mathematics Education</em>. ; , s. 802-808
-
Konferensbidrag (refereegranskat)abstract
- This theoretical paper introduces the notions of connecting, coordinating and integrating models to analyse and reflect on how models are created and developed. We define, discuss and apply these constructs to some theoretical perspectives in the present modelling discourse. We draw on an example from a model application activity within a model development sequence to illustrate these constructs. Our hope is to spark a discussion that will enhance our understanding about the nature of mathematical modelling and the teaching and learning of, and through, modelling.
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| 18. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Characterising pre-service primary teachers’ posed Fermi problems
- 2023
-
Konferensbidrag (refereegranskat)abstract
- In this paper 58 Fermi problems posed by grade 4–6 pre-service primary teachers are analysed with respect to (i) what extent the posed Fermi problems are clearly formulated and authentic for grade 4–6 students; (ii) if the Fermi problemsare inviting to, or setting up an introduction to, a relevant mathematical concept or content from the curriculum, or some relevant aspect of the real world; and (iii) what situations and contexts was used in the posed Fermi problems. Both pre-defined coding categories as well as open coding is used to analyse the 58 Fermi problems. The results provide a snapshot of the competence of pre-service primary teachers to pose problems that promote mathematical learning and learning about the proposed and diverse contexts in the problems.
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| 19. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Conformal Einstein spaces and Bach tensor generalization in n dimensions
- 2004
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we investigate necessary and sufficient conditions for an n-dimensional space, n ≥ 4, to be locally conformal to an Einstein space. After reviewing the classical results derived in tensors we consider the four-dimensional spinor result of Kozameh, Newman and Tod. The involvement of the four-dimensional Bach tensor (which is divergence-free and conformally well-behaved) in their result motivates a search for an n-dimensional generalization of the Bach tensor Bab with the same properties. We strengthen a theorem due to Belfagón and Jaen and give a basis (Uab, Vab and Wab) for all n-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship and show that the Bach tensor is the unique tensor with these properties in four dimensions. Unfortunately we have to conclude, in general that there is no direct analogue in higher dimension with all these properties.Nevertheless, we are able to generalize the four-dimensional results due to Kozameh, Newman and Tod to n dimensions. We show that a generic space is conformal to an Einstein space if and only if there exists a vector field satisfying two conditions. The explicit use of dimensionally dependent identities (some of which are newly derived in this thesis) is also exploited in order to make the two conditions as simple as possible; explicit examples are given in five and six dimensions using these tensor identities.For n dimensions, we define the tensors ?abc and ?ab, and we show that their vanishing is a conformal invariant property which guarantees that the space with non-degenerate Weyl tensor is a conformal Einstein space.
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| 20. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.
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| 21. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Developing a classification scheme of definitions of Fermi problems in education from a modelling perspective
- 2017
-
Ingår i: <em>Proceedings of the Tenth Congress of European Research in Mathematics Education </em>. - Ireland, Dublin. - 9781873769737 ; , s. 884-891
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 22. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Developing and testing a framework for analysing, comparing and visualizing content matter in and across mathematics textbooks
- 2022
-
Ingår i: The relation between mathematics education research and teachers’ professional development.. - 9789198402452 ; , s. 105-115
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 23. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Eliciting pre-service secondary teachers’ initial ideas of sampling
- 2021
-
Ingår i: <em>Sustainable mathematics education in a digitalized world. </em>. - Göteborg. ; , s. 234-244
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper investigates secondary pre-service teachers’ strategies of sampling. The work of eight groups of pre-service secondary teachers asked to devise and imple- ment a sampling strategy to answer two questions about three given populations of different sizes are analyzed. The result presented highlights the models devised and used by the groups. The paper especially discusses the pre-service teachers’ models of samplings in term of how the number of samples and sample size used were decided on in the model as fixed, interval-static, or dynamic.
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| 24. |
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| 25. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Ett modell- och modelleringsperspektiv på lärande och undervisning
- 2014
-
Ingår i: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; :4, s. 39-45
-
Tidskriftsartikel (populärvet., debatt m.m.)abstract
- I denna artikel diskuterar och exemplifierar författaren tankeavslöjande aktiviteter som stöttar elever att utveckla och förfina sin förståelse av matematiska modeller. Ett modell- och modelleringsperspektiv används också i ett försök att fånga och beskriva kritiska aspekter av lärande och undervisning.
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| 26. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Exploring students’ models of sampling and inference with nominal variables
- 2021
-
Ingår i: Quadrante: Revista de Investigação em Educação Matemática. - Lisbon, Portugal : Associacao de Professores de Matematica. - 0872-3915 .- 2183-2838. ; 30:1, s. 158-177
-
Tidskriftsartikel (refereegranskat)abstract
- Making inferences about unknown populations is central in statistical reasoning. However, little attention has been paid to empirical investigations of how and why students develop sampling models when investigating a categorical variable whose values are nominal. This paper reports on an intervention that draws on the models and modeling perspective, where 25 pre-service teachers were asked to develop a sampling model that could be used to make inferences about the number of different colored beads and the distribution of different colored beads in different sized populations. Using a thematic analysis, three main results about the characteristics of the students’ models of sampling and inference with nominal variables were identified: to catch all the low frequency colors in the population; not to overestimate the low frequency colors in the population; and, to formalize the relationships used in making inferences. These results highlight several issues about students’ understanding of the relationship between sample representativeness and sample variability and its consequences for making inferences.
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| 27. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Exploring the solving process of group solving realistic Fermi problems from the perspective of the Anthropological theory of didactics
- 2011
-
Ingår i: Proceedings of the Seventh Conference of European Research in Mathematics Education (CERME 7). ; , s. 1010-1020
-
Konferensbidrag (refereegranskat)abstract
- This paper reports on a first attempt to use the notions of ‘Research and Study Course’ (RSC) and ‘praxeologies’ within the Anthropological Theory of the Didactics (ATD) to analyse groups of students engaged in the mathematical activity of solving realistic Fermi problems. By considering so called realistic Fermi problem as a generating question in a RSC the groups’ derived sub-questions are identified and the praxeologies developed to address these are discussed.
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| 28. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Fermi problems and Fermi Problem Activity Templates as tools for identifying the knowns and unknowns in integrated STEM approaches - a proposal.
- 2023
-
Ingår i: <em>Proceedings of the 47th Annual Meeting of Japan Society for Science Education</em>. - Ehime University, Ehime, Japan. ; , s. 157-158
-
Konferensbidrag (refereegranskat)abstract
- Approaches to integrated STEM education offers opportunities as well as challenges for both teachers and students. Working on problems or projects involving more than one of the STEM disciplines gives access to interesting, motivating and relevant real-world contexts and problem situations, but at the same time increases the complexity of the problems and problem solving process. One contributing factor to this increasing complexity is the need to appreciate, negotiate and coordinate the different perspectives on the nature of knowledge and the characteristics of inquiry in the different STEM disciplines. This paper outlines and discusses a proposal for how so-called Fermi Problems and Fermi Problem Activity Templates (FPATs) can be used as a tool for teachers and students to start navigating and tackling this complexity.
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| 29. |
- Bergman Ärlebäck, Jonas, et al.
(författare)
-
Fermi problems as a hub for task design in mathematics and stem education
- 2023
-
Ingår i: Teaching Mathematics and its Applications. - : OXFORD UNIV PRESS. - 0268-3679 .- 1471-6976.
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms.
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| 30. |
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| 31. |
- Bergman Ärlebäck, Jonas, et al.
(författare)
-
FPAT-A Framework for Facilitating the Teaching and Learning of Using Fermi Problems Originating in Mathematics Education Research
- 2022
-
Ingår i: Physics Teacher. - : AMER ASSN PHYSICS TEACHERS. - 0031-921X .- 1943-4928. ; 60:7, s. 569-571
-
Tidskriftsartikel (refereegranskat)abstract
- Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order of magnitude calculations, and Fermi himself used them in his own research and physics classes. The procedure proposed by Fermi was to break the original problem down into simpler sub-problems, solve these by making reasonable estimates and educated guesses, and thereby reach a solution to the original question. In the literature, this way of working is known as the "Fermi (estimates) method."
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| 32. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Interpreting average rate of change in context
- 2012
-
Ingår i: Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. - : Western Michigan University. - 9780615697925 ; , s. 965-968
-
Konferensbidrag (refereegranskat)abstract
- This paper draws on a models and modeling perspective to investigate students’ abilities to describe and interpret non-constant average rates of change in the context of exponential decay. The results show that about half of the students could describe the behavior of the function and its rate of change, with more than half of those also referring to the problem context. Two themes in the students’ responses are discussed: describing the context as a way of describing the function, and difficulties related to the use of language in describing changing phenomena.
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| 33. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Introduction to the papers of TW6: Application and modelling
- 2023
-
Ingår i: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). - Budapest. ; , s. 1095-1102
-
Konferensbidrag (refereegranskat)
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| 34. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
IPAs - ihopparningsaktiviteter : aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga
- 2017
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 35. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
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| 36. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Matematiska modeller och modellering - vad är det?
- 2013
-
Ingår i: Nämnaren. - : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; :3, s. 21-26
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Vad är en matematisk modell? Vad innebär modellering? Denna artikel tar sig an dessa frågor, problematiserar bregreppen och undersöker hur de förhåller sig till angränsade begrepp som tillämpningar och problemlösning.
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| 37. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Mathematical modelling in upper secondary mathematics education in Sweden
- 2010
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling.The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively.The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations.From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.
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| 38. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Modelling from the Perspective of Commognition – An emerging framework
- 2013
-
Ingår i: Teaching mathematical modelling. - Dordrecht : Springer Netherlands. - 9789400765399 - 9789400765405 ; , s. 47-56
-
Bokkapitel (refereegranskat)abstract
- This bookprovides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.
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| 39. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Moving beyond a single modelling activity
- 2015
-
Ingår i: Mathematical modelling in educational research and practice. - asdf : Springer. - 9783319182711 - 9783319182728 ; , s. 293-303
-
Bokkapitel (refereegranskat)abstract
- In this theoretical chapter, we draw on a models and modelling perspective on teaching and learning to elaborate on the components of model development sequences using the lens of variation theory. We give empirical examples of how model exploration activities and model application activities can be described and understood from a variation theory perspective. The chapter concludes by presenting tentative principles for the design of such activities within a model development sequence.
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| 40. |
- Bergman Ärlebäck, Jonas, et al.
(författare)
-
Moving beyond descriptive models: Research issues for design and implementation
- 2020
-
Ingår i: AVANCES DE INVESTIGACION EN EDUCACION MATEMATICA. - : SOC ESPANOLA INVESTIGACION & EDUCACION MATEMATICA-SEIM. - 2254-4313. ; :17
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we draw on a models and modeling perspective to describe the design of a sequence of tasks, known as a model development sequence, that has been used to research the teaching and learning of mathematics. A central research goal of a models and modeling perspective is the development of principles for the design of sequences of modeling tasks and for the teaching of such sequences. We extend our earlier research by elaborating how a model development sequence can be used to support students in developing models that are not only descriptive but also have explanatory power when connected to existing mathematical models. In so doing, we elaborate language issues about representations and context as well as the implementation strategies used by the teacher.
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| 41. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
On pre-service secondary teachers’ mathematical content knowledge in statistics
- 2021
-
Ingår i: <em>Sustainable mathematics education in a digitalized world. </em>. - Göteborg : SMDF - Svensk Förening för Matematikdidaktisk Forskning. ; , s. 203-212
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we report on the use of a pre-post-test design to study pre-service secondary mathematics teachers’ mathematical content knowledge in statistics before and after their first university course in statistics. The results show that the participants were successful in the pre-test on items related to sampling, probabi- lity and the general logic of making formal statistical inferences, but struggled with items concerning distributions. Comparing the pre- and post-test reveals an increas- ing average of the participants’ scores in most statistical areas, but that topics like informal statistical inferences and distributions remain challenging for the majority of the participants.
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| 42. |
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| 43. |
- Bergman Ärlebäck, Jonas
(författare)
-
On the use of realistic Fermi problems for introducingmathematical modelling in school
- 2009
-
Ingår i: The Mathematics Enthusiast. - : Montana Council of Teachers of Mathematics & Information Age Publishing. - 1551-3440. ; 6:3, s. 331-364
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper an analytical tool referred to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme is used to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extra-mathematical knowledge used by the students during the problem solving session.
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| 44. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
On the Use of Realistic Fermi Problems in Introducing Mathematical. Modelling in Upper Secondary Mathematics
- 2010
-
Ingår i: Modeling Students' Mathematical Modeling Competencies, ICTMA 13. - Boston, MA : Springer US. - 9781441905604 - 9781441905611 ; , s. 597-609
-
Konferensbidrag (refereegranskat)abstract
- This paper reports on a study aiming to investigate the possible potential of using Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. Three groups of students- work on realistic Fermi problems were analysed using an analytic tool, referred to as the -modelling activity diagram-, adapted and developed by the author. It was observed that the processes involved in a mathematical modelling cycle were richly represented in the problem solving processes of the groups. The students also frequently used their personal extra-mathematical knowledge in the solving process in three different ways; a creative, a verifying and a social way.
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| 45. |
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| 46. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Students’ emerging models of average rate of change in context
- 2013
-
Ingår i: Proceedings of the 8th Congress of European Research in Mathematics Education (CERME 8).
-
Konferensbidrag (refereegranskat)abstract
- This paper describes a model application activity in the context of how light intensity varies depending on the distance from a point light source within a model development sequence focusing on developing students’ understanding of average rate of change. Students’ early models were found to be linearly decreasing functions and they did not distinguish between the light intensity and changes in light intensity. Most students were able to draw on several representations (most notably tables and graphs) to represent, describe and distinguish between the light intensity and changes in light intensity. Some students encountered difficulties when describing change when the rates were negative and understanding how the graphical representation of average rates of change depended on the interval width
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| 47. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence
- 2018
-
Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 50:1-2, s. 187-200
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 48. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
The Bach tensor and other divergence-free tensors
- 2005
-
Ingår i: International Journal of Geometric Methods in Modern Physics (IJGMMP). - 0219-8878. ; 2:1, s. 13-21
-
Tidskriftsartikel (refereegranskat)abstract
- In four dimensions, we prove that the Bach tensor is the only symmetric divergence-free 2-tensor which is also quadratic in Riemann and has good conformal behavior. In n > 4 dimensions, we prove that there are no symmetric divergence-free 2-tensors which are also quadratic in Riemann and have good conformal behavior, nor are there any symmetric divergence-free 2-tensors which are concomitants of the metric tensor gab together with its first two derivatives, and have good conformal behavior.
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| 49. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
The bottleneck problem in modelling revisited
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper Sfard's theory of commognition is used to investigate how two students work collaboratively to develop mathematical models in a natural school setting. The students' communication is analysed from both an insider and an outsider perspective to recreate the construction of their developed models in terms of realization trees. The analysis shows how the students draw on different discourses and that the models evolved through activities of recognition and negotiation. In particular, the students formulated their mathematical models using already known mathematical models. However, these latter models were tacit models in that they were not explicitly mentioned or discussed during the developmental process. To facilitate students’ capability to productively engage in mathematical modelling, the result of this study points to the need renegotiate the learning-teaching agreement so that it incorporates activities offering the students opportunities to practice negotiation and recognition.
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| 50. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
The clash of cultural affordances : Using cultural affordances to analyze students’ work in an activity using a mobile game app to simulate a pandemic outbreak
- 2020
-
Ingår i: Journal of Mathematics and Culture. - : North American Study Group on Ethnomathematics. - 1558-5336. ; 14:2, s. 111-131
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we use the framework of cultural affordances to analyze students’ work in an activity using a commercial mobile game app for smartphones and tablets that provided a context and simulation of a pandemic outbreak. The written work carried out by 22 upper secondary students working in pairs is analyzed, with a focus on the extent to which the students’ answers and produced graphs illustrated i) the students’ gameplay, ii) the context of the phenomena (the development and spread of a pandemic), or iii) the mathematical characteristics of the graphs. The results highlight the challenges of exploiting, leveraging, and aligning students’ gameplay with curricula learning goals in what can be seen as a clash of norms and behavior associated with the game and gameplay on the one hand, and the teaching and learning of mathematics on the other.
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