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  • 1.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. University of Skövde, Health and Education.
    The Viability of Social Constructivism as a Philosophy of Mathematics2013In: Croatian Journal of Philosophy, ISSN 1333-1108, E-ISSN 1847-6139, Vol. XIII, no 39, p. 341-355Article in journal (Refereed)
    Abstract [en]

    Attempts have been made to analyse features in mathematics within a social constructivist context. In this paper we critically examine some of those attempts recently made with focus on problems of the objectivity, ontology, necessity, and atemporality of mathematics. Our conclusion is that these attempts fare no better than traditional alternatives, and that they, furthermore, create new problems of their own.

  • 2.
    Höglund, Marlen
    University of Skövde, School of Humanities and Informatics.
    När kan jag använda mina kunskaper i matematik?: teoretisk och praktisk betydelse för grundskolans matematik2011Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I skolan anses matematiken vara ett viktigt ämne och den upptar en stor del av skolans undervisningstid. Däremot har det märkts en trend bland eleverna i grundskolan att de mer och mer ifrågasätter varför de över huvud taget måste lära sig matematik. Ren matematik som de läser i skolan kan det många gånger vara svårt att se nyttan med. Påföljande matematik blir då sedan svårare och svårare att ge bra motiveringar till varför man bör kunna.  Många elever och vuxna känner även en ren ångest när man pratar om ämnet matematik. Vad är egentligen matematik, var används den och till vad? Var kommer matematiken ifrån? Hur uppstod den? Är det intressant och relevant för elever att få kunskap om detta? Har matematikundervisningen följt den snabba samhällsutvecklingen och vad behöver vi egentligen lära oss för matematik i grundskolan? Behöver alla få undervisning i matematik? Matematiken finns överallt omkring oss och synen på matematiken eleverna erhållit har formats av hela samhället. Hur mycket påverkar läraren elevernas inställning och vad har föräldrarna för del i det hela? Studien tar upp det matematiska lärandet, matematikens användande och den matematiska fostran.

  • 3.
    Pettersson, Kerstin
    et al.
    University of Skövde, School of Life Sciences.
    Scheja, Max
    Algorithmic contexts and learning potentiality: A case study of students' understanding of calculusManuscript (Other academic)
  • 4.
    Scheja, Max
    et al.
    Stockholm Univ, Dept Educ, S-10691 Stockholm, Sweden.
    Pettersson, Kerstin
    University of Skövde, School of Life Sciences.
    Transformation and contextualisation: exploring students' conceptual understandings od threshold concept in calculus2010In: Higher Education, ISSN 0018-1560, E-ISSN 1573-174X, Vol. 59, no 2, p. 221-241Article in journal (Refereed)
  • 5.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences.
    Measuring the Power of Arithmetical Theories2005Licentiate thesis, monograph (Other scientific)
    Abstract [en]

    This thesis discusses the possibility to measure the power of extentions of Peano Aritmetic, P A. It consists of three parts, an introduction and two separately written papers. In the introduction we present the problem and briefly give an account of van Lambalgen's and raatikainen's criticism of gnenralization of two versions of Chaitin's incompleteness theorem, and reinforces the above mentioned criticism. The second paper is the main paper of the thesis, and here, using the modal logic GL, we design a measure of the power, in terms of the capacity to prove theorems, of an important set of extentions of P A.

  • 6.
    Sjögren, Jörgen
    University of Skövde, School of Engineering Science. University of Skövde, Health and Education.
    Philosophy of Mathematics and Mathematics Education: Some Reflections2014In: IDÉES FIXES: A festschrift dedicated to Christian Bennet on the occasion of his 60th birthday / [ed] Martin Kaså, Göteborg: Department of Philosophy, Linguistics and Theory of Science , 2014, p. 85-100Chapter in book (Refereed)
  • 7.
    Sjögren, Jörgen
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, Health and Education.
    Bennet, Christian
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Sweden.
    Concept Formation and Concept Grounding2014In: Philosophia (Ramat Gan), ISSN 0048-3893, E-ISSN 1574-9274, Vol. 42, no 3, p. 827-839Article in journal (Refereed)
    Abstract [en]

    Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.

  • 8.
    Torra, Vicenç
    et al.
    Institut d'Investigacío en Intellig̀encia Artificial, Consejo Superior de Investigaciones Cient́ficas, Universitat Aut̀onoma de Barcelona, Bellaterra, Catalonia, Spain.
    Stokes, Klara
    Departments of Computer Science and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain / UNESCO Chair in Data Privacy, Tarragona, Catalonia, Spain.
    Narukawa, Yasuo
    Toho Gakuen, Tokyo, Japan / Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan.
    An extension of fuzzy measures to multisets and its relation to distorted probabilities2012In: IEEE transactions on fuzzy systems, ISSN 1063-6706, E-ISSN 1941-0034, Vol. 20, no 6, p. 1032-1045Article in journal (Refereed)
    Abstract [en]

    Fuzzy measures are monotonic set functions on a reference set; they generalize probabilities replacing the additivity condition by monotonicity. The typical application of these measures is with fuzzy integrals. Fuzzy integrals integrate a function with respect to a fuzzy measure, and they can be used to aggregate information from a set of sources (opinions from experts or criteria in a multicriteria decision-making problem). In this context, background knowledge on the sources is represented by means of the fuzzy measures. For example, interactions between criteria are represented by means of nonadditive measures. In this paper, we introduce fuzzy measures on multisets. We propose a general definition, and we then introduce a family of fuzzy measures for multisets which we show to be equivalent to distorted probabilities when the multisets are restricted to proper sets

1 - 8 of 8
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