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  • 251.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Frejd, Peter
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The bottleneck problem in modelling revisitedManuskript (preprint) (Övrigt vetenskapligt)
    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.

  • 252.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Causal tensors and simple forms2002Ingår i: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 17, nr 20, s. 2748-2748Artikel i tidskrift (Refereegranskat)
  • 253.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Causal tensors in Lorentzian geometry2003Ingår i: Publications of the Spanish mathematical society, Vol. 5, s. 73-83Artikel i tidskrift (Refereegranskat)
  • 254.
    Bergqvist, Göran
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Curves and envelopes that bound the spectrum of a matrix2018Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 557Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A generalization of the method developed by Adam, Psarrakos and Tsatsomeros to find inequalities for the eigenvalues of a complex matrix A using knowledge of the largest eigenvalues of its Hermitian part H(A) is presented. The numerical range or field of values of A can be constructed as the intersection of half-planes determined by the largest eigenvalue of H(e(i theta) A.). Adam, Psarrakos and Tsatsomeros showed that using the two largest eigenvalues of H(A), the eigenvalues of A satisfy a cubic inequality and the envelope of such cubic curves defines a region in the complex plane smaller than the numerical range but still containing the spectrum of A. Here it is shown how using the three largest eigenvalues of H(A) or more, one obtains new inequalities for the eigenvalues of A and new envelope-type regions containing the spectrum of A. (C) 2018 Elsevier Inc. All rights reserved.

    Publikationen är tillgänglig i fulltext från 2020-07-24 14:59
  • 255.
    Bergqvist, Göran
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Exact probabilities for typical ranks of 2 × 2 × 2 and 3 × 3 × 2 tensors2013Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, nr 2, s. 663-667Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that the probability to be of rank 2 for a 2×2×2 tensor with elements from a standard normal distribution is π/4, and that the probability to be of rank 3 for a 3×3×2 tensor is 1/2. In the proof results on the expected number of real generalized eigenvalues of random matrices are applied. For n×n×2 tensors with n≥4 we also present some new aspects of their rank.

  • 256.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Monotone quantities for the Penrose inequality2003Ingår i: Penrose Inequalities,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 257.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Spinors and conformal curvature2005Ingår i: Publications of the Spanish mathematical societyArtikel i tidskrift (Refereegranskat)
  • 258.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    The Penrose inequality and null hypersurfaces2003Ingår i: Joint meeting of the American Mathematical Society and the Spanish Mathematical Society,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 259.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Eriksson, Ingemar
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces2007Ingår i: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 24, nr 13, s. 3437-3455Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we characterize the source-free Einstein–Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein–Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein–Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein–Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces.

  • 260.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Eriksson, Ingemar
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Senovilla, J. M. M.
    Departamento de Física Teórica, Universidad del País Vasco, Bilbao, Spain.
    New electromagnetic conservation laws2003Ingår i: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 20, nr 13, s. 2663-2668Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel–Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if the Einstein–Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, conserved tensor, which is different from the energy–momentum tensor, and nonetheless can be constructed for any test Maxwell field or any Einstein–Maxwell spacetime.

  • 261.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Eriksson, Ingemar
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Senovilla, José M M
    New conservation laws in Einstein-Maxwell spacetimes2004Ingår i: 17th International Conference on General Relativity and Gravitation,2004, 2004Konferensbidrag (Övrigt vetenskapligt)
  • 262.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Forrester, Peter J.
    University of Melbourne, Victoria, Australia.
    Rank probabilities for real random NxNx2 tensors2011Ingår i: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 16, s. 630-637Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that the probability P_N for a real random Gaussian NxNx2 tensor to be of real rank N is P_N=(Gamma((N+1)/2))^N/G(N+1), where Gamma(x) and G(x) denote the gamma and the Barnes G-functions respectively. This is a rational number for N odd and a rational number multiplied by pi^{N/2} for N even. The probability to be of rank N+1 is 1-P_N. The proof makes use of recent results on the probability of having k real generalized eigenvalues for real random Gaussian N x N matrices. We also prove that log P_N= (N^2/4)log (e/4)+(log N-1)/12-zeta'(-1)+O(1/N) for large N, where zeta is the Riemann zeta function.

  • 263.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Hoglund, A.
    Algebraic Rainich theory and antisymmetrization in higher dimensions2002Ingår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 19, nr 12, s. 3341-3355Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein-Maxwell spacetime. One of the conditions is that T2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions.

  • 264.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank2005Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 461, nr 2059, s. 2181-2195Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

  • 265.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Algebraic and differential Rainich conditions for the Bel-Robinson tensor and other higher rank tensors2004Ingår i: 17th International Conference on General Relativity and Gravitation,2004, 2004Konferensbidrag (Övrigt vetenskapligt)
  • 266.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Unique characterization of the Bel-Robinson tensor2004Ingår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 21, nr 14, s. 3499-3503Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

  • 267.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Larsson, Erik G
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska högskolan.
    Overview of recent advances in numerical tensor algebra2010Ingår i: Proceedings of Asilomar Conference on Signals, Systems and Computers, 2010, s. 3-7Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find lowrank approximations of tensors, and we describe some new results, including numerical methods, algorithms and theory, for the higher order singular value decomposition (HOSVD) and the parallel factors expansion or canonical decomposition (CP expansion).

  • 268.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Larsson, Erik G.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem.
    The Higher-Order Singular Value Decomposition Theory and an Application2010Ingår i: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 27, nr 3, s. 151-154Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    Tensor modeling and algorithms for computing various tensor decompositions (the Tucker/HOSVD and CP decompositions, as discussed here, most notably) constitute a very active research area in mathematics. Most of this research has been driven by applications. There is also much software available, including MATLAB toolboxes [4]. The objective of this lecture has been to provide an accessible introduction to state of the art in the field, written for a signal processing audience. We believe that there is good potential to find further applications of tensor modeling techniques in the signal processing field.

  • 269.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Senovilla, José M. M.
    Structure of conformal Lorentz transformations2003Ingår i: Current Trends in Relativistic Astrophysics: theoretical, numerical, observational / [ed] L. Férnadez-Jambrina, L.M. González-Romero, Springer , 2003, s. 245-251Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    The present volume contains the expanded lectures of a meeting on relativistic astrophysics, the goal of which was to provide a modern introduction to specific aspects of the field for young researchers, as well as for nonspecialists from related areas. Particular emphasis is placed on the theory of black holes and evolution, relativistic stars and jet hydrodynamics, as well as the production and detection of gravitational waves. The book is complemented by further contributions and animation supplied on the accompanying CD-ROM.

  • 270.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    A calculus lecture: What made it good?2012Ingår i: Proceedings of Norma 11: The Sixth Nordic Conference of Mathematics Education / [ed] G. H. Gunnarsdóttir, et al., Reykjavik: University of Iceland Press, 2012, s. 167-176Konferensbidrag (Refereegranskat)
    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.

  • 271.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    A classification of algebraic tasks2003Ingår i: New trends in mathematics education research: an European perspective,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 272.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Beyond the representation given - The parabola and historical metamorphoses of meaning2004Ingår i: PME - Interbational Group for the Psychology of Mathematics Education,2004, Bergen: Bergen Univeristy College , 2004, s. 1-264-1-264Konferensbidrag (Övrigt vetenskapligt)
    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.

  • 273.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    Beyond the representation given: The parabola and historical metamorphoses of meanings2015Ingår i: Refractions of mathematics education: Festschrift for Eva Jablonka / [ed] C. Bergsten & B. Sriraman, Charlotte, NC: Information Age Publishing, 2015, s. 15-48Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 274.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Datoranvändning i högskolans matematikundervisning1999Ingår i: Datorstödd eller datorstörd matematikundervisning,1998, Stockholm: Högskoleverket , 1999, s. 21-Konferensbidrag (Refereegranskat)
    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.   

  • 275.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Datrostödd eller datorstörd matematikundervisning?1999Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
  • 276.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    En gyllene pyramid: Fem trianglar och en pentagon2003Ingår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 30, nr 2, s. 36-41Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    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.

  • 277.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    En kommentar till den matematiska problemlösningens didaktik2006Ingår i: Perspektiv på kunskapens och lärandets villkor / [ed] Lisen Häggblom, Lars Burman & Ann-Sofi Röj-Lindberg, Vasa: Åbo Akademi , 2006, s. 165-176Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    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.

  • 278.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Exploiting the gap between intuitive and formal knowledge in mathematics2008Ingår i: The International Congress on Mathematical Education, ICME,2004, Copenhagen: Roskilde University , 2008Konferensbidrag (Refereegranskat)
  • 279.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Faces of Swedish research in mathematics education2002Ingår i: 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, s. 21-36Konferensbidrag (Övrigt vetenskapligt)
  • 280.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    From sense to symbol sense1999Ingår i: European research in mathematics education I.II / [ed] Inge Schwank, Osnabrück: Forschungsinstitut für Mathematikdidaktik and ERME , 1999, Vol. II, s. 126-137Konferensbidrag (Refereegranskat)
    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.

  • 281.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    How do theories influence the research on teaching and learning limits of functions?2007Ingår i: CERME,2007, Nicosia: University of Cyprus , 2007, s. 1638-Konferensbidrag (Refereegranskat)
  • 282.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Investigating quality in undergraduate mathematics lectures2007Ingår i: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 19, nr 3, s. 48-72Artikel i tidskrift (Refereegranskat)
    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.

  • 283.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Lecture notes - On lecturing in undergraduate mathematics2007Ingår i: MADIF-5, 2006, Linköping: SMDF , 2007, s. 31-Konferensbidrag (Övrigt vetenskapligt)
    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.

  • 284.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Magic circels in the arbelos2006Rapport (Övrigt vetenskapligt)
  • 285.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Magic circles in the arbelos2010Ingår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 7, nr 2&3, s. 209-222Artikel i tidskrift (Refereegranskat)
    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.

  • 286.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Matematik i tiden: Dokumentation av 12:e Matematikbiennalen, Norrköping 24-26 januari 20022002Proceedings (redaktörskap) (Övrigt vetenskapligt)
  • 287.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Mathematical approaches2018Ingår i: Encyclopedia of Mathematics Education / [ed] Steve Lerman (complete book) and Eva Jablonka (section editor), Cham: Springer, 2018, 2, s. 1-8Kapitel i bok, del av antologi (Refereegranskat)
    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...

  • 288.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    Mathematical approaches2014Ingår i: Encyclopedia of Mathematics Education / [ed] Steve Lerman, Springer, 2014, 1, s. 376-383Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    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.

  • 289.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Utbildningsvetenskap.
    Mathematics education research in Sweden: An introduction2010Ingår i: 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, s. 269-282Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    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.

  • 290.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling2017Ingår i: Quaderni di Ricerca in Didattica" QRDM (Mathematics), ISSN 1592-5137, E-ISSN 1592-4424, Vol. 27, nr 2, s. 229-233Artikel i tidskrift (Refereegranskat)
    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.

  • 291.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    News from Nordic mathematics education2014Ingår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 19, nr 1, s. 75-84Artikel, forskningsöversikt (Refereegranskat)
  • 292.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    News from Nordic mathematics education2011Ingår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 16, nr 4, s. 103-117Artikel, forskningsöversikt (Övrigt vetenskapligt)
  • 293.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    News from Nordic mathematics education2012Ingår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 17, nr 2, s. 69-84Artikel, forskningsöversikt (Övrigt vetenskapligt)
  • 294.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    News from Nordic mathematics education2013Ingår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, nr 2, s. 93-102Artikel, forskningsöversikt (Övrigt vetenskapligt)
  • 295.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Några aspekter av matematikens formelspråk2008Ingår i: Matematiska språk. Sju essäer om symbolspråkets roll i matematiken., Stockholm: Santérus Förlag , 2008, s. 127-143Kapitel i bok, del av antologi (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

       

  • 296.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions2008Ingår i: ZDM : the international journal on mathematics education, ISSN 1863-9690, Vol. 40, nr 2, s. 189-199Artikel i tidskrift (Refereegranskat)
    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.

  • 297.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Studying mathematics at university: Views of first year engineering students2016Ingår i: Didactics of mathematics in higher education as a scientific discipline: Conference Proceedings / [ed] R. Göller, R. Biehler, R. Hochmuth, H-G. Rück, Kassel, 2016, s. 458-465Konferensbidrag (Refereegranskat)
    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.

  • 298.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Symbolic computing and mathematics education1994Rapport (Övrigt vetenskapligt)
    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.

  • 299.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    The development of teacher education: Panel discussion2004Ingår i: Educating for the future: Proceedings of an International Symposiun on Mathematics Teacher Education / [ed] R. Strässer, G. Brandell, B. Grevholm, O. Helenius, Göteborg: The Royal Swedish Academy of Sciences , 2004, s. 221-226Konferensbidrag (Refereegranskat)
  • 300.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    The relationships of theory and practice in mathematics education2003Ingår i: CERME 3 Third Conference of the European Society for Research in Mathematics Education,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
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