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  • 151.
    Björk, Kim
    et al.
    Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Matematiska institutionen.
    Engdahl, Amanda
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    På vilka sätt kan lärare hjälpa elever i matematiksvårigheter?: En litteraturstudie2019Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Det finns möjligheter för elever i matematiksvårigheter att nå skolans kunskapskrav i ämnet matematik om de får hjälp iform av effektiva interventioner. Därför är det av intresse att undersöka vilka undervisningsmetoder som ingår i effektivainterventioner.Frågeställningarna för denna litteraturstudie är:• På vilka sätt kan lärare stötta elever i matematiksvårigheter?o Vilka undervisningsmetoder har visats vara gynnsamma för elever i matematiksvårigheter?o Vilka representationsformer använder lärare för att stötta elever i matematiksvårigheter?• Hur påverkar undervisnings- och representationsformer elevers matematiska förmågor?I resultatet framkommer det att effektiva interventioner inkluderar muntliga och skriftliga instruktioner (med hjälp avvisuellt stöd), datorstöd, laborativ undervisning och självbedömning samt olika kombinationer av dessa. Hur effektfull enintervention är mäts med hjälp av effektstorlek och alla artiklar som ingår i denna litteraturstudie har i metaanalyserbedömts ha stor effektstorlek.

  • 152.
    Björk, Petter
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap.
    Hur stor är sannolikheten?: En studie om traditionellt och laborativt lärande inom sannolikhetsläran2019Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Syftet med denna studie är att förklara, analysera och jämföra traditionell och laborativ undervisning inom matematikens sannolikhetslära genom learning study. Studien syftar även till att synliggöra elevernas upplevelser från de olika undervisningsmetoderna. Under en veckas matematiklektioner är klassens elever indelas i en kontroll- och testgrupp. Med hjälp av för- och eftertest, traditionell och laborativ undervisning inom sannolikhetslära, enkäter och anteckningar jämförs elevernas resultat och skillnader i elevernas uppfattningar. Learning study påvisar en ökning av elevernas kunskaper beträffande sannolikhetslära i grupperna. Eleverna i testgruppen framlägger även positiva åsikter beträffande de laborativa undervisningstillfällena.

  • 153.
    Björkqvist, Filip
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Läromedelsanalys gällande textbaserade uppgifter i matematik2018Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med studien har varit att utveckla en kunskap om vilket innehåll olika läromedel kan ha gällande textbaserade uppgifter i ämnet matematik. Arbetet är baserat på en läromedelanalys på två olika läromedel i årskurs tre som har analyserats och granskats. Förhoppningen har varit att genom arbetet upptäcka vilka kritiska aspekter de två olika läromedlen kan innehålla för eleverna när de ska lösa textbaserade uppgifter. Studien har utgått från variationsteorin när resultatet och analysen har gjorts. I resultatet har det framkommit att läroböckerna kan innehålla kritiska aspekter för eleverna, vilket kan göra att det försvårar för eleverna att utveckla sina kunskaper gällande att lösa textbaserade uppgifter i matematik. I diskussionsdelen diskuteras det om de två olika läromedlen ger eleverna möjlighet att utveckla sin förmåga att lösa textbaserade uppgifter eller om läromedlets framställning av textbaserade uppgifter inte tar hänsyn till alla kritiska aspekter när eleverna ska lösa textbaserade uppgifter.

  • 154.
    Björkström, Angela
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Is it all in their heads?: A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary school2008Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today.  Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible.  Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system.  Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled.  Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident.  These are highlighted since they are important aspects teachers should be aware of.  The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results.  Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals.  Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies.  Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable.   

  • 155.
    Blanck, Andreas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    American Option Price Approximation for Real-Time Clearing2018Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    American-style options are contracts traded on financial markets. These are derivatives of some underlying security or securities that in contrast to European-style options allow their holders to exercise at any point before the contracts expire. However, this advantage aggravates the mathematical formulation of an option's value considerably, explaining why essentially no exact closed-formed pricing formulas exist. Numerous price approximation methods are although available, but their possible areas of application as well as performance, measured by speed and accuracy, differ. A clearing house offering real-time solutions are especially dependent on fast pricing methods to calculate portfolio risk, where accuracy is assumed to be an important factor to guarantee low-discrepancy estimations. Conversely, overly biased risk estimates may worsen a clearing house's ability to manage great losses, endangering the stability of a financial market it operates.

    The purpose of this project was to find methods with optimal performance and to investigate if price approximation errors induce biases in option portfolios' risk estimates. Regarding performance, a Quasi-Monte Carlo least squares method was found suitable for at least one type of exotic option. Yet none of the analyzed closed-form approximation methods could be assessed as optimal because of their varying strengths, where although the Binomial Tree model performed most consistently. Moreover, the answer to which method entails the best risk estimates remains inconclusive since only one set of parameters was used due to heavy calculations. A larger study involving a broader range of parameter values must therefore be performed in order to answer this reliably. However, it was revealed that large errors in risk estimates are avoided only if American standard options are priced with any of the analyzed methods and not when a faster European formula is employed. Furthermore, those that were analyzed can yield rather different risk estimates, implying that relatively large errors may arise if an inadequate method is applied.

  • 156.
    Blom, Veronica
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Gelius-Lundberg, Ulrika
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Samband mellan de fyra räknesätten- en läromedelsanalys2012Independent thesis Basic level (university diploma), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Sambandet mellan de fyra räknesätten är en del i utvecklingen av den matematiska förståelsen. Syftet med denna studie är att analysera hur ett antal olika läromedel i matematik riktade till årskurs 1-3 tar upp dessa samband. Med läromedel menas då läroböcker, samt tillhörande lärarhandledningar. Resultatet visar att flertalet av de analyserade läromedlen inte tar upp alla samband, medan ett fåtal tar upp alla samband men i olika stor omfattning. Dessutom visar analysen hur viktig lärarhandledningen är för att ge eleverna fler övningstillfällen i att träna de fyra sambanden, eftersom en stor del av dessa tillfällen förekommer i lärarhandledningen och inte i läroböckerna. Lärare som endast följer ett enskilt läromedel i sin undervisning kan alltså gå miste om mycket när det gäller sambandet mellan de fyra räknesätten.

  • 157.
    Blomqvist, Charlotta
    et al.
    Berghemsskolan, Umeå.
    Gade, Sharada
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Att kommunicera om likamedtecknet2013Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 4, s. 39-42Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    I denna artikel beskriver en lärare och en forskare sitt arbete med att utveckla den muntliga kommunikationsförmågan inom matematik i en fjärdeklass. Aktionsforskning utgör bakgrunden för arbetet och likamedtecknet står i fokus när eleverna utmanas i sitt matematiska tänkande med hjälp av lappar.

  • 158.
    Bobylev, Alexander
    et al.
    Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
    Potapenko, Irina
    Russia.
    Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas2013Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 246, s. 123-144Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 159.
    Bodin, Kenneth
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Nilsson, Martin
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Constraint based particle fluids on GPGPU2011Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    We present a fluid simulation method adapted for stream parallelism on general purpose graphics processingunits (GPGPU). In this method the equations of Navier and Stokes are discretized using particles and kernelfunctions as in Smoothed Particle Hydrodynamics (SPH), but rather than using penalty methods or solving for a divergence free velocity field, incompressibility is enforced using holonomic kinematic constraints [1]. We useone constraint for each smoothed particle stating that the local density should be kept constant. Other constraintsare used for boundary conditions and multiphysics coupling. We also present a viscosity model in which theshear rate at each pseudo particle is constrained to satisfy a given constitutive law. The computation of theconstraint forces, namely, the pressure and the stresses, requires the solution system of linear equations whichhave a sparse, saddle point structure. These are solved using the Uzawa method of preconditioned conjugate gradients (CG) applied directly to the symmetric indefinite matrix. The overall simulation method has its rootsin a discrete variational principle and the SPOOK time stepping scheme for constrained mechanical systems [2].The SPOOK method is second order accurate on the positions and constraints violations, and is stable at largetime-steps, thus often allowing several orders of magnitude larger timesteps in our method compared to intraditional SPH methods. The numerical implementation on GPGPU that is the main result of this paper consistsof the following components: particle neighbour searches based on spatial decomposition; summation of kernel densities; construction of Jacobians representing the constraints on the density, boundary conditions, viscosityand multiphysics couplings; a Uzawa CG solver for the system of linear equations; and finally, discrete timestepping of velocities and positions. The CG solver is particularly suitable for stream computing since it is basedon matrix-vector multiplications. The sparse system data is stored in a compressed matrix format and the algorithms operating on this data on GPGPU are implemented in CUDA and OpenCL. Our simulation resultsinclude performance measurements, and validation of the method for benchmark problems. We achieve up totwo orders of magnitude speed-up from the GPGPU over traditional processors and together with the increased timestep efficiency of our method we arrive at interactive performance for systems with up to two million fluidparticles representing an incompressible fluid.

  • 160.
    Bonner, Richard
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Operators that coerce the surjectivity of convolution2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of multiplication by a real analytic function; they are here called pseudo-convolutions since they also generalise pseudo-differential operators. (It is shown that the elliptic real analytic pseudo-differential operators leave both the non-invertible and the invertible distributions invariant.) But when the condition of real-analyticity is relaxed, such operators may map a non-invertible distribution to one invertible -- given that the invertibility in both cases concerns the same function space. By varying the space, however, one can measure the 'loss of non-invertibily' that a non-analytic perturbation may introduce. This phenomenon is here studied using the Beurling classes of functions and measuring the regularity of operator symbols in the Denjoy-Carleman sense; the Gevrey case turns out particularly simple.

  • 161.
    Bonner, Richard F.
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mamchych, Tetyana I.
    RFB Consulting, Sweden.
    Classifying Households by the (Sobolev) Norms of their Electricity Consumption2014Inngår i: Energy Procedia, ISSN 1876-6102, E-ISSN 1876-6102, Vol. 61, s. 1870-1873Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Numerical time series, but especially periodic such, are characterized up to pertinent symmetries by families of norms. The electricity consumption by a household, recorded daily during a month’s time, say, may then be encoded in a sequence of numbers; for example, as follows: the mean daily consumption, the mean daily variation of the consumption, the variation of the variation, the variation of the variation of the variation, etc. Now, replacing each of these numbers by the digits 0, 1, or 2, to say that a number is “low”, “medium”, or “high”, in relation to a collection of households, one naturally partitions the collection by the strings of these three digits; the household labeled 102   has then medium daily consumption, low daily variation, but high variation of variation, etc. We generally discuss this innocent idea and examine it in three ways: by way of toy examples, through its mathematical model (in detail presented elsewhere) and by accordingly classifying some actual electricity consumption data.

  • 162.
    Bonner, Richard
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Mamchych, T.
    Malchuk, I.
    On the problem of mining the Web – for a curriculum2008Konferansepaper (Fagfellevurdert)
  • 163.
    Bortolin, Gianantonio
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Gutman, Per-Olof
    A new algorithm for variable selection2006Inngår i: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, s. 1309-1314Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A new method for variable selection and estimation called Iteratively Scaled Ridge Regression, ISRR, is proposed. The method is an iterative algorithm based on ridge regression. Simulation studies show that ISRR shares the properties of both subset selection and ridge regression. It selects an optimal subset of the regressor variables and is robust to small changes in the data set. The ISRR algorithm was primarily developed for linear models, but is quite simple and general and can easily be extended to more general linear and nonlinear models.

  • 164.
    Bouhuis, Krijn
    Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
    Differentiation in teaching mathematics: An observational study of eight primary school teachers in Sweden2013Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    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.

  • 165.
    Bounadi, Monir
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The Foundations of Graph Pebbling2015Independent thesis Advanced level (degree of Master (One Year)), 240 hpOppgave
    Abstract [en]

    Graph pebbling modeling started as a method for solving a combinatorialnumber theory conjecture by Erdös and Lemke. Using thismethod, Chung proved the conjecture in 1989. Since then, the literaturehas grown considerably. Several variations and possible applicationshave been discussed, in graph theory, computer science andnetwork optimization.

    The main focus in graph pebbling is graphs, mathematical structuresmodeling binary relations between vertices. To every vertex insome graph we assign a number of pebbles. If two pebbles are movedacross an edge joining two distinct vertices, one pebble arrives andone pebble is lost. This is called a pebbling step.

    The basic question in graph pebbling asks if one may from a givendistribution of pebbles on a set of vertices move to another distributionon the same set via a series of pebbling steps.

    In this Master’s thesis we approach the above question using twomodels: a deterministic, which includes the notion of a pebblingnumber, and a probabilistic, which includes the notion of a threshold.

    For both these models we clarify earlier proofs, and provide newproofs, of foundational theorems in graph pebbling. These resultsconstitute the backbone for our discussion on recent research, whichconcentrates on generalizing and extending central notions in graphpebbling, for example the generalized idea of a pebbling number:the pi-pebbling function. Simultaneously, a corollary to the so calledcover pebbling theorem is derived. This corollary lets us prove established,and newly found, theorems.

    Regarding applications in graph pebbling, we argue that one shouldgeneralize existing results, and incorporate directed graphs into abigger part of the theory. We suggest how this can be done.

  • 166.
    Brandberg, Anna-Lena
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Wennerström, Maria
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Speciallärares kommunikation med matematiksvaga elever2010Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Undersökningen beskriver den matematiska kommunikationen mellan speciallärare och matematiksvaga elever. Den empiriska datan består av två matematiklektioner från år 9 i grundskolan. Datan analyserades för att finna olika typer av kommunikation.

    Lärarna var i många delar medvetna i sitt sätt att kommunicera med eleverna och undervisningsmiljön kändes trygg. Under lektionerna observerades två parallella språk, ett vardagsanknutet och ett matematiskt språk. Det framkom att ett tydligt förhållningssätt beträffande matematiskt språk kan underlätta för elevens inlärning samt medvetandegöra läraren om den kommunikativa betydelsen i undervisningen med styrdokumentens mål i fokus.

     

  • 167.
    Brattström, Gudrun
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
    Leonardo da Pisa: Inger Christensen och Fibonacci2008Inngår i: Lyrikvännen, ISSN 0460-0762, Vol. 55, nr 6, s. 33-38Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.

  • 168.
    Britton, Tom
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Deijfen, Maria
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Liljeros, Fredrik
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Sociologiska institutionen.
    A weighted configuration model and inhomogeneous epidemics2011Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 145, s. 1368-1384Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A random graph model with prescribed degree distribution and degree dependent

    edge weights is introduced. Each vertex is independently equipped with a random number

    of half-edges and each half-edge is assigned an integer valued weight according to a distribution

    that is allowed to depend on the degree of its vertex. Half-edges with the same weight

    are then paired randomly to create edges. An expression for the threshold for the appearance

    of a giant component in the resulting graph is derived using results on multi-type branching

    processes. The same technique also gives an expression for the basic reproduction number

    for an epidemic on the graph where the probability that a certain edge is used for transmission

    is a function of the edge weight (reflecting how closely ‘connected’ the corresponding

    vertices are). It is demonstrated that, if vertices with large degree tend to have large (small)

    weights on their edges and if the transmission probability increases with the edge weight,

    then it is easier (harder) for the epidemic to take off compared to a randomized epidemic

    with the same degree and weight distribution. A recipe for calculating the probability of a

    large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the

    model is fitted to three empirical weighted networks of importance for the spread of contagious

    diseases and it is shown that

    R0

    can be substantially over- or underestimated if the

    correlation between degree and weight is not taken into account.

  • 169.
    Brunosson, Albina
    Högskolan Kristianstad, Sektionen för Lärarutbildning.
    Kökets bråkstakar: elevers förståelse för bråktal i hem- och konsumentkunskap2010Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    The aim of this study has been to investigate students’ understanding of fractions when they occur in the practical subject home economics. In order to investigate this, the learning study method was used. Learning study can be understood as a method to gain deeper understanding of what is learnt by students during a lesson to increase learning outcome.

    The variation theory framework has been utilized to analyze the results of this study. The object of learning was chosen to be addition of fractions bigger than one half when they appear in home economics. The results indicate that in order for the learners to experience the object of learning it requires that they discern some critical aspects; to distinguish between quarters and four parts, the relationship between the part and the whole in fractions, varied presentations of the same fraction along with an understanding of the meaning of the concept to double.

     

    Moreover the students have carried out a math test which tested the students’ theoretical understanding of fractions to see whether they can transfer the knowledge from one learning context to another. The result evinces that most of the learners show a good understanding of fractions in a theoretical context as well as a practical. The learning study has increased the students learning according to the object of learning

  • 170.
    Bruér, Rebecka
    et al.
    Högskolan Kristianstad, Sektionen för lärande och miljö.
    Wiklund, Jenny
    Högskolan Kristianstad, Sektionen för lärande och miljö.
    Elevers möjligheter att lära bråk2017Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med studien är att undersöka hur elever i årskurs 6 uttrycker sina kunskaper om olika aspekter av bråk, jämförelser och division samt vilka resonemang och strategier de då använder. Syftet är även att undersöka vilka möjligheter eleverna upplever de fått att lära sig detta samt vilka möjligheter lärarna upplever att de har gett eleverna att lära sig, eftersom vi vill veta orsaker till att använda strategier valdes och vilka samband det kan finnas mellan elevers kunskaper om bråks olika aspekter och deras kunskaper om jämförelser och division med bråk. Studien är förankrad i teoretiska modeller om hur bråk kan förstås, teorier om lärande samt tidigare forskning med liknande frågeställningar. Det tillvägagångssätt som valts är flermetodsforskning som omfattar kvantitativ metod för insamling och analys av en skriftlig diagnos och kvalitativ metod för insamling och tematisk analys av intervjuer med elever och lärare. Resultatet visar att eleverna hade tillräckliga kunskaper totalt sett om bråks aspekter, jämförelser och divisioner men otillräckliga kunskaper om framför allt aspekten bråk som kvot vilket medförde otillräckliga kunskaper om innehållsdivision.

  • 171.
    Brännström, Katarina
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Variationsrika uppgifter med syfte att utveckla matematiska förmågor: En analys av komplexa tal inom gymnasiekursen Matematik 42012Independent thesis Basic level (professional degree), 12 poäng / 18 hpOppgave
    Abstract [sv]

    Det finns ett behov av att kombinera förmågor och variation i undervisningen i högre kurser på gymnasiet då det uppfattas som att kurserna blir mer abstrakta, ensidiga och läroboksbundna. Syftet är att höja elevernas måluppfyllelse. Genom litteraturstudie av matematisk förmåga och variationsteori tillverkas eller väljs ut exempeluppgifter som sedan analyseras på vilket sätt de kan variera. Det visar sig att begreppsförmågan varieras mest följt av problemlösningsförmågan och båda har ovanliga uppgifter som den mest varierbara uppgiftstypen. När det gäller verklighetsnära uppgifter är det viktigt att de är anpassade till elevernas förkunskaper för att erbjuda meningsfull variation.

  • 172.
    Brännström, Åke
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Rossberg, Axel
    School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 7BL UK.
    Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces2011Inngår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, nr 3, s. 575-592Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

  • 173.
    Brännström, Åke
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Gross, Thilo
    Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
    Blasius, Bernd
    Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111 Oldenburg, Germany.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria.
    Consequences of fluctuating group size for the evolution of cooperation2011Inngår i: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, nr 2, s. 263-281Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.

  • 174.
    Brännström, Åke
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Johansson, Jacob
    Lund University.
    von Festenberg, Niels
    The Hitchhiker’s Guide to Adaptive Dynamics2013Inngår i: Games, ISSN 2073-4336, E-ISSN 2073-4336, nr 4, s. 304-328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

  • 175.
    Bråting, Kajsa
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Studies in the Conceptual Development of Mathematical Analysis2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This dissertation deals with the development of mathematical concepts from a historical and didactical perspective. In particular, the development of concepts in mathematical analysis during the 19th century is considered. The thesis consists of a summary and three papers. In the first paper we investigate the Swedish mathematician E.G. Björling's contribution to uniform convergence in connection with Cauchy's sum theorem from 1821. In connection to Björling's convergence theory we discuss some modern interpretations of Cauchy's expression x=1/n. We also consider Björling's convergence conditions in view of Grattan-Guinness distinction between history and heritage. In the second paper we study visualizations in mathematics from historical and didactical perspectives. We consider some historical debates regarding the role of intuition and visual thinking in mathematics. We also consider the problem of what a visualization in mathematics can achieve in learning situations. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. In the third paper we consider Cauchy's theorem on power series expansions of complex valued functions on the basis of a paper written by E.G. Björling in 1852. We discuss Björling's, Lamarle's and Cauchy's different conditions for expanding a complex valued function in a power seris. In the third paper we also discuss the problem of the ambiguites of fundamental concpets that existed during the mid-19th century. We argue that Cauchy's and Lamarle's proofs of Cauchy's theorem on power series expansions of complex valued functions are correct on the basis of their own definitions of the fundamental concepts involved.

     

  • 176.
    Bråting, Kajsa
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Pejlare, Johanna
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Visualizations in mathematics2008Inngår i: Erkenntnis, ISSN 0165-0106, E-ISSN 1572-8420, Vol. 68, nr 3, s. 345-358Artikkel i tidsskrift (Fagfellevurdert)
  • 177.
    Bråting, Kajsa
    et al.
    Uppsala universitet.
    Sollervall, Håkan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Stadler, Erika
    Algebra för lärare2017 (oppl. 1)Bok (Annet vitenskapelig)
  • 178.
    Bråting, Kajsa
    et al.
    Uppsala universitet, Uppsala, Sverige.
    Sollervall, Håkan
    Linnéuniversitetet, Växjö, Sverige.
    Stadler, Erika
    Stockholms universitet, Stockholm, Sverige.
    Geometri för lärare2013 (oppl. 1)Bok (Annet vitenskapelig)
  • 179.
    Bråting, Kajsa
    et al.
    Uppsala University.
    Sollervall, Håkan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Stadler, Erika
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA), Institutionen för matematikdidaktik (MD). Stockholm University.
    Geometri för lärare2013 (oppl. 1)Bok (Annet vitenskapelig)
  • 180.
    Bukina, Elena
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Efficient Numerical Solution of PIDEs in Option Pricing2011Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
  • 181.
    Bursell, Moa
    et al.
    Inst Futures Study, Box 591, SE-10131 Stockholm, Sweden..
    Jansson, Fredrik
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm Univ, Ctr Cultural Evolut, SE-10691 Stockholm, Sweden..
    Diversity preferences among employees and ethnoracial workplace segregation2018Inngår i: Social Science Research, ISSN 0049-089X, E-ISSN 1096-0317, Vol. 74, s. 62-76Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Ethno-racial workplace segregation increases already existing ethno-racial inequality. While previous research has identified discriminatory employers as drivers of workplace segregation, this study addresses the role of the employees. Sociological and social psychological theory suggest that people prefer to surround themselves with people who positively confirm their social identity or who contribute with higher group status. Through web-based surveys, we measure employee attitudes and preferences concerning ethno-racial workplace diversity, to what extent they differ by ethnicity/race, and if they contain intersectional patterns. Thereafter, we use simulation models to analyze the consequences for workplace segregation that these preferences would have, if realized. The main survey results showed that all ethno-racial groups favored their own in-group as colleagues, especially European Americans. As a secondary choice, the respondents preferred the out-group with the highest labor market status. Intersectional patterns were identified, as minority women were preferred as colleagues over minority men. Our simulation model, based on the results of two surveys on stated vs. indirectly revealed preferences, showed that employee preferences were at best not diverse enough to desegregate workplaces. When based on the most common preferences (i.e. excluding a few outliers), the simulations even suggested that these preferences can cause segregation. We relate these findings to Schelling's model of segregation.

  • 182.
    Bylund, Ronny
    Luleå tekniska universitet, Institutionen för konst, kommunikation och lärande.
    Digitala hjälpmedel eller inte?: Gymnasieelevers åsikter om digitala hjälpmedel och hur det används i matematikundervisningen2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Denna studie syftar till att visa hur digitala verktyg används i gymnasiet inommatematikundervisningen, både utav lärare och elever i norra Sverige. Ytterligare undersöksäven elevernas åsikter om dess användning samt om de anser att det underlättar derasinlärningsprocess kring matematik eller inte. Detta har gjorts med hjälp utav en enkätstudie,SAMR-modellen och förväntan-värde teorin. Totalt deltog 102 elever i undersökningen.Resultaten visar att det inte finns några uppenbara för- eller nackdelar när elever använderdigitala hjälpmedel. Elever tycker dock att dess användning är bra inommatematikundervisningen, men främst när läraren använder sig utav det. Läraren använderfrämst digitala verktyg i sina genomgångar och för att visa hur det skall användas, elevernaanvänder det främst när läraren säger till dem att göra det, på prov och för att lösa svårauppgifter som de inte kan lösa med hjälp utav papper och penna ännu.

  • 183.
    Böörs, Mikael
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Wängberg, Tobias
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Classification by Decomposition: A Partitioning of the Space of 2X2 Symmetric Games2017Independent thesis Basic level (degree of Bachelor), 10,5 poäng / 16 hpOppgave
    Abstract [en]

    Game theory is the study of strategic interaction between rational agents. The need for understanding interaction arises in many different fields, such as: economics, psychology, philosophy, computer science and biology. The purpose of game theory is to analyse the outcomes and strategies of these interactions, in mathematical models called games. Some of these games have stood out from the rest, e.g. Prisoner's Dilemma, Chicken and Stag Hunt. These games, commonly referred to as the standard games, have attracted interest from many fields of research. In order to understand why these games are interesting and how they differ from each other and other games, many have attempted to sort games into interestingly different classes. In this thesis some already existing classifications are reviewed based on their mathematical structure and how well justified they are. Emphasis is put on mathematical simplicity because it makes the classification more generalisable to larger game spaces. From this review we conclude that none of the classifications captures both of these aspects. We therefore propose a classification of symmetric 2x2 games based on decomposition. We show that our proposed method captures everything that the previous classifications caputure. Our method arguably explains the interesting differences between the games, and we justify this claim by computer experiments. Moreover it has a simple mathematical structure. We also provide some results concerning the size of different game spaces.

  • 184.
    Cajonberg, Julia
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för matematik och ämnesdidaktik.
    ”Ibland är det svårt att veta om lika med betyder att det är lika mycket eller om det betyder svaret”: En kvalitativ fallstudie om elevers förståelse för likhetstecknet och dess innebörd2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna studie är att undersöka vilka möjligheter elever i årskurs 1–3 har för att utveckla en förståelse för likhetstecknet samt vilken förståelse för likhetstecknet elever i årskurs 1–3 visar att de faktiskt har. Tre observationer genomfördes hos en lärare för att se hur läraren undervisade om, benämnde och förklarade likhetstecknet. Därefter genomfördes ett test med sjutton elever för att undersöka vilken förståelse för likhetstecknet de har. Som uppföljning av testet, intervjuades nio elever i grupper om tre för att undersöka vilken förståelse för likhetstecknet eleverna har. Observationerna, testet och intervjuerna visade att läraren benämner likhetstecknet som ”lika med” samt att majoriteten av eleverna har en relativt välutvecklad förståelse av likhetstecknet, då de med egna ord kan förklara och visa på att det ska vara lika mycket på vardera sida av likhetstecknet för att likhetstecknet ska kunna användas. Genom intervjuerna med eleverna framkom det att eleverna fått arbeta med olikhetstecknet ”skilt från” och att det underlättade deras förståelse för likhetstecknets betydelse. De har även fått arbeta med klossar och brukar regelbundet arbeta med likhetstecknets betydelse i undervisningen, främst i deras lärobok där det är ständigt återkommande.

  • 185.
    Cano, Cédric
    Karlstads universitet, Institutionen för ingenjörsvetenskap, fysik och matematik.
    Integrering av ett främmande språk i matematikundervisningen2009Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    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.

  • 186.
    Carlsson, Eva
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Smidiga övergångar inom grundskolan,men hur?: Sex matematiklärares berättelser om övergången mellan skolår 3 och 42014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The study, Mind the Gap between Grade Three and Four is written within the research fields of Mathematics Education. The research interests in the study concerns how to achieve a smooth transition between grade three and four in compulsory school.

    As a mathematics teacher I found out that the transition from one grade to another in compulsory school affects both the pupil and the mathematics teacher and not always in a satisfactory way. Formal meetings concerning handing over information about pupils are not sufficient, and there is a definite difference between what is said about the pupils during a formal meeting and what is said in more informal settings. Are their gaps that occur?

    The aim of this study is to listen to mathematics teachers´ and to illuminate their stories about handing over pupils from grade three and taking over pupils in grade four. I am searching for gaps in their stories. My goal is to safe guard the continuity concerning the changes of grades between grade three and four in compulsory school. The research questions are: What are the important factors for mathematics teacher´s concerning the transition between grade three and four? What themes and gaps concerning the transitions are revealed in their stories?

    The study is based on a theoretical framework made of; Gees (1999) theory about "language-in-use" and "the seven building blocks of language". Social constructions because the idea is to criticize and change the established order regarding the transition between grade three and grade four. I also made a choice to look at the difficulties concerning the transition as external factors and not as the shortcoming of the mathematics teachers´ therefore I use the critical perspective. Discourse is used because this study is about communication, both spoken and written.

    In order to investigate important factors for mathematics teachers concerning the transitions I interview six mathematics teachers. They are asked about the existent transition between grade three and four at their schools and what they think are important factors for transitions overall. I also videotape one formal meeting because when different methods are used it helps me verify 2

    the outcome. The transcriptions from the interviews and the formal meeting are analyzed with help from the discourse analysis based on Gee (1999).

    The analysis/result shows themes that are important and signal about gaps that could be filled by further research. Themes revealed concerns: school organization, formal/informal meetings, teaching, assessment and special pedagogy. Gaps that are visible concern the teachers’ different educations, the school-web and the curriculum, time, relations, communication, assessment, feedback, teaching methods, teaching materials, and pupils in special needs.

    I argue that its´ necessary to create a structure and make guidelines for formal conferences concerning the transition between grade three and four to minimize the discontinuity. It should also be of interest that the gaps mentioned in this study are filled, and one way to begin could be to plan for collegial work between teachers’ in different grades.

  • 187.
    Carlzon, Madeleine
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Att få grepp om begrepp: En kvalitativ studie av gymnasieelevers begreppsförståelse inom trigonometri2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Den här studien undersöker gymnasieelevers begreppsförståelse inom trigonometri. Eleverna, som samtliga läser Ma 4, besvarade anonymt två frågeformulär där det ena bestod av en öppen fråga, medan det andra var upplagt som ett test med uppgifter att lösa. Den kvalitativa analysen baseras på Tall och Vinners (1981) teori om begreppsbild och Sfards (1991) uppdelning av begreppsförståelse i de tre processerna interiorisering, kondensering och reifiering. Resultatet indikerar att elever tenderar att använda cirkeltrigonometri före triangeltrigonometri för att lösa uppgifter, men att majoriteten av deras begreppsbilder består av både och. Det visade sig att radianer var det trigonometriska begrepp eleverna hade svårast för. Detta stämmer överens med tidigare forskning på området. Tre elever analyseras djupare med avseende på hur långt de har kommit i sin utveckling av begreppsförståelse inom trigonometri. Det ges även exempel på hur utvecklingsfaserna kan ge sig till uttryck hos enskilda elever. Såväl begreppsbild som vilka stadier eleverna befinner sig på i sin begreppsförståelse varierar stort.

  • 188.
    Carrasco, Lena
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Konkret material i matematik: Hur ser elever på det?2018Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med studien är att studera vilken syn sju elever i årskurs fyra och fem har på konkret material i matematikundervisningen. Metoden som användes för att samla in data var sju semistrukturerade elevintervjuer. Resultatet visar att elevernas syn på användning av konkret material är att det ska ge dem ett visuellt stöd för konkretisering av abstrakt matematik där siffror och symboler dominerar. Resultatet visar även att eleverna tycker att konkret material ska ingå i undervisningen. Slutsatser som kan dras från den här studien stämmer överens med det teoretiska ramverk som används i tolkning av data, om eleverna lär sig med hjälp av modeller eller om elever använder sina kunskaper till att konstruera modeller. En konsekvens av denna studie kan vara att lärare behöver utveckla sin ämnesdidaktiska kompetens så att undervisningen harmonierar med centralt innehåll för årskurs fyra till sex i den rådande läroplanen för skolan.

  • 189. Cedervall, Simon
    et al.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Nonlinear observers for unicycle robots with range sensors2007Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, nr 7, s. 1325-1329Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For nonlinear mobile systems equipped with exteroceptive sensors, the observability does not only depend on the initial conditions, but also on the control and the environment. This presents an interesting issue: how to design an observer together with the exciting control. In this note, the problem of designing an observer based on range sensor readings is studied. A design method based on periodic excitations is proposed for unicycle robotic systems.

  • 190.
    Cheander, Johan
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    CSI:Math: Ett undervisningsförsök med Storyline i matematik2011Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Storyline är en undervisningsmetod som ursprungligen kommer från Skottland. Metoden används i hela världen, men har blivit väldigt populär främst i de nordiska länderna, Danmark och Norge, men också i Sverige. Storyline är ämnesövergripande och används oftast i grundskolan. Syftet med denna studie är att undersöka hur storyline lämpar sig som undervisningsmetod i matematikundervisningen i gymnasieskolan. Undervisningsförsöket är baserat på ett utgångsmaterial som heter CSI:Math. Försöket observeras och utvärderas med en enkät och en efterföljande intervju. Utifrån resultaten av undersökningarna kan slutsatsen dras att storyline inte bara fungerar väl som arbetsmetod, utan också ligger väl i linje med de senaste förändringarna av gymnasiekurserna i matematik Gy2011.

  • 191. Cheng, Daizhan
    et al.
    Wang, Jinhuan
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    An extension of LaSalle's invariance principle and its application to multi-agent consensus2008Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, nr 7, s. 1765-1770Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected.

  • 192. Chicharro, Daniel
    et al.
    Ledberg, Anders
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Centrum för socialvetenskaplig alkohol- och drogforskning (SoRAD).
    Framework to study dynamic dependencies in networks of interacting processes2012Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, nr 4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.

  • 193.
    Christoffer, Dahlqvist
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematikdidaktik (MD).
    Spela för nöje eller spela för kunskap?: Lärares uppfattningar av IT-baserade matematikspel och dess konsekvenser på elevers kunskapsutveckling2015Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
  • 194.
    Coder Gylling, Kira
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Brännström, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria.
    Effects of Relatedness on the Evolution of Cooperation in Nonlinear Public Goods Games2018Inngår i: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 9, nr 4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Evolution of cooperation has traditionally been studied by assuming that individuals adopt either of two pure strategies, to cooperate or defect. Recent work has considered continuous cooperative investments, turning full cooperation and full defection into two opposing ends of a spectrum and sometimes allowing for the emergence of the traditionally-studied pure strategies through evolutionary diversification. These studies have typically assumed a well-mixed population in which individuals are encountered with equal probability. Here, we allow for the possibility of assortative interactions by assuming that, with specified probabilities, an individual interacts with one or more other individuals of the same strategy. A closely related assumption has previously been made in evolutionary game theory and has been interpreted in terms of relatedness. We systematically study the effect of relatedness and find, among other conclusions, that the scope for evolutionary branching is reduced by either higher average degree of, or higher uncertainty in, relatedness with interaction partners. We also determine how different types of non-linear dependencies of benefits and costs constrain the types of evolutionary outcomes that can occur. While our results overall corroborate the conclusions of earlier studies, i.e. higher relatedness promotes the evolution of cooperation, our investigation gives a comprehensive picture of how relatedness affects the evolution of cooperation with continuous investments.

  • 195.
    Cohen Scalie, Natalie
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
    Vilken matematik ligger g(l)ömd?: En studie om matematikens och de övriga ämnenas inbördes förhållande i mellanstadiets kursplaner2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    ”Vilken matematik ligger g(l)ömd?” är en studie som syftar till att rannsaka matematiken i den nya läroplanen och om den håller även för övergången till det ämnesintegrerande arbete i skolan som den har för avsikt. Här finner du svaret på hur väl matematikämnets syften och centrala innehåll överensstämmer med eventuell matematik i övriga ämnens syften och centrala innehåll i Lgr 11, årskurs 4-6? Utifrån en hermeneutisk ansats med kritisk-teoretiska inslag gjordes en innehållsanalys deducerad från en övergripande definition av vad matematiken innebar. Den skulle ge kvalitativ förståelse för lärares skoltillvaro och vilken effekt den får för eleverna genom att analyseras idécentrerat. För att förenkla den kontextuella insikten gjordes detta sedan överskådligt med hjälp av en matris byggd på kategorier. De fick bearbeta alla ämnena i läroplanen och utgjordes då av delarna matematiska idéer, matematisk operationalisering och matematiskt angreppssätt samt områdena algebra, geometri och analys, vilka alla ingick i vardera delen. Efter en pilotstudie användes sedan matrisen strukturanalytiskt och förde samman matematiska komponenter av samma sort grundat på beningsbärande koder. Då syntes ett mönster av återkommande matematiska bitar i de övriga ämnena som inte tycktes vara ha någon motsvarighet i matematikämnet. Men med återkoppling till litteratur och ett granskande med hänsyn till och av tolv författares särpräglade teorier utformades en ny klarläggande modell som gick ut på att man beroende på vilket problem man tar sig för får olika vetenskaplig beskaffenhet på de matematiska bitarna algebra och geometri’s teoretiska idéer och praktiska verksamheter på väg mot en lösning. Denna modell bidrog med en ny dimension av undersökningen, som till slut visade att de saknade bitarna i själva verket var av ämnesövergripande slag och att överensstämmelsen tycktes oinskränkt.

  • 196. Cornforth, Daniel M
    et al.
    Sumpter, David J T
    Brown, Sam P
    Brännström, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Synergy and group size in microbial cooperation2012Inngår i: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 180, nr 3, s. 296-305Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Abstract Microbes produce many molecules that are important for their growth and development, and the exploitation of these secretions by nonproducers has recently become an important paradigm in microbial social evolution. Although the production of these public-goods molecules has been studied intensely, little is known of how the benefits accrued and the costs incurred depend on the quantity of public-goods molecules produced. We focus here on the relationship between the shape of the benefit curve and cellular density, using a model assuming three types of benefit functions: diminishing, accelerating, and sigmoidal (accelerating and then diminishing). We classify the latter two as being synergistic and argue that sigmoidal curves are common in microbial systems. Synergistic benefit curves interact with group sizes to give very different expected evolutionary dynamics. In particular, we show that whether and to what extent microbes evolve to produce public goods depends strongly on group size. We show that synergy can create an "evolutionary trap" that can stymie the establishment and maintenance of cooperation. By allowing density-dependent regulation of production (quorum sensing), we show how this trap may be avoided. We discuss the implications of our results on experimental design.

  • 197.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Institutionen för teknik och byggd miljö, Ämnesavdelningen för elektronik.
    A Study of Students’ Ability to Solve Text-Based Mathematical Problems with Irrelevant or Superfluous Information2008Inngår i: Mathematical Views, MAVI 14: Strobl/Salzburg, Austria, May 2008, 2008Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A limited quantitative survey has been performed in order to study the capability of students to solve text-based mathematical problems containing irrelevant or superfluous information, as well as their ability to scrutinize text and sort out the relevant information. The students took a written test with text-based problems of different amount of irrelevant or superfluous information. The capability of understanding such problems was investigated versus degree of maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant or superfluous information and ability of solving the problems. Furthermore, the results show that the degree of maturity, expressed in terms of age, has a clear influence on the results. This study has not revealed any significant difference between genders as regards ability of sorting out the relevant information.

  • 198.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Ämnesavdelningen för elektronik.
    A Study of Students’ Ability to Solve Text-Based Mathematical Problems with Irrelevant or Superfluous Information2008Inngår i: Mathematical Views, MAVI 14: Strobl/Salzburg, Austria, May 2008, 2008Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A limited quantitative survey has been performed in order to study the capability of students to solve text-based mathematical problems containing irrelevant or superfluous information, as well as their ability to scrutinize text and sort out the relevant information. The students took a written test with text-based problems of different amount of irrelevant or superfluous information. The capability of understanding such problems was investigated versus degree of maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant or superfluous information and ability of solving the problems. Furthermore, the results show that the degree of maturity, expressed in terms of age, has a clear influence on the results. This study has not revealed any significant difference between genders as regards ability of sorting out the relevant information.

  • 199.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Institutionen för teknik och byggd miljö, Ämnesavdelningen för elektronik.
    Influence of Student’s Attitudes and Beliefs on the Ability of Solving Mathematical Problems with Irrelevant Information2009Inngår i: Beliefs and attitudes in mathematics education: new research results / [ed] Jürgen Maasz and Wolfgang Schlöglmann, Rotterdam: Sense Publishers , 2009, s. 165-178Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    A limited quantitative survey has been performed in order to study how attitudes, beliefs and feelings of students may influence the ability of solving text-based mathematical problems containing irrelevant information. The survey is also analyzing their capability of scrutinizing texts and sorting out relevant information.

    The students took a written test with text-based problems of different amount of irrelevant information. The capability of understanding such problems was investigated versus degree of mathematical maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant information and the ability of solving the problems. Furthermore, attitudes, beliefs, and the degree of mathematical maturity, expressed in terms of age, have a clear influence on the results. On the other hand, this study has not revealed any significant difference between genders as regards the capability of solving text-based problems with irrelevant information.

     

  • 200.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Ämnesavdelningen för elektronik.
    Influence of Student’s Attitudes and Beliefs on the Ability of Solving Mathematical Problems with Irrelevant Information2009Inngår i: Beliefs and attitudes in mathematics education: new research results / [ed] Jürgen Maasz and Wolfgang Schlöglmann, Rotterdam: Sense Publishers , 2009, s. 165-178Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    A limited quantitative survey has been performed in order to study how attitudes, beliefs and feelings of students may influence the ability of solving text-based mathematical problems containing irrelevant information. The survey is also analyzing their capability of scrutinizing texts and sorting out relevant information.

    The students took a written test with text-based problems of different amount of irrelevant information. The capability of understanding such problems was investigated versus degree of mathematical maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant information and the ability of solving the problems. Furthermore, attitudes, beliefs, and the degree of mathematical maturity, expressed in terms of age, have a clear influence on the results. On the other hand, this study has not revealed any significant difference between genders as regards the capability of solving text-based problems with irrelevant information.

     

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