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  • 1.
    Bergman-Ärlebäck, Jonas
    et al.
    Linköping University, Linköping, Sweden.
    Blomberg, Per
    Linnaeus University, Växjö, Sweden.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik. Linnaeus University, Växjö, Sweden.
    An instructional design perspective on data-modelling for learning statistics and modelling2015Inngår i: Development of mathematics teaching: Design, Scale, Effects: Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar / [ed] Ola Helenius, Arne Engström, Tasmin Meaney, Per Nilsson, Eva Norén, Judy Sayers, Magnus Österholm, Svensk Förening för Matematisk Didaktisk Forskning (SMDF) , 2015, s. 37-46Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This theoretical and methodological paper discusses the emerging theoretical framing and methodological considerations in our efforts to develop a theoretical approach supporting instructional design for teaching and learning statistics and mathematical modelling. From an instructional design point of view aligned with the goals in governing curricula documents and real classroom constraints, we argue for the integration of the models and modelling perspective on teaching and learning mathematics with a data-modelling approach to facilitate students’ learning statistics and mathematical modelling. An application of the framework is given and future research discussed.

  • 2.
    Ebbelind, Andreas
    et al.
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Roos, Helena
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Nilsson, Per
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Learning fractions: transformations between representations from a social semiotic perspective of multimodality2012Inngår i: Proceedings of Norma 11: the sixth Nordic Conference on Mathmatics Education in Reykjavík, May 11.-14. 2011 / [ed] Gunnarsdottir, Hreinsdottir, Palsdottir, Hannula, Hannula-Sormunen, Jablonka, Jankvist, Ryve, Valero and Waege, Reykjavík: University of Iceland Press , 2012, s. 217-226Konferansepaper (Fagfellevurdert)
    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. 

  • 3.
    Eckert, Andreas
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus University, Växjö, Sweden.
    Nilsson, Per
    School of Computer Science, Physics and Mathematics, Linnaeus University, Växjö, Sweden.
    Contextualizing Sampling: Teaching Challenges and Possibilities2013Inngår i: Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education / [ed] Behiye Ubuz, Çiğdem Haser, Maria Alessandra Mariotti, Middle East Technical University , 2013, s. 766-776Konferansepaper (Fagfellevurdert)
    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.

  • 4.
    Eckert, Andreas
    et al.
    Department of Mathematics, Linnaeus University, Växjö, Sweden.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Introducing a symbolic interactionist approach on teaching mathematics: The case of revoicing as an interactional strategy in the teaching of probability2017Inngår i: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 20, nr 1, s. 31-48Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.

  • 5.
    Iversen, Kjærand
    et al.
    The Faculty of Education and Arts, Nord University, Bodø, Norway.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik. The Faculty of Education and Arts, Nord University, Bodø, Norway.
    Lower secondary school students’ reasoning about compound probability in spinner tasks2019Inngår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we investigate the different ways in which students in lower secondary school (14–15 year-olds) reason about compound stochastic events (CSE). We ask students during clinical interviews to respond to CSE-tasks in a spinner context, where two linked spinners dis-play equal or different sizes of red and white areas. We seek to enrich our knowledge of how students make sense of CSE by not focusing exclusively on sample-space grounded reasoning. We open up the analysis to how students’reasoning can reflect aspects of multiplicative reasoning in relation to The Product Law of Probability. Our results show that students have difficulty in applying well-grounded combinatorial reasoning as well as multiplicative reasoning to the tasks, but they do show intuitive reasoning that reflect aspects of The Product Law of Probability. Two ways of reasoning identified in the current study are area-based part-whole reasoning and lowest-chance reasoning.

  • 6.
    Iversen, Kjærand
    et al.
    Agder University College, Norway.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    Students' meaning-making processes of random phenomena in an ICT-environment2006Inngår i: European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, Universitat Ramon Llull , 2006, s. 601-610Konferansepaper (Fagfellevurdert)
  • 7.
    Iversen, Kjærand
    et al.
    Nord-Trøndelag University College, Røstad, Levanger, Norway; Agder University College, Kristiansand, Norway.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    Students' reasoning about one-object stochastic phenomena in an ICT-environment2007Inngår i: International Journal of Computers for Mathematical Learning, ISSN 1382-3892, E-ISSN 1573-1766, Vol. 12, nr 2, s. 113-133Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 8.
    Juter, Kristina
    et al.
    Högskolan i Kristianstad, Kristianstad, Sweden.
    Nilsson, Per
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Begreppsbildning i sociala sammanhang: att analysera matematisk aktivitet på två nivåer2011Inngår i: Matematikundervisning: vetenskapliga perspektiv / [ed] Gerd Brandell och Astrid Pettersson, Stockholm: Stockholms universitets förlag, 2011, s. 41-64Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 9.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    A Framework for Investigating Qualities of Procedural and Conceptual Knowledge in Mathematics: An inferentialist perspectiveInngår i: Journal for Research in Mathematics Education, ISSN 0021-8251, E-ISSN 1945-2306Artikkel i tidsskrift (Fagfellevurdert)
  • 10.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    An Inferentialist Perspective on How Note-taking can Constrain the Orchestration of Math-Talk2018Inngår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The aim of this study is to investigate relationships between note-taking and the orchestrating of math-talk in whole-class teaching. A lesson on (average) velocity in a Swedish Grade 6 has been observed. Taking an inferentialist stance on human understanding, the study conceptualizes teaching and learning from the perspective of how students come to be engaged in the language practice of giving and asking for reasons. The study shows how note-taking supports a teacher-student relationship where the teacher produces content and the students’ participation is reduced to consume content. It shows how note-taking can support descriptive math-talk of concepts and symbols and step-by-step procedural math-talk, connected to the goal of providing students examples of tasks, similar to the tasks in their textbook.

  • 11.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Building a local theory for the learning of experimental probability2015Inngår i: Nordic research in mathematics education: Proceedings of NORMA14, Turku, June 3–6, 2014 / [ed] Harry Silfverberg, Tomi Kärki and Markku S. Hannula, Turku: University of Turku, Department of Teacher Education , 2015, s. 318-328Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The approach of this paper builds on the assumption that there is a need to develop local, domain specific instructional theories for the learning of probability. The aim of the present paper is to explore the qualitative hypothesis of building such a theory on the combination of students’ own experimentations with samples and principles of variation. By using data from 12-13-year old students investigating the probability of obtaining a certain colour when picking, at random, one piece from a bag with six different colours of the candy, the paper shows how variations in students’ own experimentations with samples can be used as means to explore and support students’ understanding of critical features of experimental probability. 

  • 12.
    Nilsson, Per
    Institutionen för matematikdidaktik, Linnéuniversitetet, Växjö, Sweden.
    Challenges in seeing data as useful evidence in making predictions on the probability of a real-world phenomenon2013Inngår i: Statistics Education Research Journal, ISSN 1570-1824, E-ISSN 1570-1824, ISSN 1570-1824, Vol. 12, nr 2, s. 71-83Artikkel i tidsskrift (Fagfellevurdert)
    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’.

  • 13.
    Nilsson, Per
    Växjö University, School of Mathematics and Systems Engineering, Växjö, Sweden.
    Conceptual variation and coordination in probability reasoning2009Inngår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 28, nr 4, s. 247-261Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 14.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen.
    Different ways in which students handle chance encounters in the explorative setting of a dice game2007Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 66, nr 3, s. 293-315Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 15.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Experimentation in probability teaching and learning2014Inngår i: Probabilistic thinking: presenting plural perspectives / [ed] Chernoff, Egan J. och Sriraman, Bharath, Dordrecht: Springer Netherlands, 2014, 1, s. 509-532Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This chapter explores the relationship between theoretical and empirical probability in experimentation-based teaching of probability. We examine previous research and a fresh small-scale teaching experiment in order to explore probability teaching, which involves students’ (12–13 years old) experimentation with data.

    The literature review and the teaching experiment point to several challenges for teaching probability through experimentations. Students emphasize absolute frequencies and part–part relationships, which makes it difficult for them to understand the principle of replacement and end up with numerical values to probability estimates. Students also find it hard to compare and make inferences if the samples are made up with different numbers of observations.

    According to teaching strategies, the teaching experiment shows how experimentation encourages students to engage in questions of chance and probability. Among other things, it is also shown how variation of meaning-contexts supports students understanding of unfamiliar situations and how comparison-oriented questions can be used to promote students understanding of the relationship between theoretical and empirical probability.

  • 16.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen.
    Exploring Probabilistic Reasoning: A Study of How Students Contextualise Compound Chance Encounters in Explorative Settings2006Doktoravhandling, med artikler (Annet vitenskapelig)
    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.

  • 17.
    Nilsson, Per
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Exploring probabilistic reasoning: a study of how students contextualise compound chance encounters in explorative settings2010 (oppl. 1)Bok (Annet vitenskapelig)
  • 18.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    Operationalizing the analytical construct of contextualization2009Inngår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 14, nr 1, s. 61-88Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 19.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    Summaspelet: ett spel för lärande i sannolikhet2009Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 3, s. 21-25Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    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.

  • 20.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Blomberg, Per
    Linnaeus University, Växjö, Sweden.
    Berman-Ärlebäck, Jonas
    Linköpings University, Linköping, Sweden.
    Exploring realistic Bayesian modeling situations2014Inngår i: Sustainability in statistics education: Proceedings of the Ninth International Conference on Teaching Statistics / [ed] K. Makar, B. de Sousa, & R. Gould, ISI/IASE , 2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The study reported in the present paper is part of a larger project, which aims to explore possibilities and challenges in developing a teaching practice that supports students’ ability to model random dependent situations by a Bayesian approach. A central premise is that modeling should be based on situations that appear realistic to the students. Given this premise, the specific purpose of the present study is to identify and characterize uncertain situations that are realistic and suitable for a Bayesian treatment. The study involves reviewing some of the literature related to Bayesian applications. Based on that review we distinguish detecting (test) situations and construction composition situations as two general types of Bayesian modeling situations.

  • 21.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Eckert, Andreas
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Pratt, Dave
    London University, London, UK.
    Challenges and opportunities in experimentation-based instruction in probability2017Inngår i: Teaching and Learning Probability: Advances in Probability Education Research / [ed] Batanero, C. & Chernoff, E.J., Springer Netherlands, 2017Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 22.
    Nilsson, Per
    et al.
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    Iversen, Kjærand
    Nord-Trøndelag University College, Steinkjer, Norway.
    A contextual approach on learning probability2008Inngår i: Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education, Morelia. Mexico: Guevara Impresores , 2008Konferansepaper (Fagfellevurdert)
    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.

  • 23.
    Nilsson, Per
    et al.
    Matematiska och systemtekniska institutionen, Växjö universitet, Växjö, Sverige.
    Iversen, Kjærand
    Nord-Trøndelag University College, Trondheim, Norway.
    Sannolikhet och alternativa undervisningsformer2010Inngår i: Statistikk og sannsynlighet: nordisk konferanse i matematikkdidaktikk ved NTNU 23. og 24. november 2009 / [ed] Merete Lysberg, Trondheim: Nasjonalt senter for matematikk i opplæringen , 2010, s. 59-64Konferansepaper (Annet vitenskapelig)
    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.

  • 24.
    Nilsson, Per
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus University, Växjö, Sweden .
    Juter, Kristina
    Kristianstad University, Kristianstad, Sweden.
    Flexibility and coordination among acts of visualization and analysis in a pattern generalization activity2011Inngår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 30, nr 3, s. 194-205Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 25.
    Nilsson, Per
    et al.
    Institutionen för datavetenskap, fysik och matematik (DFM), Växjö, Sweden.
    Lindström, Torsten
    Institutionen för datavetenskap, fysik och matematik (DFM), Växjö, Sweden.
    Connecting Swedish compolsory schoolteachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts2012Konferansepaper (Fagfellevurdert)
    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. 

  • 26.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik. Institutionen för matematikdidaktik (MD), Linnéuniversitetet, Växjö, Sweden.
    Lindström, Torsten
    Institutionen för matematik (MA), Linnéuniversitetet, Växjö, Sweden.
    Profiling Swedish teachers’ knowledge base in probability2013Inngår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, nr 4, s. 51-72Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 27.
    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 classroom2010Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 74, nr 3, s. 241-258Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 28.
    Nilsson, Per
    et al.
    Institutionen för matematikdidaktik (MD), Linnéuniversitetet, Växjö, Sweden.
    Ryve, Andreas
    School of Education, Culture, and Communication, Mälardalen University, Växjö, Sweden .
    The nature and role of common ground in the learning of mathematics in small-group discussions2014Inngår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 58, nr 5, s. 609-623Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 29.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Ryve, Andreas
    School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Larsson, Maria
    School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Characterizing theories aimed at supporting teachers’ mathematical classroom practices2017Inngår i: CERME 10: 10th Congress of European Research in Mathematics Education, CERME , 2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we draw upon examples from a recently published systematic literature review (Ryve et al, 2015) on productive classroom practice to contribute to the research on the nature of theories for action in mathematics education. By relating the results from the review to theories and literature on educational policy research, professional development research and implementation research we construct a framework for categorizing theories aiming at supporting teachers’ actions in mathematical classroom practices.

  • 30.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Schindler, Maike
    University of Cologne, Cologne, Germany .
    The nature and use of theories in statistics education: looking back, looking forward2018Inngår i: Looking back, looking forward / [ed] M. A. Sorto, A. White, & L. Guyot, Voorburg, The Netherlands: The International Statistical Institute, 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Theories have a significant role for scientific work—also for statistics education research (SER). This paper elaborates on the use of theories in SER, based on findings of a literature review on the nature and use of theories in SER. In particular, we address theoretical issues and possible directions to further theory development in SER. Subsequently, we discuss five themes that in our view need further attention in SER. 

  • 31.
    Nilsson, Per
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Schindler, Maike
    University of Cologne, Cologne, Germany.
    Bakker, Arthur
    Utrecht University, Utrecht, The Netherlands.
    The nature and use of theories in statistics education2017Inngår i: International Handbook of Research in Statistics Education / [ed] Ben-Zvi, D.; Makar, K.; Garfield, J., Springer, 2017Kapittel i bok, del av antologi (Annet vitenskapelig)
  • 32.
    Nilsson, Per
    et al.
    School of Mathematics and Systems Engineering, Växjö University, Växjö, Sweden.
    Sollervall, Håkan
    School of Mathematics and Systems Engineering, Växjö University, Växjö, Sweden.
    Milrad, Marcelo
    School of Mathematics and Systems Engineering, Växjö University, Växjö, Sweden.
    Collaborative design of mathematical activities for learning in an outdoor setting2010Inngår i: Proceedings of CERME 6, Lyon: Institut National de Recherche Pedagogique , 2010, s. 1101-1110Konferansepaper (Fagfellevurdert)
    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.

  • 33.
    Nilsson, Per
    et al.
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Sollervall, Håkan
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Spikol, Daniel
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Mathematical learning processes supported by augmented reality2010Inngår i: 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, Bela Horizonte, Brazíl: The International Group for the Psychology of Mathematics Education (PME) , 2010, s. 337-344Konferansepaper (Fagfellevurdert)
    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.

  • 34.
    Nilsson, Per
    et al.
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Sällström, Karin
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    Nilsson, Gunilla
    Institutionen för datavetenskap, fysik och matematik (DFM), Linnéuniversitetet, Växjö, Sweden.
    On the relationship between deterministic and probabilistic reasoning in modelling the chance of a natural phenomenon2012Inngår i: Proceedings of Norma 11: the sixth Nordic Conference on Mathmatics Education in Reykjavik, May 11-14, 2011 / [ed] Guðný Helga Gunnarsdóttir ..., Reykjavík: University of Iceland Press , 2012Konferansepaper (Fagfellevurdert)
    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.

  • 35.
    Ryve, Andreas
    et al.
    School of Education, Mälardalen University, Västerås, Sweden.
    Larsson, Maria
    School of Education, Mälardalen University, Västerås, Sweden.
    Nilsson, Per
    Institutionen för matematikdidaktik (MD), Linnéuniversitetet, Växjö, Sweden.
    Analyzing content and participation in classroom discourse: dimensions of variation, mediating tools, and conceptual accountability2013Inngår i: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 57, nr 1, s. 101-114Artikkel i tidsskrift (Fagfellevurdert)
    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. 

  • 36.
    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 education2012Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 81, nr 1, s. 1-14Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 37.
    Ryve, Andreas
    et al.
    Mälardalen University, Västerås, Sweden.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Palm, Torulf
    Umeå University, Umeå, Sweden.
    Van Steenbrugge, Hendrik
    Mälardalen University, Västerås, Sweden.
    Andersson, Catarina
    Umeå University, Umeå, Sweden.
    Bergwall, Andreas
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Boström, Erika
    Umeå University, Umeå, Sweden.
    Larsson, Maria
    Mälardalen University, Västerås, Sweden.
    Vingsle, Lotta
    Umeå University, Umeå, Sweden.
    Kartläggning av forskning om formativ bedömning, klassrumsundervisning och läromedel i matematik: Delrapport från skolforsk-projektet2015Rapport (Annet vitenskapelig)
    Abstract [en]

    The current project focuses on mathematics education, and is partitioned into three subprojects mapping research on formative assessment, classroom teaching, and curriculum programs in mathematics. The rationale for focusing on these three areas is that they are all highly relevant for understanding and improving Swedish mathematics education and students’ knowing of mathematics. Therefore, the aim of the project is to map research on formative assessment, classroom teaching, and curriculum programs in mathematics education.

    The methodology of the literature review has been inspired by Gough, Oliver, and Thomas (2013), and we have focused on the mapping on journal articles published on Web of Science (WoS).

    The results from the sample of articles on formative assessment show that strategies of formative assessment in mathematics are positively correlated to students’ performance in mathematics with medium and large effect sizes. However, based on the current mapping it is difficult to specify aspects of how the formative strategies are to be implemented in order to promote students’ knowing of mathematics.

    Despite the change in perspective of what constitutes knowledge in mathematics to also include reasoning, problem-solving and communication, the map shows that research is mainly focused on examining teaching methods and their effects on students’ skills in mathematics. A closer examination of the studies that do focus on teaching for supporting students in developing competencies like reasoning and problem-solving shows that connections between and comparison of students’ solutions, as well as teachers’ ways of asking questions to support students in explaining their solutions clearly and in detail, are important for students’ learning of these competencies.

    A central finding stemming from this review of curriculum programs is the complexity involved in how the programs can support teachers in establishing classroom practices. Curriculum resources and teacher resources, as well as other influencing factors, impact the quality of instruction, and studies have begun to point out how curriculum resources and teacher resources uniquely and jointly impact classroom practices. Multiple research articles have expressed the need for teacher support in implementing curriculum programs, by means of professional development, teacher education and support provided by the curriculum programs themselves. Interesting in this regard is the state of the research field concerning the design of educative curriculum programs, and how teachers make use of such support. Studies have proposed design approaches, regarding both the actual development of educative curriculum programs as well as how to use them in teacher education to support prospective teachers’ development of knowledge. Further, although research has revealed that it is important to prepare for teaching in certain ways, we found very little research that explicitly analyzed how teachers actually prepare for teaching a mathematics lesson.

    Limitations of the project include: (1) the lack of searching in potentially relevant databases, (2) the fact that a relatively small proportion of articles found in the search have been coded, (3) that we have not engaged in deep considerations as to whether and in what ways results from international research are relevant in the Swedish context, and (4) that we therefore have not been able to synthesize the results of the study. In relation to the Swedish context (Hemmi & Ryve, 2014; Boesen et al., 2014), international research (Hattie, 2009; Smith & Stein, 2011), and the current project’s findings, we recommend that Skolforskningsinstitutet focus on two aspects of great importance for developing students’ knowing of mathematics. First, Skolforskningsinstitutet should synthesize research that supports actors, such as teachers and principals, in acting within school practices. In the case of teachers, support is needed to engage them in actively anticipating students’ thinking, using curriculum programs effectively, introducing mathematical content, acting in group work, formatively assessing students’ learning, and orchestrating whole-class mathematical discussions. Secondly, actors within school practices need support not only in initiating and implementing developments but also in institutionalizing such developments. Skolforskningsinstitutet should specify the kind of support needed in order to ensure that material, routines, competences, and organizations become integral and permanent features of Swedish school practice. 

  • 38.
    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 terms2013Inngår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 82, nr 3, s. 497-514Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 39.
    Schindler, Maike
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Hußmann, Stephan
    International Conference on Industrial Engineering and Engineering Management (IEEM), Technische Universität Dortmund, Dortmund, Germany.
    Nilsson, Per
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Bakker, Arthur
    Freudenthal Institute, Utrecht University, Utrecht, Netherlands.
    Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis2017Inngår i: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 29, nr 4, s. 471-492Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these experiences. This article presents results from an empirical study investigating sixth-grade students’ reasoning and inferring from school-based and out-of-school experiences. In particular, it addresses the order relation, which deals with students’ very first encounters with negative numbers. Here, students can reason in different ways, depending on the experiences they draw on. We study how students reason before a lesson series and how their reasoning is influenced through this lesson series where the number line and the context debts-and-assets are predominant. For grasping the reasoning’s inferential and social nature and conducting in-depth analyses of two students’ reasoning, we use an epistemological framework that is based on the philosophical theory of inferentialism. The results illustrate how the students infer their reasoning from out-of-school and from school-based experiences both before and after the lesson series. They reveal interesting phenomena not previously analyzed in the research on the order relation for integers. 

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