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  • 1.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Lundberg, Anna L. V.
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Begreppen modellering och problemlösning i skolan och i yrkeslivet2015Other (Other academic)
  • 2.
    Lundberg, Anna, L., V.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Developing a tool for analysing upper secondary school textbook tasks about proportion and proportionality2010In: The Seventh Mathematics Education Research seminar: Mathematics and Mathematics Education: Cultural and Social Dimensions / [ed] Bergsten, Christer; Jablonka, Eva; Wedege, Tine, Linköping: LiU-Tryck , 2010, p. 269-270Conference paper (Refereed)
  • 3. Order onlineBuy this publication >>
    Lundberg, Anna, L., V.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Proportionalitetsbegreppet i den svenska gymnasiematematiken: en studie om läromedel och nationella prov2011Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Proportionality is a key concept in school mathematics. It is introduced in the primary grades, and reappears in almost all mathematics courses from Grade 9 to the last course in upper secondary school. The overall aim of this study is to investigate how the mathematical concept of proportionality is handled in the Swedish upper secondary school. A general problem connected to this end is how the national curriculum is realised in textbooks and national examinations. The focus of this thesis is on how proportionality is handled in the first Swedish upper secondary course in mathematics in some textbooks and national examinations. To examine this an analysis tool based on the theoretical framework of the ATD (Anthropological Theory of the Didactic) was developed. Of interest here are relations between the different levels in the didactic transposition, concerned with exactly how the national curriculum is realised in textbooks and national examinations. For the empirical study of the material the ATD concept of mathematical organisation was used, employing an analytical tool to examine the types of tasks dealing with proportionality, techniques for solving these tasks, and theoretical models for the concept of proportionality.

    The data presented in this study gives a fairly unstructured picture of the mathematical organisations of the conceptual field of proportionality, as presented in textbooks and in the national tests. They also look different when it comes to how proportionality is handled in the textbooks and the national test for "Matematik A". The result shows that about every fourth task of the chapters and the national tests studied involved proportionality, but that there was a low variation in terms of types of tasks. Differences were observed between textbooks and national tests in terms of how solution techniques are recommended for different types of proportionality tasks. The two theoretical models of proportionality that were studied, ie. static and dynamic proportionality, are represented to approximately the same extent in both textbooks and national examinations. In geometry, it is often static proportionality, while in the field of functions it is common to use dynamic proportionality.

    Teachers should have access to knowledge of the differences between textbooks and curricula, and how they are interpreted in the national tests, so that they can make deliberate choices in their teaching activities, including exercises, to support a good variety for students linked to curriculum objectives.

  • 4.
    Lundberg, Anna, L., V.
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hemmi, Kirsti
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Proportion in Swedish upper secondary school textbook tasks.2009In: Teaching Mathematics: Retrospective and Perspectives. Proceedings of the 10th International Conference in Mathematics Education 2009 / [ed] Madis Lepik, Tallinn, Estonia: Institute of Mathematics and Natural Sciences, Tallinn University, Estonia , 2009, p. 252-260Conference paper (Refereed)
    Abstract [en]

    This study investigates what possibilities Swedish upper secondary schooltextbook tasks offer students to develop their understanding of proportion by applying an analytical tool on one textbook. We found a variety of tasks, but some proportional reasoning types were missing.

  • 5.
    Lundberg, Anna, L., V.
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg,Gothenburg,Sweden.
    Kilhamn, Cecilia
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Transposition of Knowledge: Encountering Proportionality in an Algebra Task2018In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 16, no 3, p. 559-579, article id 1571-0068Article in journal (Refereed)
    Abstract [en]

    This article reports on an analysis of the process in which knowledge to be taught was transposed into knowledge actually taught, concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical praxeology of the two different types of knowledge exposed, in the task as such and in the activity of the classroom. Through the teacher’s explicit process of reasoning, modeling, revising, solving, and repeatedly explaining the task, we found that the transposition of knowl- edge was seriously affected by the contextualization of the task. Modeling word problems about everyday situations has its limitations and can, as in this case, make the problem unsolvable unless it is accepted as a Btextbook task^ disguised as real but adjusted to the norms of school mathematics. Such constraints may obscure mathe- matical ideas afforded by the task. We conclude that learning opportunities embedded in a task do not necessarily surface when a task is treated in a classroom setting

  • 6.
    Lundberg, Anna, L. V.
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Education and Adult Learning. Linköping University, Faculty of Educational Sciences.
    Muhrman, Karolina
    Linköping University, Department of Behavioural Sciences and Learning, Education and Adult Learning. Linköping University, Faculty of Educational Sciences.
    Att konstruera matematikuppgifter på yrkesprogram2015Other (Other academic)
    Abstract [sv]

    Uppgifter har en central roll inom matematikundervisning, och eftersom utbudet av yrkesrelaterade uppgifter är begränsat är det viktigt förmatematiklärarepå yrkesprogram att kunna skapa nya sådana uppgifter.

  • 7.
    Lundberg, Anna, L., V.
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Ödmark, Krister
    Umeå Universitet, Umeå Sverige.
    Digital teknik, digitala medier och andra verktyg2015Other (Other academic)
    Abstract [sv]

    I den svenska matematikundervisningen har ett trendbrott inträffat i och med att billiga bärbara datorer, interaktiva skrivtavlor, sofistikerade mobiltelefoner och en i högre grad problembaserad undervisning blivit allt vanligare. I det övergripande syftet i ämnesplanen för matematik betonas att eleverna ska ”ges möjlighet att utveckla sin förmåga att använda digital teknik, digitala medier och även andra verktyg som kan förekomma inom karaktärsämnena” (Skolverket, 2011). Digitalaverktygfinns även med i kunskapskraven för alla betygsstegi kursen Matematik 1. Där ingår att eleven ”löser uppgifter av standardkaraktär med viss säkerhet, både utan och med digitala och andra praxisnära verktyg” (Skolverket, 2011).

    • Digital teknik (t.ex.responsprogram, utbildningsplattformar, interaktiva tavlor, applikationer, bokföringsprogram, bokningsprogram, schema, kalkylprogram)
    • Digitala medier (internet, mobiltelefoner, surfplattoroch dator)
    • Verktyg inom karaktärsämnen(sinushylla, linjaler med skala, mätverktyg, termometer, våg mm.)
  • 8.
    Muhrman, Karolina
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Education and Adult Learning. Linköping University, Faculty of Educational Sciences.
    Lundberg, Anna, L., V.
    Linköping University, Department of Behavioural Sciences and Learning, Education and Adult Learning. Linköping University, Faculty of Educational Sciences.
    Dypbukt, Wenche
    Matematikksenteret, Trondheim, Norge.
    Jens Arne, Meistad
    Matematikksenteret, Trondheim, Norge.
    Aina, Fardal
    Horten vgs skole Norge, Horten, Norge.
    Liebich, Rolf
    Dag Vassbotn.
    Ödmark, Krister
    Umeå universitet, Umeå, Sverige.
    Popov, Oleg
    Umeå universitet, Umeå, Sverige.
    Dahlberg, Johan
    Erik Dahlbergsgymnasiet, Jönköping, Sverige.
    Uppgiftsbanken: Gymnasieskola, modul: Undervisa matematik på yrkesprogram2015Other (Other academic)
    Abstract [sv]

    Denna uppgiftsbank innehåller uppgifter med varierat innehåll och svårighetsgrad. Uppgifterna är av varierande karaktär och uppfyller i olika grad kriterierna från checklistan i texten ”Att konstruera matematikuppgifter på yrkesprogram”. Uppgifterna kan användas i undervisningen eller fungera som ett diskussionsunderlag vid utveckling av infärgade uppgifter. Studera gärna uppgifterna tillsammans med yrkeslärare.

    Till uppgifterna finns stöd för hur man kan planera och arbeta med uppgifterna i klassrummet. Det finns kopplingar till centralt innehåll i Matematik 1a, yrkesämnenas centrala innehåll och examensmålen för yrkesprogrammen. Eftersom kurserna i yrkesämnena läggs ut lokalt finns det ingen samstämmighet i vilken ordning och under vilken termin de läses på olika skolor. Det kan därför vara så att det centrala innehåll i yrkesämnena inte är aktuellt just då men det kan ändå vara bra för eleverna att känna till det. Till några av uppgifterna ges för slag på hur man kan variera eller utveckla dem. I modulen Undervisa matematik på yrkesprogram del 5: Modellering och problemlösning finns några förslag på hur uppgifterna kan göras till Fermiproblem.

    I Skolverkets bedömningsportal finns uppgifter för yrkesprogram. En del av uppgifterna är lösenordsskyddade. För att komma åt det skyddade materialet behövs inloggningsuppgifter och behörighet till ämnet eller kursen. Information om hur du som lärare får inloggningsuppgifter har skickats till rektorn på din skola. Du hittar bedömningsportalen här: https://bp.skolverket.se/.

  • 9.
    Olteanu, Constanta
    et al.
    Linnéuniversitetet, Växjö, Sverige.
    Lundberg, Anna, L., V.
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Ödmark, Krister
    Umeå universitet, Umeå, Sverige.
    Interaktion i klassrum2015Other (Other academic)
    Abstract [sv]

    Vi fokuserar i denna text på hur digitala hjälpmedel och verktyg påverkar möjligheter till interaktion i klassrummet.

  • 10.
    Popov, Oleg
    et al.
    Umeå Universitet, Umeå, Sverige.
    Ödmark, Krister
    Umeå Universitet, Umeå, Sverige.
    Lundberg, Anna, L., V.
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Kommunikation och visualisering2015Other (Other academic)
    Abstract [sv]

    Denna text belyser olika aspekter av kommunikationsförmågan och dess roll i lärande av matematik på yrkesprogram. Texten är uppbyggd med en inledande del om kommunikationens roll i undervisningen, därefter presenteras en teoretisk inblick gällande ”språk och matematik” och konkreta exempel på matematiska visualiseringsuppgifter. Tanken är att ge stöd för en utveckling av de infärgade uppgifter ni skapat. Förmågan att visualisera behövs ofta för att skapa lärande vid olika problemlösningssituationer. Det har gjorts flera avgränsningar i presentationen av fältet, t ex har fokus varit på användning en av verkliga bilder och konkreta föremål och nästan uteslutit diskussioner om mentala bilder och föreställningar i matematik. Avslutningsvis presenteras några idéer om användningen av digitala verktyg för kommunikation och visualisering som stöd för formativ bedömning och lärande.

1 - 10 of 10
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