| 1. |
- Bergman Ärlebäck, Jonas, 1972-, et al.
(författare)
-
On the Use of Realistic Fermi Problems in Introducing Mathematical. Modelling in Upper Secondary Mathematics
- 2010
-
Ingår i: Modeling Students' Mathematical Modeling Competencies, ICTMA 13. - Boston, MA : Springer US. - 9781441905604 - 9781441905611 ; , s. 597-609
-
Konferensbidrag (refereegranskat)abstract
- This paper reports on a study aiming to investigate the possible potential of using Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. Three groups of students- work on realistic Fermi problems were analysed using an analytic tool, referred to as the -modelling activity diagram-, adapted and developed by the author. It was observed that the processes involved in a mathematical modelling cycle were richly represented in the problem solving processes of the groups. The students also frequently used their personal extra-mathematical knowledge in the solving process in three different ways; a creative, a verifying and a social way.
|
|
| 2. |
- Bergsten, Christer, 1949-
(författare)
-
A calculus lecture : What made it good?
- 2012
-
Ingår i: Proceedings of Norma 11. - Reykjavik : University of Iceland Press. - 9789979549659 ; , s. 167-176
-
Konferensbidrag (refereegranskat)abstract
- 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.
|
|
| 3. |
- Bergsten, Christer, 1949-
(författare)
-
A classification of algebraic tasks
- 2003
-
Ingår i: New trends in mathematics education research: an European perspective,2003.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)
|
|
| 4. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
A remark on didactic transposition theory
- 2010
-
Ingår i: Mathematics and mathematics education: Cultural and social dimensions. - Linköping : Svensk förening för matematikdidaktisk forskning (SMDF). - 9197393460 ; , s. 58-68
-
Konferensbidrag (refereegranskat)abstract
- With reference to a historical study on the relation between the production and distribution of mathematical knowledge, using calculus as an example, some assumptions in didactic transposition theory, as introduced by Yves Chevallard, are discussed. Given the prominent status of this theory, the paper intends to initiate a debate that could help lifting it out from its relative isolation within mathematics education as a research domain.
|
|
| 5. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Algebra för alla
- 1997. - 1
-
Bok (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 6. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Background document : The education and competence development of mathematics teachers in Norway and Sweden
- 2004
-
Ingår i: Educating for the future. - Göteborg : The Royal Swedish Academy of Sciences. ; , s. 9-38
-
Konferensbidrag (refereegranskat)abstract
- In this document we present the study material, which was the starting point for the symposium. It consists of experienced teacher educators' and researchers' collected knowledge from classroom and teacher education experience as well as research from the authors and colleagues. The text describes the educational system and the teacher education in Sweden and Norway and recent reforms. It concludes with the identification of some critical issues, which have been, still are or have recently appeared within the educational and competency development of mathematics teachers in Norway and Sweden.
|
|
| 7. |
|
|
| 8. |
- Bergsten, Christer, 1949-
(författare)
-
Beyond the representation given - The parabola and historical metamorphoses of meaning
- 2004
-
Ingår i: PME - Interbational Group for the Psychology of Mathematics Education,2004. - Bergen : Bergen Univeristy College. ; , s. 1-264-1-264
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 9. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Commentary on Theories of mathematics education: Is plurality a problem?
- 2010
-
Ingår i: <em>Theories of Mathematics Education: Seeking New Frontiers </em>. - New York : Springer. - 9783642007415 - 9783642007422 ; , s. 111-120
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 10. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Conceptual and procedural approaches to mathematics in the engineering curriculum : Comparing views of junior and senior engineering students in two countries
- 2017
-
Ingår i: Eurasia Journal of Mathematics, Science and Technology Education. - : Eurasia Publishing House. - 1305-8223. ; 33:3, s. 533-553
-
Tidskriftsartikel (refereegranskat)abstract
- One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between second and fourth year groups of students in their answers to a questionnaire comprising conceptually and procedurally focused mathematics problems. We also compare these students’ conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. Our data suggest that when mathematical knowledge is being recontextualised to engineering subjects or engineering design, a conceptual approach to mathematics is more essential than a procedural approach; working within the mathematical domain, however, the procedural aspects of mathematics are as essential as the conceptual aspects.
|
|
| 11. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries
- 2015
-
Ingår i: International journal of mathematical education in science and technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 46:7, s. 979-990
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 12. |
- Bergsten, Christer, 1949-
(författare)
-
Datoranvändning i högskolans matematikundervisning
- 1999
-
Ingår i: Datorstödd eller datorstörd matematikundervisning,1998. - Stockholm : Högskoleverket. ; , s. 21-
-
Konferensbidrag (refereegranskat)abstract
- 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.
|
|
| 13. |
- Bergsten, Christer, 1949-
(författare)
-
En gyllene pyramid : Fem trianglar och en pentagon
- 2003
-
Ingår i: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 30:2, s. 36-41
-
Tidskriftsartikel (populärvet., debatt m.m.)abstract
- 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.
|
|
| 14. |
- Bergsten, Christer, 1949-
(författare)
-
En kommentar till den matematiska problemlösningens didaktik
- 2006
-
Ingår i: Perspektiv på kunskapens och lärandets villkor. - Vasa : Åbo Akademi. - 9521217421 - 9789521217425 ; , s. 165-176
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 15. |
|
|
| 16. |
|
|
| 17. |
- Bergsten, Christer, 1949-
(författare)
-
Faces of Swedish research in mathematics education
- 2002
-
Ingår i: Research and action in the mathematics classroom. - Linköping : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9197393401 ; , s. 21-36
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)
|
|
| 18. |
- Bergsten, Christer, 1949-
(författare)
-
From sense to symbol sense
- 1999
-
Ingår i: European research in mathematics education I.II. - Osnabrück : Forschungsinstitut für Mathematikdidaktik and ERME. - 3925386513 ; , s. 126-137
-
Konferensbidrag (refereegranskat)abstract
- 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.
|
|
| 19. |
|
|
| 20. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Interpreting students' reasoning through the lens of two different languages of description : integration or juxtaposition?
- 2010
-
Ingår i: Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France). - Lyon : INSTITUT NATIONAL DE RECHERCHE PÉDAGOGIQUE. - 9782734211907 ; , s. 1555-1564
-
Konferensbidrag (refereegranskat)abstract
- This contribution exemplifies the interpretation of a common set of data by using two languages of description originating from different theoretical perspectives. One ac- count uses categories from a psychological and the other from a sociological per- spective. The interpretations result in different explanations for the students’ strug- gles with sense making. However, the results cannot be integrated into a combined insight, but only be juxtaposed.
|
|
| 21. |
- Bergsten, Christer, 1949-
(författare)
-
Investigating quality in undergraduate mathematics lectures
- 2007
-
Ingår i: Mathematics Education Research Journal. - 1033-2170 .- 2211-050X. ; 19:3, s. 48-72
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 22. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Knowledgeable teacher educators and linking practices
- 2008. - 1
-
Ingår i: The International Handbook of mathematics Teacher Education, Volume 4: The Mathematics Teacher Educator as a Developing Professional. - Rotterdam : Sense Publishers. - 9789087905507 ; , s. 221-246
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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
|
|
| 23. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Learning to teach mathematics : expanding the role of practicum as an integrated part of a teacher education programme
- 2009. - 1
-
Ingår i: The professional education and development of teachers of mathematics. The 15th ICMI Study. - New York : Springer. - 9780387096001 - 0387096000 ; , s. 57-70
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 24. |
- Bergsten, Christer, 1949-
(författare)
-
Lecture notes - On lecturing in undergraduate mathematics
- 2007
-
Ingår i: MADIF-5, 2006. - Linköping : SMDF. ; , s. 31-
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 25. |
|
|
| 26. |
- Bergsten, Christer, 1949-
(författare)
-
Magic circles in the arbelos
- 2010
-
Ingår i: The Mathematics Enthusiast. - Charlotte, NC : Information Age Publishing. - 1551-3440. ; 7:2&3, s. 209-222
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 27. |
- Bergsten, Christer, 1949-
(författare)
-
Mathematical approaches
- 2018. - 2
-
Ingår i: Encyclopedia of Mathematics Education. - Cham : Springer. - 9783319774879 ; , s. 1-8
-
Bokkapitel (refereegranskat)abstract
- 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...
|
|
| 28. |
- Bergsten, Christer, 1949-
(författare)
-
Mathematical approaches
- 2014. - 1
-
Ingår i: Encyclopedia of Mathematics Education. - Dordrecht : Springer. - 9789400749795 - 9789400749788 - 9789400749771 ; , s. 376-383
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 29. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Mathematics as “Meta-Technology” and “Mind-Power” : Views of engineering students
- 2013
-
Ingår i: Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education. - Ankara, Turkey : Middle East Technical University. - 9789754293159
-
Konferensbidrag (refereegranskat)abstract
- The paper reports an exploration of first year undergraduate engineering students’ rationales for choosing engineering programmes at master’s level and the potential gains for their future professions they see from studying mathematics. As a means for organising the data, we used some notions of Bourdieu’s theory of the economy of forms of social practice. The study aims to contribute to understanding differences in the students’ experiences of and interest in university mathematics.
|
|
| 30. |
- Bergsten, Christer, 1949-
(författare)
-
Mathematics education research in Sweden : An introduction
- 2010
-
Ingår i: The first sourcebook on Nordic research in mathematics education. - Charlotte, NC : Information Age Publishing. - 9781617350986 - 9781617350993 - 9781617351006 ; , s. 269-282
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 31. |
- Bergsten, Christer, 1949-
(författare)
-
Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling
- 2017
-
Ingår i: Quaderni di Ricerca in Didattica" QRDM (Mathematics). - Palermo, Italy : Gruppo Ricerca Insegnamento delle Matematiche (G R I M). - 1592-5137 .- 1592-4424. ; 27:2, s. 229-233
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 32. |
- Bergsten, Christer, 1949-
(författare)
-
News from Nordic mathematics education
- 2014
-
Ingår i: Nordisk matematikkdidaktikk. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 19:1, s. 75-84
-
Forskningsöversikt (refereegranskat)
|
|
| 33. |
- Bergsten, Christer, 1949-
(författare)
-
News from Nordic mathematics education
- 2011
-
Ingår i: Nordisk matematikkdidaktikk. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 16:4, s. 103-117
-
Forskningsöversikt (övrigt vetenskapligt/konstnärligt)
|
|
| 34. |
- Bergsten, Christer, 1949-
(författare)
-
News from Nordic mathematics education
- 2012
-
Ingår i: Nordisk matematikkdidaktikk. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 17:2, s. 69-84
-
Forskningsöversikt (övrigt vetenskapligt/konstnärligt)
|
|
| 35. |
- Bergsten, Christer, 1949-
(författare)
-
News from Nordic mathematics education
- 2013
-
Ingår i: Nordisk matematikkdidaktikk. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 18:2, s. 93-102
-
Forskningsöversikt (övrigt vetenskapligt/konstnärligt)
|
|
| 36. |
- Bergsten, Christer, 1949-
(författare)
-
Några aspekter av matematikens formelspråk
- 2008
-
Ingår i: Matematiska språk. Sju essäer om symbolspråkets roll i matematiken.. - Stockholm : Santérus Förlag. - 9789173590181 ; , s. 127-143
-
Bokkapitel (populärvet., debatt m.m.)abstract
|
|
| 37. |
- Bergsten, Christer, 1949-
(författare)
-
On the influence of theory on research in mathematics education : the case of teaching and learning limits of functions
- 2008
-
Ingår i: ZDM : the international journal on mathematics education. - : Springer-Verlag. - 1863-9690. ; 40:2, s. 189-199
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 38. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Preference for visual methods : An international study
- 1995
-
Ingår i: Proceedings of the 19th PME Conference, Recife, Brazil, July 22-27, 1995. - Recife, Brazil : Universidade Federal de Pernambuco. ; , s. 58-65
-
Konferensbidrag (refereegranskat)abstract
- There have been assertions in recent literature on visualization that students are reluctant to visualize when doing mathematics, particularly at the high school and college levels. While there is research evidence that in the classes of 'nonvisual' teachers even 'visual' students will suppress their preferred visual cognitive modes in favor of nonvisual methods used by their teachers, our data show that it is simplistic to claim that students are reluctant to visualize. In the present international study, the same instrument for measuring preference for visual methods in solving nonroutine mathematical problems was administered to students in three countries, South Africa, Sweden and the United States. Some results are analyzed here.
|
|
| 39. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Preparing pre-service mathematics teachers for STEM education : an analysis of lesson proposals
- 2019
-
Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 51:6, s. 941-953
-
Tidskriftsartikel (refereegranskat)abstract
- Based on an investigation of research literature on the role of mathematics within the context of STEM education and twenty-first century skills, this explorative study presents and analyses 19 pre-service teachers’ lesson proposals for innovative STEM activities in secondary mathematics classrooms. Drawing on a categorisation of twenty-first century skills and key concepts from Realistic Mathematics Education and Basil Bernstein’s writings, the analysis indicated a use of detailed instructions regarding what students should do but unspecified criteria for their expected knowledge productions. Rather than serving as a digital tool for problem solving, programming was used for the purpose of generalising students’ conceptual knowledge in mathematics. At the same time a focus on modelling and applications in the STEM activities tended to weaken the disciplinary character of mathematics. The learning of various twenty-first century skills was promoted to different extents. The study raises a discussion of affordances and constraints regarding students’ access to mathematical knowledge through different modes of integration of mathematics and other STEM subjects aiming to support the development of twenty-first century skills.
|
|
| 40. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Recognising knowledge criteria in undergraduate mathematics education
- 2012
-
Ingår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. - Linköping : Svensk förening för MatematikDidaktisk Forskning - SMDF. ; , s. 101-110
-
Bokkapitel (refereegranskat)abstract
- As part of a larger study on the transition between upper secondary and tertiarymathematics education, this paper reports findings from an investigation of therelation between the students’ understanding of the criteria for legitimate mathematicalknowledge and their achievement during the first year in their undergraduatemathematics studies. As a methodology, we used interviews in whichengineering students were given excerpts from different, more or less formal,mathematics textbooks and asked whether they could rank these texts as being“more or less mathematical” and explain why. The results of our case studyindicate differences in the students’ views that are related to their achievement.
|
|
| 41. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Reproduction and distribution of mathematical knowledge in higher education: constructing insiders and outsiders
- 2010
-
Ingår i: Mathematics Education and Society. - Berlin : Freie Universotät Berlin. ; , s. 130-140, s. 150-160
-
Konferensbidrag (refereegranskat)abstract
- The design and conduct of calculus courses has been and is an object of curriculardebates and reforms. By the reconstruction of the establishment of the mathematicalsub-area now called ‘calculus’ and its fundamental theorem as a piece ofinstitutionalized mathematical knowledge for the purpose of its reproduction, wereconsider the notion of knowledge recontextualization within the field of knowledgeproduction by showing that standardization of knowledge evolves in a dynamicrelationship with its production. Interviews with mathematicians suggest that they, asteachers, create different recontextualization principles. In undergraduate teachingcalculus they suggest to include the criteria of the field of knowledge production (e.g.proof) for the future ‘insiders’, while for those who will not pursue a career withinthis field, the ‘outsiders’, the criteria change towards computational efficiency.
|
|
| 42. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Secondary school mathematics students exploring the connectedness of mathematics : The case of the parabola and its tangent in a dynamic geometry environment
- 2021
-
Ingår i: The Mathematics Enthusiast. - Missoula, MT United States : University of Montana. - 1551-3440. ; 18:1-2, s. 183-209
-
Tidskriftsartikel (refereegranskat)abstract
- Drawing on the Semiotic-cultural approach and the Anthropological theory of the didactic, this paper discusses how exploration of historically framed conceptualizations of mathematical objects can establish bridges between different mathematical areas such as calculus and Euclidean geometry. A classroom intervention study in two secondary mathematics classrooms involving dynamic geometry software tools to support the construction of a parabola and its tangent and aiming at the development of representational flexibility between algebraic/ functional and geometrical approaches, illustrates how students may benefit from participation in such explorations.
|
|
| 43. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
Students interacting with an artefact designed to visualise three-dimensional analytic geometry
- 2006
-
Ingår i: CERME - Conference of the European Society for Research in Mathematics Education,2005. - Barcelona : Universitat Ramon Llull. ; , s. 71-
-
Konferensbidrag (refereegranskat)abstract
- 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.
|
|
| 44. |
- Bergsten, Christer, 1949-
(författare)
-
Studying mathematics at university : Views of first year engineering students
- 2016
-
Ingår i: Didactics of mathematics in higher education as a scientific discipline. - Kassel. ; , s. 458-465
-
Konferensbidrag (refereegranskat)abstract
- 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.
|
|
| 45. |
- Bergsten, Christer, 1949-
(författare)
-
Symbolic computing and mathematics education
- 1994
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 46. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
The construction of the ‘transition problem’ by a group of mathematics lecturers
- 2015
-
Ingår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - Prague, Czech Republic : Charles University in Prague, Faculty of Education and ERME. - 9788072908448 ; , s. 2053-2059
-
Konferensbidrag (refereegranskat)abstract
- This paper presents views of university staff about what has become called the ‘transition problem’ when students start studying mathematics at university. The data are from a focus group interview with eight experienced university lecturers at a Swedish university department that offers mathematics courses for engineering students. We use the portrayal of the problem in the literature as an axis for the discussion.
|
|
| 47. |
|
|
| 48. |
- Bergsten, Christer, 1949-, et al.
(författare)
-
The didactic divide and the education of teachers of mathematics in Sweden
- 2004
-
Ingår i: Nordisk matematikkdidaktikk. - 1104-2176. ; 9:2, s. 123-144
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 49. |
|
|
| 50. |
- Bergsten, Christer, 1949-
(författare)
-
Trying to reach the limit : The role of algebra in mathematical reasoning
- 2006
-
Ingår i: Proceedings of the 30th conference of the International group for the psychology of mathematics education, vol2. - Prag : The International Group for the Psychology of Mathematics Education. ; , s. 153-160
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
