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  • 1.
    Ebbelind, Andreas
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Roos, Helena
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Nilsson, Per
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Learning fractions: transformations between representations from a social semiotic perspective of multimodality2012In: Proceedings of Norma 11: The Sixth Nordic Conference on Mathematics Education / [ed] Gunnarsdottir, Hreinsdottir, Palsdottir, Hannula, Hannula-Sormunen, Jablonka, Jankvist, Ryve, Valero and Waege., University of Iceland Press, 2012, p. 217-226Conference paper (Refereed)
    Abstract [en]

    This study presents a tentative framework for studying the learning of fractions in the context of transformations between different forms of representations. The framework is used in an empirical sample of how eight 10-year-old students express understanding of activities which were developed to challenge them to reflect on different ways of representing aspects of the concept of fractions. The framework is based on a social semiotic perspective of multimodality.

    The analysis discloses how the framework helps in structuring our understanding of the interplay between representations in the learning of fractions. Specifically, we saw how concrete physical material and gestures complemented the symbolic and spoken language in the students’ solution strategies of different tasks. 

  • 2.
    Eckert, Andreas
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Contextualizing Sampling: Teaching Challenges and Possibilities2013In: Proceedings of the Eight Conference of European Research in Mathematics Education, European Society for Research in Mathematics Education, 2013Conference paper (Refereed)
    Abstract [en]

    The aim of the present paper is to shed light on mathematical knowledge for teaching probability. In particular we investigate critical instances when a teacher tries to keep track on the idea of sampling and random variation by allocating the discussion to an everyday context. The analysis is based on a certain episode of a longer teaching experiment. The analytical construct of contextualization was used as a means to provide structure to the qualitative analysis performed. Our analysis provides insight into the nature and role of teachers’ knowledge of content and teaching. In particular, the study suggests the idea of a meta-contextual knowledge that teachers need to develop in order to keep track of the intended object of learning when allocating their teaching to an everyday context. 

  • 3. Iversen, Kjærand
    et al.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematikdidaktik.
    Students' meaning-making processes of random phenomena in an ICT-environment2006In: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 2006Conference paper (Refereed)
  • 4. Iversen, Kjærand
    et al.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment2007In: International Journal of Computers for Mathematical Learning, ISSN 1382-3892, Vol. 12, no 2Article in journal (Refereed)
    Abstract [en]

    This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters.

    Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.

  • 5.
    Juter, Kristina
    et al.
    Kristianstad University.
    Nilsson, Per
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Begreppsbildning i sociala sammanhang: Att analysera matematisk aktivitet på två nivåer2011In: Matematikundervisning: Vetenskapliga perspektiv / [ed] Gerd Brandell, Astrid Pettersson, Stockholm: Stockholms universitets förlag, 2011, p. 41-64Chapter in book (Other academic)
  • 6.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics Education. Örebro University.
    Challenges in seeing data as useful evidence in making predictions on the probability of a real-world phenomenon2013In: Statistics Education Research Journal, ISSN 1570-1824, E-ISSN 1570-1824, Vol. 12, no 2, p. 71-83Article in journal (Refereed)
    Abstract [en]

    This study investigates the relationship between deterministic and probabilistic reasoning when students are asked to experiment on a real-world situation involving uncertainty. Twelve students, aged eight to nine years, participated in an outdoor teaching activity that called for reflection on the growth of sunflowers within the frame of a sunflower lottery. A basic feature of the situation was that the students were involved in the process of creating their own empirical data of the growth. However, the study shows not only that the students do not make use of data for predicting the outcome of an uncertain event, but also how this can be explained by students' attention to deterministic features of the situation, brought to the fore within an ecology context and connected to a conceptual principle of ‘sharing’.

  • 7.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Conceptual variation and coordination in probability reasoning2009In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 28, no 4, p. 247-261Article in journal (Refereed)
    Abstract [en]

    This study investigates students’ conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish stu- dents (12–13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space, physical/geometrical considera- tions and experimental evidence when trying to develop their understanding of compound random phenomena.The analytical construct of contextualization was used as a means to provide structure to the qualitative analysis performed. Within the frame of the students’ problem encounters during the game and how they contextualized the solutions of the problems in personal contexts for interpretations, the analysis finds four main forms of appearance, or of lim- itations in appearance, of conceptual variation and coordination among theoretical and experimental interpretations of probability.

  • 8.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematikdidaktik.
    Different ways in which students handle chance encounters in the explorative setting of a dice game2007In: Educational Studies in Mathematics, ISSN 0013-1954Article 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.

  • 9.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Elever resonerar om sannolikhet2009In: Matematikdidaktiska frågor: Resultat från en forskarskola, Göteborg: Livréna AB , 2009Chapter in book (Other (popular science, discussion, etc.))
    Abstract [sv]

    Kapitlet beskriver en studie om hur elever utan erfarenhet av undervisning i sannolikhet kan resonera om och hantera experimentella situationer som kräver förståelse av slump och sannolikhet. Samtidigt vill jag synliggöra den potential som ryms inom ramen för barns lust att upptäcka och förstå aktiviteter som fångar deras genuina intresse. Inledningsvis ges en kort bakgrunden till studien. Den följs av en diskussion av begreppen slump och sannolikhet. Jag beskriver utförligt de tärningsspel jag använt för att generera empiriskt material i studien. Därefter presenteras och karaktäriseras några av de resonemang om sannolikheter som elevernas handlingar visade prov på när de spelade. Hur elever förstår och utvecklar begrepp betraktas utifrån det sätt på vilket elevernas förståelse varierar med deras tolkningar av spelsituationerna. Som avslutning diskuterar jag hur olika aspekter av studien bidrar med idéer till att utveckla undervisning i matematik i allmänhet och i sannolikhet i synnerhet.

  • 10.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Experimentation in probability teaching and learning2014In: Probablistic thinking: Presenting plural perspectives / [ed] Egan J Chernoff and Bharath Sriraman, Springer Science+Business Media B.V., 2014, p. 509-532Chapter in book (Refereed)
    Abstract [sv]

    This chapter provides a discussion on teaching and learning probability in the relationship between theoretical and empirical probability. We examine a small-scaled teaching experiment, which involves acts of experimentation. The purpose of the experiment is particularly on exploring and illustrating critical aspect of probability teaching, which involv es students’ concrete production and experimentation with data. Developing a background for the teaching experiment we proceed with reviewing previous research, which are highlighting issues on the relationship between empirical and theoretical probability in situations of experimentation.

  • 11.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Exploring Probabilistic Reasoning: A Study of How Students Contextualise Compound Chance Encounters in Explorative Settings2006Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis aims at exploring how probabilistic reasoning arises in explorative learning situations that are random in nature. The focus is especially on what learners with scant experience of formal theories of probability do and can do when dealing with compound random situations in which they are offered opportunities to integrate different probabilistic lines of reasoning.

    Three studies were carried out for the purpose of gaining an understanding of how learners’ probabilistic reasoning is organised and re-organised in explorative, random-dependent situations. In two of the studies 12 to 13 year-old students acted within a dice-game setting, which was based on the total of two dice. The third study examined 14 to 16 year-old students’ ways of dealing with ICT-versions of compound, independent events viewed in a random-dependent ramified structure.

    To uncover the basis and the content of the students’ reasoning, behaviour has been regarded in terms of intentions. That is, to understand and make sense of the students’ reasoning, their activities have been matched and re-matched with conjectures about their intents to fulfil certain goals.

    Although the students were acting on the same learning material, the analyses revealed various kinds of probabilistic reasoning among the students. It has been argued that students’ various ways of dealing with chance encounters may be understood and explained with reference to the ways in which they interpret the learning situations. Thus, this thesis suggests that probabilistic reasoning takes form through a process of contextualisation, i.e. through a compound process where the cognitive activity oscillates between interpretations and reflections about context, the focal event and new information that comes into play.

    This thesis reveals that students, prior to instruction, are able to devise ideas of an underlying probability distribution in the case of compound random phenomena. The students bring into the discussion geometrical and numerical considerations, as well as arguments reflecting principles of the law of large numbers.

  • 12.
    Nilsson, Per
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Exploring probabilistic reasoning: A study of how students contextualise compound chance encounters in explorative settings2010 (ed. 1)Book (Other academic)
  • 13.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Operationalizing the analytical construct of contextualization2009In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 14, no 1, p. 61-88Article in journal (Refereed)
    Abstract [en]

    This article elaborates on the construct of contextualization, which constitutes a constructivist contextual view on learning. Principles of constructivism and contextualization are operationalized into a set of four analytical categories, that teacher and researchers can use for organizing thinking about teaching and learning mathematics. The categories are discussed and verified throughout the design and analysis of a classroom compatible learning activity, which is supposed to promote probabilistic reasoning.Suggestions for developing the operationalization are discussed and, on account of that, the article invites for future efforts, where the explanatory power of contextualization and its analytical categories are further explored.

  • 14.
    Nilsson, Per
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Summaspelet: Ett spel för lärande i sannolikhet2009In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    Summaspelet är ett tärningsspel som innehåller element av slumpkaraktär. Författaren har utvecklat och använt olika varianter av spelet för att studera hur elever resonerar om och tänker kring olika aspekter av sannolikhet i sammansatta slumpförsök. Vi får en presentation av spelet och diskussion om varianter av spelet.

  • 15.
    Nilsson, Per
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Iversen, Kjærand
    Nord-Trøndelag University College.
    A CONTEXTUAL APPROACH ON LEARNING PROBABILITY2008In: Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education., Morelia. Mexico: Guevara Impresores , 2008Conference paper (Refereed)
    Abstract [en]

    This paper focuses on the learning of probability. The analytical construct of contextualization is used to explain how students deal with compound random phenomenon in an explorative ICT setting. In this setting the students were offered opportunities to interact with different representations of such phenomenon. The analysis follows a specific group of two students. The analysis shows how students’ understanding of the compound events varies with their interpretations of the situation. In particular, we notice how the two students differ when trying to connect theoretical and experimental representations of probability.

  • 16.
    Nilsson, Per
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Iversen, Kjærand
    Nord-Trøndelag University College.
    Sannolikhet och alternativa undervisningsformer2009In: Statistikk og Sannsynlighet / [ed] Merete Lysberg, Tronheim: NTNU-trykk , 2009Conference paper (Other academic)
    Abstract [en]

    Temat för presentationen var lärande och undervisning i sannolikhet. Presentationen var uppdelad i två delteman. Per inledde med att diskuterade lärande och undervisning i sannolikhet utifrån det tärningsspel han använt i sina studier. Kjærands presentation fokuserade relationen mellan multiplikativt tänkande och elevers sätt att resonera om sannolikhet. Kjærand kopplade detta sedan till Flexitree, som är ett datorprogram där elever ges möjlighet att resonera om sannolikhetsutfall, genererade av trädstrukturer. Några klassiska resultat med relevans för de båda inriktningarna utgjorde bakgrund och utgångspunkt för diskussionerna.

  • 17.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Juter, Kristina
    Kristianstad University, Sweden.
    Flexibility and coordination among acts of visualization and analysis in a pattern generalization activity2011In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 30, no 3, p. 194-205Article in journal (Refereed)
    Abstract [en]

    This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students’ attempt to reach a general formula for a three-dimensional pattern generalizing task.

    The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate the number of blocks in a three-dimensional tower of different heights. The students’ activity was video- and audio-taped, fully transcribed and lasted for 50 min.

    The analysis discloses several instances of how the students were linking acts of visualization and analysis to reach a general formula. However, regarding flexibility, we found that it was more natural for the students to change visual format than to change analytical position and direction in their attempts to generalize the three-dimensional pattern of the task in a closed formula.

  • 18.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Lindström, Torsten
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Connecting Swedish compolsory schoolteachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts2012Conference paper (Refereed)
    Abstract [en]

    This paper reports on a survey on teachers’ content knowledge of probability and with connecting such knowledge to the teachers’ level of education, teaching years and self-assessments of probability concepts. Twenty-nine teachers in compulsory school answered a questionnaire calling for reflection on these issues. The teachers’ responses disclose that the teachers find probability to be a difficult subject. The survey reports that the teachers have low confidence in understanding key concepts of probability and that they have difficulties in applying the concepts in probability tasks. The test indicates no correlation between teaching years and confidence or between teaching years and results on the probability tasks. 

  • 19.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Lindström, Torsten
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Profiling Swedish Teachers' Knowledge Base in Probability2013In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, no 4, p. 51-72Article in journal (Refereed)
    Abstract [en]

    This paper aims at profiling Swedish teachers’ knowledge base in probability. 43 teachers in compulsory school answered a questionnaire on probability estimation tasks and concept tasks. In the concept tasks, they were challenged to explain their solutions and the content involved in the probability estimation tasks. We distin- guish five patterns in the teachers’ knowledge profile: 1) a basic understanding of the theoretical interpretation of probability, 2) problems with structuring compound events, 3) difficulty with conjunction and conditional probability, 4) a higher degree of common content knowledge than of specialized content knowledge and 5) limited understanding of random variation and principles of experimental probability.

  • 20.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ryve, Andreas
    Department of Education, Stockholm University and Department of Education, University of Oxford.
    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.

  • 21.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Ryve, Andreas
    Mälardalens högskola.
    The nature and role of common ground in the learning of mathematics in small-group discussions2014In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 58, no 5, p. 609-623Article in journal (Refereed)
    Abstract [en]

    This study investigates the nature and role of common ground in group learning of mathematics by means of the analytical constructs of focal projects and contextualization. The analysis investigates two students (12–13 years old) playing a dice game, where their task is to distribute a set of markers based on the total of two dice. The analysis shows how consistency between the students' focal projects became crucial in their progression from a uniform to a non-uniform distribution of the markers used in the game. The task system and concrete manipulatives became important in furthering the students' explorations. In the frame of a frequency context, we also discuss how a contextualization may restrict certain aspects of probability from coming into play during such explorations.

  • 22.
    Nilsson, Per
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Sollervall, Håkan
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Milrad, Marcelo
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Collaborative design of mathematical activities for learning in an outdoor setting2009In: Proceedings of the 6th Conference of the European Society for Research in Mathematics Education, CERME 6: January 28th-February 1st 2009, Lyon (France), 2009, p. 1101-1110Conference paper (Refereed)
    Abstract [en]

    In recent years, teaching mathematics in an outdoor setting has become popular among teachers, as it seems to offer alternative ways to motivate children’s learning. These new learning possibilities pose crucial questions regarding the nature of how mathematical activities should be designed for outdoors settings. In this paper we describe our current work related to the design and implementation of mathematical activities in this particular environment in which a specific mathematical content was used as the central component in the design. We illustrate our collaborative design approach and the results from observations of two activities. Our initial results provide us with valuable insights that can help to better understand how to design and implement this kind of educational activities.

  • 23.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Sollervall, Håkan
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Spikol, Daniel
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Mathematical learning processes supported by augmented reality2010In: Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education: Mathematics in different settings : PME 34, Belo Horizonte, Brazil / [ed] Márcia Pínto & Teresinha Kawasaki, Belo Horizonte, Brazil: PME , 2010, p. 337-344Conference paper (Refereed)
    Abstract [en]

    The authors of this paper are involved in an ongoing project with the aim of investigating ICT-supported activities for the learning of mathematics where real-world images are mixed with computer-generated 3D images. The present paper explores the ways in which four students (15 years old) try to make sense of a task that calls for reflection on the concept of scale. The analysis shows how this specific kind of learning activity can challenge students to vary and coordinate among representations offered within the activity, thereby creating opportunities to extend and strengthen their networks of knowledge elements associated with the current learning object.

  • 24.
    Nilsson, Per
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Sällström, Karin
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Nilsson, Gunilla
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    On the relationship between deterministic and probabilistic reasoning in modelling the chance of a natural phenomenon2012In: Proceedings of Norma 11: the sixth Nordic Conference on Mathmatics Education in Reykjavik, May 11-14, 2011, 2012Conference paper (Refereed)
    Abstract [en]

    This study aims at investigating the relationship between deterministic and probabilistic reasoning when students are asked to model and predict the outcomes of a real-world situation involving uncertainty. Twelve students, aged 8-9 years, participated in an outdoor located teaching activity which called for reflection on the growing of sunflowers. Based on the analysis, and previous research, the study suggests to structure an analysis on the relationship between deterministic and probabilistic reasoning according to four analytical relationships: Deterministic model and deterministic behaviour; Deterministic model and probabilistic behaviour; Probabilistic model and deterministic behaviour; Probabilistic model and probabilistic behaviour.

  • 25.
    Roos, Helena
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Nilsson, Per
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    An Inclusive Perspective on a Pedagogy for Students in Special Needs in Mathematics2012In: Evaluation and Comparison of Mathematical Achievment: Dimensions and Perspectives : proceedings of MADIF 8 : the eighth Swedish mathematics education research seminar, Umeå, January 24-25, 2012 / [ed] C. Bergsten, E. Jablonka & M. Raman, 2012, p. 217-218Conference paper (Refereed)
  • 26.
    Ryve, Andreas
    et al.
    Mälardalens högskola.
    Larsson, Maria
    Mälardalens högskola.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Analyzing content and participation in classroom discourse: Dimensions of variation, mediating tools, and conceptual accountability2013In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 57, no 1, p. 101-114Article in journal (Refereed)
    Abstract [en]

    Balancing content and students’ participation in the mathematics classroom is an area of both practical and theoretical interest. In this article we relate and contribute to these two interests by analyzing classroom data from an intervention project aiming at teaching mathematics through problem solving. The study shows that several aspects such as mediating tools, the teacher’s conceptual accountability and interactional moves play important roles in the nature of the co-construction of critical dimensions of variation. We therefore suggest that an analysis of content and participation in the mathematics classroom would benefit from drawing on several theoretical sources. As such, the study could be seen as a contribution to recent elaborations on developing variation theory for analyzing the enacted object of learning. 

  • 27. Ryve, Andreas
    et al.
    Nilsson, Per
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Mason, John
    Establishing mathematics for teaching within classroom interactions in teacher education2011In: 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.

  • 28.
    Ryve, Andreas
    et al.
    Mälardalens högskola.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Pettersson, Kerstin
    Stockholms universitet.
    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.

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