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  • 1. Andersson, Charlotta
    et al.
    Andrén, Sanna
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Tuominen, Jane
    Skapa behov av multiplikation2020Inngår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 4, s. 11-15Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [sv]

    Kan multiplikation förstås på något annat sätt än som upprepad addition? Här prövar författarna ett nytt sätt att undervisa om multiplikation. Genom att arbeta med indirekt mätning skapas ett behov av multiplikation.

  • 2.
    Annerberg, Anna
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Pedagogiskt arbete.
    Teledahl, Anna
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Successful integration of mathematics and vocational subjects: Professional relations between different groups of teachers2018Inngår i: ECER 2018 “Inclusion and Exclusion, Resources for Educational Research?” took place 3 – 7 September at the Free University Bolzano., 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Vocational education and training (VET) is an important part of the EU aim to have 75% of its working-age population in work by 2020.  VET research which is focused on developing effective teaching is getting increased attention from the educational research community. A special area of interest for VET research is the integration of traditional theoretical subjects such as mathematics and English in vocational courses. Integration of subjects, if successfully organized, has proven to generate improved learning outcomes. What, then, are the factors that render such projects successful?

    Previous research on integration projects has highlighted the importance of organizational framing such as time allotted for planning, scheduling, infrastructure and management support. Soft values such as relations, cooperation, pedagogical values, and perspectives, have however, not received as much attention in research. The aim of this study is therefor to contribute with knowledge about how teachers, who have been successful in integrating subjects, relate to each other We have chosen to examine how teachers talk about their cooperation and their understanding of the subject content, which in this case is mathematics. The study has taken place at a Swedish upper secondary school which offers only vocational education, and where they have had an active integration project, for several years. The teachers and the school management have identified the project as successful based on improved learning outcomes as well as an increased interest in pursuing more advanced mathematics courses. The Swedish National Agency for Education have also highlighted the project as an example of productive integration.

    Theoretically we have chosen to focus on teachers’ room for maneuver or freedom to act professionally in relation to each other (Annerberg, 2007). To deal with relations and room for maneuver we use theories that derives from the power perspectives of Foucault (Foucault 1997, 2011). The professional relations between teachers are examined with theories of “professional identity” (Gustafson, 2010) and the room for maneuver is closely related to Parding´s “discretionary power” (2007). We consider power discourses (professional identities and relations) as mediated by language (Fairclough, 2010). 

    The study has a qualitative approach and focuses on the discourses that emerge in the teachers’ talk. There are two groups of respondents; eight vocational teachers who each have been interviewed, and six math teachers who have each been interviewed but also engaged in six group interviews during one year. The interviews were semi-structured and they were transcribed and analysed using a thematic content analysis (Vaismoradi, et al, 2013). The group interviews focused on a particular theme and different data, provided by the researchers, were used as a base for the discussions. Examples of such data include interviews with students, curricular documents and statements regarding mathematics.  Discussions during group interviews were recorded and transcribed in the same manner as the individual interviews. 

    The results show that the relations between vocational teachers and mathematics teachers are described differently. The feature that they have in common however is a mutual respect and a recognition of the other groups’ competence as teachers. Most of the vocational teachers talk about themselves as teachers with very good relations to students, they meet the students often and the students value their expertise. They also talk about mathematics in very positive terms and as something that is valuable and useful in their vocation. All vocational teachers do not talk about the integration project as quite as successful as the mathematics teachers do. It seems that one of the most important elements to the way the project is described as successful is the way the mathematics teachers have approached their vocational counterparts with modesty and a genuine interest in identifying the various ways in which mathematics is part of the different professions. This identification has also involved finding ways to incorporate this “workers’ mathematics” into the mathematics teaching. The school has also tried to develop similar integration projects in other subjects. These projects have however been less successful and the vocational teachers argue that identifying these subjects in their vocations is more challenging, hence the cooperation is also less fruitful. 

    One important aspect of the relations between the vocational teachers and the mathematics teachers is the fact that the school offers only vocational programmes. There are no theoretical programmes. The school has an ambition to act as a model of a workplace where teachers act as managers rather than teachers and this creates an environment in which power and status does not come from having theoretical knowledge but rather in having being able to develop and sustain good relationships to the students and in being an expert in the various vocations.

    Annerberg, A. (2016). Gymnasielärares skrivpraktiker: skrivande som professionell handling i en digitaliserad skola. Diss. Örebro: Örebro universitet, 2016. Örebro.

    Fairclough, N. (2010). Critical discourse analysis: the critical study of language (2nd ed.). Harlow: Longman.

    Foucault, M., Bjurström, C. G., & Torhell, S.-E. (2011). Vetandets arkeologi. Lund: Arkiv.

    Foucault, M., & Ewald, F. (1997). ”Il faut défendre la société”: cours au Collège de France (1975-1976). Paris: Gallimard.

    Frelin, A. (2010). Teachers’ relational practices and professionality. Uppsala: Institutionen för didaktik, Uppsala University.

    Gustafson, N. (2010). Lärare i en ny tid: om grundskollärares förhandlingar av professionella identiteter. Diss. Umeå : Umeå universitet, 2010. Umeå.

    Parding, K. (2007). Upper secondary teachers’ creation of discretionary power : the tension between profession and organisation. Luleå: Division of Industrial Processes, Department of Human Work Sciences, Luleå University of Technology.

    Vaismoradi, M., Turunen, H. & Bondas, T. (2013). Content analysis and thematic analysis: Implications for conducting a qualitative descriptive study. Nurs Health Sci. 2013 Sep; 15(3):398-405. 

  • 3.
    Barmé, Elin
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    En varierad matematikundervisning: Hur matematiklärare i årskurs F-3 varierar undervisningsformer2018Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Denna studie behandlar hur lärare i årskurs F-3 varierar sin matematikundervisning. Syftet med studien är att utifrån ett lärarperspektiv undersöka vilka olika undervisningsformer som används av ett antal matematiklärare i årskurs F-3 samt vad dessa lärare anser om variation i matematikundervisningen.Fyra lärare, en från varje årskurs från förskoleklass till årskurs 3, har deltagit i studiens undersökningar. Undersökningsmetoder har varit icke deltagande observation av en matematiklektion med varje lärare samt en kvalitativ semistrukturerad intervju med varje lärare. Resultaten visade på att den traditionella undervisningsformen var den vanligaste undervisningsformen som användes och matematikdiskussioner var den vanligaste alternativa undervisningsformen som användes. Ju högre upp i årskurserna undersökningarna gjordes desto mindre användes alternativa undervisningsformer. En ökad andel resurser under matematiklektionerna skulle bidra till ökade möjligheter till att variera undervisningen.

  • 4.
    Bergstrand, Mattias
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Digitala verktyg i matematik: Elevers arbete med matematik i digitala verktyg2017Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna undersökning är att undersöka hur elever använder det matematiska innehållet i olika digitala verktyg. För att få svar på detta har observationer och enkätundersökningar gjorts. Resultaten har analyserats med utgångspunkt i ett teoretiskt ramverk där användningar av digitala verktyg kan vara ersättande, förstärkande och transformerande. Resultaten visar att digitala verktyg kan vara ersättande i vissa avseenden och förstärkande eller transformerande i andra.

    Fulltekst (pdf)
    fulltext
  • 5.
    Buskqvist, My
    et al.
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Olsson, Sara
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Kärleksfull matematikundervisning - vägen till framgång?: - En kvalitativ intervju- och literaturstudie...2008Independent thesis Basic level (degree of Bachelor)Oppgave
    Abstract [sv]

    Utgångspunkten i vår undersökning var att grundskolans matematikundervisning sedan länge är präglad av enskild räkning i läroboken och graden av modernisering är låg. Detta grundar vi dels på egen erfarenhet och dels på forskning vi läst tidigare. När elever får problem med matematiken i skolan läggs skulden på eleverna istället för på skolan och lärarens undervisning. Syftet med vårt arbete var att få en bild av vad skolan och den enskilde läraren kan göra för att förändra/förbättra förutsättningarna i matematik för grundskolans elever. Undersökningens frågeställningar var: Vilka faktorer kan ligga bakom elevers utveckling efter ett icke godkänt nationellt prov i matematik i skolår 5? Vad kan skolan och den enskilde läraren göra för att förändra/förbättra förutsättningarna i matematik för grundskolans elever? Vi valde att söka svar på våra frågor dels genom att göra en litteraturstudie och dels genom att intervjua fyra elever som inte blivit godkända på nationella ämnesprovet i matematik i skolår 5. Vi har också intervjuat deras lärare (fem stycken) i skolår 4-6 och skolår 7-9. Utifrån våra resultat kunde vi dra slutsatsen att matematikundervisning inte enbart handlar om bra didaktiska metoder utan snarare om kärlek till och engagemang för eleverna. Våra elever verkar trivas med den kunskapssyn som Lpo 941 vilar på där skolan ska se till varje unik individ och utforma undervisningen därefter. Grundskolans matematikundervisning präglas fortfarande av enskild räkning i läroboken, visade både våra intervjuer och vår litteraturstudie. Detta trots att en enorm mängd forskning talar emot detta ensidiga arbetssätt och istället förespråkar en varierad undervisning. Våra resultat visade också att det extra stöd elever får är undervisning i liten grupp där undervisningen till stor del sker på samma ensidiga sätt. För att lyckas med matematiken menar elever att lärarens engagemang och tilltro till deras förmåga är den viktigaste faktorn. Andra faktorer som påverkar elevernas resultat är den egna motivationen och lusten att lära. Resultaten visar också att betygen har betydelse för elevernas motivation. Det finnas alltså mycket man kan göra för att förbättra situationen i skolan. De två främsta faktorerna som krävs är engagerade lärare och en varierad undervisning.

    Fulltekst (pdf)
    FULLTEXT01
  • 6.
    Charrière, Lionel
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Det vet man inte, men så tror jag!: Om hur elever i årskurs 9 löser sannolikhetsuppgifter2014Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 7.
    Cortas Nordlander, Maria
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Dissection of text-based mathematical tasks in the multilingual classroom: A pilot study2019Konferansepaper (Fagfellevurdert)
  • 8.
    Damberg, Sofie
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Lärares uppfattningar om matematik och deras syn på relevant centralt innehåll i matematik på yrkesprogram: En studie om lärares uppfattningar om matematik och relevant matematiskt innehåll för elever på fordonsprogrammet2020Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Skolverket har för avsikt att till hösten 2021 införa nya kursplaner i matematik. Kursen matematik 1a, som läses av elever på yrkesprogram, kommer att få ett nytt centralt innehåll där en del av matematiken ska kopplas till respektive yrkesprogram. Denna del, som får namnet Matematik inom karaktärsämnen och yrkesliv, lämnas dock outsagd och det blir upp till matematiklärare att fylla denna med relevant innehåll för respektive yrkesprogram. I denna studie undersöker jag vilken matematik som lärare uppfattar vara relevant att koppla till karaktärsämnena för elever på fordonsprogrammet. Det görs genom en kvalitativ studie där både matematiklärare och yrkeslärare på fordonsprogrammet intervjuas. Då forskning visar att lärare påverkas i sitt val av innehåll av bland annat deras uppfattningar om ämnet tittar jag även närmare på vilka uppfattningar lärarna har om matematik med hjälp av tre perspektiv på matematik framtagna av Pehkonen och Törner (2004).

    Resultaten visar att lärare som besitter ett av perspektiven på matematik verkar ha svårare att se matematiken i karaktärsämnet. Den visar även att matematiklärare har svårt att själva välja ut relevant innehåll av matematik för elever på fordonsprogrammet och således söker stöd hos karaktärsämneslärare för koppling till verkligheten. Studien visar slutligen på den matematik som enligt lärarna är relevant för elever på fordonsprogrammet med en del konkreta exempel.

  • 9.
    Danielsson, Helena
    et al.
    Högskolan Dalarna, Akademin Humaniora och medier, Bild.
    Taflin, Eva
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Multimodal mathematical context and video as a tool for teachers´assessment2015Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Multimodal mathematical context And video as a tool for teachers´ assessment 

    Helena Danielsson, PhD, Associate professor Art and media education - hdn@du.se 

    Eva Taflin, PhD, Senior Lecturer Mathematics education - evat@du.se

    Dalarna University

    This presentation will discuss some experiences from a four year school research study. The aim of our research was to examine teachers develop when they were part of collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. Our study had two focus; one was to investigate methods and tools that teachers can use to develop their ability in assessment when their students where working with multimodal tasks and the other was to examine how video can be used by teachers wanting to obtain knowledge about assessing.

    Our study is based on several theories about when teachers collaborate to create new knowledge. The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. A basic assumption of the framework here is that meanings are made and communicated in mathematics through a wide range of semiotic modes. By using video as an essential tool in our research our framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners are also needed.

    We will choose to highlight some findings that concern the following themes: The use of tasks for assessment, The collaborative talk, The equipment, Ethical dilemmas. Most common was one choice of esthetical mode at a time (combined with written and verbal text), but there were also lessons with mixtures such as stations with different activities. Collaborative talks were evaluated as a meaningful way of sharing knowledge, and the video tool for this, although it raised important ethical discussions. Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work. In this way the project highlighted more general aspects of school development.

    The relevance to Nordic educational research also concerns teachers´ use of collaborative talks in assessment work, multimodal tasks in mathematics and video as a research tool in general.

  • 10.
    Danielsson, Helena
    et al.
    Högskolan Dalarna, Akademin Humaniora och medier, Bild.
    Taflin, Eva
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Multimodal mathematical context and video as a tool for teachers´assessment2014Inngår i: Conference proceedings - 4th international Designs for Learning conference 6-9th May 2014, 2014Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Project aims and research questions

    This presentation will discuss some experiences from a three year school research study now in its’ final stage. The aim of our research is to examine what kinds of knowledge teachers develop when they are part of collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. Theses specific lessons are designed with multimodal mathematical tasks and students work in a multimodal process. The project has been formulated in close collaboration between teachers, other community representatives and us as researchers. Our study has two focus; one is to investigate methods and tools that teachers can  use to develop their ability in assessment when their students are working with multimodal tasks and the other is to examine how video can be used by teachers wanting to obtain knowledge about assessing “creative and aesthetics learning processes” (Skolverket, 2011).

    The research questions are: How can teachers and pupils assess mathematics abilities shown through creative and esthetic learning processes? How can video be used as a method to contribute to teacher professional development regarding formative and summative assessment? What kind of tools do teachers believe they need in order to assess pupils knowledge in multimodal processes?

    A part of  the study is (together with the teachers) to construct a matrix for assessment of students´ mathematical abilities. The matrices that are created are meant to be adapted to a completed lesson which was characterized by a multimodal task, a task in which not only the spoken or written word is important but also activities and interactions by way of documents, glances and gestures. The multimodal task might accommodate various forms of work – such as laboratory activities with different materials. The matrices that are created within the project framework are planned to be adapted for use by both teachers and students.

    Theoretical framework

    Our study is based on several theories about when teachers collaborate to create new knowledge (Carlgren 2012). The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. Other theories that are relevant for the study are Jaworskijs (1991) Teaching Triad as developed into inquiry and development of the teachers´ competence, along with Cobbs Design Theory (2000), where the specific mathematics is identified in the school discourse. The design theories expressed in different texts are used, e.g. by Kress & Van Leeuwen (2001); Kress (2010); Selander & Kress (2010), and concerning the discourse work and by Jewitt (2011; 2012) more explicit for the analyze work

    The epistemological view we represent is inspired by Vygotsky´s (1978) theory of ZDP and cultural aspects in communication. The study uses sociocultural theory as described by Säljö (2005; 2012). By using multimodal tasks we presume that multimodal tasks contribute toa more qualifiedlearning in which students candevelop theirown explanations, solve problems withdifferentstrategies dispute and present mathematical arguments, discussand comparesolutionspresentedbyvariousforms of representation (Taflin 2007). Previous studies (e.g. Danielsson 2002; Öhman Gullberg 2006; Leijon 2010) have shown that different modalities of “production forms” and media reception may even influence theexperienceofauthenticityand ownershipin a different waythan traditionalschoolwork. A basic assumption of the framework here is therefor that meanings are made and communicated in mathematics through a wide range of semiotic modes  (Jewitt 2011; Machin 2011).

    By using video as an essential tool in our research our framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners are also needed. Appropriate theories are taken from Aull Davies (2008); Pink (2012); Schön (1991); Spencer (2011) and also from Heikkilä & Sahlström (2003).From (audio-)visual cultural theories we are inspired by Wingstedt (2012) who speak ofmultimodalityfor exponential growthofunderstanding.

    Methods

    The study has been conducted in two steps. First a prestudy over one year, where two primary schools participated (focus on four classes; grade 5 and grade 9). Knowledge gained from the prestudy was used in a more extended study and during the two last years we have had contact with teachers from different schools and levels in four municipalities. With the exception of two researchers we have a group of class teachers from grade 1 to grade 9 participating (about 15 regularly active, while others have been participating at some elected occasions). Two headmasters, two doctorial students and a film maker are also connected to the project.  

    Data collection has been made by both us as researchers, by the teacher themselves and by a professional film maker. In order to learn more about video as a tool we wanted to experiment with different kinds of video equipment in order to examine their functionality for use in a school context. The participating teachers were allowed to use different models but could also choose to use other techniques such as audio recording, photographs, scanning or material copying. Furthermore, they were offered to let students try these it, as part of developing self-assessment and peer assessment. All multimodal tasks in the math lessons were prepared and organized by the teachers themselves. In their second lesson they decided to sometimes try similar ones – in order to develop comparable material, perhaps useful for the matrix discussion. The teachers´ ambition was to design tasks to see if and how they could work to support teachers' assessment of pupils' skills. The researchers empiric data collection, however, both in the prestudy and the second phase of the main study, followed by the same order; Information and presentation sessions in all places and classes. Filming of lessons. After that the film maker edited the material into shorter parts. The edited excerpts were used in a situation of stimulated recall. At this occasion both teachers, colleagues and researchers took part in a video recorded collaborative talk for analysis session (using  two cameras). This process was repeated in altogether seven seminars. The video recordings from the seven meetings along with photographs and audio recordings were presented later on at a summing up meeting, where all the main participants took part.

    We are currently in the process of preparing survey questions, addressed to the teachers, for the final data collection.

     Some findings

    As the final results not yet complete, we have chosen to highlight some findings that we consider of interest to discuss and reflections upon. They concern the following themes: The framework for assessment, Editing concerns, The equipment,  ethical dilemmas.

    Framework for assessment:  Quite early in the project the teachers at one of the schools made a framework (matrix) in order to test it for assessment in maths – and made it available for use by other teachers in the project (that meant that four different municipalities were able to test it). These frameworks were made from the point of view that the multimodal tasks were designed as a  “creative and esthetical learning process”. Interesting here was that the teachers also active in the first grades in school also tried parts of this advanced models. In the project matrices constructed for art education also played a role in maths.

    Editing concerns: The edited video material was critical in the analyse process. Through the edited film teachers were reminded about moments in the lesson – they saw or heard details that could give a more complete picture of the lesson.

    The equipment: The qualities of video cameras of different sizes were discussed a lot. One finding was that sound was sometimes more important than the pictures. In some classes the teachers preferred to use only sound recording in order to be more discrete. In other classes mainly stills were used and copies made of pupils work.

    Ethical dilemmas: The use of video recording, stills or sound material raised unexpected ethical issues. In some schools there were immigrant children with protected identities. Other classes contained students with neurological diagnoses. The parents of these children were hesitant to letting their children be filmed. How could we as researchers handle this? The ethic council at our university expressed doubts about the use of video at all while observing children in a school context. Is this attitude similar in other countries, other university councils? We live in a society where the use and presence of digital resources is increasing, but authorities views here might raise limitations to the use of video as a visual research method. The task, in our opinion, must be to learn how to handle this, not to avoid it. Our studies give an insight into information that can be used to increase this ability.

    In summary all the teachers formulated their personal designed tasks in order to test different modes.  Most common was one choice of esthetical mode at a time (combined with written and verbal text), but there were also lessons with mixtures such as stations with different activities. Teachers commented that the reflection time at the end of lessons became of great importance to sum up questions around the pupils individual learning processes - something they partly developed and stressed more after watching the film excerpts.

    Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work, and in some cases the teachers received no support from their headmaster. In this way the project highlighted more general aspects of school development.

  • 11.
    Danielsson, Helena
    et al.
    Högskolan Dalarna, Akademin Humaniora och medier, Bild.
    Taflin, Eva
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Rapport från projektet Multimodala uppgifter och bedömning i matematik: Video och kollaborativa samtal som metod vid lärares bedömning av elevers matematiska kunskaper2015Rapport (Annet vitenskapelig)
    Abstract [en]

    This research will discuss some experiences from a four year school research study. It was conducted in cooperation with teachers from four municipalities in Dalarna. The aim of the research was to examine teachers´ professional development when they participated in collaborative discussions based on video recordings and video edited material from specific lessons in their own practice. The study had two foci one was to investigate methods and tools that teachers can use to develop their ability to assess their students while working on multimodal tasks. The other was to examine how video can be used by teachers wanting to obtain knowledge about assessing students. The study is based on several theories about when teachers collaborate to create new knowledge. The first is the design theoretical approach – where visual ethnography and a semiotic approach contribute to problematize the use and mixture of different modes. A basic assumption of the framework here is that meanings are made and communicated in mathematics through a wide range of semiotic modes. By using video as an essential tool in the research the framework theories concerning visual ethnography, video documentation and individuals as reflective practitioners were also needed. The findings can be divided into the following themes: the use of tasks for assessment, collaborative discussion, equipment, ethical dilemmas. Collaborative discussions were evaluated as a meaningful way of sharing knowledge. The use of video recordings in association with these discussions raised important ethical issues. Working with the assessment framework was of great interest to the teachers but it took a lot of time from their ordinary work. In this way the project highlighted more general aspects of school development. The research also concerns teachers´ use of collaborative discussions in assessment work, multimodal tasks in mathematics and video as a research tool in general.

    Fulltekst (pdf)
    fulltext
  • 12.
    Danielsson, Stina
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Håller din lärobok i matematik måttet?: En modell för granskning av hur läroböcker i matematik förhåller sig till rådande styrdokuments centrala innehåll2012Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 13.
    Dimenäs, Jörgen
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Pedagogiskt arbete.
    Taflin, Eva
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Handledares och den handleddes roller i lärarutbildningens verksamhetsförlagda delar2020Konferansepaper (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 14.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet.
    Algebraic thinking and level of generalisation: students’ experiencing of comparisons of quantities2019Inngår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 4, nr 3-4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article explores grade 1 students’ different ways of experiencing quantity comparisons after participating in teaching designed as a learning activity using tasks from the Davydov curriculum. A phenomenographic analysis generated three hierarchical ways of experiencing comparisons: counting numerically, relating quantities, and conserving relationships. The first category comprises arithmetic ways of thinking, whereas the second and third categories comprise algebraic ways of thinking. Algebraic thinking was identified as reflections on relationships between quantities at different levels of generalisation. The implications of these results in relation learning activity theory are discussed.

  • 15.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Identifying algebraic reasoning about fractions2018Inngår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg, Lovisa Sumpter, Umeå, Sweden: PME , 2018, s. 255-262Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The issue for this paper is to identify algebraic reasoning through students´sense-making actions, during a lesson, where students and a teacher develop learning models for mixed numbers. The analysis focuses the students’ work, trying to make sense of the unknown fractional part of the number. This unknown part was elaborated when the students suggested to “add a little bit more” to construct equality. The un-known part developed to a fractional part with help of an emerging learning model containing algebraic symbols: B=W+p/a. In this activity. The potentialities in the students’ algebraic reasoning were identifyed as: an additive relationship between the integer and the fractional part of the number, and a multiplicative relationship between the numerator and the denominator in this fractional part.

    Fulltekst (pdf)
    FULLTEXT01
  • 16.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Rationella tal som tal: Algebraiska symboler och generella modeller som medierande redskap2015Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In this study the teaching of mathematics has been developed in relation to rational numbers and towards a learning activity. At the same time topic-specific mediated tools have been studied. The iterative model for learning study has been used as research approach.

    The purpose of the study was to explore what in an algebraic learning activity enables knowledge of rational numbers to develop. The specific questions answered by the study are how an algebraic learning activity can be formed in an otherwise arithmetic teaching tradition, what knowledge is mediated in relation to different mediated tools and what in these tools that enable this knowledge.

    The result of the study shows how an algebraic learning activity can be developed to support the students to understand rational numbers even in an arithmetic teaching tradition. The important details that developed the algebraic learning activity were to identify the problem to create learning tasks and the opportunity for the students to reflect that are characteristic of a learning activity. The result also shows that the mediating tools, the algebraic symbols and the general model for fractional numbers, have had significant importance for the students' possibilities to explore rational numbers. The conditions for the algebraic symbols seem to be the possibilities for these symbols to include clues to the meaning of the symbol and that the same symbol can be used in relation to several of other mediated tools. The conditions in the general model consisted of that the integer numbers and the rational numbers in the model could be distinguished and that the students could reflect on the meaning of the different parts. The general model consists of the algebraic symbols, developed in the learning activity. The algebraic symbols make the structure of the numbers visible and the general model mediates the structure of additive and multiplicative conditions that are contained in a rational number.

    The result of the study contributes in part to the field of mathematics education research by examining Elkonin's and Davydov's Mathematical Curriculum in a western teaching practice and in part to a development of the model of Learning study as a didactical research approach by using an activity-theoretical perspective on design and analysis.

    Fulltekst (pdf)
    FULLTEXT01
  • 17.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet.
    Bergkvist, Anna-Mia
    Södertörns högskola.
    Öppna eller stängda skolor – en fråga även om bildning och lärande2020Inngår i: S.O.S - Skola och Samhälle, ISSN 2001-6727Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Fulltekst (pdf)
    fulltext
  • 18.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Eriksson, Inger
    Stockholms universitet, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Matematik som teoretiskt arbete - utveckling av matematiska modeller för rationella tal i åk 42016Inngår i: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 4, nr 1, s. 6-24Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The teaching of rational numbers to young students (grade 4-6) is known to be difficult. It is for instance difficult for students to understand that fractions and decimal numbers may represent the same value, or that fraction has a specific place on the number line, i.e. that it is a number among other numbers. The purpose of this article is to discuss and exemplify how students can be involved in a theoretical exploration of fractions as numbers. The basis of the students’ exploration was a designed situation where they were to make measurements of wooden rods where the measurements did not make an equal, i.e. “a little bit” was missing. With these measurements students in joint discussions were able to design a general model for fractions. Such a model could be used as a tool in discussions of “the whole” and “its parts” in fractions. The article is based on data from a series of Learning studies conducted in a grade 4 in an intercultural school in 2012-2013.

    Fulltekst (pdf)
    FULLTEXT01
  • 19.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sumpter, Lovisa
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Fractions and algebraic reasoning2017Konferansepaper (Fagfellevurdert)
    Fulltekst (pdf)
    FULLTEXT01
  • 20.
    Eriksson, Inger
    et al.
    Stockholms universitet, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Setting an object of knowledge in motion through Davydov’s learning activity2017Inngår i: Book of Abstracts, 2017, s. 111-111Konferansepaper (Fagfellevurdert)
  • 21.
    Erixon, Eva-Lena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Convergences and influences of discourses in an online professional development course for mathematics teachers2017Inngår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 22, nr 1Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Despite the ever-increasing number of online professional development (OPD) courses, few studies have examined online education for mathematics teachers. This article reports on a case study of discourses in an OPD course for mathematics teachers concerning the convergence and influence of discourses in course seminar discussions and in mathematics teaching in school when course participants are given the task of translating their insights into actual teaching, with a focus on the participants’ discussions of their own and one another’s video-recorded lessons. The analysis shows that there is a convergence of discourses in the seminars and in the school context related to a focus on concepts and everyday life connections. However, the study also suggests that there is a risk of students remaining outside in an ”everyday discourse”, in which knowledge of mathematics might be useful, but mathematics is discussed in imprecise and simplified terms.

  • 22.
    Erixon, Eva-Lena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Learning activities and discourses in mathematics teachers’ synchronous oral communication online2016Inngår i: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 18, nr 3, s. 267-282Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    There is increasing interest in the provision of online professional development (OPD) for teachers. This case study contributes to the field of research on professional development in the context of activities and discourses relating to mathematics teachers’ synchronous oral communication online. The purpose of this article is to explore the activities on offer in this communication and to identify the discourses that mathematics teachers may create in their meaning-making activities. An analysis of an online community in the form of a professional development course for mathematics teachers has, therefore, been conducted. The analysis shows that there is a lack of reciprocal participation and a shortcoming in creating a reflective learning environment, which can probably be partly explained by the specific mode of digital conversation. The discourses created by the mathematics teachers in their meaning-making activities focused mainly on sharing experiences about the teaching of mathematics.

  • 23.
    Erixon, Eva-Lena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Örebro universitet, Institutionen för humaniora, utbildnings- och samhällsvetenskap.
    Matematiklärares kompetensutveckling online: policy, diskurs och meningsskapande2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Different forms of professional development online are becoming increasingly common for teachers and the aim of the thesis is to contribute knowledge about online professional development for mathematics teachers and the relationship between professional development, educational policy, and mathematics teaching practice. In the thesis, professional development refers to organized professional development in terms of university courses.

    The thesis consists of four studies, each of which has been presented in the form of an article. The four studies together explore transnational and national policy discourses, meaning-making activities that can be distinguished in online professional development, discourses pertaining to mathematics teaching in the classroom and in the subsequent seminar discussions in the course, and teachers’ experience of professional development online. The different arenas have been explored using the concept of discourse with reference to Fairclough, Gee, and Sfard. The term ”discourse” refers primarily to communication and language in use.

    The result of the studies indicates that the participants have not been offered enough opportunities to reflect on how or whether the use of several concepts and everyday life connections really deepened the students’ understanding of the mathematical content. Moreover, the analysis of the interviews with the participants shows that it was difficult for them to deepen their reflections in the synchronous communication online. There is a lack of reciprocal participation and reflection in the conversation and it is hard for the participants to get an idea of how the others respond to their messages. When a participant has completed his or her message the next speaker continues with a new message and as a result, the communication often takes a new direction instead of allowing in-depth reflection.

    Fulltekst (pdf)
    FULLTEXT01
  • 24.
    Erixon, Eva-Lena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Bjerneby-Häll, Maria
    Mathematics teachers’ meaning making in an online professional development course2014Konferansepaper (Fagfellevurdert)
  • 25.
    Erixon, Eva-Lena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Taflin, Eva
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Problem solving in mathematics: An analytic tool for teachers2011Inngår i: Proceedings of Norma 11: The sixth nordic conference on mathematics education, 2011Konferansepaper (Fagfellevurdert)
  • 26.
    Erixon, Eva-Lena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Wahlström, Ninni
    Linnéuniversitetet.
    In-service training programmes for mathematics teachers nested in transnational policy discourses2015Inngår i: European Journal of Teacher Education, ISSN 0261-9768, E-ISSN 1469-5928, Vol. 39, nr 1, s. 94-109Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Results in mathematics on international knowledge surveys like Programme for International Student Assessment (PISA )and Trends in International Mathematics and Science Study (TIMSS) have become one of the most important factors for the perceived success or failure of schools and even entire education systems in the policy arena. In this article we explore the complex recontextualising processes that occur when translating educational policy into actual programmes for teachers’ education. First, the transnational education policy discourse(s) of teachers´ in-service training with a focus on mathematics will be explored. Second, we examine how this transnational discourse is recontextualised in a national policy discourse resulting in a national reform programme for in-service training of mathematics teachers in Sweden. In a third step, concrete teacher training courses in mathematics are examined. The result shows a convergence between the official policy discourse and the pedagogic recontextualising field in terms of a broad teaching repertoire and peer discussions about reflections on certain common objects of learning.

  • 27.
    Fahlström, Magnus
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Less is more - how to communicate simple but distinct2014Inngår i: Summer School On Scientific Visualization And Presentation: Falun 16-18 June, 2014, 2014, s. 18-18Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    When you present something you want the recipients to perceive the content the way you intend without ambiguity. A picture is worth a thousand words is a famous phrase. If this phrase is true - how do one control the thousand words? In this session I will present some ideas for my research in the light of the theme- Scientific Visualization and Presentation. My research is about class room noise and the impact on students chance of learning as intended. I will address questions such as: In what way is it useful to transform future results to a form of: Wasted Learning Units?

  • 28.
    Fahlström, Magnus
    et al.
    Högskolan Dalarna, Akademin Industri och samhälle, Mikrodataanalys.
    Teledahl, Anna
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Students’ use of images for documenting their problem solving2017Konferansepaper (Annet vitenskapelig)
  • 29.
    Grundén, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Linnéuniversitetet, Institutionen för matematik (MA).
    Diversity in meanings as an issue in research interviews2017Inngår i: Mathematics Education and Life at Times of Crises: Proceedings of the 9th International Conference of Mathematics Education and Society / [ed] Anna Chronaki, Volos, Greece: University of Thessaly Press , 2017, s. 503-512Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Taking the social, political, and ethical dimensions of mathematics education seriously means not only researching these issues, but also designing and assessing research with these dimensions in mind. When designing an interview study about planning in mathematics, diversity in meanings was recognized and participants and their voices were foregrounded. In this paper, the design is related to perspectives on interviews, meaning as both durable and transient, and quality criteria such as reproducibility and bias. Theoretical assumptions had consequences for how meaning was seen, but also for relevance of the chosen quality criteria. Findings suggest that not only design, but also assessment of quality in interview studies have to be discussed in relation to the theoretical assumptions the studies build on. 

  • 30.
    Grundén, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Educational planning in mathematics as a part of macro-sociological structures2017Inngår i: ICT in mathematics education: the future and the realities: Proceedings of MADIF10 / [ed] Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist, Göteborg: Göteborgs universitet, 2017, s. 149-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    All teachers in mathematics somehow plan for their teaching. They have con- siderations and make decisions that will in uence what is happening in the classroom and thereby also what opportunities their students have to learn mathematics. Considerations and decisions are made in a social practice with power relations operating both within the practice itself and between practices. In a forthcoming study about planning of mathematics teaching these power relations will be explored. In this presentation different methods for exploring the power relations are discussed.

  • 31.
    Grundén, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Linnaeus University.
    Planning in mathematics teaching: a varied, emotional process influenced by others2020Inngår i: LUMAT: International Journal on Math, Science and Technology Education, E-ISSN 2323-7112, Vol. 8, nr 1, s. 67-88Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 32.
    Grundén, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Tensions between representations and assumptions in mathematics teaching2019Inngår i: Proceedings of the Tenth International Mathematics Education and Society Conference / [ed] Jayasree Subramanian, Hyderabad, India: Mathematics Education and Society , 2019, Vol. 2Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Mathematics teaching and mathematics teachers are part of cultural, societal, and educational structures. These structures and different actors within the structures construct mathematics teaching differently and influence the scope of action that teachers hold. To explore the mechanisms behind this influence, Fairclough’s concepts of representations and assumptions were used to analyze common themes in interviews with six Swedish mathematics teachers. Results showed that there is diversity in ways of representing and that three groups of actors are visible in the representations: teachers, official actors, and students and parents. Results also revealed tensions between representations and assumptions that have consequences for teachers’ considerations and decisions about their mathematics teaching.

  • 33.
    Grundén, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Linnéuniversitetet.
    Sterner, Helén
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Linnéuniversitetet.
    Balancing interests in a research project through internal ethical engagement2020Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In educational design research projects, there are long-term relationships between researcher and participants. Hence, in addition to external ethical engagement, researchers have to engage in internal ethical issues, which became evident when a researcher suggested mathematical content for an intervention. The suggestion was both appealing to and uncomfortable for the teachers, and this ambiguity made power relations between the researcher and the participants visible. In the moment, the researcher made decisions about the content that might not be the best. This situation made visible the importance of internal ethical engagement in advance, for example, by thinking about how we care for our participants and for what and whom we are responsible.

    Fulltekst (pdf)
    fulltext
  • 34.
    Hammenborg, Helene
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik. Högskolan Dalarna, Akademin Utbildning och humaniora, Pedagogiskt arbete.
    Från grej till kvadrat: Om begreppsförståelse inom geometri utifrån läromedel2012Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    One of the purposes of this work was to find out what it means to have a conceptual understanding of geometry. It describes how the geometry evolved from history and the geometry that is taught in grade one to nine and collage. The area examined was based on fundamental geometric objects for example two- and three- dimensional objects and its characteristics and especially focusing on the areas of perimeter, area and volume. The literature- review showed that the conceptual understanding was primary to developing a good knowledge of geometry. The second purpose of his study examined whether pupils achieved the goals in geometry by working with a Mathematics Book. It was the newest Mathematics-book that gave the best conditions for this, while the oldest was missing key parts.

    Fulltekst (pdf)
    fulltext
  • 35.
    Harvey, Frida
    et al.
    Örebro University.
    Teledahl, Anna
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Örebro University.
    Teacher Professional Development and Collegial Learning: A literature review through the lens of Activity System2019Inngår i: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education / [ed] Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M., Utrecht, Netherlands, 2019Konferansepaper (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 36.
    Hjerpe, Olof
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Feedback II: Hur feedback i form av feedbackfrågor påverkar elevers resonerande vid matematisk problemlösning2018Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    I den här kvalitativa studien undersöks hur elevers resonemang vid matematisk problemlösning påverkas av feedback given i form av frågor enligt en given modell. Elever i åk 7 har fått arbeta med ett matematiskt problem och i arbetet fått muntliga feedbackfrågor av olika bestämda typer som beskrivs närmare i §3.4. Studien visar hur lärares variation av feedbackfrågor kan påverka hur elever resonerar vid arbete med matematiska problem.

  • 37.
    Isberg, Jenny
    et al.
    Högskolan Dalarna, Akademin Hälsa och samhälle, Idrotts- och hälsovetenskap.
    Grundén, Helena
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Kvalitet i undervisning - med fokus på förmågor2012Konferansepaper (Annet vitenskapelig)
    Abstract [sv]

    Skolans huvudsakliga uppdrag är lärande (Utbildningsdepartementet, 2010) och läraren är den enskilt viktigaste faktorn för elevernas kunskaper (Hattie, 2009). Skolinspektionens nationella granskningar av undervisningen i matematik samt idrott och hälsa visar att undervisningen inte bedrivs i enlighet med styrdokumenten. I matematik framkom att många lärare inte är medvetna om kursplanens innebörd och att undervisningen präglas av enskilt räknande i läroböcker (Skolinspektionen, 2009). I idrott och hälsa visade det sig att undervisningen inte följer den bredd av aktiviteter som kursplanen anger och att det var ett fåtal aktiviteter, så som bollspel och bollekar, som dominerade lektionerna och att hälsoperspektivet nästan inte alls förekom (Skolinspektionen, 2010). Som ett led i att förbättra kvaliteten i undervisningen lyfts i Lgr11 ämnesspecifika förmågor fram som långsiktiga mål som eleverna ska ges möjlighet att utveckla (Skolverket, 2011). Bakgrunden till två projekt som genomförs med lärare i matematik samt idrott och hälsa i två kommuner är en tanke om att en förutsättning för att undervisning utifrån de långsiktiga målen ska kunna ske är att de lärare som planerar och genomför undervisningen förstår innebörden av de ämnesspecifika förmågorna, samt att en ökad medvetenhet om dessa ska öka kvaliteten i undervisningen. Projekten inleddes med en undersökning av lärares uppfattningar och kunskaper om de ämnesspecifika förmågorna och hur kursplanens delar förhåller sig till varandra. Resultaten av dessa undersökningar visar att lärare i de båda ämnena är osäkra både på förmågornas innebörd och hur kursplanens delar förhåller sig till varandra. Många lärare har heller inte förstått förmågornas roll vid planering av undervisning.

  • 38.
    Isberg, Jenny
    et al.
    Högskolan Dalarna, Akademin Hälsa och samhälle, Idrotts- och hälsovetenskap.
    Larsson, Hed Kerstin
    Högskolan Dalarna, Akademin Utbildning och humaniora, Naturvetenskap.
    Bjerneby Häll, Maria
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Förskolor som miljöer för ett omsorgsfullt lärande med fokus på matematik, naturvetenskap och teknik2012Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

    Hur kan miljöer i förskolan utformas för att stimulera till lärande i matematik, naturvetenskap och teknik? Vilka förutsättningar för barns utveckling och lärande ger olika miljöer?

    I ett pågående forskningsprojekt studeras hur olika förskolemiljöer på olika sätt kan bidra till att utveckla barns lärande i matematik, naturvetenskap och teknik. Miljö innefattar den fysiska miljön, de material barn har tillgång till i lek för att bygga, skapa och konstruera och för att lära genom att upptäcka, undersöka och pröva olika lösningar, hur rum används och verksamheten organiseras, såväl inomhus som utomhus.

    Projektet är mångvetenskapligt både till sin karaktär och med avseende på forskare knutna till projektet. Matematik, naturvetenskap och teknik i förskolan har nära kopplingar till andra målområden, som språkutveckling, skapande och värdegrundsfrågor. Med kunskaper om bl.a. biologi, energi och materia får människor också redskap för att kunna bidra till en hållbar utveckling. Förskolan ska enligt Lpfö 98/10 medverka till att barn tillägnar sig ett varsamt förhållningssätt till natur och miljö. Ett omsorgsfullt lärande kan på så sätt även bidra till att barn utvecklar en omsorgsfull relation till naturen och miljön.

     Fokus för undersökningen är i vilken utsträckning den fysiska och pedagogiska miljön ger barn förutsättningar att möta matematik, naturvetenskap och teknik i olika sammanhang, på ett varierat sätt och genom olika uttrycksformer. Variation är ett nyckelbegrepp och syftar både på variation mellan förskolor som miljöer för lärande, och variation inom en förskola som miljö för lärande. 

    Seminariet bygger på forskning och det pågående projektet om förskolemiljöer. Konkreta exempel på analys av data från undersökningen, bl.a. i form av fotografier hämtade från olika förskolor, presenteras under seminariet.

     

  • 39.
    Isberg, Jenny
    et al.
    Högskolan Dalarna, Akademin Hälsa och samhälle, Idrotts- och hälsovetenskap.
    Larsson, Hed Kerstin
    Högskolan Dalarna, Akademin Utbildning och humaniora, Naturvetenskap.
    Bjerneby Häll, Maria
    Högskolan Dalarna, Akademin Utbildning och humaniora, Matematikdidaktik.
    Miljöer för små barns lärande i matematik, naturvetenskap och teknik2012Konferansepaper (Annet vitenskapelig)
    Abstract [sv]

    Miljöns betydelse för barns lärande framhålls av forskare (Sheridan, Pramling Samuelsson & Johansson, 2009). I läroplanen (Lpfö 98/2010) understryks vikten av att miljön är öppen, innehållsrik och inbjudande. Med miljö syftas här på vilka material barn har tillgång till i lek, för att bygga, skapa och konstruera och för att lära genom att upptäcka, undersöka och pröva olika lösningar, hur rum används och verksamheten organiseras såväl utomhus som inomhus. Persson (2008) konstaterar att det finns förvånansvärt lite forskning om barns lärande i matematik och naturvetenskap och om den fysiska miljöns betydelse för lärande i förskolan, och han hänvisar till forskare som menar att de rumsliga och fysiska förutsättningarna för barns lärande inte tagits i beaktande i pedagogisk forskning. Barns aktiva lärande sker med hela kroppen och det är genom kroppen och sinnena som människan upplever olika fenomen (Merleau-Ponty, 1962). I sin studie av småbarns möten med matematik visar Björklund (2007) att barn använder sin kropp som utgångspunkt, barnets kroppsliga upplevelser och erfarenheter utgör grunden för förståelse av företeelser i omvärlden.

    I föreliggande mångvetenskapliga forskningsprojekt1 studeras förskolemiljöer med fokus på i vilken utsträckning den fysiska och pedagogiska miljön ger barn förutsättningar att möta matematik, naturvetenskap och teknik i olika sammanhang och på olika sätt. Resultaten hittills har visat på nödvändigheten av att även rikta uppmärksamhet mot pedagogerna i förhållande till förskolans fysiska och pedagogiska miljö. Det är pedagogen som är ansvarig för miljön, skapare av miljön, och därmed den som påverkar det lärande, lärandets innehåll och form, som möjliggörs i miljön. Thulin (2011) beskriver i sin avhandling pedagogen som iscensättare av en pedagogisk miljö som kan möjliggöra barns lärande i naturvetenskap. Pedagogen är samtidigt den som kan berätta om de resonemang som förs och motiv som finns till att miljön utformats på ett visst sätt. Den genomförda datainsamlingen har också tydliggjort behovet av att fördjupa studien genom återkommande kontakter och besök i samma förskolemiljöer, samt nödvändigheten av att samtala med pedagoger ansvariga för miljöns utformning och för förändringar i den fysiska miljön. Variation är ett nyckelbegrepp och syftar både på variation mellan förskolor, variation inom en förskola, och variation med avseende på lärandets objekt.

  • 40.
    Jäder, Jonas
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Med uppgift att lära: om matematikuppgifter som en resurs för lärande2019Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [sv]

    Elevers möjligheter att utveckla sin kunskap i matematik påverkas av de uppgifter de arbetar med. Det är möjligt att göra en distinktion mellan rutinuppgifter och matematiska problem. En rutinuppgift är en uppgift som en elev kan lösa genom att använda en välbekant metod, eller genom att imitera en förlaga. För att lösa ett matematiskt problem behöver däremot eleven konstruera en för henne ny lösningsmetod. För att utveckla sin matematiska kunskap behöver elever möta såväl rutinuppgifter som matematiska problem. Problemlösning kan skapa förutsättningar för en elev att utveckla såväl en kreativ problemlösningsförmåga, som en konceptuell, matematisk förståelse.

    Avhandlingen består av fem studier med ett fokus på matematikuppgifter, där studie 1-3 syftade till att undersöka vilka möjligheter att arbeta med matematisk problemlösning som elever i gymnasieskolan erbjuds. Detta undersöktes genom läroboksanalyser, studier av elevers arbete med uppgifter och av elevers uppfattningar om matematik. Uppgifter i läroböcker från 12 länder analyserades (studie 1) och ungefär 10 procent av dessa var matematiska problem. Eleverna arbetade (studie 2) nästan uteslutande med de uppgifter som av läroboksförfattarna kategoriserats som enkla och utan att arbeta problemlösande. Bland dessa uppgifter var andelen matematiska problem 4 procent. Inte heller bland uppgifter som kategoriserats som till exempel ’problemlösning’ eller ’utforska’ var matematiska problem i övervikt. Resultaten var relativt lika för de tolv ländernas läroböcker. Elevers uppfattningar om att rutinarbete är säkrare och något som är rimligt att förvänta sig i matematik (studie 3) kan ha en ytterligare påverkan på deras möjligheter att arbeta problemlösande. Med tanke på de positiva effekter som påvisats för elever som arbetar med problemlösning verkar elevers möjligheter att arbeta med problemlösning begränsade. Det finns potential i att såväl utveckla innehållet i läroböckerna för att öka andelen matematiska problem, som i ett medvetet uppgiftsurval från dessa läroböcker.

    Syftet med studie 4 och 5 var att fördjupa förståelsen för problemlösning. Ett analytiskt ramverk har utvecklats för att identifiera kreativa, konceptuella och andra utmaningar i elevers problemlösning. Respektive utmaning karaktäriserades för att ytterligare fördjupa förståelsen för dessa och för problemlösning. Elevers arbete med matematiska problem (studie 4) och lärares förväntningar på de utmaningar elever möter vid problemlösning (studie 5) studerades. Konceptuella och kreativa utmaningar visade sig vara de mest centrala vid elevers problemlösning. Genom den karaktäristik som knöts till respektive utmaning kan svårigheter med att identifiera, framför allt kreativa utmaningar, och relationen mellan uppgift och utmaning diskuteras.

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  • 41.
    Jäder, Jonas
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet.
    Task design with a focus on conceptual and creative challenges2019Inngår i: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019). / [ed] Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M., Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. , 2019, s. 4234-4241Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Tasks are an important part of the education in mathematics. In an ongoing study, an analytic framework for identifying challenges in students mathematical task solving has been developed, and the conceptual and the creative challenge has been defined. Preliminary results indicate that considerations are needed to include these challenges in mathematical tasks. This paper takes off from there to describe a structure for selection and (re)design of tasks. The aim is to be able to discuss the basis for the structure. A further aim is to develop a support for teachers, test designers, textbook authors and others, in creating tasks with specific learning goals.

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  • 42.
    Jäder, Jonas
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Lithner, Johan
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Sidenvall, Johan
    Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
    Mathematical problem solving in textbooks from twelve countries2020Inngår i: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 51, nr 7, s. 1120-1136Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook. There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks. Textbook descriptions indicating problem solving did not guarantee that a task solution had to be constructed without the support of an available template.

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  • 43.
    Jäder, Jonas
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Linköping University.
    Sidenvall, Johan
    Linköping University; School Administration, Municipality of Hudiksvall.
    Sumpter, Lovisa
    Department of Mathematics and Science Education, Stockholm University.
    Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving2017Inngår i: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 15, s. 759-776Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were found deductively and include expectations, motivational beliefs and security. When it comes to reasoning, a variety of approaches were found. Even though the tasks were designed to demand more than imitation of algorithms, students used this method and failed to solve the task. © 2016 Ministry of Science and Technology, Taiwan

  • 44.
    Karlsson, Lennart
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Matematiska samband i en algebraisk lärandemiljö: Studiens syfte är att undersöka om eleverna får djupare förståelse för matematik genom att arbeta med matematiska samband i en algebraisk lärandeverksamhet2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
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  • 45.
    kilicaslan, Pinar
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Lärares användning av digitala verktyg vid problemlösning i matematikundervisningen för årskurs 7-92020Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Användning av digitala verktyg inom matematikundervisningen är väsentlig i dagens digitaliserade värld. De olika verktygen ger möjlighet för lärare att arbeta på olika sätt och tillåter elever att undersöka olika matematiska förhållanden inte minst inom problemlösning, som både är en förmåga och ett kunskapsområde inom matematik. Syftet med denna studie var att undersöka lärarnas användning av digitala verktyg vid problemlösning i matematikundervisningen för årskurs 7-9, med utgångspunkt i lärarnas beskrivningar. Användandet undersöktes med utgångspunkt i rollerna ersättande, förstärkande samt transformerandet. Studien genomfördes genom intervjuer med sex matematiklärare för högstadiet, där resultatet visade att lärarna beskriver användningen av digitala verktyg vid problemlösning som ersättande, förstärkande, ersättande/förstärkande eller transformerande. Den förstärkande användningen var framträdande då varje lärare beskrev minst en användning av ett digitalt verktyg som kunde klassas inom kategorin.

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  • 46.
    Larsson, Daniel
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Elevers möjligheter att utveckla kreativt matematiskt resonemang genom lärarskapade problemlösningsuppgifter2020Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med studien är att med utgångspunkt i lärarskapade problemlösningsuppgifter undersöka elevers möjligheter till kreativt matematiskt resonemang, CMR, som innebär att eleven skapar en ny eller återupptäcker en för eleven glömd lösningsmetod. Studien genomförs som en kvalitativ uppgiftskategorisering där utvalda problemlösningsuppgifter ur Kunskapsmatrisens uppgiftsbank analyseras genom att undersöka möjligheten till imitation av lösningsmetod genom lärobokens övningar och exempel. Uppgifterna är skapade av verksamma lärare i landet och urvalet har medvetet gjorts för att fokusera på uppgifter där problemlösning är i fokus, både ur ett innehålls- och förmågeperspektiv.

    Resultatet visar att lärarskapade problemlösningsuppgifter som ett komplement till läroboken inte ökar möjligheten för eleverna att erbjudas CMR i undervisningen eftersom andelen CMR i dessa uppgifter ligger på samma nivå som i läromedlen. Studiens analys av lärarskapade problemlösningsuppgifter pekar tydligt på att uppfattningen om att problemlösning och CMR inte är till för alla elever tydligt lever kvar i klassrummen eftersom CMR saknas bland uppgifterna som i Kunskapsmatrisen bedöms med lägst svårighetsgrad

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  • 47. Liljekvist, Yvonne
    et al.
    Mellroth, Elisabet
    Olsson, Jan
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet.
    Boesen, Jesper
    Conceptualizing a local instruction theory in design research: report from a symposium2017Inngår i: ICT in mathematics education: the future and the realities. Proceedings of MADIF10. The tenth research seminar of the Swedish Society for Research in Mathematics Education. Karlstad, January 26–27, 2016 / [ed] Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist, Göteborg: SMDF/NCM , 2017, s. 119-128Konferansepaper (Fagfellevurdert)
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  • 48.
    Olsson, Jan
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet, Institutionen för tillämpad utbildningsvetenskap.
    GeoGebra, Enhancing Creative Mathematical Reasoning2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The thesis consists of four articles and this summarizing part. All parts have focused on bringing some insights into how to design a didactical situation including dynamic software (GeoGebra) to support students’ mathematical problem solving and creative reasoning as means for learning. The four included articles are:

    I. Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62.

    II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21.

    III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review)

    IV. Olsson, J., & Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review)

    Background

    A common way of teaching mathematics is to provide students with solution methods, for example strategies and algorithms that, if followed correctly, will solve specific tasks. However, questions have been raised whether these teaching methods will support students to develop general mathematical competencies, such as problem solving skills, ability to reason and acquire mathematical knowledge. To merely follow provided methods students might develop strategies of memorizing procedures usable to solve specific tasks rather than drawing general conclusions. If students instead of being provided with algorithms, are given the responsibility to construct solution methods, they may produce arguments for why the method will solve the task. There is research suggesting that if those arguments are based on mathematics they are more likely to develop problem solving and reasoning-skill, and learn the included mathematics better. In such didactic situations, where students construct solutions, it is important that students have instructions and tasks that frame the activity and clarify goals without revealing solution methods. Furthermore, the environment must be responsive. That is, students need to receive responses on their actions. If students have an idea on how to solve (parts of) the given problem they need to test their method and receive feedback to verify or falsify ideas and/or hypotheses. Such activities could be supported by dynamic software. Dynamic software such as GeoGebra provides features that support students to quickly and easily create mathematical objects that GeoGebra will display as visual representations like algebraic expressions and corresponding graphs. These representations are dynamically linked, if anything is changed in one representation the other representations will be altered accordingly, circumstances that could be used to explore and investigate different aspects and relations of these objects. The first three studies included in the thesis investigate in what way GeoGebra supports creative reasoning and collaboration. These studies focus questions about how students apply feedback from GeoGebra to support their reasoning and how students utilize the potentials of GeoGebra to construct solutions during problem solving. The fourth study examine students’ learning outcome from solving tasks by constructing their methods.

    Methods

    A didactical situation was designed to engage students in problem solving and reasoning supported by GeoGebra. That is, the given problems were not accompanied with any guidelines how to solve the task and the students were supposed to construct their own methods supported by GeoGebra. The students were working in pairs and their activities and dialogues were recorded and used as data to analyse their engagement in reasoning and problem solving together with their use of GeoGebra. This design was used in all four studies. A second didactical situation, differing only with respect of providing students with guidelines how to solve the task was designed. These didactical situations were used to compare students’ use of GeoGebra, their engagement in problem solving and reasoning (study III) and students’ learning outcome (study IV) whether the students solved the task with or without guidelines. In the fourth study a quantitative method was applied. The data from study IV consisted of students’ results during training (whether they managed to solve the task or not), their results on the post-test, and their grades. Statistical analysis where applied.

    Results

    The results of the first three studies show qualitative aspects of students solving of task with assistance of GeoGebra. GeoGebra was shown to support collaboration, creative mathematical reasoning, and problem solving by providing students with a shared working space and feedback on their actions. Students used GeoGebra to test their ideas by formulating and submitting input according to their questions and hypotheses. GeoGebra’ s output was then used as feedback to answer questions and verify/falsify hypotheses. These interactions with GeoGebra were used to move the constructing of solutions forward. However, the way students engage in problem solving and reasoning, and using GeoGebra to do so, is dependent on whether they were provided with guidelines or not. Study III and IV showed that merely the students who solved unguided tasks utilized the potential of GeoGebra to explore and investigate the given task. Furthermore, the unguided students engaged to a larger extent in problem solving and creative reasoning and they expressed a greater understanding of their solutions. Finally study IV showed that the students who managed to solve the unguided task outperformed, on posttest the students who successfully solved the guided task.

    Conclusions

    The aim of this thesis was to bring some insights into how to design a didactical situation, including dynamic software (GeoGebra), to support students' mathematical problem solving and creative reasoning as means for learning. Taking the results of the four studies included in this thesis as a starting point, one conclusion is that a didactical design that engage students to construct solutions by creative reasoning supported by GeoGebra may enhance their learning of mathematics. Furthermore, the mere presence of GeoGebra will not ensure that students will utilize its potential for exploration and analysis of mathematical concepts and relations during problem solving. The design of the given tasks will affect if this will happen or not. The instructions of the task should include clear goals and frames for the activity, but no guidelines for how to construct the solution. It was also found that when students reasoning included predictive argumentation for the outcomes of operations carried out by the software, they could better utilize the potential of GeoGebra than if they just, for example, submitted an algebraic representation of a linear function and then focused on interpreting the graphical output.

    Fulltekst (pdf)
    FULLTEXT01
  • 49.
    Olsson, Jan
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet.
    The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems2017Inngår i: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, s. 1-21Artikkel i tidsskrift (Fagfellevurdert)
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    fulltext
  • 50.
    Olsson, Jan
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Umeå universitet.
    Granberg, Carina
    Umeå universitet.
    Dynamic software, task solving with or without guidlines, and learning outcomes2019Inngår i: Technology, Knowledge and Learning, ISSN 2211-1662, E-ISSN 2211-1670, Vol. 24, nr 3, s. 419-436Artikkel i tidsskrift (Fagfellevurdert)
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