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  • 1.
    Abens, Maria
    University of Gävle, Department of Mathematics, Natural and Computer Sciences.
    Outdoor Education in Mathematics: Can it be implemented?2008Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This study examines outdoor education in mathematics at an international school under the IB PYP curriculum. Students spend most of their time indoors with the exception of lunch recess. Outdoor education provides a new and different way for both teachers and students to get fresh air. Research indicates that children who spend more time outdoors suffer less from allergies and other health problems. In the study, teachers and parents were given questionnaires, and three mathematics lessons were conducted outdoors.  Students were later interviewed in groups. Most parents and teachers were positive to the idea of academic outdoor lessons in any subject. Teachers saw some difficulties implementing it because of time, weather and behavioural problems with students outside. Furthermore, they agreed that children should spend more time outside and that the children’s health might benefit. Most of the students enjoyed the outdoor mathematics lessons. They were positive towards outdoor education in any subject.

  • 2.
    Ali, Rafef
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Matematik och estetiska lärprocesser: en studie om ämnesintegration av estetiska verktyg i matematikundervisning.2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med undersökningen var att observera hur lärarna arbetar med matematik i årskurserna F-3, med fokus på hur estetiska verktyg används i matematikundervisningen. Studien är baserad på klassobservationer i två årskurser i de tidigare skolåren F-3 samt elev- och lärarintervjuer och ämnade lyfta estetiska lärprocesser samt hur de spelar in på elevernas upplevelser vad gäller ämnesintegration i matematikundervisning. Resultaten visar att estetiska verktyg används mer med yngre elever och mindre ju äldre eleverna blir. Lärarna i denna studie påpekade att ett ämnesövergripande arbetssätt och att blanda in olika sinnen främjar elevernas inlärning. Majoriteten av de intervjuade lärarna betonade att det gäller att hitta en balans mellan olika metoder för att skapa en varierad undervisning. 

  • 3.
    Allaire, G.
    et al.
    Ecole Polytechnique, Palaiseau Cedex, France.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway.
    Piatnitski, A.
    Lebedev Physical Institute RAS, Moscow, Russia.
    Homogenization and concentration for a diffusion equation with large convection in a bounded domain2012In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, no 1, p. 300-330Article in journal (Refereed)
    Abstract [en]

    We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests.

  • 4.
    Allaire, G.
    et al.
    Ecole Polytechnique, Palaiseau Cedex, France.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway; Ecole Polytechnique, Palaiseau Cedex, France.
    Piatnitski, A.
    Narvik University College, Narvik, Norway; Lebedev Physical Institute RAS, Moscow, Russia.
    Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer2012In: SeMA Journal, ISSN 1575-9822, Vol. 58, no 1, p. 53-95Article in journal (Refereed)
    Abstract [en]

    The paper deals with the homogenization of a non-stationary convection-diffusion equation defined in a thin rod or in a layer with Dirichlet boundary condition. Under the assumption that the convection term is large, we describe the evolution of the solution’s profile and determine the rate of its decay. The main feature of our analysis is that we make no assumption on the support of the initial data which may touch the domain’s boundary. This requires the construction of boundary layer correctors in the homogenization process which, surprisingly, play a crucial role in the definition of the leading order term at the limit. Therefore we have to restrict our attention to simple geometries like a rod or a layer for which the definition of boundary layers is easy and explicit.

  • 5.
    Andersson Younas, Nikolina
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    För att eleverna verkar tänka bättre när de får prata: Vilka metoder kan man hitta hos lärare som främjar diskussioner i matematik2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med arbetet är att söka reda på olika metoder lärare använder i klassrumssituationer för att stödja elevernas utveckling i matematiska uttryck gällande muntlig kommunikation mellan elever och lärare. Arbetet är baserat på observationer av tre lärare i årskurs 4, 6 och 9. Insamlad information från observationerna har resulterat i tre olika lektionsstrukturer och ett antal frågemodeller. Gemensamt i samtliga lektioner är att eleverna får först diskutera och berätta innan läraren blanda sig i; läraren har använt elevernas samtal för att bygga vidare och utgår på det sättet utifrån elevernas kunskaper. Vissa lektioner har fokus legat i diskussionen och elevers presentation av sina lösningar för klassen. I andra lektioner har läraren använt en specifik didaktisk metod för att stimulera diskussionen och elevernas förståelse. Samtliga lärare uttrycker att ett mål de haft är att eleverna skall få chansen att diskutera och ge uttryck för sina tankar verbalt.

  • 6.
    Andréasson, Frida
    University of Gävle, Faculty of Engineering and Sustainable Development.
    Barns sätt att benämna och uppfatta geometriska former: En observation och intervjustudie med förskolebarn2010Independent thesis Basic level (university diploma), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med arbetet är att undersöka hur barn i åldrarna tre till sex år uppfattar de geometriska formerna i sin närmiljö, utan att någon vuxen påvisar formerna. I undersökningen ingår även att se vilka former barnen känner till och hur de benämner formerna. Metoderna som använts i undersökningen är intervjuer och observationer. Huvudresultatet var att barnen såg olika geometriska former i sin förskolemiljö. Hur barnen benämnde formerna varierar mellan matematisk benämning och vardagsbenämning och även egen påhittad benämning. Att förskolorna arbetar olika med matematik gör ingen skillnad för hur barnen benämner formerna.

    Viktig Slutsats: Barnen benämner de geometriska formerna med samma benämning som de vuxna i barnens omgivning använder sig av.

  • 7.
    Angermann, Lutz
    et al.
    Clausthal University of Technology, Clausthal, Germany..
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Yatsyk, Vasyl
    O. Ya, Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    Mathematical models for scattering and generation of plane wave packets on layered cubically polarisable structures2013In: Far East Journal of Applied Mathematics, ISSN 0972-0960, Vol. 81, no 1-2, p. 1-31Article in journal (Refereed)
    Abstract [en]

    The paper deals with different formulations of mathematical models for the analysis of processes of resonance scattering and generation of plane wave packets on isotropic, nonmagnetic, linearly polarised media with a nonlinear, layered dielectric structure of cubic polarisability. For each formulation, sufficient conditions for the existence and, partially, uniqueness of the corresponding solution are derived.

  • 8.
    Angermann, Lutz
    et al.
    Technische Universität Clausthal, Institut für Mathematik, Clausthal-Zellerfeld, Germany .
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Yatsyk, Vasyl V.
    O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine .
    Eigenmodes of linearised problems of scattering and generation of oscillations on cubically polarisable layers2015In: Inverse Problems and Applications / [ed] Larisa Beilina, Springer-Verlag New York, 2015, Vol. 120, p. 67-80Conference paper (Refereed)
    Abstract [en]

    In the frequency domain, the resonant properties of nonlinear structures are determined by the proximity of the scattering/generation frequencies of the nonlinear structures to the complex eigenfrequencies of the corresponding homogeneous linear spectral problems with the induced nonlinear permeability of the medium. Here the case of cubically polarisable, canalising, and decanalising layers is considered.

  • 9.
    Asami-Johansson, Yukiko
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Linköpings universitet, Matematiska institutionen.
    Designing Mathematics Lessons Using Japanese Problem Solving Oriented Lesson Structure: A Swedish case study2015Licentiate thesis, monograph (Other academic)
    Abstract [en]

    This licentiate thesis is concerned with applying the Japanese problem solving oriented (PSO) teaching approach to Swedish mathematics classrooms. The overall aim of my research project is to describe and investigate the viability of PSO as design tool for teaching mathematics. The PSO approach is a variation of a more general Japanese teaching paradigm referred to as “structured problem solving”. These teaching methods aim to stimulate the process of students’ mathematical thinking and have their focus on enhancing the students’ attitudes towards engaging in mathematical activities. The empirical data are collected using interviews, observations and video recordings over a period of nine months, following two Swedish lower secondary school classes. Chevallard’s anthropological framework is used to analyse which mathematical knowledge is exposed in the original Japanese lesson plans and in the lessons observed in the classrooms. In addition, Brousseau’s framework of learning mathematics is applied to analyse the perception of individual students and particular situations in the classroom.

    The results show that the PSO based lesson plans induce a complex body of mathematical knowledge, where different areas of mathematics are linked. It is found that the discrepancy between the Japanese and Swedish curriculum cause some limitations for the adaptation of the lesson plans, especially in the area of Geometry. Four distinct aspects of the PSO approach supporting the teaching of mathematics are presented.

  • 10.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Concept definition and concept image: in the case of equations2007In: Ämnesdidaktik ur ett nationellt och internationellt perspektiv: rapport från Rikskonferensen i ämnesdidaktik, Kristianstad: Kristianstad University Press , 2007, p. 89-98Conference paper (Refereed)
    Abstract [en]

    The purpose of this study is to analyse what kind of conceptions secondary school teachers in mathematics have about equations and how these conceptions are related to the formal definition of the concept of equation. Data was gathered by interviews and questionnaires. Both newly graduated and experienced secondary school teachers were participated in this study. The phenomenographic research approach in order to analyse research outcomes was applied in the investigation. From a phenomenographic analysis of the interview transcripts I found that some patterns could be identified in them and the three qualitatively distinct categories of description about equations could be discerned among the teachers’ conceptions. The research results indicated that equations were apprehended as a procedure, as an answer and as a ‘rewritten’ expression.

  • 11.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Matematikdidaktik för blivande 4-9-lärare2001Report (Other academic)
  • 12.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Mathematics teachers' conceptions about concept learning in algebra2007In: Current state of research on mathematical beliefs XII: proceedings of the MAVI-7 [i.e. MAVI-12] Workshop, May 25-28, 2006, Helsinki: University of Helsinki , 2007, , p. 12Chapter in book (Other academic)
    Abstract [en]

    In this article I discuss the mathematics teachers’ conceptions about concept learning in algebra from school and university time. The study has a focus on the particular topic of equations. The data was gathered by interviews and questionnaires. Both newly graduated and experienced secondary school teachers were participated in this study. The phenomenographic research method in order to analyse research outcomes was applied in the investigation. The research results indicated that the teachers experience the learning of equations from school and university time on four qualitatively different ways. Learning was apprehended as doing routine problems, as memorizing and reproduction of rules and models, as doing applications and as interaction with other students.

  • 13.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Mathematics teachers' conceptions about equations2006Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    The aim of this study is to describe and to clarify the mathematics teachers’ subject matter and pedagogical content conceptions about equations. As the basis of these conceptions, the teachers’ experiences of the concept learning of equations from their own school time are described. The early research of conceptions has been concentrated on pupils’ conceptions of the topic as a contrast to scientific conceptions since the middle of the 1970s. Research of teachers’ conceptions of mathematics and mathematics teaching and learning has grown during the last decade. However, in these studies teachers’ conceptions of a specific content area in mathematics have not been investigated. In the theoretical background of the research, different traditions of school mathematics learning and teaching are treated. By using theories of experiential learning, it has been possible to study such learning situations and experiences, which may lead to the development of subjective conceptions of mathematical concepts. In order to understand difficulties concerning the concept formation in mathematics the theory of the concept image and the concept definition as well as the theory based on the duality of mathematical concepts have been studied. The acquired experiences from school time seem to lay the basis of both the teachers’ subject matter and pedagogical content-specific conceptions and decisions. Different components in teacher knowledge base together with current research both in teachers’ subject matter and pedagogical content knowledge are therefore presented at the end of the theoretical framework. By combining different kinds of methods like questionnaires, recorded interviews, videotape recording of six lessons in mathematics and observations the research empirical material was collected. In this investigation, five novice, five expert and 75 student teachers in mathematics participated. The preliminary investigation included 30 student teachers. In the study the phenomenographic approach is used in order to reveal differences between the teachers’ conceptions and experiences about equations. The research results indicate that equations are not apprehended as complete, static objects. Conceptions about equations reveal that equations are closely related to the symbols x and y and solving procedures. The teachers’ experiences of learning and teaching of mathematics may have formed their conceptions. The conceptions about equations seem to be based on the teachers’ experiences in arithmetic and their first impressions of learning the process of solving equations. The teachers apprehend equation teaching as a study of procedures rather than as a study of central ideas and concepts of algebra. Both aspects are however equally important at compulsory school, since the teaching of algebra should develop pupils’ ability both to use and to understand the basic algebraic concepts. Some of the teachers do not have a clear conception what the pupils should attain in algebra at compulsory school according to the specific goals in Swedish mathematics curriculum. The research results further show that both the expert and the novice teachers have various apprehensions of the pupils’ difficulties concerning equations.

  • 14.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Teachers’ knowledge about the equation concept2002In: International group for the psychology of mathematics education PME 26, 2002, p. 1-335Conference paper (Other academic)
  • 15.
    Attorps, Iiris
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Uppfattningar hos lärare av ekvationsbegreppet2003Report (Other academic)
    Abstract [en]

    Syftet med min studie är att beskriva hur matematiklärare uppfattar begreppet ekvation. Min målsättning är också att undersöka lärarnas erfarenheter av ekvationsinlärning från grundskolan till universitetsnivån. Tio lärare från grundskolans högstadium har deltagit i undersökningen. Fem är nyutexaminerade lärare med mindre än ett års yrkeserfarenhet. Data i undersökningen samlades in genom enkäter och intervjuer. Undersökningsresultat analyserades genom fenomenografisk metod. Resultatet pekar på att lärarnas uppfattningar av ekvationsbegreppet avviker från den formella begreppsdefinitionen. De känner osäkerhet inför matematiska symboler, bokstavsuttryck och lösningsprocedurer. Deras skolerfarenheter visar att de har använt största delen av tiden till att utveckla algoritmiska färdigheter istället för matematisk förståelse.

  • 16.
    Attorps, Iiris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Björk, Kjell
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Radic, Mirko
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Generating the patterns of variation with GeoGebra: the case of polynomial approximations2016In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 47, no 1, p. 45-57Article in journal (Refereed)
    Abstract [en]

    In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group. 

  • 17.
    Attorps, Iiris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Björk, Kjell
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Radic, Mirko
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Tossavainen, Timo
    University of Eastern Finland, Finland.
    Varied ways to teach the definite integral concept2013In: International Electronic Journal of Mathematics Education, ISSN 1306-3030, Vol. 8, no 2-3, p. 81-99Article in journal (Refereed)
    Abstract [en]

    In this paper, we report on a collaborative teaching experiment based on the Learning Study model (LS model) which grounds on the Variation Theory. Until today, most of such studies have focused on the teaching and learning of elementary school mathematics; ours was carried out in undergraduate mathematics education. In the following, we discuss how we managed to promote students’ conceptual learning by varying the treatment of the object of learning (the concept of definite integral and the Fundamental Theorem of Calculus) during three lectures on an introductory course in calculus. We also discuss the challenges and possibilities of the LS model and the Variation Theory in the development of the teaching of tertiary mathematics in general. The experiment was carried out at aSwedish university. The data of the study consists of the documents of the observation of three lectures and the students’ answers to the pre- and post-tests of each lesson. The analysis of learning results revealed some critical aspects of the definite integral concept and patterns of variations that seem to be effective to a significant degree. For example, we found several possibilities to use GeoGebra to enrich students’ learning opportunities.

  • 18.
    Attorps, Iiris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Björk, Kjell
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Radic, Mirko
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Viirman, Olov
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Teaching Inverse Functions at Tertiary level2013In: CERME 8: Proceedings of the EightŠ Congress of the European Society for Research in Mathematics Education, Antalya: Middle East Technical University , 2013, p. 2524-2533Conference paper (Refereed)
    Abstract [en]

    This study is a part of an ongoing research that attempts to explain the relationship between the teachers’ instructional practise and students’ learning in the context of functions and function inverses. The question in this paper is how the use of technology as a pedagogical tool may contribute to the understanding of the inverse function concept. An engineering student group (n =17) was taught functions and inverse functions with the assistance of GeoGebra. In our theoretical framework we apply Variation theory together with the theory of Concept image and Concept definition. The data were gathered by doing a pre and post test concerning inverse functions. Our experiment revealed that students’ concept images in the post test were more developed compared with the results in the pre test.

  • 19.
    Attorps, Iiris
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Johansson, Eva
    Area och omkrets i förskoleklass2008In: Nämnaren, ISSN 0348-2723, Vol. 35, no 1, p. 34-36Article in journal (Other academic)
    Abstract [sv]

    Här beskrivs ett antal undervisningstillfällen kring begreppen area och omkrets i en förskoleklass. I planeringen har lärarna utgått från att barnen ska samarbeta, kommunicera med varandra, använda flera sinnen, reflektera över sitt och andras tänkande samt dokumentera och sätta egna ord på det de varit med om.

  • 20.
    Attorps, Iiris
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Kellner, EvaUniversity of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för naturvetenskap.
    Conceptions and beliefs in mathematics and science education including MAVI XIII2008Conference proceedings (editor) (Other academic)
  • 21.
    Attorps, Iiris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Kellner, Eva
    University of Gävle, Faculty of Health and Occupational Studies, Department of Occupational and Public Health Sciences, Biology.
    School-€“University Action Research: Impacts on Teaching Practices and Pupil Learning2017In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 15, no 2, p. 313-330Article in journal (Refereed)
    Abstract [en]

    The aim of this article is to describe a design and implementation of a school–university action research project about teaching and learning biology and mathematics in primary school. Nine teachers in grades 1 to 6, in collaboration with two researchers, were using content representation (CoRe) in learning study (LS)-inspired cycle as pedagogical tools when planning, implementing, and reflecting on lessons and pupil learning. By using pre- and post-tests, the teachers acquired knowledge about pupil subject-specific knowledge and learning. Some examples are given on how the tools in the project influenced the teaching practices and pupil learning. This research design brought together university and school practitioners to work collaboratively in a professional learning community, which developed teaching and learning in biology and mathematics.

  • 22.
    Attorps, Iris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Hector, Sören
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Radić, Mirko
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Creating the patterns of variation with GeoGebra when teaching derivative graphs for first year engineering students2015In: International Journal of Engineering ,Science and Innovative Technology, ISSN 0949-149X, E-ISSN 2277-3754, Vol. 31, no 6, p. 1605-1612Article in journal (Refereed)
    Abstract [en]

    The present study investigates how technology assisted and designed teaching influences engineering students’ understanding of the connection between the graph of a function and its derivatives. An engineering student group (n = 27) was taught with the assistance of GeoGebra while a control group (n =20) was taught in a traditional way. The data of the study consist of the documents and photos of the observation of two lectures and the students’ answers to the pre and post tests. In our theoretical framework we discuss the distinction between conceptual and procedural knowledge. When creating the teaching sequences we applied variation theory. In the analysis of the students’ pre and post tests results we applied statistical methods. Our experiment revealed that the GeoGebra-assisted teaching design created more opportunities for students to grasp the connection between a function and its derivatives.

  • 23. Order onlineBuy this publication >>
    Attorps, Iris
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Radic, Mirco
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Variationsteoretiskt perspektiv på matematikundervisningen2016In: Ämnesdidaktiska utmaningar - inom matematik, naturvetenskap och teknik / [ed] Mikael Björling, Gävle: Gävle University Press , 2016, 1, p. 15-26Chapter in book (Other academic)
  • 24. Barrera, Tony
    et al.
    Spångberg, Daniel
    Hast, Anders
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Bengtsson, Ewert
    Vectorized table driven algorithms for double precision elementary functions using Taylor expansions2009In: APLIMAT 8th international conference, 2009, p. 231-246Conference paper (Refereed)
    Abstract [en]

    This paper presents fast implementations of the inverse square root and arcsine, both in double precision. In single precision it is often possible to use a small table and one ordinary Newton-Raphson iteration to compute elementary functions such as the square root. In double precision a substantially larger table is necessary to obtain the desired precision, or, if a smaller table is used, the additional Newton-Raphson iterations required to obtain the precision often requires the evaluation of other expensive elementary functions. Furthermore, large tables use a lot of the cash memory that should have been used for the application code.

    Obtaining the desired precision using a small table can instead be realised by using a higher order method than the second order Newton-Raphson method. A generalization of Newton's method to higher order is Householder's method, which unfortunately often results in very complicated expressions requiring many multiplications, additions, and even divisions.

    We show how a high-order method can be used, which only requires a few extra additions and multiplications for each degree of higher order. The method starts from the Taylor expansion of the difference of the value of the elementary function and a starting guess value for each iteration. If the Taylor series is truncated after the second term, ordinary Newton iterations are obtained. In several cases it is possible to algebraically simplify the difference between the true value and the starting guess value. In those cases we show that it is advantageous to use the Taylor series to higher order to obtain the fast convergent method. Moreover, we will show how the coefficients of a Chebyshev polynomial can be fitted to give as little error as possible for the functions close to zero and in the same time reduce the terms in the Taylor expansion.

    In the paper we benchmark two example implementations of the method on the x86_64 architecture. The first is the inverse square root, where the actual table (to 12 bit precision) is provided by the processor hardware. The inverse square root is important in many application programs, including computer graphics, and explicit particle simulation codes, for instance the Monte Carlo and Molecular Dynamics methods of statistical mechanics. The other example is the arcsine function, which has a slow converging Taylor expansion and where no tables are provided by the hardware. The vectorized versions of the implementations of the inverse square root are 3.5 times faster than compiled code on the Athlon64 and about 5 times faster on the Core 2. The scalar version of the arcsine function is, depending on order and table size, between 2 and 3 times faster than the compiled code, and the vectorized version is between 3 and 4 times faster on the Athlon64, while it is between 4 and 5 times faster than the compiled version on the Core 2.

  • 25.
    Berg, Hanna
    et al.
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences.
    Svedberg, Emma
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences.
    Lekande lätt att lära matematik: en handledning i matematik för förskolans personal2017Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Forskning visar på att allt fler förskollärare anser att det är svårt att lära ut matematik till yngre barn. För att bidra till ökad matematikundervisning samt förståelse framställdes en produkt, i form av en handledning. Handledningen riktar sig till förskolepersonal som arbetar med barns lärande av matematik. Detta gjordes främst för att all förskolepersonal ska kunna vara delaktig i undervisningen.

    Handledningen innefattade fyra olika matematiska avsnitt med varierande aktiviteter som kallades talraden, geometri, mönster samt mätning. De utvalda aktiviteterna stöds i handledningen främst av Bishops matematiska aktiviteter och mål från förskolans läroplan samt vetenskaplig grund i form av forskning. Handledningen provades av intresserad förskolepersonal från tre olika förskolor. De 14 personerna som provade materialet svarade sedan på en utvärderingsenkät som handledningen reviderades utifrån. Under arbetets gång gavs tillfälle att presentera handledningen för en grupp förskolechefer. De lämnade sina åsikter som sedan jämfördes med förskolepersonalens svar. Resultatet visade att handledningen fyller en funktion i matematikundervisningen i förskolan samt att den fungerar både i teori och praktik. Slutsatsen som dras är att handledningen bidrar till att underlätta matematikundervisningen.

  • 26.
    Bergholm, Marie
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Linköpings universitet, Matematiska institutionen.
    Gymnasieelevers kommunikativa strategier i matematikklassrummet: En fallstudie av ett smågruppsarbete om derivata2014Licentiate thesis, monograph (Other academic)
    Abstract [en]

    This case study takes its focus on upper secondary school students’ work in small groups with a problem related to the derivative. The analysis aims to identify factors that promote or hinder an individual’s participation in and development of the mathematical communication in the classroom. The theoretical basis of the study is Anna Sfard’s commognitive framework, where learning mathematics is seen as participating in a mathematical discourse.

    For more than a decade, reports about Swedish students’ decreasing levels of school mathematical knowledge have been put forward. Research points to various factors behind this development. The prevailing educational culture, where students largely work individually from the textbook, is seen as one explanation for the deterioration in the results, and that teaching does not give students the opportunity to develop all the required competencies in the curriculum. To achieve this, both research and the new Swedish curriculum from 2011 emphasize the importance of student communication in mathematics. In this perspective, there is a need to highlight the differences in student participation in the communication of mathematics in the classroom, particularly in the context of small group learning, and how this is assumed to influence students’ opportunities for learning.

    The focus of the research is directed towards the participants’ contributions to the group’s mathematical discourse, i.e. when they communicate about mathematical objects or processes, and how these affect students’ opportunities and participation in the communication. Focus is also directed to the communication that involves participants in the group, what the students are doing and how they evaluate each other’s way to participate in the mathematical discourse in the classroom. This type of communication is in the framework referred to as subjectifying, and is assumed to affect the individual’s mathematical learning.

    Data collection methods used are interviews, audio and video recordings, as well as “smart pens” to combine verbal and written communication. In the first step of the analysis, the mathematical discourse was studied regarding differences in the content of the participants’ utterances. The second step of analysis focused on the interaction flow of the group to understand more of the differences in each student’s participation and contribution to the communication.

    The results point to big differences regarding participation and content in student communication, both at group level and individual level. The development of students’ mathematical discourse benefits from the use of multiple mediators to represent the mathematical objects. When connections to a previously acquired discourse are offered, this leads to discursive advancements. Students were observed to have difficulties to interpret and use the formal mathematical symbolic language that would support their mathematizing. Students’ interpretation of the equality sign, the sign for inequality, and the symbol f´(x) on a process level, create obstacles to developing the mathematical discourse in the desired direction. The discourse about the participants and their own traits  (identification) constitutes about 10% of all utterances and are almost all negative reviews, frequently used in order to exclude or incorporate themselves or others from participating in the mathematizing activity.

    This research study points to a need for more knowledge about how mathematics teachers can best organize work in small groups to increase student engagement and the quality of their mathematizing. The study also indicates the importance of mathematics teachers highlighting and varying the use of different mediators to represent the mathematical objects to learn. The case study also highlights the importance of building up a permissive environment in which students do not evaluate themselves and others, but instead dare to ask questions that will make them increasingly involved in the mathematical discourse. A need emerges for further research not only on the assessment between teacher and student, but also on the assessment that goes on in the classroom between the students, which can affect what roles they take or are assigned to in the classroom. This can be assumed to be of great importance to the way students communicate about mathematics with other students in the classroom, which is also likely to influence learning.

  • 27.
    Bergström Lissmyr, Jannice
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    En kvalitativ studie om lärarens syn på lässvårigheters påverkan på matematikinlärningen: samt andra svårigheters påverkan2017Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med den här studien är att undersöka hur lärare ser på lässvårigheters påverkan på matematikinlärningen i årskurserna 4–6. Metodvalet är inom det didaktiska forskningsområdet, arbetet består av en litteraturbakgrund, observationer och intervjuer med sex verksamma lärare och en specialpedagog för att undersöka deras syn på hur lässvårigheter kan påverka matematikinlärningen.

     

    Resultatet visar att det kan finnas ett samband mellan lässvårigheter och matematiksvårigheter. Det som framkommer i arbetet är att det finns bakomliggande faktorer som påverkar läsinlärningen och matematikinlärningen. Det är flera delar som påverkar inlärningen, en del är den som är kopplad till de språkliga inlärningsförmågorna, som är en bristande fonologisk förmåga, läsförståelsen och ett svagt arbetsminne. När eleven har svårt med dessa faktorer påverkar det även möjligheten till inlärning i matematik. Förutom de här svårigheterna visar resultatet att de emotionella känslorna påverkar elevers förmåga att prestera. En av de emotionella känslorna som påverkar eleven är motivation och intresse för de som ska läras, om det inte finns motivation och intresse sker ingen inlärning. Det som forskare och lärare är absolut överens om är att ett dåligt självförtroende är det som påverkar eleven mest vid inlärningen. Ett dåligt självförtroende kan leda till blockeringar inte bara för läsinlärningen utan för övriga ämnen i skolan så som matematik.

  • 28.
    Björkman, Maria
    University of Gävle, Faculty of Engineering and Sustainable Development.
    Övningar med förskolebarn i naturen: En undersökning om barns matematikkunskaper2013Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna undersökning har jag genomfört tre olika övningar i matematik i naturen med några förskolebarn i åldern fyra år för att ta reda på deras kunskap i räkning, jämförelseord och sortering. Mitt syfte var att se hur utvecklad barnens kunskap var i de av Gelman och Gallistels principer som övningen innehöll. Resultatet visade att barnen hade goda kunskaper i de övningar som utfördes. Den metod jag använde var att gå ut i skogen till en välbekant plats. Där fick barnen genomföra övningarna med hjälp av kottar, stenar, pinnar och löv. 

    Den erferanhet jag gjorde var att jag fick se att barnens kunskaper bland annt kunde visas med hjälp av deras sinnen och genom lek.

  • 29.
    Brand, Katharina
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Lekfull matematik i förskolan2014Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet i denna undersökning har varit att undersöka hur utvecklad barnens antalsräkning är i olika åldrar genom att framförallt studera antalsprincipen och abstraktionsprincipen. Genomförande har skett i olika åldersgrupper där barnen har fått fiska ankor med matematikuppdrag under ankornas magar i form av prickar att räkna. Observationer har gjorts under aktiviteterna där jag antecknat barnens svar i ett färdigt kryssprotokoll. Studien visar hur barn hanterar antalsräkning i lekfulla aktiviteter där det blir inspirerande att lära sig räkna genom att räkna prickar på ankorna, samt att para ihop dem efter utseende. Resultatet visade att barnen har goda kunskaper i antalsräkning där pekräkningen användes. Vid ögonräkningen visade barnen bristande kunskaper.

  • 30.
    Brandt, Sven Anders
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Land management, GIS.
    Modeling and visualizing uncertainties of flood boundary delineation: algorithm for slope and DEM resolution dependencies of 1D hydraulic models2016In: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 30, no 6, p. 1677-1690Article in journal (Refereed)
    Abstract [en]

    As flood inundation risk maps have become a central piece of information for both urban and risk management planning, also a need to assess the accuracies and uncertainties of these maps has emerged. Most maps show the inundation boundaries as crisp lines on visually appealing maps, whereby many planners and decision makers, among others, automatically believe the boundaries are both accurate and reliable. However, as this study shows, probably all such maps, even those that are based on high-resolution digital elevation models (DEMs), have immanent uncertainties which can be directly related to both DEM resolution and the steepness of terrain slopes perpendicular to the river flow direction. Based on a number of degenerated DEMs, covering areas along the Eskilstuna River, Sweden, these uncertainties have been quantified into an empirically-derived disparity distance equation, yielding values of distance between true and modeled inundation boundary location. Using the inundation polygon, the DEM, a value representing the DEM resolution, and the desired level of confidence as inputs in a new-developed algorithm that utilizes the disparity distance equation, the slope and DEM dependent uncertainties can be directly visualized on a map. The implications of this strategy should benefit planning and help reduce high costs of floods where infrastructure, etc., have been placed in flood-prone areas without enough consideration of map uncertainties.

  • 31.
    Bring, Johan
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Statistics.
    Bring, Annika
    Department of Neuroscience, Uppsala University, Uppsala, Sweden.
    Measuring gait - how the choice of measure can affect the statistical results and the clinical interpretation2017In: European Journal of Physiotherapy, ISSN 2167-9169, E-ISSN 2167-9177, Vol. 19, no 1, p. 8-12Article in journal (Refereed)
    Abstract [en]

    Aims: The aim of this study was to illustrate how the choice of gait measure could affect the statistical analysis of data and the resulting clinical conclusions. Methodology: A descriptive design in which the results from different tests from 10 patients with normal pressure hydrocephalus illustrates the potential to generate different clinical conclusions. Major findings and principal conclusion: The results illustrate how the choice of measure can affect the statistical results and the clinical interpretation of a study. It is possible to have the paradoxical situation in which one group has a better walking ability if the variable speed is used but the other group has a better walking ability if the variable time is used. An important message is that the choice of measurement and the transformation of data are not primarily statistical issues. If the statistical results are to be useful for clinical decisions, the variables used must be directly related to the utility for the subjects. An understanding of the clinical relevance of different outcomes is required. The distinction between when numbers are purely descriptive and when numbers represent a valuation is subtle and difficult to comprehend.

  • 32.
    Bring, Johan
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Statistics.
    Thuresson, Marcus
    Three Points for a Win in Soccer: Is It Fair?2011In: CHANCE: New Directions for Statistics and Computing, ISSN 0933-2480, Vol. 24, no 3, p. 47-53Article in journal (Refereed)
    Abstract [en]

    Most sports have to change their rules and scoring systems once in a while to adapt to external changes or improve the quality of their sport. The driving force behind many changes has been an attempt to make the games more exciting and suitable for television broadcasting.

    For example, in April 2009, the World Squash Federation changed the rules in squash so points are awarded in every rally (ball played), compared to the traditional rules in which players only could score a point in their own serve.

  • 33.
    Broqvist, Madeleine
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Problemlösning bland yngre elever2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med uppsatsen är att undersöka vilka stragier som lärare i lågstadiet anser är mest lämpade för yngre elever, och vilka metoder lärarna använder sig av i sin undervisning. Studien har en kvalitativ ansats, och intervjuer och klassrumsobservationer har genomförts med två lärare. Lärarna hade varit yrkesverksamma i cirka 10 år men arbetade inte på samma skola. Studien har genomförts i en kommun i Mellansverige. Strategierna som eleverna använde sig mest av var att rita sina lösningar och att jobba med laborativa material. Undervisningen innehöll mycket diskussioner bland eleverna. Lärarna betonade att de ville att eleverna skulle reflektera i sina tankegångar och sätta ord på sina tankeprocesser.

  • 34.
    Bäckman, Kerstin
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences, Curriculum studies.
    Children´s Play as a Starting Point for Teaching Mathematics in Preschool2014In: POEM: Online Proceedings, 2014Conference paper (Refereed)
    Abstract [en]

    This presentation contributes to the knowledge about how children learn about and explore mathematics in their everyday activities. Children´s mathematical encounters in play activities give them experiences as a base for education. The understanding of children’s mathematical encounters in play and teachers’ teaching is presented as teachable and learnable moments in ‘here-and-now’ situations. The data used for this study consists of video recordings of young children’s play in four Swedish preschools. In the presentation I use two examples to illustrate and discuss how children’s play can be a starting point for teachers’ teaching.  The results display that a teacher’s questions in play can support children’s explorations if the teacher observes, recognizes the mathematical content and asks questions.

  • 35.
    Bäckman, Kerstin
    University of Gävle, Faculty of Education and Business Studies, Department of Culture Studies, Religious Studies and Educational Sciences, Curriculum studies.
    Preschool Children’s Perspectives in Mathematical Learning2011In: Rights and Education, 2011Conference paper (Refereed)
  • 36.
    Bäckman, Kerstin
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences, Curriculum studies.
    Teaching Mathematics in Swedish Preschool - Didactic Situations2014In: 24th EECERA Conference : ‘Us, Them & Me: Universal, Targeted or Individuated Early Childhood Programmes’: Abstract Book, 2014, p. 94-Conference paper (Refereed)
    Abstract [en]

    The aim with this paper is to present research about teaching in preschool and the meaning of education in the preschool context within the perspective of quality. More specific the research focus on teaching mathematics and didactical considerations.Teaching mathematics always consists of several components with teacher, children and the mathematical content as three major parts. One of these basic components includes preschool teachers' intentions, choices and actions in which the goal is to create opportunities for children's learning in mathematics. Another component is the children, with their own experiences, intentions and their own choices. A third component is the mathematical content of the teaching situation (Brousseau, 1997). Play is a keyconcept in mathematical activities (Bishop, 1992) and in teaching of a mathematical content (Brousseau, 1997).The research focus is on didactic situations and more specifically the social interaction in teaching so-called didactic contract (Brousseau, 1997). Didactic contract can be understood as the dilemma between the educational goals and the participants’ intentions. A case study illustrates didactic situations in one Swedish preschool.Permissions has been gathered from the parents. The ethical rules for researcher in Sweden have been followed.The findings show the teachers use of play aspects in didactic situations expands the learning opportunities. The didactic contract in teaching give learning opportunities for children. Preschool teachers use of play in didactic situations make the teacher's aware of the mathematical and didactic considerations in relation to context and thereby improve the teaching of mathematical content.

  • 37.
    Bögvad, Rikard
    et al.
    Department of Mathematics, Stockholm University, Stockholm, Sweden.
    Källström, Rolf
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Geometric interplay between function subspaces and their rings of differential operators2006In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 359, no 5, p. 2075-2108Article in journal (Refereed)
    Abstract [en]

    We study, in the setting of algebraic varieties, finite-dimensional spaces of functions $V$ that are invariant under a ring $\Dc^V$ of differential operators, and give conditions under which $\Dc^V$ acts irreducibly. We show how this problem, originally formulated in physics \cite{kamran-Milson-Olver:invariant,turbiner:bochner}, is related to the study of principal parts bundles and Weierstrass points \cite{EGA4,laksov-thorup}, including a detailed study of Taylor expansions. Under some conditions it is possible to obtain $V$ and $\Dc^V$ as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of $\Dc^V$ are of this type, and that there are many more - in particular, arising from toric varieties.

  • 38.
    Chechkina, Alexandra
    et al.
    Lomonosov Moscow State University, Moscow, Russia.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway.
    Pettersson, Klas
    Narvik University College, Narvik, Norway.
    Spectral asymptotics for a singularly perturbed fourth order locally periodic elliptic operator2015In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 93, no 1-2, p. 141-160Article in journal (Refereed)
    Abstract [en]

    We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic operator with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and the dependence of the coefficients on the slow variable lead to localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a rescaled function that is constructed in terms of the jth eigenfunction of fourth or second order effective operators with constant coefficients.

  • 39.
    Chiadò Piat, V.
    et al.
    Politecnico di Torino, Torino, Italy.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway.
    Piatnitski, A.
    Narvik University College, Narvik, Norway; P.N. Lebedev Physical Institute RAS, Moscow, Russian Federation.
    Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions2013In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 3, p. 1302-1327Article in journal (Refereed)
    Abstract [en]

    This paper is aimed at homogenization of an elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of localization of the eigenfunctions. Moreover, the limit behavior of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive estimates for the rate of convergence. 

  • 40.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    University of Gävle, Department of Technology and Built Environment, Ämnesavdelningen för elektronik.
    A Study of Students’ Ability to Solve Text-Based Mathematical Problems with Irrelevant or Superfluous Information2008In: Mathematical Views, MAVI 14: Strobl/Salzburg, Austria, May 2008, 2008Conference paper (Refereed)
    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.

  • 41.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    University of Gävle, Department of Technology and Built Environment, Ämnesavdelningen för elektronik.
    Influence of Student’s Attitudes and Beliefs on the Ability of Solving Mathematical Problems with Irrelevant Information2009In: Beliefs and attitudes in mathematics education: new research results / [ed] Jürgen Maasz and Wolfgang Schlöglmann, Rotterdam: Sense Publishers , 2009, p. 165-178Chapter in book (Other academic)
    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.

     

  • 42.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Electronics.
    Komplexa tal är inte så komplexa!2010Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Abstraktion kan ofta utgöra ett hinder för lärande i matematik. Momentet med komplexa tal är inte något undantag. Varför ska man acceptera att i2=-1? Hur kan lärare introducera det på ett pedagogiskt sätt? Visualisering kan vara ett väsentligt led i att underlätta studenters lärande, ge dem en känsla av lägre abstraktion och härigenom vara nyckeln till djupare förståelse. Artikeln beskriver en visuell ansats som uppfyller kravet på lättillgänglighet. Metoden bygger på upprepade rotationer i det komplexa talplanet, vilket åskådliggör och konkretiserar komplexa tal genom visualisering.

  • 43.
    Eckefjord, Deborah
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Utomhusmatematikens möjligheter: En kvalitativ studie om hur lärare i F-3 arbetar med utomhusmatematik och uppfattar dess effekter för elevernas lärande2017Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien var att undersöka vilka möjligheter matematikundervisning utomhus kan ge för elevernas utveckling och lärande. Syftet var även att undersöka hur utomhusmatematik kan användas som ett komplement till den traditionella inomhusundervisningen i ämnet matematik. Studien baserades på en kvalitativ forskningsansats där kvalitativa semistrukturerade intervjuer och ostrukturerade observationer användes som metoder för att besvara studiens forskningsfrågor. Sex lärare i F-3 intervjuades och två observationer på två olika skolor genomfördes. Resultatet visar att utomhusmatematiken kompletterar matematikundervisningen inomhus genom ett samspel mellan arbetssätt och miljöer. Resultatet visar även på flera positiva effekter med utomhusmatematik så som verklighetsanknytning, motivation, fysisk aktivitet, hälsa, sinnligt lärande, tillåtande miljö och sociala effekter.  De positiva effekter utomhusmatematiken medföljer för elevernas utveckling och lärande bör uppmärksamma fler lärare om dess möjligheter. 

  • 44.
    Edling, Patrik
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences, Educational science. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Lärares val av metod i matematikundervisningen: Med fokus på elever med svenska som andraspråk2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Detta arbete har som huvudsyfte att analysera några erfarna lärares olika metoder och val av material i sin matematikundervisning, och hur de motiverar sina val för att genomföra en likvärdig undervisning för alla elever - med fokus på elever med svenska som andraspråk. I detta arbete har jag valt att intervjua fyra lärare från två olika skolor. Då syftet med detta arbete var att analysera lärares val av metoder vid matematikundervisningen utgick jag från lärarnas egna perspektiv. Med inspiration från grounded theory har en kvalitativ dataanalys genomförts från intervjuerna. Både intervjuerna och litteraturgenomgången visar att det inte finns något rätt eller fel vid val av undervisningsmetod, men att vissa metoder ibland fungerar bättre än andra. Det gäller att hitta det sätt som fungerar i den grupp man jobbar i för tillfället. De egenskaper som verkar lysa igenom som några av de viktigare egenskaperna hos en lärare är att vara flexibel.

  • 45.
    Ertas, Cihan
    University of Gävle, Faculty of Education and Business Studies, Department of Educational sciences.
    Matematik: En studie om hur några förskollärare undervisar matematik inom förskolan2016Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Matematiken är ett av inslagen i förskolans verksamhet och i förskolans läroplan (Skolverket, 2010) betonas att förskolan ska sträva efter att varje barn utvecklar sin förmåga att använda matematik för att undersöka, reflektera över och prova olika lösningar av egna och andras problemställningar. I läroplanen betonas också att förskolan ska sträva efter att varje barn utvecklar sin förmåga att urskilja, uttrycka, undersöka och använda matematiska begrepp och samband mellan begrepp. Syftet med denna studie är att undersöka hur några förskollärare synliggör den matematiska undervisningen i sin verksamhet. I denna studie valdes intervju som metod där sju förskollärare från olika förskolor intervjuades. Studiens resultat visar olika tillvägagångssätt som förskollärarna använder sig av i sin matematiska undervisning. Det framkom att förskollärarna till stor del synliggör matematiska begrepp och antal, medan matematisk problemlösning förekom i mindre skala. 

  • 46.
    Forsman, Jenny
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Lärande med estetiska lärprocesser i Matematik: Problemlösning med hjälp av estetiska lärprocesser - slöseri med tid eller en väg till kunskap?2016Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien är att undersöka estetiska lärprocesser i matematisk problemlösning då eleverna arbetar tillsammans i grupp. Vidare undersöks elevperspektivet på den estetiska lärprocessen. Studien utförs i en årskurs ett där eleverna får lösa ett matematiskt problem i grupp. Eleverna dokumenterar med en film hur det löser problemet. Elevernas perspektiv undersöks genom att de besvarar en enkät om deras upplevelser. Resultatet av studien är att samtliga grupper löser problemet med hjälp av olika strategier. Genom att eleverna diskuterar och reflekterar med varandra kan de till viss del inspirera varandra till olika lösningsstrategier och lösningar. Slutsatserna resulterar i att problemlösning med estetiska lärprocesser är inspirerande för eleverna och resurskrävande för verksamheten. Genom estetiska lärprocesser kan eleverna konkretisera och reflektera över problemet samt lösa det utan hjälp av den ordinarie matematikboken.

  • 47.
    Gunnarsson, Therese
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Automatisera multiplikationstabellerna - är det nödvändigt?: Matematiklärares uppfattning om automatisering av multiplikationstabellerna samt framgångsrika automatiseringsmetoder.2017Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med arbetet är att skapa en bild av matematiklärares uppfattning om automatisering av multiplikationstabellerna samt att redogöra för både för- och nackdelar med automatiserad kunskap. Syftet är även att belysa och diskutera olika automatiseringsmetoder som på olika sätt främjar eller hindrar elevernas matematikutveckling. Det gjordes en digital enkätundersökning där urvalet utgörs av 333 frivilliga matematiklärare representerade från olika undervisningsnivåer. Resultatet visar att matematiklärare anser att det är nödvändigt att eleverna automatiserar multiplikationstabellerna för att få en chans att utvecklas inom matematiken på bästa sätt, men att det kan ske på olika sätt, med olika metoder. Den mest fördelaktiga metoden verkar vara att kombinera färdighetsträning med att lära ut beräkningsstrategier för att kunskapen ska bestå.     

  • 48.
    Hallström, Linnea
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Digitala verktyg inom matematikundervisningen i samband med den nya ämnesplanen i matematik.2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna undersökande uppsats är att utreda hur digitala verktyg används i matematikundervisningen idag och hur stor förändring den kommande revideringen av ämnesplanen kommer kräva av lärare och skolor när det gäller matematikundervisningen. Undersökningen sker via en enkätundersökning som skickats ut till matematiklärare i Sverige. Därigenom framkommer det att ca 90% av de 209 responderande matematiklärarna i gymnasiet anser sig använda digitala hjälpmedel idag. Dock dras slutsatsen att implementerandet av digital teknik, med tillhörande pedagogiskt genomtänkt undervisning och tillhörande arbetsuppgifter, är något som inte kommer existera automatiskt vid införandet av den reviderade ämnesplanen. Istället kräver detta mer tid och kunskap från lärarkåren för att en möjlighet till utökat lärande för eleverna ska existera. Med andra ord är fortbildning och utökad erfarenhet för lärare inom den slags användning som uttrycks av ämnesplanen ett måste för ett produktivt införande av digitala verktyg i gymnasieskolans matematikundervisning.

  • 49.
    Haraldsson, Natalia
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Laborativ matematikundervisning på lågstadiet: En studie om fem lågstadielärares arbetssätt och perspektiv på ämnet2018Independent thesis Basic level (degree of Bachelor), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med detta examensarbete är att undersöka hur några lågstadielärare ser på den laborativa matematikundervisningen med elever samt hur deras perspektiv på ämnet samt deras arbetssätt förhåller sig till den i studien använda forskningen. För att få svar på dessa frågor har jag använt mig av den kvalitativa metoden som kallas för ostrukturerad intervju (Bryman, 2012). Alla de intervjuade lärarna verkar se laborativt arbetssätt som ett viktigt och självklart inslag i matematikundervisning för alla elever. Detta arbetssätt skapar möjligheter för alla elever och läraren att lära av varandra oavsett elevernas individuella förutsättningar. Det laborativa arbetssättet både beskrivs och används som källa till elevens fördjupade långsiktiga matematiklärande och hennes ökade motivation i lärprocessen. Lärarna lyfter även arbetssättets inkluderande roll i matematikklassrummet. De inslag som verkar centrala i lärarnas laborativa undervisning är: gemensam introduktion, stödjande frågor till eleven, progression och långsiktighet i arbetet.

    Utifrån de ovanför beskrivna resultaten verkar lärarnas arbetssätt i hög grad överensstämma med de forskningsansatser som jag har valt att utgå ifrån i mitt arbete.

  • 50.
    henriksson, elin
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
    Matematiksagor i förskolan: Ett arbetsmaterial för förskollärare2014Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
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