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  • 1.
    Andersen, Jørgen Ellegaard
    et al.
    CTQM, Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark.
    Fjelstad, Jens
    Department of Physics, Karlstad University, Karlstad, Sweden.
    On Reducibility of Mapping Class Group Representations: The SU(N) case2010In: Noncommutative structures in mathematics and physics / [ed] Stefaan Caenepeel, Jürgen Fuchs, Simone Gutt, Christophe Schweigert, Alexander Stolin, Freddy Van Oystaeyen, Brussels: Koninklijke vlaamse academie van Belgie voor Wetenschappen en kunsten, 2010, p. 27-45Conference paper (Refereed)
    Abstract [en]

    We review and extend the results of [1] that gives a condition for reducibility of quantum representations of mapping class groups constructed from Reshetikhin-Turaev type topological quantum field theories based on modular categories. This criterion is derived using methods developed to describe rational conformal field theories, making use of Frobenius algebras and their representations in modular categories. Given a modular category C, a rational conformal field theory can be constructed from a Frobenius algebra A in C. We show that if C contains a symmetric special Frobenius algebra A such that the torus partition function Z(A) of the corresponding conformal field theory is non-trivial, implying reducibility of the genus 1 representation of the modular group, then the representation of the genus g mapping class group constructed from C is reducible for every g\geq 1. We also extend the number of examples where we can show reducibility significantly by establishing the existence of algebras with the required properties using methods developed by Fuchs, Runkel and Schweigert. As a result we show that the quantum representations are reducible in the SU(N) case, N>2, for all levels k\in \mathbb{N}. The SU(2) case was treated explicitly in [1], showing reducibility for even levels k\geq 4.

  • 2.
    Andersen, Jørgen Ellegaard
    et al.
    Center for Quantum Geometry of Moduli Spaces, University of Aarhus, Århus, Denmark.
    Fjelstad, Jens
    Department of Physics, Karlstad University, Karlstad, Sweden.
    Reducibility of quantum representations of mapping class groups2010In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 91, no 3, p. 215-239Article in journal (Refereed)
    Abstract [en]

    In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.

  • 3.
    Banaem, Hossein Yousefi
    et al.
    Tehran University of Medical Science, Tehran, Iran.
    Ahmadian, Alireza
    Tehran University of Medical Science, Tehran, Iran.
    Saberi, Hooshangh
    Tehran University of Medical Science, Tehran, Iran.
    Daneshmehr, Alireza
    University of Tehran, Tehran, Iran.
    Khodadad, Davood
    Tehran University of Medical Science, Tehran, Iran.
    Brain tumor modeling: glioma growth and interaction with chemotherapy2011In: International Conference on Graphic and Image Processing (ICGIP) / [ed] Yi Xie & Yanjun Zheng, SPIE - International Society for Optical Engineering, 2011, Vol. 8285, article id 82851MConference paper (Refereed)
    Abstract [en]

    In last decade increasingly mathematical models of tumor growths have been studied, particularly on solid tumors which growth mainly caused by cellular proliferation. In this paper we propose a modified model to simulate the growth of gliomas in different stages. Glioma growth is modeled by a reaction-advection-diffusion. We begin with a model of untreated gliomas and continue with models of polyclonal glioma following chemotherapy. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter. Tumor growth is characterized by a dangerous change in the control mechanisms, which normally maintain a balance between the rate of proliferation and the rate of apoptosis (controlled cell death). Result shows that this model closes to clinical finding and can simulate brain tumor behavior properly.

  • 4.
    Bergwall, Andreas
    Örebro University, School of Science and Technology.
    Conceptualizing reasoning-and-proving opportunities in textbook expositions: Cases from secondary calculus2017In: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017) / [ed] Dooley, T., & Gueudet, G., Dublin, Ireland: European Society for Research in Mathematics Education , 2017, p. 91-98Conference paper (Refereed)
    Abstract [en]

    Several recent textbook studies focus on opportunities to learn reasoning-and-proving. They typically investigate the extent to which justifications are general proofs and what opportunities exist for learning important elements of mathematical reasoning. In this paper, I discuss how a particular analytical framework for this might be refined. Based on an in-depth analysis of certain textbook passages in upper secondary calculus textbooks, I make an account for analytical issues encountered during this process and identify aspects of reasoning-and-proving in textbooks that might be missed unless the framework is refined. Among them there are characterizations of generality, use of different representations, logical and mathematical structure, and ordering of material and student activities. Finally, implications beyond textbook research are discussed.

  • 5.
    Bergwall, Andreas
    Örebro University, School of Science and Technology.
    On a generality framework for proving tasks2015In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer; Nada Vondrova, Prague: Charles University in Prague, Faculty of Education and ERME , 2015, p. 86-92Conference paper (Refereed)
    Abstract [en]

    In this paper I present an analytic framework for generality in textbook proving tasks that involve functions. The framework is discussed in relation to results obtained when analysing tasks in integral calculus. The results show that the frameworks’ categories are easily distinguishable if the functions are explicitly described. The results are also promising regarding the possibility to clarify differences between textbooks. The analysed sections exemplify that there is not necessarily a correlation between the number of general proving tasks and the opportunities for students to engage in reasoning about arbitrary functions. Limitations and possible refinements of the framework are also discussed.

  • 6.
    Bergwall, Andreas
    et al.
    Örebro University, School of Science and Technology.
    Hemmi, Kirsti
    Åbo Akademi University, Åbo, Finland; Uppsala University, Uppsala, Sweden.
    The State of Proof in Finnish and Swedish Mathematics Textbooks: Capturing Differences in Approaches to Upper-Secondary Integral Calculus2017In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 19, no 1, p. 1-18Article in journal (Refereed)
    Abstract [en]

    Students’ difficulties with proof, scholars’ calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related reasoning in integral calculus, a key subject in transitioning from secondary to tertiary education. We analyze expository sections and nearly 2000 students’ exercises in the four most frequently used Finnish and Swedish textbook series. Results indicate that Finnish textbooks offer more opportunities for learning proof than do Swedish textbooks. Proofs are also more visible in Finnish text-books than in Swedish materials, but the tasks in the latter reflect a higher variation in nature of proof-related reasoning. Our results are compared with methodologically similar U.S. studies. Consequences for learning and transition to university mathematics, as well as directions for future research, are discussed.

  • 7.
    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 multimodality2012In: 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, 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. 

  • 8.
    Fjelstad, Jens
    et al.
    Department of Mathematics, Uppsala University, Uppsala.
    Fuchs, Jürgen
    Teoretisk fysik, Karlstads Universitet, Karlstad.
    Mapping class group representations from Drinfeld doubles of finite groupsManuscript (preprint) (Other academic)
    Abstract [en]

    We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.

  • 9.
    Gulliksson, Mårten
    et al.
    Örebro University, School of Science and Technology.
    Mazur, Stepan
    Örebro University, Örebro University School of Business.
    An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection2019In: Computational Economics, ISSN 0927-7099, , p. 21Article in journal (Refereed)
    Abstract [en]

    Covariance matrix of the asset returns plays an important role in the portfolioselection. A number of papers is focused on the case when the covariance matrixis positive definite. In this paper, we consider portfolio selection with a singu-lar covariance matrix. We describe an iterative method based on a second orderdamped dynamical systems that solves the linear rank-deficient problem approxi-mately. Since the solution is not unique, we suggest one numerical solution that canbe chosen from the iterates that balances the size of portfolio and the risk. The nu-merical study confirms that the method has good convergence properties and givesa solution as good as or better than the constrained least norm Moore-Penrose solu-tion. Finally, we complement our result with an empirical study where we analyzea portfolio with actual returns listed in S&P 500 index.

  • 10.
    Hagström, Malin
    et al.
    Örebro University, School of Science and Technology.
    Wetterstrand, Frida
    Örebro University, School of Science and Technology.
    EPA blir STAR: Problemlösning i matematik2018In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 1, p. 37-40Article in journal (Other (popular science, discussion, etc.))
  • 11.
    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-environment2006In: European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, Universitat Ramon Llull , 2006, p. 601-610Conference paper (Refereed)
  • 12.
    Nilsson, Per
    Växjö University, School of Mathematics and Systems Engineering, Växjö, Sweden.
    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.

  • 13.
    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.

  • 14.
    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 (ed. 1)Book (Other academic)
  • 15.
    Nilsson, Per
    Växjö universitet, Matematiska och systemtekniska institutionen, Växjö, Sweden.
    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.

  • 16.
    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 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.

  • 17.
    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 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.
    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 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.
    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.

  • 20.
    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 setting2010In: Proceedings of CERME 6, Lyon: Institut National de Recherche Pedagogique , 2010, 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.

  • 21.
    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 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, Bela Horizonte, Brazíl: The International Group for the Psychology of Mathematics Education (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.

  • 22.
    Nyroos, Mikaela
    et al.
    Umeå University, Umeå, Sweden.
    Bagger, Anette
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education, Umeå, Sweden.
    Silfver, Eva
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education, Umeå, Sweden.
    Sjöberg, Gunnar
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education, Umeå, Sweden.
    Exploring the presence of test anxiety and its relation to mathematical achievement in a sample of grade 32012In: Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274, p. 151-160Article in journal (Refereed)
    Abstract [en]

    The present study aims at exploring if a sample of Swedish grade 3 pupils reported any test anxiety and whether there were any relations to performance in different mathematical areas. Overall, test anxiety explained 20% of the variance for the total mathematical score, with the subscale “thoughts” as the significant predictor. The model of test anxiety also explained Number understanding, Mass and Time, Patterns, and Mathematical problems; however Mental arithmetic and Written arithmetic algorithms were not significantly explained by the model. Test anxiety seems not to be a major problem in this sample; still, significant negative correlations were found, which likely might influence the pupils in some aspects.

  • 23.
    Pettersson, Angelica
    Örebro University, School of Science and Technology.
    Något om regressionsanalys2009Independent thesis Basic level (degree of Bachelor), 15 credits / 22,5 HE creditsStudent thesis
    Abstract [sv]

    En gren inom statistikteorin är den så kallade Regressionsanalysen där man studerar hur data från exempelvis ett stickprov kan anpassas till en graf. Skrivandet av denna uppsats har haft som syfte att studera några av de metoder som finns att tillgå vid bestämning av de ingående parametrarna i de enklare fallen av regression. Dessutom ges i de avslutande kapitlen exempel på den del inom regressionsanalysen som kallas Styckvis Linjär Regression eller Piecewise Linear Regression.

  • 24.
    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 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. 

  • 25.
    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.

  • 26.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Hussman, Stephan
    Technical university Dortmund, Dortmund, Germany.
    Ein Kontext für negative Zahlen ‒ auch für die Multiplikation: English: A context for negative numbers ‒ also for multiplication2014In: Mathematik lehren: Die Zeitschrift für den Unterricht in allen Schulstufen, ISSN 0175-2235, no 183, p. 28-32Article in journal (Other academic)
    Abstract [de]

    Der Beitrag stellt eine Konzept zur Einführung der negativen Zahlen sowie eine entsprechende Lernumgebung vor, das im Rahmen eines Unterrichtsprojekts erarbeitet wurde. Dazu wurde der tragfähige Kontext “Guthaben und Schulden" weiterentwickelt. Dieser kann beim Aufbau eines inhaltlichen Verstehens, das die Bedeutung von “Minus mal Minus" nicht auf eine Regel reduziert, hilfreich sein.          

  • 27.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Hussmann, Stephan
    IEEM, Technische Universität Dortmund, Dortmund, Germany.
    About students’ individual concepts of negative integers ‒ in terms of the order relation2013In: Proceedings of the eighth congress of the European Society of Research in Mathematics Education: Cerme 8 / [ed] Behiye Ubuz, Çiğdem Haser, Maria Alessandra Mariotti, Ankara: Middle East Technical University , 2013, p. 373-382Conference paper (Refereed)
    Abstract [en]

    We investigated sixth graders’ individual concepts of negative integers right before they were introduced to the “world" of the negatives. In order to investigate students’ first ideas of negative numbers, we initially investigated their ideas concerning the order relation of integers. With a qualitative data analysis utilizing a theoretical lens concerning individual concept formation, we gained insight into the students’ individual procedures and conceptions as well as into how the procedures are linked to the students’ previous knowledge.

  • 28.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Chadalavada, Ravi
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Creativity in the eye of the student: Refining investigations of mathematical creativity using eye-tracking goggles2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (PME) / [ed] C. Csíkos, A. Rausch, & J. Szitányi, 2016Conference paper (Refereed)
    Abstract [en]

    Mathematical creativity is increasingly important for improved innovation and problem-solving. In this paper, we address the question of how to best investigate mathematical creativity and critically discuss dichotomous creativity scoring schemes. In order to gain deeper insights into creative problem-solving processes, we suggest the use of mobile, unobtrusive eye-trackers for evaluating students’ creativity in the context of Multiple Solution Tasks (MSTs). We present first results with inexpensive eye-tracking goggles that reveal the added value of evaluating students’ eye movements when investigating mathematical creativity—compared to an analysis of written/drawn solutions as well as compared to an analysis of simple videos.

  • 29.
    Seidouvy, Abdel
    Örebro University, School of Science and Technology.
    Exploring student collaboration during Data Generation in the Statistics Classroom: An Inferentialist Perspective2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This dissertation explores student collaboration during data generation in statistics. The first aim is to put the semantic theory of inferentialism to work and develop a theoretical lens for exploring student collaboration during data generation. The second is to use the previously developed inferentialist lens regarding collaboration to better understand data generation processes in the statistics classroom. Two studies were conducted in Swedish 5th and 7th grade classes. The first involved 7th-grade students collaboratively engaged in experimentation with paper helicopters and their flight durations. The second study involved 5th graders experimenting with paper frogs and their jump lengths. The analyses reveal that inferentialism is a meaningful perspective for exploring student collaboration. One salient theoretical contribution of this thesis is that the inferentialist concept of norms helps avoid the dichotomy between social and individual facets of collaboration and learning that have plagued research on collaboration. However, by using the inferentialism lens, the social and individual can be regarded in their intertwined and dynamic natures. The thesis also illustrates how the formulation of tasks, social conditions, and norms mutually condition students’ learning opportunities. It is also demonstrated that data generation processes can also involve conceptual learning opportunities. The results offer ideas concerning which classroom conditions and manners of formulating tasks may contribute to such conceptual learning opportunities

    List of papers
    1. An inferentialist account of students’ collaboration in mathematics education
    Open this publication in new window or tab >>An inferentialist account of students’ collaboration in mathematics education
    2019 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050XArticle in journal (Refereed) Epub ahead of print
    Abstract [en]

    Collaboration is an increasingly popular topic in mathematics education due to its potential to foster students’learning. The purpose of this article is to draw attention to the semantic philosophical theory of inferentialism and its value for investigating students’ collaboration. We suggest that Brandom’s inferentialism can serve as a valuable theoretical resource to overcome certain issues of existing theoretical view-points on student collaboration. In particular, we argue that inferentialism may help to understand the individual and social nature of collaboration as intertwined. We illustrate our inferentialist approach using data from two scenes taken from video-recorded group work sessions from a fifth and seventh grade primary school class in Sweden. The topic in both classes was data generation in statistics.

    Place, publisher, year, edition, pages
    Springer, 2019
    Keywords
    Collaboration, Data generation, Inferentialism, Norms, Philosophy
    National Category
    Mathematics Didactics
    Identifiers
    urn:nbn:se:oru:diva-76042 (URN)10.1007/s13394-019-00267-0 (DOI)
    Funder
    Swedish Research Council, 2012-04811
    Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
    2. Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology
    Open this publication in new window or tab >>Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology
    2018 (English)In: Topics and Trends in Current Statistics Education Research / [ed] Gail Burrill, Dani Ben-Zvi, Springer, 2018, p. 153-171Chapter in book (Refereed)
    Abstract [en]

    Informal statistical inference and informal inferential reasoning (IIR) are increasingly gaining significance in statistics education research. What has not sufficiently been dealt with in previous research is the social nature of students’ informal inferences. This chapter presents results from a study investigating seventh grade students’ IIR in an experiment with paper helicopters. It focuses on students’ reasoning on the best rotor blade length, addressing statistical correlation. We study how students draw inferences when working in a group; and how their inferences emerge socially in their IIR. For grasping the reasoning’s social nature and its normativity, we use inferentialism as background theory. The results illustrate how students’ informal inferences are socially negotiated in the group, how students’ perceived norms influence IIR, and what roles statistical concepts play in students’ IIR.

    Place, publisher, year, edition, pages
    Springer, 2018
    Series
    ICME-13 Monographs, ISSN 2520-8322, E-ISSN 2520-8330
    Keywords
    Generalization from data, Inferentialism, Informal inferential reasoning (IIR), Informal statistical inference (ISI), Informal statistical reasoning, Norms, Social
    National Category
    Mathematics Didactics
    Identifiers
    urn:nbn:se:oru:diva-76043 (URN)10.1007/978-3-030-03472-6_7 (DOI)978-3-030-03471-9 (ISBN)978-3-030-03472-6 (ISBN)
    Funder
    Swedish Research Council, 2012-04811
    Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
    3. Designing for responsibility and authority in experiment based instruction in mathematics: The case of reasoning with uncertainty
    Open this publication in new window or tab >>Designing for responsibility and authority in experiment based instruction in mathematics: The case of reasoning with uncertainty
    2017 (English)In: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10) / [ed] Dooley, T.; Gueudet, G., Dublin, Ireland: Institute of Education, Dublin City University, Ireland , 2017, p. 3740-3747Conference paper, Published paper (Refereed)
    Abstract [en]

    This study examines principles of task design concerning the concept of uncertainty in the area of statistics. A purpose is to promote and support students reasoning competency involving the aspects authority and responsibility. By using inferential role semantics as a background theory, we examine students' reasoning by means of how they show authority and responsibility for statements in the reasoning process. Statistical tasks where students generate and analyze their own data formed the basis for this pilot study conducted with seventh grade students in Sweden. The students were able to reflect on how their actions and consequences of their actions influence their reasoning with uncertainty. The study describes the findings, and presents principles to inform the design of innovative learning environments that promote authority and responsibility in reasoning in the domain of uncertainty.

    Place, publisher, year, edition, pages
    Dublin, Ireland: Institute of Education, Dublin City University, Ireland, 2017
    Keywords
    Design principles, uncertainty, responsibility, authority
    National Category
    Mathematics Didactics
    Identifiers
    urn:nbn:se:oru:diva-76044 (URN)000467053304094 ()978-1-873769-73-7 (ISBN)
    Conference
    10th Congress of the European-Society-for-Research-in-Mathematics-Education (CERME10), Dublin, Ireland, February 1-5, 2017
    Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
    4. Data generation in statistics – both procedural and conceptual: An inferentialist analysis
    Open this publication in new window or tab >>Data generation in statistics – both procedural and conceptual: An inferentialist analysis
    2018 (English)In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11 / [ed] J. Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren, & O. Olande, Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, p. 191-200Conference paper, Published paper (Refereed)
    Abstract [en]

    Data generation in statistics education is often conducted by the students them-selves; however, the question of what learning opportunities the data generation process offers has only been studied to a small extent. This paper investigates to what extent data generation is an observational and procedural vs. a conceptual activity. We inquire into this question based on an empirical study where eleven year old students measured the jump lengths of paper frogs. Our analysis draws on stu-dents’ discussions in group work, and it uses inferentialism as a background theory. Our results indicate that students’ discussions are conceptual to a certain extent and provide various learning opportunities for the students.

    Place, publisher, year, edition, pages
    Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018
    Series
    Skrifter från Svensk Förening för MatematikDidaktisk Forskning, ISSN 1651-3274 ; 13
    National Category
    Mathematics Didactics
    Identifiers
    urn:nbn:se:oru:diva-76045 (URN)978-91-984024-2-1 (ISBN)
    Conference
    The eleventh research seminar of the Swedish Society for Research in Mathematics Education (MADIF11), Karlstad, Sweden, January 23–24, 2018
    Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-20Bibliographically approved
    5. Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
    Open this publication in new window or tab >>Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
    2019 (English)In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 24, no 2, p. 25-47Article in journal (Refereed) Published
    Abstract [en]

    Students’ peer collaboration efforts in mathematics and statistics is a topic that has increasingly gained attention in research. In any collaboration, authority relations play a role for how meaning is constituted: Whenever things are discussed and decision sare made, authority is involved in a sense that some arguments or persons may be more convincing and powerful than others. In this article, we investigate how authority changes dynamically in type and in distribution as groups of fifth grade students collaborate in data generation processes. We identify and categorize authority using an epistemological framework, which is based on the philosophical theory of inferentialism. The results show that the three different types of authority described in inferentialism are all identifiable in students’ collaborative work. We also find and categorize further types of authority connected to the statistics group work, some of which are hardly addressed in previous research.

    Place, publisher, year, edition, pages
    Göteborg, Sweden: NOMAD, 2019
    National Category
    Mathematics Didactics
    Identifiers
    urn:nbn:se:oru:diva-76046 (URN)
    Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-05Bibliographically approved
  • 30.
    Sjöberg, Gunnar
    et al.
    Umeå University, Department of science and mathematics education, Umeå, Sweden.
    Silfver, Eva
    Umeå University, Department of science and mathematics education, Umeå, Sweden.
    Bagger, Anette
    Umeå University, Department of science and mathematics education, Umeå, Sweden.
    Disciplined by tests2015In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 20, no 1, p. 55-75Article in journal (Refereed)
    Abstract [en]

    This article reports on a Swedish research project on the reintroduction of national tests in mathematics for nine- to ten-year-old pupils. Data were collected over a period of three years (2010-2012) by video recording test situations in different classrooms and by conducting video-stimulated recall interviews with children. The aim is to explore and analyse the testing situation and how it creates different positions for children. We conclude that discourses of testing, caring and competition, sometimes strengthening and sometimes shadowing each other and thereby, produce knowledge in children about success and failure in mathematics, positioning children as ‘winners’ or ‘losers’. The tests are interpreted as a technology – a form of disciplinary power that functions at the level of the body (Foucault, 1980).

  • 31.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Hernandez Bennetts, Victor
    Örebro University, School of Science and Technology.
    Schaffernicht, Erik
    Örebro University, School of Science and Technology.
    Reconstructing gas distribution maps via an adaptive sparse regularization algorithm2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 7, p. 1186-1204Article in journal (Refereed)
    Abstract [en]

    In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.

  • 32.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Lukyanenko, Dmitry V.
    Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russian Federation.
    Yagola, Anatoly G.
    Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russian Federation.
    An optimal regularization method for convolution equations on the sourcewise represented set2015In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 23, no 5, p. 465-475Article in journal (Refereed)
    Abstract [en]

    In this article, we consider an inverse problem for the integral equation of the convolution typein a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a prioriinformation (sourcewise representation) based on optimal recovery theory we propose a new method. Theregularization and optimization properties of this method are proved. An optimal minimal a priori error ofthe problem is found. Moreover, a so-called optimal regularized approximate solution and its correspondingerror estimation are considered. Eciency and applicability of this method are demonstrated in a numericalexample of the image deblurring problem with noisy data.

  • 33.
    Ögren, Magnus
    et al.
    Örebro University, School of Science and Technology. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark; Department of Chemistry, Nano-Science Center, University of Copenhagen, Copenhagen, Denmark.
    Nyström, Marcus
    Lund University Humanities Laboratory, Lund, Sweden.
    Jarodzka, Halszka
    Open University, Heerlen, The Netherlands.
    There’s more to the multimedia effect than meets the eye: is seeing pictures believing?2017In: Instructional science, ISSN 0020-4277, E-ISSN 1573-1952, Vol. 45, no 2, p. 263-287Article in journal (Refereed)
    Abstract [en]

    Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.

1 - 33 of 33
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