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  • 51.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Trigonometric and cylindrical polynomials and their applications in electromagnetics2019In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed)
    Abstract [en]

    Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

  • 52.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Kuzmina, Ekaterina
    Moscow Technological University MIREA, Moscow, Russia.
    On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides2018In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper (Refereed)
    Abstract [en]

    Theory of complex waves (see e.g. [1] and references therein) accumulated a big volume of results. However, its biggest drawback remains which brakes significantly the development of the theory: absence of rigorous proofs of the existence of complex waves. In this respect, studies of complex waves in open metal-dielectric waveguides has been essentially enhanced when two new families of symmetric (angle-independent) complex waves have been identified [2, 3] in a dielectric rod (DR) and Goubau line (GL) with homogeneous dielectric cover: surface complex waves occurring as perturbations of real surface waves caused by the presence of lossy dielectric, and pure complex waves which have no counterpart in the set of real waves. Existence of the latter family of complex waves has been shown using a special technique and the proof [3] of the existence of an infinite set of complex roots of the dispersion equation (DE) describing waves in DR and GL.

    In this work, a development of the analytical and numerical methods [2, 3] are considered for the analysis of the electromagnetic wave propagation in metal-dielectric waveguides with multi-layered dielectric filling. The first step constitutes extension of the results obtained for symmetric complex waves in DR and GLto the case of non-symmetric (angle-dependent) waves, and the second step, to multi-layered dielectric covers. Both steps are accomplished using specific forms of DEs obtained in [3]by construction analytical continuation of the functions involved in DEs to multi-sheet Riemann surfaces of the spectral parameter and applying appropriate generalization the techniques [4]forfinding complex roots of the DEs.

    Calculation ofnon-symmetric complex waves employs numerical solution of the DEs with the help of parameter differentiation in the complex domain using multi-parameter setting and analysis of implicit functions of several complex variables [5] and reduction [2, 3] to numerical solution of auxiliary Cauchy problems.

    1. A. S. Raevskiiand S. B. Raevskii, Complex Waves, Radiotekhnika, Moscow, 2010.

    2. E. Kuzmina and Y. Shestopalov, “Waves in a lossyGoubau line,”10th European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland, 2016, doi: 10.1109/EuCAP.2016.7481368.

    3. E. Kuzmina and Y. Shestopalov, “Complex waves in a dielectric rod and Goubau line,” 19th Int. Conf. on Electromagneticsin Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 963-966, doi: 10.1109/ICEAA.2017.8065417.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

    5.Y. Shestopalov,“On unique solvability of multi-parameter waveguide inverse problems, ”19th Int. Conf. on Electromagnetics in Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 372-376, doi: 10.1109/ICEAA.2017.8065253.

  • 53.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Sheina, Elena
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Smirnov, Alexander
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems2018In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper (Refereed)
    Abstract [en]

    Development of the methods and algorithms [1, 2] are considered for the numerical solution to the forward problem of the electromagnetic wave scattering by inhomogeneous dielectric inclusions in a waveguide of rectangular cross section and inverse problem of reconstructing parameters of the dielectric inclusions from the values of the transmission coefficient of the scattered electromagnetic wave. The codes are developed implementing an FDTD method that employs the PML-layer technique. Numerical modeling and simulations are performed for the analysis of the wave propagation in waveguides of rectangular cross section loaded with parallel-plane layered media (layered dielectric diaphragms) and such diaphragms containing cubic dielectric inclusions. Validation is carried out of the results of calculations using closed-form solution [3] to the canonical single-layer structure.

    Progress in analytical - numerical investigations of the solutions to the forward and inverse waveguide problems are largely based on a recent discovery [4] of the singularities and extrema in the complex domain of the transmission coefficient of layered dielectric diaphragms. In fact, the knowledge of the location of singularity and extrema sets of the scattering matrix allows one to justify correct determination of real or complex permittivity of each layer of the diaphragm by specifying domains in the complex plane where the transmission coefficientis one-to-one; that is, the domains that do not contain singularities and where unique permittivity reconstruction is therefore possible. Forthe forward problem of the scattering of a normal waveguide mode by a single-and three-layer diaphragms with a dielectric cube, it is shown [1, 2] that variation in the values of the transmission coefficient can be up to two orders of magnitude less than that of the permittivity of the inclusion. Taking into account this result and the presence of singularities, improvements are proposed of the numerical method, algorithms and codes implementing the calculations. The results of modeling and computations are validated by comparing with experimental and measurement data [3]. The requirements are formulated that should be imposed on the accuracy of computations and measurements necessary to reconstruct numerically permittivity of the inclusion from the amplitude and phase of the transmitted wave with the prescribed accuracy.

    1. E. Sheina, A. Smirnov,Y. Shestopalov,and M.Ufimtsev,“FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy,”Progress in Electromagnetics Research Symposium (PIERS),St Petersburg, Russia, 2017, pp. 3188-3195, doi:10.1109/PIERS.2017.8262306.

    2.E. Sheina, A. Smirnov, and Y. Shestopalov, “Influence of standing waves on the solution of the inverse problem ofreconstructing parameters of a dielectric inclusion in a waveguide,”URSI Int. Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 2016,pp. 643-646, doi:10.1109/URSI-EMTS.2016.7571479.

    3. Yu. G. Smirnov, Yu. V. Shestopalov, and E. D. Derevyanchuk, “Inverse problem method for complex permittivity reconstruction of layered media in a rectangular waveguide,”Physica Status Solidi(C), 11,5-6, 2014,pp. 969–974, doi:10.1002/pssc.201300697.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

  • 54.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, Maxim
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.
    New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 55.
    Sköld Runnfors, Rebecca
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Digitala verktygs påverkan på grundskoleelevers motivation inom matematiken2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
  • 56.
    Smirnov, Yuri
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line2019In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed)
    Abstract [en]

    The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

  • 57.
    Strandberg, Lovisa
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Att tala naturvetenskap: Kommunicera naturvetenskap i lågstadiet2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Den här uppsatsen ger en insikt i hur elever på lågstadiet kommunicerar för att förstå och göra sig förstådda inom naturvetenskap. Att ”tala naturvetenskap” handlar om mer än vetenskapliga begrepp och att en elev kan rabbla inlärda svar eller försöka lista ut vilka svar läraren vill höra. Genom intervjuer med elevpar från årskurs ett, två och tre undersöks hur barn på lågstadiet kommunicerar om naturvetenskapliga fenomen. Studien syftar även till att ta reda på hur elever på lågstadiet använder sig av varandras tankar när de talar om naturkunskap. Kan de hjälpa varandra att komma framåt? Resultatet från intervjuerna visar att eleverna använder sig av vardagsspråk framför naturvetenskapliga begrepp men att deras sätt att tala ändå är naturvetenskapligt.

  • 58.
    Trulsson, Madeleine
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Praktisk matematik: Hur man kan arbeta mer praktiskt inom ämnet matematik2019Independent thesis Basic level (university diploma), 20 credits / 30 HE creditsStudent thesis
  • 59.
    Ukic, Sejla
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Det ska vara en utmaning, men inte för svårt: En studie om hur fem lärare organiserar sin undervisning med matematisk problemlösning2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna studie är att undersöka lärares perception av matematisk problemlösning i årskurs F-3 samt hur lärare strukturerar upp sin undervisning och på vilket sätt de väljer problemlösningsuppgifterna. För att besvara studiens forskningsfrågor utfördes en kvalitativ undersökning i form av semistrukturerade intervjuer med fem verksamma lärare. Resultatet av studien påvisar att lärarna strukturerar upp sin undervisning i tre olika faser, dock finns det både likheter och olikheter i faserna. Gemensamt för majoriteten av lärarna är att de organiserar så att samarbete och kommunikation har ett naturligt inslag i undervisningen, trots att lärarnas definition av matematisk problemlösning i vissa avseende avviker från varandra samt forskning. Vidare påvisar resultatet att lärarna förespråkar att eleverna använder sig av konkret material/ rita som problemlösningsstrategier. Problemlösningsuppgifterna som eleverna arbetar med väljs främst ur läroböcker i samband med det matematiska området som är aktuellt, vilket kan medföra att problemen övergår till att vara rutinuppgifter. 

  • 60.
    Viirman, Olov
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Kristiansand, Norway.
    Nardi, Elena
    School of Education, University of East Anglia, Norwich, UK.
    Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modelling activities2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 2, p. 233-252Article in journal (Refereed)
    Abstract [en]

    Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

  • 61.
    Walid, Mohammad Adham
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Simulation of train passage2019Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The project simulates the passage of a moving train on the railway when it is passing a level crossing. The project uses hardware and software to simulate the signals that the relays, which are connected to the track, get when a train is passing the level crossing. This simulation is to evaluate a new level crossing system that is called Alex and will be used in Sweden in the future. One set of relays and two Alex systems will be installed at the Swedish school of transportation (Trafikverksskolan) in Ängelholm at a simulated level crossing for testing and training purposes. The project also evaluates the reactions of the relays of any level crossing without running any real train on them.

  • 62.
    Wallström, Åsa
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Matematikdidaktik utomhus, varför inte?: En undersökning om F-3 lärare och deras möjligheter till utomhusdidaktik2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med detta arbete var att undersöka lärarnas inställning till att bedriva matematik utomhus och deras tankar och uppfattningar kring ämnet. Min studie baserades på kvalitativa semistrukturerade intervjuer av sex olika lärare från olika skolor i Gävleborgs län. Resultatet från min undersökning visar att många lärare är positivt inställda till att vara utomhus och de innehar kunskapen om att barnen finner glädje med att bedriva matematik med inslag av att vara ute kopplat till rörelseaktiviteter. För att främja utomhusmatematik och inse dess fördelar och betydelsefullhet är det av stor vikt att lärarna bortser från bekvämligheter och undanflykter. Eleverna är det primära och lärarnas uppgift är att finna genvägar och underlätta för elevernas framgång i matematik.

  • 63.
    Wieveg, Jessica
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Klassrummet – en dynamisk lärmiljö: -En studie om hur tre lärare arbetar med att individanpassa matematikundervisningen2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 64.
    Wiklund, Annie
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Att arbeta med problemlösning: En studie om hur tre lärare använder problemlösning i matematikundervisningen2019Independent thesis Basic level (university diploma), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med uppsatsen är att undersöka vilka problemlösningsstrategier lärare använder sig av i undervisningen, samt vilka metoder lärare använder när de undervisar ele-verna i problemlösning. Studien grundar sig i kvalitativa undersökningar genom klassrums ob-servationer och semistrukturerade intervjuer med tre lärare. Lärarna arbetade på två olika skolor i samma kommun i Mellansverige. Resultatet visar att lärarna undervisar eleverna i flertalet strategier som de kan tillämpa i sin problemlösning, men vissa strategier använts mer frekvent än andra. Studien visar även lärarnas medvetenhet om vad som gynnar eleverna i undervis-ningen av problemlösning. Samtliga lärare är medvetna om att problemlösningsförmågan är något som utvecklas under lång tid och att det krävs många tillfällen till övning. Undervisningen om strategier att tillämpa är av stor vikt för elevernas framgång. I denna undervisning har lära-ren en stor del i om och hur eleverna utvecklas.

  • 65.
    Winberg, Emma
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Motivation till lärande: Hur kan mellanstadieelever motiveras till att jobba med matematik i skolan?2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
  • 66.
    Zhao, Xuhui
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Electronics.
    Automatic analysis for continuous integration test failures2019Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    CI (Continuous Integration) is a software development practice which became more and more popular in last decade. Ericsson followed the trends and used CI several years. Because of the complexity of RBS (Radio Base Station) software few levels of CI have been implemented there. In RCS (RBS Control System) module CI there are many automatic JCAT (Java Common Auto Tester) test loops running every day and some of them failed. This thesis tries to find a way to classify these test failures automatically, so efficiency and lead time can be improved.

    Two methods are presented and investigated in this report, rule matching and machine learning. After analysis and comparisons rule matching approach is selected because it does not require huge effort in the initial phase and rule matched data can be used as labeled data for machine learning. This approach requires manual work to add new rules continuously but with correctly defined rules the accuracy is 100%, if the rule is general it can classify one type of issue including the ones which never happen before.

    One analysis system is designed and implemented, and only small update is required to the result report block of the CI flow. One matching example is showed and according to estimation this method could save many man hours every year.

  • 67.
    Ängskog, Per
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Electronics. Department of Electromagnetic Engineering, KTH Royal Institute of Technology, Stockholm, Sweden.
    Bäckström, Mats
    Department of Electromagnetic Engineering, KTH Royal Institute of Technology, Stockholm, Sweden.
    Samuelsson, Carl
    Saab Aeronautics, Linköping, Sweden.
    Kangashaka Vallhagen, Bengt
    Saab Aeronautics, Linköping, Sweden.
    Shielding Effectiveness and HPM Vulnerability of Energy-Saving Windows and Window Panes2019In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, Vol. 61, no 3, p. 870-877Article in journal (Refereed)
    Abstract [en]

    In this paper, we report results from shielding effectiveness measurements on energy-saving windows and individual, coated window panes of different generations, as well as results from high-power microwave irradiation on single panes. Shielding effectiveness was measured with two complementary methods: first, with near isotropic irradiation in nested reverberation chambers, and the other with irradiation at normal incidence in a semianechoic chamber. The measurements show that the construction of the energy conserving windows has a clear impact on how well they attenuate radio frequency signals. The more modern the window or pane, the higher is the shielding effectiveness. The high-power irradiation on coated panes showed that depending on the type of coating, hotspots can build up causing the coating to crack and, hence, deteriorate the shielding effectiveness. These results may serve as guidance when reviewing high-altitude electromagnetic pulse (EMP), high-power microwave, or intentional electromagnetic interference protection of critical infrastructures, and provide assistance in the work with reduction of compromising emanations.

  • 68.
    Åhr, Simon
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Framtagning av ett multiplexerat datainsamlingssystem för mätning av små elektriska strömmar2019Independent thesis Basic level (university diploma), 180 HE creditsStudent thesis
  • 69.
    Öberg, Karin
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Det behövs ett nytt verktyg för att reparera bristande baskunskaper i matematik: En studie om Elevate My Math´s effekter hos svensla gymnasieelever2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Mätningar av kunskaperna inom matematik hos svenska elever har under en längre tid visat på en nedåtgående trend. Samtidigt läser vi dagligen om den svenska lärarkårens höga arbetsbelastning. Syftet med det här examensarbetet är att undersöka en hållbar lösning, som både vänder den nedåtgående kunskapstrenden hos eleverna och dessutom underlättar lärarnas arbete. I Examensarbetet undersöks elevernas upplevelser samt kunskapsutveckling då de  arbetar med det digitala verktyget Elevate My Math.

    Undersökningen, som är både kvantitativ och kvalitativ görs i en ekonomiklass där halva klassen får arbeta med Elevate My Math och den andra halvan får jobba med ett material som vanligtvis används inom undervisningen. Resultaten visar att eleverna upplevelse av att arbeta med Elevate My Math är mycket positiv. Samtidigt visar resultatet att vidare forskning behövs för att säkerställa elevernas kunskapsutveckling vid användandet av Elevate My Math.

  • 70.
    Öhman, Johanna
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. 19881121-1542.
    Lärares syn och attityd på användandet av digitala verktyg inom matematikämnet2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
  • 71.
    Örnblom, Anna
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
    Strategier vid problemlösning i matematik: Lärares arbete med problemlösning i matematik i de lägre årskurserna2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Denna studie har genomförts för att undersöka om och hur lärare i de lägre årskurserna arbetar med och lär ut problemlösning i matematik. Metoder som använts för att undersöka detta är enkät och intervju. Totalt har 16 lärare svarat på enkäten och 4 lärare har deltagit i en kvalitativ intervju. Resultatet redovisar att alla deltagande lärare arbetar aktivt med problemlösning i matematik. De använder olika arbetssätt, strategier och lösningsstrategier i sitt arbete med att undervisa i problemlösning.

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