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  • 101.
    Bartolini Bussi, M G
    et al.
    Universita' di Modena e Reggio Emilia, Modena, Itlay.
    Gade, Sharada
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Janvier, M
    Kahane, J-P
    Matsko, V
    Maschietto, M
    Ouvrier-Buffet, C
    Saul, M
    Mathematics in context: focusing on students2009Inngår i: Challenging Mathematics In and Beyond the Classroom – The 16th ICMI Study / [ed] E. J. Barbeau and P. J. Taylor, New York: Springer Science+Business Media B.V., 2009, s. 171-203Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This chapter presents nine case studies in which school students engage in challenging mathematics outside their immediate classroom environment. In each case, students are encouraged to collaborate in investigations that go beyond the standard curriculum and creatively use the ingredients of the particular context. In Italy, students visit a mathematical laboratory to understand and utilize mathematical machines. Morning assembly at an Indian school brings students from many classes together in the solution of mathematical problems. Four of the projects are from France: students analyze the configuration of a heap of sand, pursue astronomical investigations with software, obtain a flavor of research by having secondary school teams investigate interesting problems, and are presented at all levels with open-ended research problems. There are three programs from the United States, the first, an advanced geometry sequence for secondary students completing the regular syllabus early, the second, activities arising from exhibits in an art museum, and the third, using the school lawn to deepen student understanding of geometric constructions. All such activities need to be evaluated for their effectiveness, so that they move from just being initiatives of dynamic individuals to serve as the foundation for systemic improvements in the way in which students learn, understand and use mathematics. In the early part of this chapter, we briefly mention how research into such activities might be approached.

  • 102.
    Bartoszek, Krzysztof
    Gdansk University of Technology.
    A Graph – String Model of Gene Assembly in Ciliates2006Inngår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2006, Vol. 10, s. 521-534Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.

  • 103.
    Bartoszek, Krzysztof
    Gdansk University of Technology, Poland.
    A Graph – String Model of Gene Assembly in Ciliates [Grafowo-tekstowy model rekombinacji DNA u orzęsek]2006Inngår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2006, s. 521-534Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.

  • 104.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    Signerska, Justyna
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    The Fundamental Group, Covering Spaces and Topology in Biology2006Inngår i: Conference materials 9th International Workshop for Young Mathematicians "Topology", 2006, s. 19-29Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.

  • 105.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology.
    Signerska, Justyna
    Gdansk University of Technology.
    The Fundamental Group, Covering Spaces and Topology in Biology2006Inngår i: Conference materials IX International Workshop for Young Mathematicians: Topology, 2006, s. 19-29Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.

  • 106.
    Bashardanesh, Zahedeh
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    Flexibility and Robustness of Biochemical Switches2011Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 107.
    Basieva, Irina
    et al.
    City University of London, UK.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments2017Inngår i: QUANTUM INTERACTION, QI 2016 / [ed] DeBarros, JA; Coecke, B; Pothos, E, Springer, 2017, s. 49-56Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Analogy between the two slit experiment in quantum mechanics (QM) and the disjunction effect in psychology led to fruitful applications of the mathematical formalism of quantum probability to cognitive psychology. These quantum-like studies demonstrated that quantum probability (QP) matches better with the experimental statistical data than classical probability (CP). Similar conclusion can be derived from comparing QP and CP models for a variety of other cognitive-psychological effects, e.g., the order effect. However, one may wonder whether QP covers completely cognitive-psychological phenomena or cognition exhibits even more exotic probabilistic features and we have to use probabilistic models with even higher degree of nonclassicality than quantum probability. It is surprising that already a cognitive analog of the triple slit experiment in QM can be used to check this problem.

  • 108.
    Basieva, Irina
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Ohya, Masanori
    Yamato, Ichiro
    Quantum-like interference effect in gene expression: glucose-lactose destructive interference2011Inngår i: Systems and Synthetic Biology, ISSN 1872-5325, Vol. 5, nr 1, s. 56-64Artikkel i tidsskrift (Fagfellevurdert)
  • 109. Bauso, Dario
    et al.
    Dia, Ben Mansour
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Tembine, Hamidou
    Tempone, Raul
    Mean-Field Games for Marriage2014Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, nr 5, s. e94933-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article examines mean-field games for marriage. The results support the argument that optimizing the long-term wellbeing through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

  • 110.
    Beach, Dennis
    et al.
    Högskolan i Borås, Institutionen för Pedagogik.
    Player-Koro, Catarina
    Högskolan i Borås, Institutionen för Pedagogik.
    Authoritative Knowledge in Initial Teacher Education: Studying the Role of Subject Textbooks through Two Ethnographic Studies of Mathematics Teacher Education.2012Inngår i: Journal of Education for Teaching, ISSN 0260-7476, E-ISSN 1360-0540, Vol. 38, nr 2, s. 115-125Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Two related ethnographic research projects on mathematics teacher education in Sweden are presented in this paper. They represent a response to recent policy developments that reaffirm the value of authoritative subject studies content as the central and most important component in the professional knowledge base of would-be teachers and concomitant increases in the amount of subject studies in teacher education. These policy changes, in Sweden at least, lack scientific research support and the article argues that these policies need to be seriously rethought, as the increased emphasis on subject content may undermine the development of key professional skills.

  • 111.
    Begum, Rabeya
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    The roles of teachers and types of questions in the science classroom: A study of communication patterns in high school level biology lessons2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    Teacher-student communication in the classroom is crucial for effective student learning and a teacher can play different roles by asking related questions. Teachers use of the right questions at the right moment stimulates and invites the students to have a closer look, reinvestigate or revisit the problem. The teachers play various roles while asking the questions to continue the classroom discourse. Therefore, the purpose of this study was to investigate various roles of a high school teacher in a science classroom discourse. The study also pursued how these roles are related to the types of questions asked by the teacher during classroom communication. A framework, constructed by Chen and his colleagues, has been used to categorize types of teachers’ roles to find the relationship between the roles of the teachers and the types of questions asked in a science class.  A case study has been presented in this report with observations from two high school level biology lessons.  Both audio and video recording were deployed to capture the lessons as well as a notebook was maintained. These recordings have been transcribed for a qualitative data analysis. In this study, five types of questions have been observed in two biology lessons: concept, confirmation, remembering, challenging and encouraging. Furthermore, based on Chen and his colleagues Framework, only three roles of the teacher was found: dispenser, coach, and participant. The findings revealed that the concept, confirmation and remembering types of questions are related to the teacher role as dispenser, the challenging types of questions are related to the role as coach and encouraging type of questions are related to the teacher’s participant role. The teacher acted mostly as a dispenser in the classroom discourses. There were some rooms where the teacher might exercise more as a coach and participant to improve the classroom interaction. No connection between the content of the questions and the role of the teachers was found from the observations. Therefore, this study suggests that further research should be continued with a broader scope to analyze the teachers’ questioning roles, its relationship with the content of the questions and its impact to promote student learning.

  • 112.
    Beilina, Larissa
    et al.
    Chalmers University, Gothenburg University.
    Shestopalov, YuriKarlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.
    Inverse problems and large-scale computations2013Konferanseproceedings (Fagfellevurdert)
  • 113.
    Belova, Anna
    et al.
    Högskolan i Halmstad, Akademin för informationsteknologi.
    Shmidt, Tamara
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS).
    Ehrhardt, Matthias
    AMNA, Bergische Universität Wuppertal, Wuppertal, Germany.
    Meshfree methods in option pricing2012Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A meshfree approximation scheme based on the radial basis function (RBF) methods is presented for the numerical solution of the options pricing model. This work deals with the valuation of the European, Asian and American options. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. Next, the option price is approximated in space with RBF. In case of American options a penalty method is used, i.e. the free boundary is removed by adding a small and continuous penalty term to the Black-Scholes equation. Finally, we present a comparison of analytical and finite difference solutions and numerical results. © 2012 MANT.

  • 114.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    Högskolan i Skövde, Institutionen för vård och natur. Högskolan i Skövde, Forskningsspecialiseringen Hälsa och Lärande.
    The Viability of Social Constructivism as a Philosophy of Mathematics2013Inngår i: Croatian Journal of Philosophy, ISSN 1333-1108, E-ISSN 1847-6139, Vol. XIII, nr 39, s. 341-355Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Attempts have been made to analyse features in mathematics within a social constructivist context. In this paper we critically examine some of those attempts recently made with focus on problems of the objectivity, ontology, necessity, and atemporality of mathematics. Our conclusion is that these attempts fare no better than traditional alternatives, and that they, furthermore, create new problems of their own.

  • 115.
    Bennevall, Marcus
    Linköpings universitet, Matematiska institutionen.
    Creativity in Mathematics Curricula – An International Comparison between Singapore, Hong Kong, Sweden, and Norway2017Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Studies have shown that creative mathematically founded reasoning (CMR) outperforms algorithmic reasoning (AR) in regards to retention and (re)construction of knowledge. This suggests that creativity should be encouraged in national high-school mathematics curricula. The aim of the present study is to compare how creativity is framed in different national high-school mathematics curricula, using the following definition: creativity is the characteristics of people, processes, and environments which lead to new and original products that are useful or otherwise attractive to an individual or a society. Utilizing content and discourse analysis, the present study thus contrasts how the high-school mathematics curricula of Singapore, Hong Kong, Sweden, and Norway handle and value creativity, and also examines which role creativity takes in each curricula.

    Findings suggest that Singapore’s curriculum emphasizes creativity the most, and frequently does so in relation to assessment. Hong Kong’s curriculum is found to emphasize creativity in diverse ways, often using words with connotations to playfulness. Analysis of Sweden’s curriculum indicates a relatively minute focus on creativity, tending to put it in a teacher-centered context. A feature of Norway’s curriculum is an increasing emphasis on creativity as courses approach tertiary education. This also suggests a rising value of creativity in its curriculum. A similar though not as pronounced trajectory is found also in Singapore’s curriculum. In the Asian and Norwegian curricula, creativity is expressed both as a means and an end, while in Sweden’s curriculum it is only seen as an end.

    The results are discussed in terms of potential reasons for the prominent national features, and the study also includes an evaluation of the aptness of the suggested definition of creativity, a review of the limitations of the study, as well as propositions for further research. Finally, two recommendations are given to the National Agency for Education in Sweden – Skolverket – based on the results of the study: 1) diversify the emphasis on creativity in the curriculum, and 2) ensure alignment between what teachers value and what Skolverket values with respect to creativity.

  • 116.
    Berg, Birgitta
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Eriksson, Marie-Therése
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Likhetstecknet - Att öka förståelsen i förskoleklass med hjälp av Learning study metoden: Ett laborativt arbetssätt där till och med namn kan väga jämnt!2010Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna empiriska studie är att undersöka hur lärare kan erbjuda möjligheter för 6-åringar att vidga sin förståelse av likhetstecknets innebörd. Undersökningen är inspirerad av Learning Study metoden vilket är en metod som har sin utgångspunkt i variationsteorin. Barnens initiala förmågor analyseras före planeringen av undervisningen och det ger en uppfattning om barnens kunskaper. Utifrån det planeras lektionerna och de aspekter som är de mest kritiska för barnen lyfts och på så sätt utvecklas deras kunskap. Vår slutsats är att det är viktigt att arbeta utifrån ett variationsinriktat lärandeperspektiv. Barnen lyckas bra i de uppgifter där de får laborera med konkret material.

     

     

  • 117.
    Berggren, Jacob
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Landhammar, Anna
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Johansson, Emma
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    ”Man kan ju skriva också” -Kommunikation, inte bara en muntlig förmåga: - En analys av kommunikationsförmågan inom matematiken2018Independent thesis Advanced level (professional degree), 240 hpOppgave
    Abstract [sv]

    Som ett led i att förbättra kvaliteten på matematikundervisning fokuserar den senaste versionen av läroplanen på förmågor som elever ska ges möjlighet att utveckla. Kommunikationsförmågan är en av dessa som nämns i styrdokumenten och som denna studie kommer att behandla. Våra erfarenheter, likväl som Skolinspektionen, har visat att alla lärare inte planerar och undervisar enligt styrdokumenten. Denna studie kommer därför att undersöka hur lärare definierar kommunikationsförmågan i matematikämnet samt vilka metoder och arbetssätt de låter eleverna använda för att utveckla denna förmåga.

    Genom intervjuer och observationer av matematiklektioner ska studien ge en bild av hur lärare i årskurs 4-6 tänker och arbetar för att utveckla just kommunikationsförmågan.

    Resultatet av detta visar att de intervjuade lärarnas definition av kommunikationsförmågan är relativt likvärdiga, det handlar om att prata matematik. Däremot skiljer det sig hur de väljer att arbeta med att låta eleverna utveckla förmågan. De metoder som väljs för att fokusera på just kommunikationsförmågan är främst problemlösning i par eller grupp, men också genomgångar och gemensamma diskussioner. Resultatet i denna studie visar även att få av lärarna nämner eller tillämpar kommunikation via skrift. Inte förrän de har tänkt igenom och analyserat förmågan på ett djupare plan beskriver de att även en skriftlig version är viktig att beakta.

  • 118.
    Berglin, Emmy
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Ett matematikproblem man vill eller kan lösa: En studie om hur elever med olika förutsättningar tar sig an samma problemuppgift2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Den empiriska studien handlar om hur alla elever kan gynnas av samma problemlösningsuppgifter och hur detta visar sig. Vilka strategier väljer elever när de arbetar med valda uppgifter och hur uppmärksammas dessa genom observation och intervju. Tre matematiska förmågor kommer att synliggöras i denna empiriska studie och hur dessa förmågor kan komma att visa sig hos elever som arbetar med problemlösning. En skola för alla är något som kan tolkas olika, i denna studie kommer främst tidigare forskning att förklara begreppet och vad det kan innebära för elever. Fokuset i studien är problemlösning och hur elever arbetar med detta i skolan, utifrån olika faser att ta sig an ett problem. 

  • 119.
    Bergling, Fredrik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Applications of Quantiles In Portfolio Management2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 120.
    Berglund, Jessica
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Vill du spela bingo med mig?: En studie med laborativt material för att utveckla elevers kunskaper om positionssystemet2019Independent thesis Advanced level (degree of Master (Two Years)), 240 hpOppgave
    Abstract [sv]

    Studiens syfte är att med hjälp av en learning study med förtest och eftertest undersöka elevers förkunskaper om positionssystemet samt om elever genom laborativt material kan fördjupa sina kunskaper om positionssystemet. Studiens teoretiska utgångspunkt är hämtad från variationsteorin. Att arbeta med ett laborativt material möjliggör för eleverna att utveckla en utökad förståelse för positionssystemet med basen 10. En av slutsatserna från denna studie är att ett variationsteoretiskt perspektiv på undervisningen underlättar lärandet.

  • 121.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Doerr, Helen M.
    Syracuse University.
    At the core of modelling: Connecting, coordinating and integrating models2015Inngår i: Proceedings of the 9th Congress of European Research in Mathematics Education / [ed] K. Krainer & N. Vondrová, 2015, s. 802-808Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This theoretical paper introduces the notions of connecting, coordinating and integrating models to analyse and reflect on how models are created and developed. We define, discuss and apply these constructs to some theoretical perspectives in the present modelling discourse. We draw on an example from a model application activity within a model development sequence to illustrate these constructs. Our hope is to spark a discussion that will enhance our understanding about the nature of mathematical modelling and the teaching and learning of, and through, modelling.

  • 122.
    Bergner, Julia
    et al.
    University of California, Riverside, USA.
    Hackney, Philip
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. University of California, Riverside, USA.
    Group actions on Segal operads2014Inngår i: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 202, nr 1, s. 423-460Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spaces. We then extend this result to give a Quillen equivalence between the model structures for simplicial operads equipped with a group action and the corresponding Segal operads.

  • 123.
    Bergner, Julia
    et al.
    University of California, Riverside, USA.
    Hackney, Philip
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. University of California, Riverside, USA.
    Reedy categories which encode the notion of category actions2015Inngår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 193-222Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard group actions on categories and on operads.

  • 124.
    Bergqvist, Ewa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    A verbal factor in the PISA 2003 mathematics items: Tentative analyses2009Inngår i: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education: In Search for Theories in Mathematics Education, Thessaloniki, Greece: PME , 2009, s. 145-152Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This study uses a statistical method to identify verbal items among mathematical items from PISA 2003. The verbal items are preliminary analysed and compared to the non-verbal items concerning number of text lines, response types, cognitive level, and competences measured. The results show that the verbal items, to a higher percentage than the non-verbal items, measures the reproduction competency, are straigh­t­forward, and of open constructed-response type. These results and proposed further analyses are discussed.

  • 125.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Dyrvold, Anneli
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012Inngår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, s. 61-70Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 126.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Dyrvold, Anneli
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Österholm, Magnus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012Inngår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, s. 61-70Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 127.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Dyrvold, Anneli
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012Inngår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, s. 61-70Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 128.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Theens, Frithjof
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Relations between linguistic features and difficulty of PISA tasks in different languages2016Inngår i: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, s. 125-125Konferansepaper (Fagfellevurdert)
  • 129.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Theens, Frithjof
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Österholm, Magnus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Relations between linguistic features and difficulty of PISA tasks in different languages2016Inngår i: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, Vol. 1, s. 125-125Konferansepaper (Fagfellevurdert)
  • 130.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    A theoretical model of the connection between the process of reading and the process of solving mathematical tasks2010Inngår i: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, s. 47-57Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.

  • 131.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Österholm, Magnus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    A theoretical model of the connection between the process of reading and the process of solving mathematical tasks2010Inngår i: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, s. 47-57Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.

  • 132.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Communicating mathematics or mathematical communication?: An analysis of competence frameworks2012Inngår i: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2: opportunities to learn in mathematics education / [ed] Tai-Yih Tso, 2012, s. 67-74Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.

  • 133.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Österholm, Magnus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Monash University, Australia.
    Communicating mathematics or mathematical communication?: An analysis of competence frameworks2012Inngår i: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2: opportunities to learn in mathematics education / [ed] Tai-Yih Tso, 2012, s. 67-74Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.

  • 134.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Österholm, Magnus
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Språkbrukets roll i matematikundervisningen2014Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2014, nr 1, s. 27-31Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

  • 135.
    Bergqvist, Ewa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Österholm, Magnus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Språkbrukets roll i matematikundervisningen2014Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2014, nr 1, s. 27-31Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

  • 136.
    Bergström, Jonas
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Dummigan, Neil
    Mégarbané, Thomas
    Ibukiyama, Tomoyoshi
    Katsurada, Hidenori
    Eisenstein Congruences for SO(4, 3), SO(4, 4), Spinor, and Triple Product L-values2018Inngår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, nr 2, s. 230-250Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4, 3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4, 4) and the L-function is a triple product L-function.

  • 137.
    Bergström Lissmyr, Jannice
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    En kvalitativ studie om lärarens syn på lässvårigheters påverkan på matematikinlärningen: samt andra svårigheters påverkan2017Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    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.

  • 138.
    Bergwall, Andreas
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Conceptualizing reasoning-and-proving opportunities in textbook expositions: Cases from secondary calculus2017Inngår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017) / [ed] Dooley, T., & Gueudet, G., Dublin, Ireland: European Society for Research in Mathematics Education , 2017, s. 91-98Konferansepaper (Fagfellevurdert)
    Abstract [en]

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

  • 139.
    Bergwall, Andreas
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    On a generality framework for proving tasks2015Inngår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer; Nada Vondrova, Prague: Charles University in Prague, Faculty of Education and ERME , 2015, s. 86-92Konferansepaper (Fagfellevurdert)
    Abstract [en]

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

  • 140.
    Bergwall, Andreas
    et al.
    Örebro universitet, Institutionen för naturvetenskap och teknik.
    Hemmi, Kirsti
    Åbo Akademi University, Åbo, Finland; Uppsala University, Uppsala, Sweden.
    The State of Proof in Finnish and Swedish Mathematics Textbooks: Capturing Differences in Approaches to Upper-Secondary Integral Calculus2017Inngår i: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 19, nr 1, s. 1-18Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 141.
    Bernhoff, Niclas
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations2017Inngår i: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, Vol. 10, nr 4, s. 925-955Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 142.
    Bernhoff, Niclas
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation2015Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 159, nr 2, s. 358-379Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 143.
    Bernhoff, Niclas
    et al.
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Vinerean, Mirela
    Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
    Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants2016Inngår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 165, nr 2, s. 434-453Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 144.
    Bertolino, Mattias
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Jonnarth, Arvi
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Monte Carlo methods applied to tree-structured decision processes2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 145.
    Bertse, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    A simulational approach to parking2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 146.
    Bild, Elina
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Lundkvist, Julia
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Skolan i den digitala världen: En designstudie om integrering av ett digitalt verktyg i matematikundervisningen2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Denna designstudie inriktar sig på integrering av ett digitalt verktyg i en specifik undervisningskontext. Studien utgår från ett sociokulturellt perspektiv och fokus ligger således på undervisningssituationen som helhet. Sociala interaktioner i form av möten mellan elever, lärare och artefakter genomsyrade undersökningen. Enligt den cykliska process som karaktäriserar design research bearbetades systematiskt integreringen av det digitala verktyget Matteappen, med målet att skapa en undervisningssituation som främjar elevers utveckling av taluppfattning. Totalt genomfördes tre cykler bestående av planering, genomförande och analys för att utforma designprinciper och ramar anpassade till den specifika kontexten. Resultatet visar att integreringen av Matteappen bidrog positivt till elevernas inställning till matematikundervisningen. Det visar även att självständighet främjas och att effektiv individanpassning möjliggörs. I den aktuella kontexten fungerade integreringen bäst i samband med en möblering där eleverna satt i par. Graden av social interaktion visade sig ha stor betydelse. En viktig slutsats som kan dras är att Matteappen inte kan stå på egna ben i undervisningen utan måste integreras på ett didaktiskt genomtänkt sätt för att bidra till elevernas utveckling och lärande.  

  • 147.
    Birky, Geoffrey
    et al.
    Georgetown University.
    Campbell, Connie M
    Millsaps College, USA.
    Raman, Manya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Sandefur, James
    Georgetown University.
    Somers, Kay
    Moravian College, USA.
    One problem, nine student-produced proofs2011Inngår i: The College Mathematics Journal, ISSN 0746-8342, E-ISSN 1931-1346, Vol. 42, nr 5, s. 355-360Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The context of this paper is a project aimed at meeting the challenges of teaching an introduction-to-proof course at our own institutions. These courses are typically taken by second year students intending to major in mathematics or computer science and are taught in sections of 15 to 24 students. These students benefit from being given the freedom to explore different methods of proof without the presumption that they will use a certain method.  This is the story of how what could have been a routine, closed problem became an open one.

  • 148.
    Bisenius Sellgren, Kajsa
    Södertörns högskola, Lärarutbildningen.
    En studie om elevers val av metoder vid subtraktionsberäkningar2010Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this qualitative study of students’ methods of calculating subtractions, I have used interviews, subtraction exercises and analysis of teaching material. The purpose of my study was to explore which methods students in grade three uses when calculating subtractions. I also wanted to highlight which strategies the students use and their comprehension of the concept of subtraction. In the study, I also highlight the different pedagogical ideas on which the teaching material is based on and the students’ choice of methods.  The study shows that the students choose to use the methods”deduct” and “kind of number” independently. Further it also shows that the students choose to switch from the method “deduct” to “kind of number” when the numbers in the exercises are further up on the number axis. When asked, the students answered that subtraction means “minus” which they in turn explained as removing something, an explanation confirmed by the Swedish Academy dictionary. The students’ choice of methods and teaching material is based on different fundamental pedagogical view.

     

  • 149. Bjarnadóttir, Kristín
    et al.
    Furinghetti, FulviaKrüger, JennekePrytz, JohanUppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.Schubring, GertSmid, Harm Jan
    "Dig where you stand" 5: Proceedings of the fifth international conference on the history of mathematics education. September 19-22, 2017, at Utrecht University, the Netherlands2019Konferanseproceedings (Fagfellevurdert)
  • 150.
    Björk, Annika
    et al.
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
    Nilsson, Sara
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
    ”Det finns jättemycket luckor, att de inte förstår”: –      En studie om barns och pedagogers kunskap i antalsuppfattning.2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Matematik finns överallt men trots det har vi genom studien fått fram att ”det finns jättemycket luckor, att de inte förstår”.  Detta citat är hämtat ifrån en av våra intervjuer och speglar vårt resultat. Studien är kvalitativ och vi har intervjuat pedagoger samt låtit barn, i förskola och årskurs 1, utföra matematikuppgifter. I denna studie har vi fokuserat på grunderna i matematik. Syftet med studien har varit att utröna kunskaper inom antalsuppfattning hos barn. Vi har även belyst pedagogernas kunskaper inom antalsuppfattning samt hur de arbetar med detta. I studien har vi influerats av Piagets och Vygotskijs tankar om hur barn lär. Resultaten i vår studie har analyserats med inspiration av hermeneutiken. Resultaten visar att det finns okunskap hos både barn och pedagoger gällande antalsuppfattning. Det gäller bland annat barn som helt saknar kunskaper inom detta samt att pedagoger uppfattar att subitizing, se stycke 3.4., och ett till ett-principen, se stycke 3.5., är detsamma som antalsuppfattning. Pedagoger behöver djupare förståelse för de matematiska begreppen inom den grundläggande matematiken. Det i sin tur kan medföra ett tydligare matematiskt språk vilket kan underlätta kommunikationen sinsemellan. I sin tur kan det möjliggöra för pedagoger att tillsammans lättare kunna utveckla barns matematiska färdigheter som de behöver i sin vardag som vuxna samhällsmedborgare. 

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