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  • 1.
    Albarracín, Lluís
    et al.
    Universitat Autònoma de Barcelona.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Civil, Elisabeth
    Universitat Autònoma de Barcelona.
    Gorgorió, Núria
    Universitat Autònoma de Barcelona.
    Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes2019In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 16, no 1-2, article id 10Article in journal (Refereed)
    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.

  • 2. Andersson, Carina
    et al.
    Losand, Elin
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Att uppleva räta linjer och grafer – erfarenheter från ett forskningsprojekt2015In: Nämnaren 2014:4, no 1, p. 21-27Article in journal (Other (popular science, discussion, etc.))
  • 3.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Conformal Einstein spaces and Bach tensor generalization in n dimensions2004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we investigate necessary and su±cient 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 Jaén and give a basis (Uab, V ab and Wab) for all n-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship Bab = 1/2Uab + 1/6V ab 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 our-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 babc and Bab, 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.

  • 4.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Designing, implementing and evaluating mathematical modelling modules at the upper secondary level2009Report (Other academic)
    Abstract [en]

    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.

  • 5.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Ett modell- och modelleringsperspektiv på lärande och undervisning2014In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 4, p. 39-45Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    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.

  • 6.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Exploring the solving process of group solving realistic Fermi problems from the perspective of the Anthropological theory of didactics2011In: Proceedings of the Seventh Conference of European Research in Mathematics Education (CERME 7) / [ed] M. Pytlak, T. Rowland, & W Swoboda, 2011, p. 1010-1020Conference paper (Refereed)
    Abstract [en]

    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.

  • 7.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Matematiska modeller och modellering - vad är det?2013In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3, p. 21-26Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    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.

  • 8.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mathematical modelling in upper secondary mathematics education in Sweden2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    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.

    List of papers
    1. Towards understanding teachers’ beliefs and affects about mathematical modelling
    Open this publication in new window or tab >>Towards understanding teachers’ beliefs and affects about mathematical modelling
    2009 (English)Conference paper, Published paper (Other academic)
    Abstract [en]

    Work in progress on a framework aiming at capturing teachers’ beliefs about mathematical models and modelling is presented. It is suggested that the belief structure of mathematical models and modelling as perceived by teachers fruitfully might be explored as partly constituted of the teachers’ beliefs about the real world, the nature of mathematics, school mathematics, and applying and applications of mathematics. Some aspects of the suggested framework are explored using two case study interviews. It is found that the two teachers do not have any well formed beliefs about mathematical models and modelling, and that the interpreted beliefs structure of the teachers contain inconsistencies which are made explicit within the framework. The empiric findings also suggest some modifications of the framework.

    National Category
    Pedagogy
    Identifiers
    urn:nbn:se:liu:diva-54316 (URN)
    Conference
    CERME 6 - Sixth Conference of European Research in Mathematics Education Lyon, France, January 28 - February1
    Available from: 2010-03-09 Created: 2010-03-09 Last updated: 2018-09-01
    2. On the use of realistic Fermi problems for introducingmathematical modelling in school
    Open this publication in new window or tab >>On the use of realistic Fermi problems for introducingmathematical modelling in school
    2009 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 6, no 3, p. 331-364Article in journal (Refereed) Published
    Abstract [en]

    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.

    Place, publisher, year, edition, pages
    Montana Council of Teachers of Mathematics & Information Age Publishing, 2009
    Keywords
    Fermi problems, Fermi estimates, Modelling cycles, Mathematical modelling, Modelling activity diagram
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-54664 (URN)
    Available from: 2010-03-30 Created: 2010-03-30 Last updated: 2017-12-12
    3. First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
    Open this publication in new window or tab >>First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
    2009 (English)Conference paper, Published paper (Other academic)
    Abstract [en]

    This paper reports on the first results from a study investigating Swedish upper secondary students’ (11th – 12th grade) mathematical modelling competency. Using non-parametric statistical methods the data from 381 students are analysed and the students’ modelling competency is described in terms of seven subcompetencies. Possible factors affecting the students’ mathematical competency such as attitudes toward modelling, previous experiences, last taken mathematics course, grade, class and gender were also investigated.

    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-54317 (URN)
    Conference
    14th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA 14), University of Hamburg, 27th to 31st July, Germany
    Available from: 2010-03-09 Created: 2010-03-09 Last updated: 2014-06-23Bibliographically approved
    4. Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
    Open this publication in new window or tab >>Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
    2009 (Swedish)Report (Other academic)
    Abstract [en]

    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.

    Place, publisher, year, edition, pages
    Linköping University: Linköping Universtity Electronic Press, 2009. p. 93
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2009:8
    National Category
    Mathematics Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-54267 (URN)LiTH-MAT-R-2009-8 (ISRN)
    Available from: 2010-03-05 Created: 2010-03-05 Last updated: 2014-06-23
    5. Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
    Open this publication in new window or tab >>Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
    2009 (English)Report (Other academic)
    Abstract [en]

    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.

    Place, publisher, year, edition, pages
    Linköping University: Linköping Universtiy Electronic Press, 2009. p. 219
    National Category
    Mathematics Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-54269 (URN)LiTH-MAT-R-2009-9 (Local ID)LiTH-MAT-R-2009-9 (Archive number)LiTH-MAT-R-2009-9 (OAI)
    Available from: 2010-03-05 Created: 2010-03-05 Last updated: 2014-06-23
  • 9.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On the use of realistic Fermi problems for introducingmathematical modelling in school2009In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 6, no 3, p. 331-364Article in journal (Refereed)
    Abstract [en]

    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.

  • 10.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Towards understanding teachers’ beliefs and affects about mathematical modelling2009Conference paper (Other academic)
    Abstract [en]

    Work in progress on a framework aiming at capturing teachers’ beliefs about mathematical models and modelling is presented. It is suggested that the belief structure of mathematical models and modelling as perceived by teachers fruitfully might be explored as partly constituted of the teachers’ beliefs about the real world, the nature of mathematics, school mathematics, and applying and applications of mathematics. Some aspects of the suggested framework are explored using two case study interviews. It is found that the two teachers do not have any well formed beliefs about mathematical models and modelling, and that the interpreted beliefs structure of the teachers contain inconsistencies which are made explicit within the framework. The empiric findings also suggest some modifications of the framework.

  • 11.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Using a Models and Modeling Perspective (MMP) to frame and combine research, practice- and teachers’ professional development2017In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017Conference 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.

  • 12.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Albarracín, Lluís
    Serra Húnter Fellow, Universitat Autònoma de Barcelona, Spain.
    Developing a classification scheme of definitions of Fermi problems in education from a modelling perspective2017In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017, p. 884-891Conference 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.

  • 13.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    On the Use of Realistic Fermi Problems in Introducing Mathematical. Modelling in Upper Secondary Mathematics2010In: Modeling Students' Mathematical Modeling Competencies, ICTMA 13 / [ed] Richard Lesh, Peter L. Galbrait, Christopher R. Haines and Andrew Hurford, Springer US , 2010, p. 597-609Conference paper (Refereed)
    Abstract [en]

    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.

  • 14.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Blomberg, Per
    Örebro University.
    Nilsson, Per
    Linnaeus University, Sweden.
    An instructional design perspective on data-modelling for learning statistics and modelling2015In: Development of mathematics teaching: Design, Scale, Effects : Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar, Umeå, 2015, p. 37-46Conference 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.

  • 15.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Claesson, Marcus
    Kungsgårdsgymnasiet Norrköping.
    Hällgren, Malin
    Birgittaskolan vuxenutbildning Linköping.
    Lindh, Sofia
    Hagagymnasiet Norrköping.
    Lundell, Mia
    Djäkneparksskolan Norrköping.
    Nordling, Mattias
    Anders Ljungstedts gymnasium Linköping.
    IPAs - ihopparningsaktiviteter: aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga2017Report (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.

  • 16.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Doerr, Helen M.
    Syracuse University.
    At the core of modelling: Connecting, coordinating and integrating models2015In: Proceedings of the 9th Congress of European Research in Mathematics Education / [ed] K. Krainer & N. Vondrová, 2015, p. 802-808Conference paper (Refereed)
    Abstract [en]

    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.

  • 17.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Doerr, Helen M.
    Department of Mathematics, Syracuse University, Syracuse, NY, USA.
    Moving beyond a single modelling activity2015In: Mathematical modelling in educational research and practice: Cultural, social and cognitive influences Part III / [ed] Gloria Ann Stillman, Werner Blum and Maria Salett Biembengut, asdf: Springer, 2015, p. 293-303Chapter in book (Refereed)
    Abstract [en]

    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.

  • 18.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Doerr, Helen M.
    Syracuse University.
    Preserving students’ independence by encouraging students self-evaluation2015In: Nordic research in mathematics education – Proceedings of NORMA14, Turku: The Finnish Research Association for Subject Didactics , 2015, p. 257-266Conference paper (Refereed)
  • 19.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Doerr, Helen M.
    Department of Mathematics, Syracuse University, Syracuse, USA.
    Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence2018In: 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)
    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.

  • 20.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Doerr, Helen M.
    Syracuse University, NY, USA .
    O'Neil, AnnMarie H.
    Syracuse University, NY, USA .
    A Modeling Perspective on Interpreting Rates of Change in Context2013In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 15, no 4, p. 314-336Article in journal (Refereed)
    Abstract [en]

    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.

  • 21.
    Bergman Ärlebäck, Jonas
    et al.
    Syracuse University, USA.
    Doerr, Helen M.
    Syracuse University, USA.
    O’Neil, AnnMarie H.
    Syracuse University, USA.
    Interpreting average rate of change in context2012In: Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education / [ed] L. R. Van Zoest, J.-J. Lo, & J. L. Kratky, Western Michigan University , 2012, p. 965-968Conference paper (Refereed)
    Abstract [en]

    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.

  • 22.
    Bergman Ärlebäck, Jonas
    et al.
    Syracuse University, NY, USA .
    Doerr, Helen M.
    Syracuse University, NY, USA .
    O’Neil, AnnMarie H.
    Syracuse University, NY, USA .
    Students’ emerging models of average rate of change in context2013In: Proceedings of the 8th Congress of European Research in Mathematics Education (CERME 8), 2013Conference paper (Refereed)
    Abstract [en]

    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

  • 23.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Edgar, Brian
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    The Bach tensor and other divergence-free tensors2005In: International Journal of Geometric Methods in Modern Physics (IJGMMP), ISSN 0219-8878, Vol. 2, no 1, p. 13-21Article in journal (Refereed)
    Abstract [en]

    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.

  • 24.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    First results from a study investigating Swedish upper secondary students' mathematical modelling competencies2010In: EIMI 2010 Conference: Educational interfaces between mathematics and industry : proceedings / [ed] Araújo, Adérito; Fernandes, António; Azevedo, Assis; Rodrigues, José Francisco, Lissabon: Centro Internacional de Matemática , 2010, p. 63-74Conference paper (Refereed)
  • 25.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Modelling from the Perspective of Commognition – An emerging framework2013In: Teaching mathematical modelling: Connecting to research and Practice / [ed] Gloria Ann Stillman, Gabriele Kaiser, Werner Blum, Jill P. Brown, Springer Netherlands, 2013, p. 47-56Chapter in book (Refereed)
    Abstract [en]

    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.

  • 26.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    The bottleneck problem in modelling revisitedManuscript (preprint) (Other academic)
    Abstract [en]

    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.

  • 27.
    Doerr, Helen M.
    et al.
    Syracuse University.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Fostering students’ independence in modelling activities2015In: Proceedings of the 9th Congress of European Research in Mathematics Education / [ed] Krainer & N. Vondrová, 2015, p. 855-862Conference paper (Refereed)
  • 28.
    Doerr, Helen M.
    et al.
    Syracuse University, NY, USA.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Costello Staniec, Andria
    Syracuse University, NY, USA.
    Design and Effectiveness of Modeling-Based Mathematics in a Summer Bridge Program2014In: Journal of Engineering Education, ISSN 1069-4730, E-ISSN 1524-4873, Vol. 103, no 1, p. 92-114Article in journal (Refereed)
    Abstract [en]

    Background

    Since students' success in their first-semester college mathematics course is a key factor in their success in engineering, many summer bridge programs for underrepresented students focus on their preparation in mathematics. However, research on the design and efficacy of such programs is limited. We examine the design and effectiveness of a modeling-based approach to mathematics for entering freshmen engineering students.

    Purpose

    The study addresses two questions: Does a modeling-based mathematics course in a bridge program positively affect students' performance in their first-semester college mathematics course? To what extent does a sequence of modeling tasks support the development of students' concepts of average rates of change?

    Design/Method

    This quasi-experimental study compared two cohorts of bridge program students over six years to examine the effectiveness of a modeling-based mathematics course on first-semester mathematics course grades. Pre- and post–tests measured changes in students' concepts of average rates of change.

    Results

    The modeling-based mathematics course closed the previous letter grade gap between bridge program participants and non-participants in the first mathematics course. We also found significant course grade gains for students who took the modeling-based mathematics course compared with a previous cohort who took a traditional summer mathematics course.

    Conclusions

    These results suggest that the modeling-based mathematics course, with its focus on the development of engineering students' abilities to model changing phenomena, was effective in improving students' concepts of average rate of change and their first-semester mathematics course grade.

  • 29.
    Doerr, Helen M.
    et al.
    Syracuse University, NY, USA.
    Bergman Ärlebäck, Jonas
    Syracuse University, NY, USA.
    O’Neil, AnnMarie H.
    Syracuse University, NY, USA.
    An integrated modeling approach to a summer bridge course2012In: Proceedings of the 119th ASEE (American Society for Engineering Education) annual conference & exposition, 2012Conference paper (Refereed)
  • 30.
    Doerr, Helen M.
    et al.
    Syracuse University, USA.
    Bergman Ärlebäck, Jonas
    Syracuse University, USA.
    O’Neil, AnnMarie H.
    Driver Middle School, USA .
    Interpreting and communicating about phenomenon with negative rate of change2013In: Proceedings of the 120th ASEE (American Society for Engineering Education) annual conference & exposition, 2013Conference paper (Refereed)
  • 31.
    Doerr, Helen M.
    et al.
    Syracuse University, USA.
    Bergman Ärlebäck, Jonas
    Syracuse University, USA.
    O’Neil, AnnMarie H.
    Syracuse University, USA.
    Teaching practices and exploratory computer simulations2013In: Computers in The Schools, ISSN 0738-0569, E-ISSN 1528-7033, Vol. 30, no 1-2, p. 102-123Article in journal (Refereed)
    Abstract [en]

    While computing technologies are widely available in secondary schools, these technologies have had only limited impact on chang- ing classroom practices. In part, this can be attributed to an under- developed understanding of the role of the teacher in engaging in classroom practices that can support student learning with technol- ogy. In this qualitative study, we analyzed the teaching practices that supported pre-college students’ learning of a conceptually rich and deep topic (the average rate of change) when using an ex- ploratory computer simulation environment. The results illustrate the demands placed on teachers when faced with the generation of student ideas from their interactions with the simulation and three broad categories of teaching practices in response to these demands: (a) pressing students for representations, (b) harvest- ing student ideas, and (c) sorting out and refining student ideas. These findings contribute to evolving frameworks for understanding meaningful and productive technology use in teaching secondary mathematics. 

  • 32.
    Doerr, Helen M.
    et al.
    Syracuse University, NY, USA.
    Bergman Ärlebäck, Jonas
    Syracuse University, NY, USA.
    O’Neil, AnnMarie H.
    Syracuse University, NY, USA.
    Teaching practices, technology and student learning2012In: Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2012) / [ed] L. R. Van Zoest, J.-J. Lo, & J. L. Kratky, Western Michigan University , 2012, p. 1065-1072Conference paper (Refereed)
    Abstract [en]

    While computing technologies are widely available in secondary schools, these technologies have had only limited impact on changing classroom practices. Partly, this can be attributed to an underdeveloped understanding of the role of the teacher in engaging in classroom practices that can support student learning with technology. In this study, we analyzed the teaching practices that supported students’ learning of a conceptually rich and deep topic (the average rate of change) when using an exploratory computer simulation environment. The results illustrate the demands placed on teachers when faced with the multiplicity of student ideas generated by their interactions with the simulation and three aspects of a teaching practice in response to those demands. These findings contribute to evolving frameworks for understanding meaningful and productive technology use in teaching secondary mathematics.

  • 33.
    Doerr, Helen M.
    et al.
    Syracuse University, NY, USA.
    Ärlebäck, Jonas Bergman
    Syracuse University, NY, USA.
    O’Neil, AnnMarie H.
    Syracuse University, NY, USA.
    Teaching practices and modelling changing phenomena2013In: Proceedings of the 8th Congress of European Research in Mathematics Education (CERME 8), 2013Conference paper (Refereed)
    Abstract [en]

    While much research has demonstrated the positive impact of mathematical modelling on student learning, considerably less research has focused on the teaching practices that are needed to support modelling approaches to student learning. In this study, we examined the characteristics of teaching in a classroom setting where the students engaged in a sequence of model development tasks designed to support their abilities to create and interpret models of changing physical phenomena. The results illustrate the demands that modelling tasks place on teachers, ways of responding to those demands, and suggest needed pedagogical shifts in teaching practices.

  • 34.
    English, Lyn D.
    et al.
    Queensland University of Technology, Australia.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mousolides, Nicholas
    Department of Education, University of Cyprus, Nicosia, Cyprus .
    Reflections on progress in mathematical modelling research2016In: 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)
  • 35.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies2009Conference paper (Other academic)
    Abstract [en]

    This paper reports on the first results from a study investigating Swedish upper secondary students’ (11th – 12th grade) mathematical modelling competency. Using non-parametric statistical methods the data from 381 students are analysed and the students’ modelling competency is described in terms of seven subcompetencies. Possible factors affecting the students’ mathematical competency such as attitudes toward modelling, previous experiences, last taken mathematics course, grade, class and gender were also investigated.

  • 36.
    Geiger, Vincent
    et al.
    Learning Sciences Institute Australia, Faculty of Education and Arts, Australia.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Interpreting curricula to find opportunities for modeling: case studies from Australia and Sweden2016In: 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)
  • 37.
    Jankvist, Uffe Thomas
    et al.
    Aarhus University, Danish School of Education, Denmark.
    Sánchez Aguilar, Mario
    Instituto Politécnico Nacional, CICATA Legaria, Mexico.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Wæge, Kjersti
    Norwegian Centre for Mathematics Education, Norwegian University of Science and Technology (NTNU), Norway.
    Introduction to the papers of TWG23:Implementation of research findings in mathematics education2017In: Proceedings of the Tenth Congress of European Research in Mathematics Education  / [ed] T. Dooley, & G. Gueudet, Ireland, Dublin, 2017, p. 3769-3775Conference 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.

  • 38.
    Jiménez, Leslie
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Using the Mathematical Working Space model as a lens on geometry in the Swedish mathematics upper secondary curriculum2018In: 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 (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.

  • 39. Johnsson, Kerstin
    et al.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Godissugen! En tankeavslöjande aktivitet för att introducera området funktioner2014In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 4, p. 46-51Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    I den här artikeln diskuteras en aktivitet som introducerar funktioner i åk 8 genom att utmana eleverna att skapa mening av sådant de redan kan. Läraren arbetar med så kallade tankeavslöjande aktiviteter för att utmana elever på olika nivåer inom ramen för en och samma aktivitet.

  • 40.
    Lee, Hollylynne S.
    et al.
    North Carolina State University, Raleigh, USA.
    Doerr, Helen M.
    Syracuse University, NY, USA.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Pulis, Tyler
    North Carolina State University, Raleigh, USA.
    Collaborative design work of teacher educators: A case from statistics2013In: Proceedings of the Thirty-Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Broadening Perspectives on Mathematics Thinking and Learning / [ed] Mara V. Martinez & Alison Castro Superfine, Chicago, IL: University of Illinois at Chicago , 2013, p. 357-364Conference paper (Refereed)
    Abstract [en]

    Our study, situated within graduate-level courses for teachers focused on statistics, illustrates work across institutions for making sense of teachers' statistical thinking. Using a common assessment instrument, we identify and discuss four items that indicate strong statistcal thinking and two that highlight concepts with which the teachers struggle. We discuss potenital course elements that may be contributing to areas of success. Implications for collaborative course (re)design and shared assessment items are discussed.

1 - 40 of 40
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