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  • 1. Adolfsson, Sandra
    Matematikverkstad: hur kan lärare och elever arbeta där?2010Student paper other, 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The starting point of this work has been to get knowledge about teachers working in a mathematical workshop with the students. I also wanted to investigate what students think about math, both within the workshop and in traditional teaching.

    To achieve this I chose to interview a teacher in charge within the framework of a mathematical workshop, and six students in the 5th grade. I also did a lesson observation with the purpose to see how well the teacher’s tutoring agrees with the results of the interview.

    In this study I have discovered that the lessons in the mathematical workshop are planned after what the students are working with in the textbook. The teacher opens the lessons with the whole class and then splits it up in groups. In the interview the respondent conveys the importance of discussions among the students where they can explain their thoughts, especially for the weaker students that, thanks to the discussions are able to show their knowledge more. This is something I did not see during my lesson observation, however. The students also seemed to miss this when I spoke to them in the interview. They describe that they cannot see the connection between what they learn in the workshop and the textbook.

  • 2.
    Beilina, Larissa
    et al.
    Chalmers University, Gothenburg University.
    Shestopalov, YuriKarlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Inverse problems and large-scale computations2013Conference proceedings (editor) (Refereed)
  • 3.
    Bernhoff, Niclas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations2017In: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, Vol. 10, no 4, p. 925-955Article in journal (Refereed)
    Abstract [en]

    We consider some extensions of the classical discrete Boltzmann equation to the cases of multicomponent mixtures, polyatomic molecules (with a finite number of different internal energies), and chemical reactions, but also general discrete quantum kinetic Boltzmann-like equations; discrete versions of the Nordheim-Boltzmann (or Uehling-Uhlenbeck) equation for bosons and fermions and a kinetic equation for excitations in a Bose gas interacting witha Bose-Einstein condensate. In each case we have an H-theorem and so for the planar stationary half-space problem, we have convergence to an equilibrium distribution at infinity (or at least a manifold of equilibrium distributions). In particular, we consider the nonlinear half-space problem of condensation and evaporation for these discrete Boltzmann-like equations. We assume that the flow tends to a stationary point at infinity and that the outgoing flow is known at the wall, maybe also partly linearly depending on the incoming flow. We find that the systems we obtain are of similar structures as for the classical discrete Boltzmann equation (for single species), and that previously obtained results for the discrete Boltzmann equation can be applied after being generalized. Then the number of conditions on the assigned data at the wall needed for existence of a unique solution is found. The number of parameters to be specified in the boundary conditions depends on if we have subsonic or supersonic condensation or evaporation. All our results are valid for any finite number of velocities.

  • 4.
    Bernhoff, Niclas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 159, no 2, p. 358-379Article in journal (Refereed)
    Abstract [en]

    We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for a general discrete model of a quantum kinetic equation for excitations in a Bose gas. In the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations. These systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete Boltzmann equation. Then a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete kinetic equation can be made. The number of additional conditions that need to be imposed for well-posedness is given by some characteristic numbers. These characteristic numbers are calculated for discrete models axially symmetric with respect to the x-axis. When the characteristic numbers change is found in the discrete as well as the continuous case. As an illustration explicit solutions are found for a small-sized model.

  • 5.
    Bernhoff, Niclas
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants2016In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 165, no 2, p. 434-453Article in journal (Refereed)
    Abstract [en]

    An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a well-known fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. For binary mixtures also the concept of supernormal DVMs was introduced, meaning that in addition to the DVM being normal, the restriction of the DVM to any single species also is normal. Here we introduce generalizations of this concept to DVMs for multicomponent mixtures. We also present some general algorithms for constructing such models and give some concrete examples of such constructions. One of our main results is that for any given number of species, and any given rational mass ratios we can construct a supernormal DVM. The DVMs are constructed in such a way that for half-space problems, as the Milne and Kramers problems, but also nonlinear ones, we obtain similar structures as for the classical discrete Boltzmann equation for one species, and therefore we can apply obtained results for the classical Boltzmann equation.

  • 6.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Potapenko, Irina
    Russia.
    Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 246, p. 123-144Article in journal (Refereed)
    Abstract [en]

    A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau-Fokker-Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation process very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O(root epsilon), where epsilon is a parameter of approximation being equivalent to the time step Delta t in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu. (C) 2013 Elsevier Inc. All rights reserved.

  • 7.
    Bouhuis, Krijn
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Differentiation in teaching mathematics: An observational study of eight primary school teachers in Sweden2013Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    According to the Swedish curriculum for the primary school, the teachers have to meet the different conditions and demands of all the pupils. A way of meeting the different conditions and demands of all the pupils is differentiation. The aim of this study was to contribute to the discussion about differentiation in the classroom on the subject of mathematics in Swedish primary school.

    Differentiation means that the teacher adapts his teaching to the different learning styles, interests and levels of the pupils. The main question of this exam paper is: How do teachers in Swedish primary school differentiate during their mathematics lessons? In order to get an answer to this question eight teachers were observed during their mathematics lessons. An observation instrument, newly developed by the University of Utrecht, was used for this.

    The main parts of the observed lessons were whole class instruction and working independently, alone or in groups. The teachers’ instructions varied from concrete acts, the use of pictures and schedules to formal tasks. The teachers used the different principles of how a child is learning mathematics in their instructions as well. For example: understanding the concept and development of strategies. Another way of differentiation is to give the pupils freedom to choose their own working style while working individually. This kind of differentiation was not observed often during the eight lessons.

    This study shows that teachers in Swedish primary school are differentiating. However the differentiation can be improved and implemented more often. Furthermore it is unclear if the teachers differentiate consciously, which would mean that their level of consciousness could probably be increased.

  • 8.
    Cano, Cédric
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Integrering av ett främmande språk i matematikundervisningen2009Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Content and Language Integrated Learning (CLIL) is a relatively new method for learning a foreign language. CLIL programs are growing in popularity and more and more schools are adopting it all around the world. There is still no special education for the teachers working with CLIL, though research suggests it may be an effective method for achieving good results.To get a realistic view of the work of a CLIL teacher, I have interviewed four different mathematic teachers who work at CLIL international schools in Spain with English as the foreign language. I have compared their methods and experiences with the main ideas of current research in this particular field.The survey shows that the teachers’ views about how CLIL is to be used do not completely correspond to that of the research. My conclusion is therefore that training in CLIL is needed.

  • 9.
    Dahlin, Malin
    Karlstad University.
    Digitala verktyg i matematik på lågstadiet2017Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
  • 10.
    Derevyanchuk, E.
    et al.
    Russia .
    Smirnov, Yurij
    Russia.
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Permittivity determination of thin multi-sectional diaphragms in a rectangular waveguide2013In: Proceedings of the International Conference Days on Diffraction 2013, 2013, p. 32-35, article id 6712799Conference paper (Refereed)
    Abstract [en]

    In this paper we consider the inverse problem of the permittivity determination of thin multisectional diaphragm in a rectangular waveguide. We perform a detailed analysis for one-, two- and three-sectional thin diaphragms. Numerical results are presented.

  • 11.
    Erlandsson, Markus
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Införandet av programmering i grundskolan: En studie om motiven bakom införandet av programmering för elever i lägre åldrar på statlig och lokal nivå2017Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
  • 12.
    Fernström, Mikael
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Utvecklas modelleringsförmågan nu?: Elevers potentiella utveckling i att modellera inom en specifik modelleringsmodul anpassad för kursen Matematik 5 på gymnasiet.2019Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Mathematical modelling is one of the competences students will have the possibility to develop in upper secondary school. However, it is not entirely obvious among teachers what modelling really means and it is questionable if the learning activities that are being used in relation to modelling education today really are effective. This study focuses on the students’ potential development within a series of lessons, a so-called modelling module, adapted for the course Mathematics 5 in upper secondary school. The students’ potential development is studied based on their involvement in the various sub-processes that are considered to be the modelling process as a hole. The result indicates that the modelling module involves students in all of these sub-processes. At the same time, the results show this is not self-evident and some of the subprocesses seem to be harder to involve the students in than others.

  • 13.
    Fredriksson, Anders
    Karlstad University, Faculty of Technology and Science.
    Tron på praktisk och laborativ matematik i undervisningen -relevant eller överdriven?: Landsomfattande jämförelse av 1000 elevers betyg2008Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Som student på lärarutbildningen fick jag bland annat lära mig om olika inlärningsstilar och om vikten av varierade arbetsformer i undervisningen. Något förenklat menar vissa forskare att man kan skilja den teoretiskt lagde eleven från den mer praktiskt lagde, vilket betyder att en mix av teoretisk och praktisk/laborativ undervisning skapar bra förutsättningar för att så många som möjligt ska kunna ta del av den. Inte minst viktigt är detta i ämnet matematik och budskapet från Skolverket är det samma vad gäller detta ämne.

    Denna uppsats handlar om matematikundervisningen på högstadiet, det vill säga grundskolans senare år, åk 7-9. Den är kopplad till de faktorer som styr vårt lärande och om elevernas förståelse för matematik gagnas av praktiska och laborativa övningar eller inte.

     

    Då det i diskussioner om dagens matematikundervisning ofta framkommer att användandet av den praktiska/laborativa matematikundervisningen på högstadiet borde vara större, har jag i denna studie valt att undersöka om dess inverkan verkligen är så viktig som görs gällande.

    Är tron på praktisk och laborativ matematikundervisning relevant eller överdriven?

    Med hjälp av litteratur, samtal med lärare och pedagoger och en betygsjämförelse har jag försökt att hitta fakta som belyser den praktiska/laborativa undervisningens betydelse för studieresultatet i matematik. I studien har 1038 elever med betyg G i matematik deltagit och deras betyg i matematik, idrott och slöjd har jämförts och analyserats.

    Resultatet visar att hälften av alla dessa elever uppvisar ett bättre betyg i idrott såväl som i slöjd. Detta resultat kan ses som en indikation på att elever med betyg G i matematik är mer praktiskt lagda och främjas av en praktiskt orienterad undervisning.

  • 14.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Schaumann, Gregor
    Max-Planck-Institut für Mathematik, Bonn.
    Schweigert, Christoph
    Hamburg University.
    A trace for bimodule categories2017In: Applied Categorical Structures, ISSN 0927-2852, E-ISSN 1572-9095, Vol. 25, no 2, p. 227-268Article in journal (Refereed)
    Abstract [en]

    We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued tracefor 1-morphisms in the tricategory of finite tensor categories. It is defined by a universalproperty that is a categorification of Hochschild homology of bimodules over an algebra.We present several equivalent realizations of this 2-functor and show that it has a coherent cyclic invariance.Our results have applications to categories associated to circles in three-dimensional topological field theories with defects. This is made explicit for the subclass of Dijkgraaf-Wittentopological field theories.

  • 15.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Schweigert, Christoph
    Hamburg University.
    Stigner, Carl
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Higher genus mapping class group invariants from factorizable Hopf algebras2014In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 250, p. 285-319Article in journal (Refereed)
    Abstract [en]

    Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the category of bimodules over a finite-dimensional factorizable ribbon Hopf algebra H. For any such Hopf algebra we find an invariant of Map_{g,n} for all values of g and n. More generally, we obtain such invariants for any pair (H,omega), where omega is a ribbon automorphism of H. Our results are motivated by the quest to understand correlation functions of bulk fields in two-dimensional conformal field theories with chiral algebras that are not necessarily semisimple, so-called logarithmic conformal field theories.

  • 16. Granli, Karin
    Problemlösning: - att välja strategi2010Independent thesis Basic level (university diploma), 15 credits / 22,5 HE creditsStudent thesis
    Abstract [en]

    Abstract

    By finding out the pupils' choice of strategies for problem solving, we as teachers, can get a better understanding of their way of thinking, and thus also help them develop in their learning of mathematics. In a classroom environment where several different strategies could be found, the pupils' learning is facilitated as they, with the help of classmates, find positive and negative attributes of different kinds of strategies. The pupils are, in other words, each other's resources, rather than competitors. The main point is that the classroom environment, as well as the role of the teacher in the classroom, are both key elements for good mathematics learning.

    In order to increase the understanding of the pupils' choice of learning strategies, a survey was performed based on two school classes, one third grade and one six grade class at the same school. Both classes received the same mathematical problem to work with, and the strategies observed were analyzed and compared. The results show that the pupils' choice of strategies in the two grades did not differ significantly.

  • 17.
    Hansson, Maria
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013).
    Verklighetsanknuten matematik: En intervjustudien med lärare2015Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of this study was to identify which thought's teachers had on the curriculum and its term to connect mathematics with reality, and how to combine this with concept of mathematics. The results presented in this report are based on interviews with seven teachers.

    The results showed that mathematics connected to reality can be interpreted from two basic principles. 1. To adapt the teaching to the pupils’ everyday life and by that facilitate learning here and now. 2. To prepare the pupils for their future so they feel secure and confidence in using mathematics. It was also based on these two approaches that the teachers' view of how the teaching of mathematics connected to reality became visible. For those who had the con-venience of that the students should learn here and now, was working with everyday math and to experiment with practical material current. The long-term approach, learning for life, as-sumed to work with problem solving in which interaction, discussion and argument were im-portant parts. Some of the teachers, who thought that facilitate learning here and now was how to connect mathematics to reality also thought about teaching, unconsciously or con-sciously, as learning for life.

  • 18.
    Hedberg, Stefan
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Reed-Muller kod av första ordningen2006Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    En säker informationskanal med hög överföringskvalitet krävs i dessa dagar när informationsöverföringen ökar för varje år som går. Det finns olika sätt att skapa detta. Antingen genom att se till att överföringsmediet är av mycket hög kvalitet eller att skapa en skyddsmekanism som gör att de överföringsfel som kan uppstå kan detekteras och även korrigeras om man önskar detta. Denna uppsats handlar om detta, att kunna detektera och korrigera fel. Denna gren inom matematiken kallas kodningsteori.

    Uppsatsen presenterar grunden för kodningsteorin, för att sedan presentera några vanligt förekommande kodningsalgoritmer, Hamming koder, BCH koder, Reed-Solomon. Jag går in på djupet av en av de absolut äldsta kodningsalgoritmerna, en kod som presenterades 1954 av David E. Muller, något senare presenterade en annan föregångare inom kodningsteori, Irving S. Reed, en avkodningsalgoritm för Mullers kod. Denna kod blev känd under namnet Reed-Muller kod.

    Jag presenterar teorin bakom Reed-Muller kod och hur ett Reed-Muller kodord skapas med hjälp av teorin. Jag visar också hur man avkodar Reed-Muller kod med hjälp av olika algoritmer där Irving S. Reeds algoritm står i centrum. För att testa kodning och avkodning i simulerad verklighet används datorprogrammet Matlab. Slutligen presenteras hur kodnings- och avkodningsalgoritmer kan skapas med hjälp av grindnät.

  • 19.
    Johansson, Anton
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Bi-directional flow in the Social Force Model2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    We use the social force model to study the behaviour of two crowds of pedestrians in a bi-directional flow. There are two main goals of the project. The first goal is to study the effects of perception anisotropy on lane formation of the two crowds. The perception anisotropy models the fact that people actually do not perceive their surroundings equally well in all directions, i.e they have a field of vision. The second goal is to develop pedestrian viscosity indices to characterize the motion of the crowds. Our concepts of viscosity indices estimate how fluid the motion of the crowds are. We develop two viscosity indices. A lane viscosity index which gives information of the flow on large timescales, and a space-dependent viscosity index which can pinpoint where in space the motion is less fluid. Our results indicate that there is a small correlation between the perception anisotropy and the lane formation of the two crowds. The two viscosity indices work as intended but more refinement is needed to cope with simultaneous space-time changes.

  • 20.
    Jonsson, Daniel
    Karlstad University, Faculty of Technology and Science.
    Att lära in matematik utomhus: Fördelar och nackdelar2009Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Children are able to learn mathematics in many different ways. To study and learn mathematics out of doors are not so common in today's nine-year compulsory school, but can work as a perfect complement to the usual teaching methods. The purpose of this essay is to make researches into advantages and disadvantages with outdoor mathematics. The conclusions of this essay are based on results from six structured interviews with teachers at a school in the west of Sweden, as well as literature and research. All of the teachers that have been interviewed in this essay, have experience of working with mathematics out of doors. Outdoor mathematics helps to put mathematics in a concrete form. The outdoor environment gives children a good chance to use all of their senses, which can confirm old and new knowledge, at the same time as they get the opportunity to use their whole bodies. Disadvantages with outdoor mathematics are often related to shortage of staff and increased planning from the teacher's side. In the end, the attitudes of the teacher are the major obstacle when it comes to outdoor mathematics.

  • 21.
    Jonsson, Johan
    Karlstad University, Faculty of Technology and Science.
    Ändliga grupper2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    Uppsatsen börjar med definitionen av en grupp och fortsätter med grundläggande begrepp och egenskaper hos grupper såsom undergrupper, homomorfismer, isomorfismer, normala undergrupper, faktorgrupper och permutationsgrupper. Sedan behandlas konjugerade undergrupper, konjugatklasser och klassekvationen med vars hjälp det visas att en grupp med ordning $p^{2}$ är abelsk. Vidare behandlas direkta och semidirekta produkter av grupper. Det konstateras att omvändningen till Lagranges sats i allmänhet inte gäller men att Sylows satser finns istället. Med hjälp av den tidigare teorin visas sedan att de enda enkla grupperna med ordning mellan 1 och 60 är av primtalsordning. Det visas också vilka olika grupper som finns med ordning upp till och med 15. Uppsatsen avslutas med en introduktion av datorprogrammet GAP.

  • 22.
    Liljekvist, Sara
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Svenska elevers sjunkande matematikkunskaper: möjliga orsaker och framtida insatser2013Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    National and international studies, such as PISA and TIMSS, which are part of the national evaluation system, are carried out continuosly. Skolverket, in collaboration with researchers, are responsible for the implementation, evaluation, and analysis of the studies. National results show an increasing percentage of pupils who do not reach the goals in mathematics. The last completed international studies PISA 2009 and TIMSS 2007 show an impaired trend of knowledge, in international comparison. Moreover, studies also show that the differences between schools and also within the same school in Sweden have increased. In summary, the analysis of the studies shows that the Swedish students' math skills have been declining over time. The purpose of this report is to examine possible causes, essential factors that are affecting and future actions in order to achieve better results. Completed national and international studies and analysis show a range of factors that are affecting Swedish students´ declining mathematic skills. However, this report clarifies the big complexity that is revealed when results are being analyzed. This is due to a multitude of factors of influence of underlying causes. Nevertheless, results and analysis show that teachers’ skills are a strong factor which affects and influences the progression and accumulation of knowledge.

  • 23.
    Liljekvist, Yvonne
    et al.
    Uppsala University, Uppsala, Sweden.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Olin-Scheller, Christina
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Department of Educational Studies (from 2013).
    Professional Learning Communities in a Web 2.0 World: Rethinking the Conditions for Professional Development2017In: Teacher Empowerment Toward Professional Development and Practices: Perspectives Across Borders / [ed] Ismail Hussein Amzat, Nena P. Valdez, Singapore, Singapore: Springer, 2017, p. 269-280Chapter in book (Refereed)
    Abstract [en]

    The new technologies, in particular social media in Web 2.0, enable rapid change in people’s behaviour, which needs to be considered in research on teacher empowerment and teacher professional development and growth. In this chapter we discuss how teachers in an informal, yet structured, way use social media to expand their professional learning communities beyond the local school context in Sweden. This is an example of how a new behaviour is emerging among teachers that changes the opportunities and the frames for professional development and growth. Through teachers’ engagement in social media, such as Facebook, extended professional learning communities arise and teachers’ professional development and growth become evident. Global levels influence local levels: teachers from different schools engage in structured discussions related to everyday practice, such as issues of learning goals in pre-school or topics related to a specific course in upper secondary school. The teachers’ arena for professional development and growth has changed, which means that the context of teacher empowerment is rapidly changing too. Consequently, the chapter includes theoretical reflections on professional learning communities in a Web 2.0 world and how this phenomenon may affect our approach to enhancing teachers’ professional development.

  • 24.
    Lloyd, Emma
    Karlstad University.
    Förstelärare i matematik: En kvalitativ intervjustudie om hur förstelärarens arbete i skolämnet matematik kan se ut2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The Swedish national agency of education has written reports about what the first-teacher do in general. The purpose with this study is to exemplify what the first-teacher in mathematics do and what it possibly can result in, both for colleagues and pupils. By making qualitative interviews with seven first-teachers in mathematics the study illustrates how they work and what outcome they experience. The results show that the first-teacher assignments differs, for example, one teacher does nothing above her regular teaching in her assignment more than having a title. Another first-teacher actively work with screening to assess pupils’ knowledge in mathematics, enables teaching of practical mathematics and is responsible for different projects in developing competence for colleagues. The first-teachers work is done under different conditions, such as time assigned to the mission, number of pupils at the school they work at and other on-going projects. Something that is crucial for the first-teacher efforts is, in part, how committed principal and school leadersare, and what demands they make, partly how passionate and skilful the first-teacher is herself.

  • 25.
    Mellqvist, Johanna
    Karlstad University.
    Taluppfattning i årskurs 1: En studie om lärares tankar och arbetssätt2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The aim of this study is to investigate how teachers teaching 2nd Grade primary school in mathematics work with number sense and what methods they primary use in their teaching. This study also investigates, from a teacher’s perspective, the extent of which the pupils are using their number sense both in basic mathematics and later in life. 

     

    The study has been conducted by a questionnaire where 75 teachers answered the survey. The survey was submitted through three Facebook groups and teachers who have been teaching 2nd Grade mathematics got the possibility to answer the questionnaire during a period of three weeks. 

     

    The result of the study shows that most teachers believe that number sense is vital in almost all areas of mathematics stated in the survey. Teachers also believed that number sense is of great importance for the pupils, both when it comes to the basics of mathematics but also later in life. Teachers find it difficult to precisely define number sense. However, the teacher considers number sense to be of significant importance for the pupils. According to the survey, most frequently used teaching methods in early mathematics are review and concrete material. 

  • 26.
    Mets, Regina
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Surfplatta som ett verktyg till matematik: Samspelet mellan barnen i förskolan2014Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This study deals with how the new tablet device can be used in daily practice in a pre-school,

    and how new technology is perceived by the children. I conducted a study using observations and interviews on a four to five year department.

    The reason I chose the pre-school I chose was because i have practiced there and hoped that

    the children would recognize me and feel more comfortable with answering questions.

    With interviews and observations I wanted to find out if the usage of tablets can be used in pre-schools. My conclusion is that it can be used advantageously for educational purposes.

  • 27.
    Muntean, Adrian
    Technical University of Eindhoven, Netherlands.
    On the interplay between fast reaction and slow diffusion in the concrete carbonation process: A matched-asymptotics approach2009In: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 44, no 1, p. 35-46Article in journal (Refereed)
  • 28.
    Narimanyan, A.
    et al.
    University of Bremen.
    Muntean, Adrian
    University of Bremen.
    Mathematical modelling driven by two industrial applications: A moving-boundary approach2006In: Mathematical Modelling and Analysis, ISSN 1392-6292, E-ISSN 1648-3510, Vol. 11, no 3, p. 295-314Article in journal (Refereed)
    Abstract [en]

    This note emphasizes the application of the moving‐boundary methodology in the modelling of two processes of particular industrial relevance. The first model explains the application of the Stefan and Signorini type boundary conditions in the modelling of the thermal cutting of metals by a plasma beam, while the second model shows how interface kinetic conditions, employed within the framework of a two‐phase Stefan‐like model, can describe the dynamics of an aggressive reaction front in concrete‐based materials. Our formulations provide a conceptually new approach towards the understanding of the involved physical processes. The connection between the two models is discussed as well. It relies on the presence of non‐equilibrium conditions driving the moving interface.

  • 29.
    Nordström, Lisa
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Lärobokens möjligheter för utveckling av det algebraiska tänkandet: En granskning av läroböcker för grundskolans senare år2019Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Mathematics education in Sweden is heavily influenced by textbooks. Being based on the Swedish curriculum and adapted to its content, the textbooks carry great weight in relation to the pupils’ teaching experience. Algebraic knowledge comprises an important role in the learning of mathematics. The aim of this study is to identify what characterizes the algebraic content in Swedish textbooks and curriculums for the lower secondary school. Researchers within mathematics education have previously published studies related to this aim in the lower level of elementary school. Five Big Ideas were identified and used as a framework to characterize the algebraic content in earlier studies. Those five Big Ideas were also used as a framework in this study. The results show that the algebraic content in lower secondary school is largely composed of methods for using variables. Methods and aspects suitable for solving equations were also frequently represented.

  • 30.
    Palmér, Hanna
    et al.
    Linnaeus University, Sweden.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Young student's feelings towards problem-solving tasks: What does "success" imply?2018In: Views and Beliefs in Mathematics Education: The Role of Beliefs in the Classroom / [ed] Benjamin Rott, Günter Törner, Joyce Peters-Dasdemir, Anne Möller & Safrudiannur, Springer, 2018, p. 69-78Conference paper (Refereed)
    Abstract [en]

    According to the Swedish curriculum, problem-solving is to be part of mathematics teaching from preschool continuing throughout all grades in school. However, little is known about young students’ feelings towards problem-solving tasks. This paper reports on an educational design research study investigating the potential in teaching problem-solving in preschool classes (6-year-olds). Two examples are presented showing how the students evaluate their feelings towards the problem-solving tasks they have been working on. The results show that understanding a task from the beginning or being able to solve it quickly are not necessary prerequisites for young students to experience enjoyment when working with the tasks. Quite the opposite, the majority of the students evaluated the tasks as fun and accessible, even though their initial solutions were often incorrect and they had to struggle a lot to solve the problems.

  • 31.
    Pettersson, Annika
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Grafisk och algebraisk representation: Gymnasieelevers förståelse av linjära funktioner2016Licentiate thesis, monograph (Other academic)
    Abstract [en]

    This thesis concerns upper secondary students’ understanding of algebraic and graphic representation of linear functions. Components of the students’ concept images, so-called ‘concept elements’, were studied as a way to capture their understanding. Four aspects affect the graphical view of a linear function, namely the parameter k, the parameter m, the scale of the coordinate axes and the domain of the function. Concerning the scale of the coordinate axis, there is a need to distinguish between two kinds of slope. When the scale of x-axis is changed, the k-value of the function, the so-called analytic slope, is constant but the visual slope changes. The tasks were designed so that three aspects were held constant in each task and one was varied. The study is qualitative and consists of two sub- studies. In the first, six students worked with two tasks involving the parameters k and m in the dynamic software GeoGebra. In the second, eight students were interviewed about a task concerning functions with different domains. Both studies also involved a task concerning the aspect of slope in a non-homogeneous coordinate system (a system with different scales on the axes). The results indicate three main findings: Firstly, students displayed difficulties in distinguishing between analytic and visual slope. Secondly, the word ‘start value’ can lead to conceptual problems when there is no visible intercept between the graphical representation of the function and the y-axis. Thirdly, the students displayed almost no concept elements in relation to the domain of a function.

  • 32.
    Podlipenko, Yury
    et al.
    Kiev Natl Univ, Kiev, Ukraine..
    Shestopalov, Youri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Guaranteed Estimates of Linear Continuous Functionals of Solutions and Right-hand Sides of the Helmholtz Equation in the Domains with Infinite Boundaries under Uncertainties2013In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, p. 65-69Conference paper (Refereed)
    Abstract [en]

    We consider the construction of guaranteed estimates of linear continuous function als of the unknown solutions and right-hand sides of the Helmholtz equation; the boundary value problems under study are associated with the wave diffraction by a bounded body D situated in a domain Omega is an element of R-n, n = 2, 3, whose boundary partial derivative Omega stretches to infinity (e.g., a wedge or a layer) and Green's function Phi(k) (x, y), (x, y is an element of Omega, x not equal y) corresponding to wave number k with k > 0 and boundary condition (I)k (x, y)vertical bar y is an element of Omega = 0 is known [4]. Here, for a function u(y) defined in (Omega) over bar Bu(y)vertical bar(y is an element of partial derivative Omega) + beta partial derivative u(y)/partial derivative y vertical bar(y is an element of partial derivative Q), alpha, beta = 0, 1, alpha + beta = 1, v is outward normal to aft We assume that right-hand sides of the equations entering the problem statement are not known; the only available information is that they belong to a bounded set of the space of square-integrable functions. In order to solve these estimation problems we need additional data: observations in the form of certain linear transformations of the solution distorted by noise. The latter are realizations of the random fields with the unknown second moment functions belonging to a given bounded set in the appropriate functional space. The approach set forth in and developed in this study allows us to obtain optimal estimates of the unknown solution or righthand sides of the equations and linear functionals, i.e., estimates sought in the class of functionals linear with respect to observations for which the maximal mean-square estimation error taken over all elements belonging to the aforementioned sets takes minimal value. Such estimates are called minimax or guaranteed estimates. We obtain representations for these estimates and estimation errors in terms of solutions to certain integro-differential or integral equations in bounded subdomains of domain Omega \ D.

  • 33.
    Podlipenko, Yury
    et al.
    Russia.
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties2013In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, p. 135-167Article in journal (Refereed)
    Abstract [en]

    We are looking for linear with respect to observations optimal estimates of solutions and right-hand sides of Maxwell equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms of solutions to special variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. © Springer International Publishing Switzerland 2013.

  • 34.
    Schalley, Andrea C.
    University of Munich.
    Das mathematische Weltbild der Maya2000Book (Refereed)
    Abstract [de]

    In acht Kapiteln zu Schriftsystem, religiösem Weltbild, Zahlensystem, Kalendersystem, Arithmetik und Astronomie bringt das Buch eine Gesamtdarstellung des mathematisch-astronomischen Wissens der Maya nach aktuellem Erkenntnisstand.

  • 35.
    Smirnov, A. P.
    et al.
    Moscow MV Lomonosov State Univ, Moscow, Russia..
    Semenov, A. N.
    Moscow MV Lomonosov State Univ, Moscow, Russia..
    Shestopalov, Youri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    FDTD Simulation of Waveguide with Non-uniform Dielectric Slab2013In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, p. 76-83Conference paper (Refereed)
    Abstract [en]

    Scattering in the time domain of electromagnetic waves in the elongated waveguide with non-uniform dielectric slab is considered. Electromagnetic field components are computed and investigation of energy transport in the guide is performed by using Finite Difference Time Domain (FDTD) method for various frequency ranges. Computation for the non-stationary Maxwell equation system is performed by efficient 3D FDTD solver EMWSolver3D created by this paper authors. Simulation is performed for the H10-mode scattering from dielectric slab inclusions. Numerical computations for large-scale problems solution have been implemented on supercomputers of the last generation. The simulation of an empty waveguide without dielectric inclusions has shown that numerical dispersion arising during waves travelling in waveguide causes solution errors. Numerical phase velocity is shown to differ from the analytical phase velocity with the lapse of time that obstructs accurate finding of attenuation and propagation factors. In this respect method similar to Total Field/Scattered field has been proposed to specify waveguide mode with respect to numerical dispersion. The analytical solution of finite-difference equation for the H10-mode has been found for this purpose. Usage of the methods described above has allowed the authors to compute the values of waveguide attenuation and propagation factors for different configurations of dielectric slab.

  • 36.
    Smirnov, Alexander
    et al.
    Chalmers University, Gothenburg University.
    Semenov, Alexey
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions2013In: Inverse Problems and Large-Scale Computations / [ed] Larisa Beilina, Yury V. Shestopalov, Springer, 2013, Vol. 52, p. 113-118Conference paper (Refereed)
    Abstract [en]

    We consider scattering in the time domain of electromagnetic waves from inhomogeneous dielectric inclusions in a 3D waveguide of rectangular cross section. All electromagnetic field components are calculated, and transport of energy in the guide is investigated using finite difference time domain (FDTD) method in different frequency ranges. An efficient 3D FDTD EMWSolver3D solver for the nonstationary Maxwell equation system is used. The model computations are performed for the H10-mode scattering from parallelepiped-shaped dielectric inclusions. Attenuation and propagation factors are calculated for the transmitted modes and field distributions are visualized. The present method can be used for a wide class of waveguide problems that meet substantial difficulties as far as numerical solution by conventional FDTD methods is concerned due to complex geometries or computational requirements. The solver employs algorithms of parallel computations and is implemented on supercomputers of last generation for solving large-scale problems with characteristic matrix dimensions achieving 1012.

  • 37.
    Smirnov, Yu. G.
    et al.
    Penza State Univ, Penza, Russia..
    Shestopalov, Yuri
    Derevyanchuk, E. D.
    Penza State Univ, Penza, Russia..
    Reconstruction of Permittivity and Permeability Tensors of Anisotropic Materials in a Rectangular Waveguide from the Reflection and Transmission Coefficients at Different Frequencies2013In: PIERS 2013 STOCKHOLM: Progress In Electromagnetics Research Symposium, 2013, p. 290-295Conference paper (Refereed)
    Abstract [en]

    This paper is devoted to the study of inverse problem of the permittivity and permeability tensor reconstruction of anisotropic materials in the form of diaphragms (sections) in a single-mode waveguide of rectangular cross section from the transmission and reflection coefficients measured. Results of numerical modeling are presented for different types of anisotropic materials. The developed solution techniques for the inverse problem under study can be applied in optics, nanotechnology, and design of microwave devices.

  • 38.
    Smirnov, Yu.G.a
    et al.
    Penza State University, Russian Federation.
    Shestopalov, Youri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Derevyanchuk, E.D.a
    Penza State University, Russian Federation.
    Permittivity determination of multi-sectional diaphragm with metamaterial layers in rectangular waveguide2013Conference paper (Refereed)
    Abstract [en]

    In this paper we consider the inverse problem of the permittivity determination of a multi-sectional diaphragm with metamaterial layers. Based on the developed recursive method of the solution to the inverse problem we perform a detailed analysis for a three-sectional diaphragm. Copyright © 2013 The Electromagnetics Academy.

  • 39.
    Tomasek, P.
    et al.
    Tomas Bata Univ Zlin, Zlin, Czech Republic..
    Shestopalov, Youri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Parameter Optimization of Waveguide Filters Employing Analysis of Closed-form Solution2013In: PIERS 2013  Stockholm: Progress In Electromagnetics Research Symposium, Cambridge, MA: Electromagnetics Academy , 2013, p. 296-299Conference paper (Refereed)
    Abstract [en]

    This work aims at computation and optimization of transmission coefficients of waveguide filters formed by one- or multi-sectional diaphragms in a waveguide of rectangular cross-section. An approach for designing band-stop and band-pass filters is proposed employing analysis of closed-form solutions and numerical multi-parameter optimization.

  • 40.
    Viirman, Olov
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Högskolan i Gävle.
    The function concept and university mathematics teaching2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis concerns the teaching of mathematics at university level, with a particular focus on the teaching of the function concept. The main aim of the thesis is describing and analysing the teaching practices of university mathematics teachers regarding the function concept, and how this concept is constituted through these practices. To this end, video recordings of lectures by seven mathematics teachers at three Swedish universities were analysed using a discursive perspective, Sfard’s commognitive framework. The observed teaching was traditional in form, with teachers using “chalk talk” – simultaneously talking and writing on the board. The results show that the teaching practices of the teachers belong to two distinct but intertwined discourses – a mathematical discourse, and a discourse of mathematics teaching. Classifications of important aspects of these discourses are presented, and it is found that the teachers’ discursive practices, while sharing overall form, still display considerable differences. Other results include an analysis of the levels of objectification displayed by the teachers in their discursive constitution of the function concept. The study contributes to a small but growing body of empirical research on university mathematics teaching practice.

  • 41.
    Österholm, Magnus
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Tomas
    Umeå universitet, Institutionen för tillämpad utbildningsvetenskap.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Uppsala universitet.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Utvärdering av Matematiklyftets resultat: slutrapport2016Report (Other (popular science, discussion, etc.))
    Abstract [sv]

    Matematiklyftet är en fortbildning för alla lärare i Sverige som undervisar i matematik. Den genomfördes 2012-2016. Kärnan i fortbildningen var det kollegiala lärandet. Lärare arbetade tillsammans med olika moduler som var och en bestod av didaktiskt material att använda vid planering, diskuss-ioner och genomförande av matematikundervisning, samt vid kollegiala reflektioner och diskussioner. Genom modulerna belystes primärt fyra olika didaktiska perspektiv: (1) att undervisa matematik utifrån förmågorna, (2) bedömning för lärande och undervisning i matematik, dvs. formativ bedömning, (3) rutiner/interaktioner i klassrummet och (4) klassrumsnormer/sociomatematiska normer.

    Denna rapport presenterar en utvärdering av Matematiklyftets resultat där det undersökts i vilken utsträckning Matematiklyftet har bidragit till att utveckla en bestående undervisningskultur och en bestående fortbildningskultur. Utvärderingen syftar också till att identifiera faktorer som gynnar eller missgynnar Matematiklyftets resultat och ska även fungera både formativt och summativt. Det innebär att både slutsatser om hur Matematiklyftet har uppnått målen att utveckla undervisnings- och fortbildningskulturen och slutsatser om hur stöd till planeringar och genomförande av liknande fort-bildningssatsningar formuleras. Urvalet i utvärderingen består av 35 grund-och gymnasieskolor. På varje skola har tre lärare slumpmässigt valts ut att ingå i utvärderingen, dvs. totalt 105 lärare. I utvärderingen ingår också varje skolas rektor och representant för skolhuvudman. Skolorna har besökts vid två tillfällen för att kunna undersöka förändring i undervisnings- och fortbildningskultur. Datamaterialet består av observationer av matematiklektioner och av kollegiala samtal, intervjuer och enkäter med lärare och rektorer, samt intervjuer med representanter för skolhuvudmän. I datamaterialet ingår även insamlade dokument (t.ex. fortbildningsplaner och kopior av undervisningsmaterial) och bakgrundsinformation om de besökta skolorna (från externa databaser). Denna rapport utgör slutrapporten för utvärderingen av Matematiklyftets resultat. Nedan redovisas utvärderingens huvudsakliga resultat tillsammans med rekommendationer inför framtida fortbildningssatsningar av samma typ som Matematiklyftet.

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