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  • 1.
    Boesen, Jesper
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Palm, Torulf
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    The relation between types of assessment tasks and the mathematical reasoning students use2010In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 75, no 1, p. 89-105Article in journal (Refereed)
    Abstract [en]

    The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.

  • 2.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    A research framework for creative and imitative reasoning2008In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 67, no 3, p. 255-267Article in journal (Refereed)
    Abstract [en]

    This conceptual research framework addresses the problem of rote learn- ing by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of different reasoning types

     

  • 3.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Mathematical reasoning in task solving.2000In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 41, p. 165-190Article in journal (Refereed)
    Abstract [en]

    An earlier study (Lithner 1998) treated the question “what are the main characteristics and background of undergraduate students’ difficulties when trying to solve mathematical tasks?” This paper will focus on, and extend, the part of the earlier study that concerns task solving strategies. The results indicate that focusing on what is familiar and remembered at a superficial level is dominant over reasoning based on mathematical properties of the components involved, even when the latter could lead to considerable progress.

     

  • 4.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Students’ mathematical reasoning in university textbook exercises2003In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 52, no 1, p. 29-55Article in journal (Refereed)
    Abstract [en]

    Video recordings of three undergraduate students’ textbook-based home- work are analysed. A focus is on the ways their exercise reasoning is mathematically well- founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive reasoning attempts are made.

     

  • 5.
    Palm, Torulf
    Umeå University, Faculty of Science and Technology, Department of mathematics.
    Impact of authenticity on sense making in word problem solving2008In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 67, no 1Article in journal (Refereed)
  • 6.
    Ryve, Andreas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Nilsson, Per
    Pettersson, Kerstin
    Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms2013In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 82, no 3, p. 497-514Article in journal (Refereed)
    Abstract [en]

    Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students' attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.

  • 7.
    Sundström (Raman), Manya
    Department of Learning and Teaching, New Brunswick, USA.
    Key ideas: What are they and how can they help us understand people view proof?2003In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 52, no 3, p. 319-325Article in journal (Refereed)
    Abstract [en]

    This paper examines the views of proof held by university level mathematics students and teachers.  A framework is developed for characterizing people's views of proof, based on a distinction between public and private aspects of proof and the key ideas which link these two domains.

1 - 7 of 7
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