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  • 1.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen.
    Different ways in which students handle chance encounters in the explorative setting of a dice game2007In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 66, no 3, p. 293-315Article in journal (Refereed)
    Abstract [en]

    The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were tape-recorded and fully transcribed, the students were encouraged to explore strategies for winning a specifically designed dice game based on the sum of two dice. The dice game included four different set-ups of dice designed to bring to the fore different aspects of probability modelling and to offer the student the opportunity to encounter small differences in the mathematical structure of the sample space and of the probability distribution between the four different set-ups. The study describes strategies that the students use when confronted with these different set-ups, what their activities imply in terms of resources in handling random phenomena and what the dice game offers in terms of opportunities for learning probability. In order to explain such meaning-making processes the students’ activities are viewed from a perspective that takes into consideration how the students’ understanding varies with their interpretations of the situation they are confronted with, i.e., how they contextualize the different set-ups of the dice game. The results show how the students, during the course of the game, reorganize their interpretations of the mathematical content confronting them, and how a variation of guiding principles becomes the object of exploration. Approaches of extremes and a number model are described as a means for the students to identify and assign probabilities for the total of two dice.

  • 2.
    Nilsson, Per
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus University, Växjö, Sweden .
    Ryve, Andreas
    Department of Education, Stockholm University, Stockholm, Sweden; Department of Education, University of Oxford, Oxford, United Kingdom.
    Focal event, contextualization, and effective communication in the mathematics classroom2010In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 74, no 3, p. 241-258Article in journal (Refereed)
    Abstract [en]

    The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12-13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.

  • 3.
    Ryve, Andreas
    et al.
    Mälardalen University, Västerås, Sweden; Stockholm University, Stockholm, Sweden; University of Oxford, Oxford, United Kingdom .
    Nilsson, Per
    Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik (DFM), Växjö, Sweden.
    Mason, John
    Open University, Milton Keynes, United Kingdom.
    Establishing mathematics for teaching within classroom interactions in teacher education2012In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 81, no 1, p. 1-14Article in journal (Refereed)
    Abstract [en]

    Teacher educators’ processes of establishing “mathematics for teaching” in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the establishment of mathematics for teaching is dependent on the use of keywords from the mathematics education domain, the introduction of variation, and the use of generic communicative strategies. As such, the study could be seen as a contribution to ongoing research on how mathematics teacher educators interactively deal with mathematics for teaching.

  • 4.
    Ryve, Andreas
    et al.
    School of Education, Mälardalen University, Västerås, Sweden; Umeå University, Umeå, Sweden .
    Nilsson, Per
    Institutionen för matematikdidaktik (MD), Linnéuniversitetet, Växjö, Sweden .
    Pettersson, Kerstin
    Stockholm University, Stockholm, Sweden.
    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 12-13 old students playing a dice game as well as data from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms are crucial in students’ attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and link between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.

  • 5.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology. Faculty of Human Sciences, University of Cologne, Cologne, Germany.
    Lilienthal, Achim J.
    Örebro University, School of Science and Technology.
    Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 1, p. 123-139Article in journal (Refereed)
    Abstract [en]

    Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in mathematics even though they may not apply in this domain. This article investigates to what extent the EMH applies in mathematics - geometry in particular - and aims to lift the discussion of what inferences can be validly made from eye-tracking data. We use a case study to investigate the need for a refinement of the use of the EMH. In a stimulated recall interview, a student described his original thoughts perusing a gaze-overlaid video recorded when he was working on a geometry problem. Our findings contribute to better a understanding of when and how the EMH applies in the subdomain of geometry. In particular, we identify patterns of eye movements that provide valuable information on students' geometry problem solving: certain patterns where the eye fixates on what the student is processing and others where the EMH does not hold. Identifying such patterns may contribute to an interpretation theory for students' eye movements in geometry - exemplifying a domain-specific theory that may reduce the inherent ambiguity and uncertainty that eye tracking data analysis has.

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