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  • 1.
    Ashjari, Hoda
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Jablonka, Eva
    Luleå tekniska universitet, Luleå.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Recognizing texts in undergraduate mathematics2012In: Proceedings 36th Conference of the International Group for the Psychology of Mathematics Education: Opportunities to Learn in Mathematics Education, Taipei-Taiwan, July 18-22, 2012. / [ed] Tso, T.Y., Department of Mathematics, National Taiwan Normal University; Taiwan Association of Mathematics Education , 2012, p. 4-245-Conference paper (Refereed)
    Abstract [en]

    Findings from interviews investigating how Swedish first year engineering students recognize undergraduate mathematics texts as being more or less “mathematical”. The results indicate a relation between the students’ understanding of the principles for knowledge classification and their success in their mathematics studies.

  • 2.
    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.

  • 3.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    A calculus lecture: What made it good?2012In: Proceedings of Norma 11: The Sixth Nordic Conference of Mathematics Education / [ed] G. H. Gunnarsdóttir, et al., Reykjavik: University of Iceland Press, 2012, p. 167-176Conference paper (Refereed)
    Abstract [en]

    This paper reports from a study that investigates, from a student and a teacher perspective, the fact that the large group lecture format prevails and attracts students in undergraduate mathematics education despite the many arguments put forward against the educational value of lectures. The focus here is on students’ views on specific aspects of one calculus lecture they just attended.

  • 4.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    A classification of algebraic tasks2003In: New trends in mathematics education research: an European perspective,2003, 2003Conference paper (Other academic)
  • 5.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Beyond the representation given - The parabola and historical metamorphoses of meaning2004In: PME - Interbational Group for the Psychology of Mathematics Education,2004, Bergen: Bergen Univeristy College , 2004, p. 1-264-1-264Conference paper (Other academic)
    Abstract [en]

      Tracking the history of a mathematical object reveals a double influence on its development - from inside and outside the pure mathematical realm. From a semiotic point of view, a chain of metamorphoses of meanings is created, which becomes critical as the mathematical object by the social process of didactic transposition is turned into a presented object of teaching and learning. As an example, by representing the mathematical object -parabola- by means of its historical progression within classical geometry, analytic geometry, and dynamic geometry software, it is seen, by using analytic tools from semiotics, anthropo¬logical theory of didactics, and embodied cognition, how and why students- concept images and problem solving techniques may become disconnected and instrumental.

  • 6.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Beyond the representation given: The parabola and historical metamorphoses of meanings2015In: Refractions of mathematics education: Festschrift for Eva Jablonka / [ed] C. Bergsten & B. Sriraman, Charlotte, NC: Information Age Publishing, 2015, p. 15-48Chapter in book (Other academic)
  • 7.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Datoranvändning i högskolans matematikundervisning1999In: Datorstödd eller datorstörd matematikundervisning,1998, Stockholm: Högskoleverket , 1999, p. 21-Conference paper (Refereed)
    Abstract [sv]

     För att få en översiktlig bild av datoranvändningen i den svenska högskolans matematikundervisning genomfördes under våren 1998 en enkätundersöknng. Kursansvariga (eller motsvarande) lärare för kurser i matematik och matemaisk statistik besvarade frågor om bl.a. typ och omfång av datorstöd och argument för eller emot anvädningen av datorer i undervisningen. Resultatet kan sammanfattas i bl.a. följande slutsatser: stadig ökning av datoranvändning under de senaste tre åren til ca 50% av kurserna i matematik och ca 80% av kurserna i matemaisk statistik; stor skillnad mellan olika högskolor; ingen större skillnad mellan utbildningr (lärarutbildningar speciell situation) eller kurser (utom "tillämpade"); formerna för datoranvändning varierar i allmänhet inte så mycket; argumenten för och emot datoranvändning i matematikundervisningen varierar men ryms inom fem till sex kategorier; stor skillnad mellan högskolor i miniräknarpolicy på skriftlig tentamen i matematik, där totalt ca 1/3 av kurserna tillåter miniräknare; argumenten mot miniräknare på skriftlig tentamen i matematik är många och "motståndet" är starkt på flera håll: det finns ett uttalat intresse hos många lärare att utveckla datorstödet i matematikundervisningen.   

  • 8.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Datrostödd eller datorstörd matematikundervisning?1999Collection (editor) (Other academic)
  • 9.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    En gyllene pyramid: Fem trianglar och en pentagon2003In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 30, no 2, p. 36-41Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Den regelbundna femhörningen, pentagonen, är ett enkelt geometriskt objekt som innehåller förvånansvärt mycket matematik. Från detta objekt kan man konstruera flera andra som trianglar och femuddiga stjärnor. Gemensamt för alla dessa figurer är att de har starka anknytningar till det gyllene snittet. Från pentagonen kan man även konstruera ett tredimensionellt objekt – en gyllene pyramid.

  • 10.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    En kommentar till den matematiska problemlösningens didaktik2006In: Perspektiv på kunskapens och lärandets villkor / [ed] Lisen Häggblom, Lars Burman & Ann-Sofi Röj-Lindberg, Vasa: Åbo Akademi , 2006, p. 165-176Chapter in book (Other academic)
    Abstract [sv]

     Grundat på en klassificering av teoretiska perspektiv, aspekter av matematiska problem, kunskapsbildning och undervisning, presenteras en epistemologisk modell för problemslösningens roll i en matematisk praktik.

  • 11.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Exploiting the gap between intuitive and formal knowledge in mathematics2008In: The International Congress on Mathematical Education, ICME,2004, Copenhagen: Roskilde University , 2008Conference paper (Refereed)
  • 12.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Faces of Swedish research in mathematics education2002In: Research and action in the mathematics classroom: Proceedings of MADIF 2, the 2nd Swedish Mathematics Education Research Seminar, Göteborg, January 26-27, 2000 / [ed] Christer Bergsten, Göte Dahland, Barbro Grevholm, Linköping: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2002, p. 21-36Conference paper (Other academic)
  • 13.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    From sense to symbol sense1999In: European research in mathematics education I.II / [ed] Inge Schwank, Osnabrück: Forschungsinstitut für Mathematikdidaktik and ERME , 1999, Vol. II, p. 126-137Conference paper (Refereed)
    Abstract [en]

    In this theoretical paper figurative aspects of algebraic symbolism are discussed and related to the theory of image schemata, opening up for one way of understanding the development of symbol sense in mathematics. The ideas of mathematical forms (referring to spatial characteristics of mathematical formulas), and form operations, are at the core of this analysis.

  • 14.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    How do theories influence the research on teaching and learning limits of functions?2007In: CERME,2007, Nicosia: University of Cyprus , 2007, p. 1638-Conference paper (Refereed)
  • 15.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Investigating quality in undergraduate mathematics lectures2007In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 19, no 3, p. 48-72Article in journal (Refereed)
    Abstract [en]

    The notion of quality in undergraduate mathematics lectures is examined by using theoretical notions and research results from the literature and empirical data from a case study on lecturing on limits of functions. A systemic triangular model is found to catch critical quality aspects of a mathematics lecture, consisting of mathematical exposition, teacher immediacy, and general quality criteria for mathematics teaching. Mathematical exposition involves the dynamic interplay of mathematical content, mathematical process, and institutionalisation. The discussion is a contribution to an increased pedagogical awareness in undergraduate mathematics teaching.

  • 16.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Lecture notes - On lecturing in undergraduate mathematics2007In: MADIF-5, 2006, Linköping: SMDF , 2007, p. 31-Conference paper (Other academic)
    Abstract [en]

    Lectures is a common teaching format in undergraduate mathematics. This study sets up to investigate the notion of a quality lecture, based on a literature review and a case study in a beginning calculus course. Critical aspects discussed include information delivery, connections, rigour-intuition, algebraic-imagistic modes, gestures, socio-mathematical norms, a mathematical mind, inspiration, personalisation, and general quality criteria for mathematics teaching, al of which came into play in the lecture studied.

  • 17.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Magic circels in the arbelos2006Report (Other academic)
  • 18.
    Bergsten, Christer
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Magic circles in the arbelos2010In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 7, no 2&3, p. 209-222Article in journal (Refereed)
    Abstract [en]

    In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.

  • 19.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Matematik i tiden: Dokumentation av 12:e Matematikbiennalen, Norrköping 24-26 januari 20022002Conference proceedings (editor) (Other academic)
  • 20.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mathematical approaches2018In: Encyclopedia of Mathematics Education / [ed] Steve Lerman (complete book) and Eva Jablonka (section editor), Cham: Springer, 2018, 2, p. 1-8Chapter in book (Refereed)
    Abstract [en]

    Research in mathematics education is interdisciplinary. According to Higginson (1980), mathematics, philosophy, psychology, and sociology are contributing disciplines to mathematics education (similar to what Michael Otte called Bezugsdisziplinen; Otte et al. 1974, p. 20). Linguistics and semiotics could be added. Framing of research, by means of theories or methods from these, amounts to different approaches, mathematics itself being one obvious choice. According to one view, mathematics education as a research field belongs to mathematics: at the second International Congress on Mathematical Education (ICME) in Exeter, Zofia Krygowska suggested that mathematics education should be classified as “a part of mathematics with a status similar to that of analysis or topology” (Howson 1973, p. 48). Another view sees mathematics education as an autonomous science (didactics of mathematicsas Hans Georg Steiner in 1968 called the new discipline he wanted to establish; see...

  • 21.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Mathematical approaches2014In: Encyclopedia of Mathematics Education / [ed] Steve Lerman, Springer, 2014, 1, p. 376-383Chapter in book (Other academic)
    Abstract [en]

    Research in mathematics education is interdisciplinary. According to Higginson (1980), mathematics, philosophy, psychology, and sociology are contributing disciplines to mathematics education (similar to what Michael Otte called Bezugsdisziplinen; Otte et al. 1974, p. 20). Linguistics and semiotics could be added. Framing of research, by means of theories or methods from these, amounts to different approaches, mathematics itself being one obvious choice. According to one view, mathematics education as a research field belongs to mathematics: at the second International Congress on Mathematical Education (ICME) in Exeter, Zofia Krygowska suggested that mathematics education should be classified as “a part of mathematics with a status similar to that of analysis or topology” (Howson 1973, p. 48). Another view sees mathematics education as an autonomous science (didactics of mathematics as Hans Georg Steiner in 1968 called the new discipline he wanted to establish; see Furinghetti et al. 2008, p. 132), strongly linked to mathematics, as expressed at ICME1 in Lyon 1969: “The theory of mathematical education is becoming a science in its own right, with its own problems both of mathematical and pedagogical content. The new science should be given a place in the mathematical departments of Universities or Research Institutes, with appropriate qualifications available” (quoted in Furinghetti et al. 2008, p. 132). However, in many countries, mathematics education research has an institutional placement mainly in educational departments.

  • 22.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Mathematics education research in Sweden: An introduction2010In: The first sourcebook on Nordic research in mathematics education: Norway, Sweden, Iceland, Denmark and contributions from Finland / [ed] Sriraman, B., Bergsten, C., Goodchild, S., Pálsdóttir, G., Dahl Søndergaard, B., & Haapasalo, L., Charlotte, NC: Information Age Publishing , 2010, p. 269-282Chapter in book (Other academic)
    Abstract [en]

    Iceland, Denmark and contributions from Finland provides the first comprehensive and unified treatment of historical and contemporary research trends in mathematics education in the Nordic world. The book is organized in sections co-ordinated by active researchers in mathematics education in Norway, Sweden, Iceland, Denmark, and Finland. The purpose of this sourcebook is to synthesize and survey the established body of research in these countries with findings that have influenced ongoing research agendas, informed practice, framed curricula and policy. The sections for each country also include historical articles in addition to exemplary examples of recently conducted research oriented towards the future. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside the Nordic countries. This Sourcebook includes over 50 chapters from the Nordic world. Section I- Norwegian Research in Mathematics Education Section Editor: Simon Goodchild Introduction to the Norwegian part of the Sourcebook of Nordic Research in Mathematics Education Simon Goodchild The development of mathematics education as a research field in Norway - an insider's personal reflections, Trygve Breiteig and Simon Goodchild Section II- Swedish Research in Mathematics Education Section Editor: Christer Bergsten Mathematics education research in Sweden - An introduction Christer Bergsten Some theoretical orientations of Swedish research Learning difficulties and mathematical reasoning Johan Lithner, Torulf Palm Section III - Icelandic Research in Mathematics Education Section Editors: Guðbjörg Pálsdóttir, Bharath Sriraman Mathematics Education in Iceland: Explaining the Non-homogeneity in a Homogenous System, Guðný Helga Gunnarsdóttir, Guðbjörg Pálsdóttir, Bharath Sriraman The History of Public Education in Mathematics in Iceland and its Relations to Secondary Education, Kristín Bjarnadóttir Section IV - Danish Research in Mathematics Education Section Editors: Bettina Dahl, Bharath Sriraman Section V- Contributions from Finland Section Editor: Lenni HaapasaloShow.

  • 23.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling2017In: Quaderni di Ricerca in Didattica" QRDM (Mathematics), ISSN 1592-5137, E-ISSN 1592-4424, Vol. 27, no 2, p. 229-233Article in journal (Refereed)
    Abstract [en]

    Considering the ‘popularity’ of mathematical modelling as an arena for using mathematisation as didactic principle, teachers’ conceptions of mathematical modelling in relation to how they view their main task as mathematics teachers, as well what use the mathematics students learn at school might be, was investigated drawing on interview data. While the teachers generally separated ‘reality’ and ‘mathematics’, the potential diversity of mathematical descriptions and the problematic nature of any “translation” were generally not discussed. Overall goals of teaching mathematics such as understanding, interest and usefulness were emphasised rather than relating modelling to mathematisation as didactic principle.

  • 24.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    News from Nordic mathematics education2014In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 19, no 1, p. 75-84Article, review/survey (Refereed)
  • 25.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    News from Nordic mathematics education2011In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 16, no 4, p. 103-117Article, review/survey (Other academic)
  • 26.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    News from Nordic mathematics education2012In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 17, no 2, p. 69-84Article, review/survey (Other academic)
  • 27.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    News from Nordic mathematics education2013In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, no 2, p. 93-102Article, review/survey (Other academic)
  • 28.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Några aspekter av matematikens formelspråk2008In: Matematiska språk. Sju essäer om symbolspråkets roll i matematiken., Stockholm: Santérus Förlag , 2008, p. 127-143Chapter in book (Other (popular science, discussion, etc.))
    Abstract [sv]

       

  • 29.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions2008In: ZDM : the international journal on mathematics education, ISSN 1863-9690, Vol. 40, no 2, p. 189-199Article in journal (Refereed)
    Abstract [en]

     After an introduction on approaches, researh frameworks and theories in mathematics education research, three didactical research studies on limits of functions with different research frameworks are analysed and compared with respect to their theoretical perspectives. It is shown how a chosen research framework defines the world in which the reearch lives, pointing to the difficult but necessary task to compare research results within a common field of study but conducted within different frameworks.

  • 30.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Studying mathematics at university: Views of first year engineering students2016In: Didactics of mathematics in higher education as a scientific discipline: Conference Proceedings / [ed] R. Göller, R. Biehler, R. Hochmuth, H-G. Rück, Kassel, 2016, p. 458-465Conference paper (Refereed)
    Abstract [en]

    As part of a larger project investigating the transition from secondary to tertiary mathematics educa-tion in Sweden, interviews with 60 engineering students at the end of their first year of study sug-gest that shifts during the transition from individualised to collective study approaches and from de-pendent to apprenticed student positions, as well as student life, contribute to students’ views on university studies as a generally highly valuable experience.

  • 31.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Symbolic computing and mathematics education1994Report (Other academic)
    Abstract [en]

    A lab sequence with the computer algebra system Maple was integrated in one of the analysis courses for beginning engineering students. The students appreciated the labs, but questionned their value for the learning of analysis. There was a significant shift over time toward a higher appreciation of the labs, and most students wanted Maple in the course. No significant differences were found in mathematical achievement or attitudes between the lab and control groups. The plotting function of Maple was valued for learning and understanding analysis. Data indicate, however, that the symbolic computational feature of a computer algebra system will not be fully appreciated until students are familiar with the computations. It thus seems necessary, when planning to use a computer algebra system as a learning tool, to explicate the intended learning paradigm, how the computational facilities of the system are to be used, and what kind of mathematical competence students develop and get out of the course. A conclusion from this study is that the use in education of thus type of technology is appreciated by the students, but that early in an analysis course it should be used mainly as a support to imagery, and that only later in the course automated algebraic computations should be used for example as a problem solving tool.

  • 32.
    Bergsten, Christer
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    The relationships of theory and practice in mathematics education2003In: CERME 3 Third Conference of the European Society for Research in Mathematics Education,2003, 2003Conference paper (Other academic)
  • 33.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Trying to reach the limit: The role of algebra in mathematical reasoning2006In: Proceedings of the 30th conference of the International group for the psychology of mathematics education, vol2 / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prag: The International Group for the Psychology of Mathematics Education , 2006, p. 153-160Conference paper (Other academic)
    Abstract [en]

    In this paper the role of algebra in students- mathematical reasoning about limits of functions in undergraduate mathematics is analysed, considering the students- edu¬cational setting. Data from a video study where six students worked in pairs to solve problems on limits of functions, and an analysis of their calculus lectures, indicate that algebra is at the same time a key and a lock to reach the limit in these problems. This double effect is related to the mathematical organisation taught, as well as the students- sense of authority as internal or external.

  • 34.
    Bergsten, Christer
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Tvillingcirklar2009In: Normat - Nordisk matematisk tidskrift, ISSN 0801-3500, Vol. 57, no 1, p. 22-31Article in journal (Refereed)
    Abstract [en]

    This ties with previous articles on the arbelos of Archimedes, but instead of starting with two tangent circles, enclosed in a common tangent circle, no conditions are imposed on the two. We then get two cases, whether the circles intersect or not, and a detailed study is made on the nesuing circles. Much of the motivation for this paper is how the problems can be used to illustrate the power of various dynamic geometry software available on the market since the 80's.

  • 35.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Vad är en parabel?2006In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 33, no 1, p. 45-48Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Med parabeln som exempel visas hur den historiskt-kulturella utvecklingen av idéer, uttrycksformer, metoder och verktyg kan berika och utveckla ett matematiskt begrepp och hur detta kan uppfattas. Vilka didaktiska problem och möjligheter ger detta i dagens skola?

  • 36.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Why do students go to lectures?2011In: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Svoboda, Rzeszów, Poland: University of Rzeszów, Poland , 2011, p. 1960-1970Conference paper (Refereed)
    Abstract [en]

    This paper investigates, from a student perspective, the fact that, despite arguments put forward against the educational value of large group lectures, this teaching format prevails and attracts students in undergraduate mathematics education.

  • 37.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Dahland, GöteGöteborg University, Sweden.Grevholm, BarbroUniversity of Agder, Norway.
    Research and action in the mathematics classroom: proceedings of MADIF 2, the 2nd Swedish Mathematics Education Research Seminar, Göteborg, January 26-27, 20002002Collection (editor) (Refereed)
  • 38.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Engelbrecht, Johann
    University of Pretoria, South Africa.
    Kågesten, Owe
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries2015In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 7, p. 979-990Article in journal (Refereed)
    Abstract [en]

    This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in some detail from two interviews with professional engineers, selected to represent two different ‘poles’ of engineering work. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering work, as well as some common across contexts. Both interviewees feel that conceptual mathematics is more important for engineering work, although the role of the procedural aspect was seen by one of the interviewees also to be important, but in a very intricate way.

  • 39.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Fransson, Torbjörn
    Växjö universitet.
    Students interacting with an artefact designed to visualise three-dimensional analytic geometry2006In: CERME - Conference of the European Society for Research in Mathematics Education,2005, Barcelona: Universitat Ramon Llull , 2006, p. 71-Conference paper (Refereed)
    Abstract [en]

     To investigate students- ways of working with concrete materials in mathematics, a three-dimensional static artefact was constructed and made available to upper secondary students, with pre-knowledge only in two-dimensional coordinate geo¬metry, for solving problems about planes and straight lines in space. Artefact interactivity was generally high, even students also disregarded the model to work only numerically with the coordinates, building on know¬ledge about lines in two dimensions. The model was used when trying to convince other students in the group. 

  • 40.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, Barbro
    Challenges in mathematics education: Proceedings of MADIF 3 : the 3rd Swedish Mathematics Education Research Seminar, Norrköping, January 23-25, 20022003Conference proceedings (editor) (Refereed)
  • 41.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, BarbroHøgskolen i Agder.
    Conceptions of mathematics: proceedings of norma 01 : the 3rd Nordic Conference on Mathematics Education, Kristianstad, June 8-12, 20012005Collection (editor) (Other academic)
    Abstract [en]

     Proceedings of Norma01, Third Nordic Conference on Mathematics Education, Kristianstad 2001

  • 42.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, BarbroUniversitetet i Agder.
    Developing and researching quality in mathematics teaching and learning2007Collection (editor) (Refereed)
  • 43.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, Barbro
    Knowledgeable teacher educators and linking practices2008In: The International Handbook of mathematics Teacher Education, Volume 4: The Mathematics Teacher Educator as a Developing Professional / [ed] Barbara Jaworski and Terry Woods, Rotterdam: Sense Publishers , 2008, 1, p. 221-246Chapter in book (Other academic)
    Abstract [en]

    The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes. Volume 4 of this handbook has the title The Mathematics Teacher Educator as a Developing Professional. The volume seeks to complement the other three volumes by focusing on knowledge and roles of teacher educators working with teachers in teacher education processes and practices. In this respect it is unique. Chapter authors represent a community of teacher educators world wide who can speak from practical, professional and theoretical viewpoints about what it means to promote teacher education practice. The volume is in 3 main sections. In the first we focus on Challenges to and Theory in Mathematics Teacher Education. Here authors write from perspectives of theory and/or challenge and relate this to examples and insights from their practice. The second section, Reflection On Developing as a Mathematics Teacher Educator has four autobiographical chapters in which authors delineate their experiences as teacher educators and relate these to theoretical and/or moral standpoints. In Section 3, Working With Prospective and Practising Teachers: What We Learn; What We Come to Know, authors write from perspectives on practice - in many cases, the practices in which they themselves have engaged - and relate this to theoretical perspectives and rationales for teacher education programmes. The volume also has an introductory chapter in which the purpose and content of the volume is set out, and a final chapter that syntheses themes and issues from the chapters as a whole, offering an overview of the field and suggesting future directions. Bibliographical Information for the complete set: VOLUME 1: Knowledge and Beliefs in Mathematics Teaching and Teaching Development Peter Sullivan, Monash University, Clayton, Australia and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-541-5, hardback: 978-90-8790-542-2, ebook: 978-90-8790-543-9 VOLUME 2: Tools and Processes in Mathematics Teacher Education Dina Tirosh, Tel Aviv University, Israel and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-544-6, hardback: 978-90-8790-545-3, ebook: 978-90-8790-546-0 VOLUME 3: Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks Konrad Krainer, University of Klagenfurt, Austria and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-547-7, hardback: 978-90-8790-548-4, ebook: 978-90-8790-549-1 VOLUME 4: The Mathematics Teacher Educator as a Developing Professional Barbara Jaworski, Loughborough University, UK and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-550-7, hardback: 978-90-8790-551-4, ebook: 978-90-8790-552-1

  • 44.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, BarbroHøgskolen i Agder.
    Mathematics and language: proceedings of MADIF 4 : the 4th Swedish Mathematics Education Research Seminar, Malmö, January 21-22, 20042004Collection (editor) (Other academic)
    Abstract [en]

     Proceedings of the 4th Swedish Mathematics Education Research Seminar, Malmö 2004 

  • 45.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, Barbro
    Realfag Høgskolen i Agder.
    The didactic divide and the education of teachers of mathematics in Sweden2004In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 9, no 2, p. 123-144Article in journal (Refereed)
    Abstract [en]

    On a background of tradition versus renewal, a discussion on recent teacher education reforms in Sweden is given. A balance of different aspects of content and a need for research are seen as critical for the formation of mathematics teacher education. A conception of a -didactic divide- between disciplinary and pedagogical knowledge is used as an analytic tool to describe the rationale behind the design of the reforms. Empirical data from student teachers enrolled in the new teacher education programme highlight how the structure and content of the programme contribute to overcoming the divide.

  • 46.
    Bergsten, Christer
    et al.
    Linköping University, Faculty of Educational Sciences. Linköping University, Department of Mathematics, Applied Mathematics.
    Grevholm, Barbro
    Favilli, Franco
    Learning to teach mathematics: expanding the role of practicum as an integrated part of a teacher education programme2009In: The professional education and development of teachers of mathematics. The 15th ICMI Study, New York: Springer , 2009, 1, p. 57-70Chapter in book (Other academic)
    Abstract [en]

    The premise of the 15th ICMI Study is that teachers are key to students' opportunities to learn mathematics. What teachers of mathematics know, care about, and do is a product of their experiences and socialization, together with the impact of their professional education. The Professional Education and Development of Teachers of Mathematics assembles important new international work- development, research, theory and practice - concerning the professional education of teachers of mathematics. As it examines critical areas to reveal what is known and what significant questions and problems warrant collective attention, the volume also contributes to the strengthening of the international community of mathematics educators. The Professional Education and Development of Teachers of Mathematics is of interest to the mathematics education community as well as to other researchers, practitioners and policy makers concerned with the professional education of teachers.

  • 47.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Grevholm, BarbroUniversitetet i Agder.Lingefjärd, ThomasGöteborgs universitet.
    Perspectives on mathematical knowledge2009Collection (editor) (Other academic)
  • 48.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Grevholm, BarbroUniversitetet i Agder.Strömskag Måsöval, HeidiSör-Tröndelag University College.Rönning, FrodeSör-Tröndelag University College.
    Relating practice and reserch in mathematics education: Proceedings of the Fourth Nordic Conference on Mathematics Education2007Collection (editor) (Other academic)
  • 49.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Häggström, Johan
    Lindberg, Lisbeth
    Algebra för alla1997 (ed. 1)Book (Other academic)
    Abstract [sv]

    Bakom titeln Algebra för alla ligger tanken att alla lärare som arbetar med matematik i grundskola och gymnasieskola ska ha glädje av innehållet och målet att alla elever ska möta matematikens generaliserande kraft. Syftet med materialet är att avdramatisera arbetet med skolalgebra samt att uppmärksamma och stimulera möjligheterna att arbeta med olika uttrycksformer. I boken ingår ett stort antal elevaktiviteter och studieuppgifter för lärare samt litteraturförslag.

  • 50.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Jablonka, Eva
    Luleå tekniska universitet.
    Commentary on Theories of mathematics education: Is plurality a problem?2010In: Theories of Mathematics Education: Seeking New Frontiers / [ed] B. Sriraman, B. & L. English, New York: Springer , 2010, p. 111-120Chapter in book (Other academic)
    Abstract [en]

    The chapter by Steve Lerman provides a powerful analysis that helps to make sense of the changing nature of the discourse in mathematics education as a research domain, of its knowledge structure and of the positions of researchers in relation to intellectual traditions ‘outside’ the field as well as in relation to changing pedagogic modes. The reading invited us to expand on the conceptualisation of knowledge structures and discourses in mathematics education as a research domain.

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