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  • 1.
    Abdulhamid, Lawan
    et al.
    University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. University of the Witwatersrand, Johannesburg, South Africa.
    Primary mathematics teachers’ responses to students’ offers: An ‘elaboration’ framework2018In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 51, p. 80-94Article in journal (Refereed)
    Abstract [en]

    Responding constructively ‘in-the moment’ to student offers is described as a critical, and yet difficult, aspect of skilful and responsive teaching. South African evidence points to limited evaluation of student offers in schools serving poor communities. In this paper, we present and discuss an ‘elaboration’ framework emerging from a grounded analysis of data drawn from video recordings of 18 mathematics lessons prepared and conducted by four in-service primary school teachers in South Africa. This analysis led to a categorization of the situations in which teacher responses to student offers occurred, and the nature and range of these responses. Three response situations are identified within the framework: breakdown, sophistication, and individuation/collectivization, with a range of response (and non-response) categories in each situation. Literature on responsive feedback is drawn in to explore hierarchies and relationships between the emergent categories within situations of elaboration. The elaboration framework provides a tool for lesson observation, and a model for thinking about developments in responsive teaching.

  • 2.
    Askew, Mike
    et al.
    Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings2020In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704Article in journal (Refereed)
    Abstract [en]

    The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive and multiplicative relations have been theorized. We examine how the connections between these can be considered through a focus on number line representations and children positioning and comparing numbers. The responses of a cohort of South African Grade 1 learners’ (6- and 7-year-olds) to a numerical magnitude estimation task and to a numerical comparison task are analysed and the findings compared to those in the international literature, some of which argue that children’s early, informal, understandings of cardinality and ordinality are underpinned by an intuitive logarithmic model relating number order and size. A main finding presented here is that the responses from learners in this study exhibited a better fit with an exponential model of the relationship between cardinality and ordinality. These findings raise questions about whether some of the findings in previous research are as universal as sometimes claimed.

  • 3.
    Askew, Mike
    et al.
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramdhany, Viren
    University of Johannesburg, South Africa.
    Tshesane, Herman
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Teaching for structure and generality: Assessing changes in teachers mediating primary mathematics2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 2, Research reports (A-K) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 41-48Conference paper (Refereed)
    Abstract [en]

    From a sociocultural perspective that a teacher’s use of mediational means is central to student learning, this paper presents an analysis of six teachers and their mediating, across a two-three year time gap. Drawing on the Mediating Primary Mathematics framework – developed to examine the type and quality of mediational means – we propose two composite assessments of quality of mediation – extent and depth – that indicate the extent to which teaching addresses mathematical structure and generality. The findings reveal a range of differences in these two assessments for each of the six teachers, but that all six teachers were more coherent in their use of mediational means in the later lesson than in the earlier one. These findings have implications for other schooling systems and researchers seeking to improve the quality of mathematics instruction.

  • 4.
    Askew, Mike
    et al.
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramsingh, Valerie
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Takane, Thulelah
    School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Roberts, Nicky
    Centre for Education Practice Research, University of Johannesburg, Johannesburg, South Africa.
    Multiplicative reasoning: An intervention’s impact on foundation phase learners’ understanding2019In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 9, no 1, article id a622Article in journal (Refereed)
    Abstract [en]

    Background: Given the context of low attainment in primary mathematics in South Africa, improving learners’ understanding of multiplicative reasoning is important as it underpins much of later mathematics.

    Aim: Within a broader research programme aiming to improve Foundation Phase (Grades 1–3, 7–9-year-olds) learners’ mathematical performance, the aim of the particular research reported on here was to improve learners’ understanding of and attainment in multiplicative reasoning when solving context-based problems.

    Setting: The research was conducted in a suburban school serving a predominantly historically disadvantaged learner population, and involved teachers and learners from three classes in each of Grades 1–3.

    Methods: A 4-week intervention piloted the use of context-based problems and array images to encourage learners to model (through pictures and diagrams) the problem situations, with the models produced used both to support problem solving and to support understanding of the multiplicative structures of the contexts.

    Results: Cleaning the data to include those learners participating at all three data points – pre-, post-and delayed post-test – provided findings based on 233 matched learners. These findings show that, on average, Grade 1 learners had a mean score average increase of 22 percentage points between the pre-test and the delayed post-test, with Grades 2 and 3 having mean increases of 10 and 9 percentage points, respectively.

    Conclusion: The findings of this study demonstrate that young learners can be helped to better understand and improve their attainment in multiplicative reasoning, and suggest the usefulness of trialling the intervention model more broadly across schools. 

  • 5.
    Avery, Helen
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Centre for Middle Eastern Studies, Lund University, Sweden.
    Acquérir les gestes qu’il faut: les mathématiques scolaires comme interaction et savoir-faire2019In: AREF 2019: Livret des résumés, 2019, p. 286-287Conference paper (Refereed)
    Abstract [en]

    The paper presents the synthesis of a series of studies on support measures for pupils with additional languages in Sweden, with a particular focus on the consequences of language support measures for teaching and learning school mathematics. The analysis identifies several critical aspects in mathematics teaching when the pupils transition from one school system to another, and particularly when they do not yet have a shared language to communicate among each other or with their teachers. Three aspects with relevance to language support will be discussed and illustrated with examples from the studies: the notion of mathematics as a formal language; the notion of levels and absolute progression in mathematics; the notion that learning mathematics means understanding "concepts".

  • 6.
    Avery, Helen
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Centre for Middle Eastern Studies, Lund University, Sweden.
    De la nation-foyer à la nation-forteresse: quelles implications pour l’éducation des réfugiés en Suède?2019In: AREF 2019: Livret des résumés, 2019, p. 209-210Conference paper (Refereed)
    Abstract [en]

    The tensions between tendencies to support and reject that can be observed in reception measures for newly-arrived students in Sweden are a consequence both of the general climate of hostility towards immigration in Europe, and features particular to Sweden. The paper summarises the historical background to the present situation, from the 1960s onwards, and points to some of the impacts for teachers and for civil society. The analysis will above all focus on three diverging but parallell trends and which overlap: dynamics of integration, dynamics of competition and social segregation; dynamics of 'securitisation'. These dynamics evolve within different conceptualisations of education, but also relate to social developments and conflicting visions for society as a whole.

  • 7. Björklund, C.
    et al.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Implementing a structural approach in preschool number activities: Effects of an intervention programManuscript (preprint) (Other academic)
  • 8. Björklund, C.
    et al.
    Kullberg, A.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Venkat, H.
    Critical ways of using fingers in arithmetic problem solving – a study of Swedish 5-yearolds2018Conference paper (Refereed)
  • 9.
    Björklund, Camilla
    et al.
    University of Gothenburg, Sweden.
    Alkhede, Maria
    University of Gothenburg, Sweden.
    Kullberg, Angelika
    University of Gothenburg, Sweden.
    Reis, Maria
    University of Gothenburg, Sweden.
    Marton, Ference
    University of Gothenburg, Sweden.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Teaching finger patterns for arithmetic development to preschoolers2018Conference paper (Refereed)
    Abstract [en]

    In this paper we describe the empirical and theoretical meaning behind how finger patterns are taught to facilitate the development of preschool children’s perception of the first ten natural numbers. An intervention programme, informed by Variation theory of learning, included 65 five-year-olds and teachers at seven preschool departments in Sweden. The programme aimed at developing teaching activities and artefacts to promote children discerning necessary aspects of the first ten numbers. The design of the programme is significant to describe and evaluate as basis for forthcoming analyses of the learning outcomes, as a pedagogical approach that stands in contrast to common preschool teaching practice in Sweden is adopted.

  • 10.
    Björklund, Camilla
    et al.
    Department of Education, Communication and Learning, University of Gothenburg, Sweden.
    Kullberg, Angelika
    Department of Pedagogical, Curricular and Professional studies, University of Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Structuring versus counting: critical ways of using fingers in subtraction2019In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 1, p. 13-24Article in journal (Refereed)
    Abstract [en]

    The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4–5-year-olds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children’s finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered. 

  • 11.
    Björklund, Camilla
    et al.
    Department of Education, Communication and Learning, University of Gothenburg, Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Validating a theory of children’s ways of experiencing numbers2019In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education / [ed] U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis, 2019Conference paper (Refereed)
  • 12.
    Boesen, Jesper
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. National Center for Mathematics Education, University of Gothenburg, Göteborg, Sweden.
    Lithner, Johan
    Umeå Mathematics Education Research Centre, Umeå University, Umeå, Sweden.
    Palm, Torulf
    Umeå Mathematics Education Research Centre, Umeå University, Umeå, Sweden.
    Assessing mathematical competencies: an analysis of Swedish national mathematics tests2018In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 62, no 1, p. 109-124Article in journal (Refereed)
    Abstract [en]

    Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

  • 13.
    Carlgren, Ingrid
    et al.
    Stockholms universitet.
    Eriksson, Inger
    Stockholms universitet.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Learning study2017In: Undervisningsutvecklande forskning: exemplet learning study / [ed] Ingrid Carlgren, Malmö: Gleerups Utbildning AB, 2017, p. 17-30Chapter in book (Other academic)
  • 14.
    Dahlin, Evelina
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Vet du hur mycket klockan är?: En läromedelsanalys om tid- och klockuppgifters utrymme i svenska läromedel2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This study has been done within mathematic education. The purpose of the study is to analyse how much space time- and clock assignments are given in relation to other quantities in two popular teaching materials. Analysis and interpretations of assignments from the two teaching materials have been the basis for the study.

     The study has been restricted to containing teaching materials for grade 1-3. This subject was chosen because the curriculum in mathematic can be seen as rather slim when it comes to time and the clock, therefore it can be interesting to see how much space these assignments get in the different teaching materials. The study has its foundation in the sociocultural perspective, which means that humans learn in interplay with one another.  The sociocultural perspective is the most central perspective of the curriculum for the elementary school  (Skolverket, 2018) and is also strongly connected to the five mathematical abilities the study contains. The result also shows that the five mathematical abilities are not clearly shown through the assignments of the teaching materials. The result also shows that the five mathematical abilities are not revealed in a clear way through the assignments in the teaching materials. However, the five mathematical abilities can be made more visible through interpretations by those who work with the teaching material. Teacher manuals proved helpful to some degree when it comes to interpretation of what abilities that can be learned through the assignments.

  • 15.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Differences in pre-school teachers' ways of handling a part-part-whole activity2018Conference paper (Refereed)
    Abstract [en]

    The data in this paper draws from an eight-month intervention study based on the idea that children need to discern the first ten natural numbers as relations of parts and whole to develop their arithmetic skills. In order to implement educational activities according to this conjecture, a group of Swedish preschool teachers worked closely with a research team, planning, enacting and analyzing activities. In this paper I describe how nine pre-school teachers, across 67 video-recorded films, handled one of these activities, called the ‘snake game’ with their groups of 5-year-old children. Using analysis based on variation theory, the results point to differences in the enactment of the ‘snakegame’ in terms of if and how the teachers foregrounded the structural aspects of numbers embedded in the activity.

  • 16.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Different learning possibilities from the same activity - Swedish preschool teachers’ enactment of a number relation activityManuscript (preprint) (Other academic)
  • 17.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Teaching for the learning of additive part-whole relations: The power of variation and connections2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, results from four empirical studies and a re-analysis are synthesized with what can constitute a structural approach to teaching and learning additive part-whole relations among learners aged four to eight years. In line with a structural approach to additive relations, the relations of parts and whole are in focus from the outset and are seen as the basis for addition and subtraction (Davydov 1982; Neuman, 1987). This approach was introduced by the researches in two intervention studies across different contexts. The researches collaborated with teachers in planning part-whole activities, teachers teaching them in their own settings, and then reflecting on them together with the research team. The empirical material consists of video-recorded lessons (Grade 3), small-group teaching (preschool) and individual video-recorded task-based learner interviews (with preschoolers). The teaching episodes and interviews were analyzed on a micro-level, using analytical tools and concepts from variation theory (Marton, 2015). To deepen the knowledge, a re-analysis was also conducted with the purpose of identifying qualitative differences in teachers’ enactments of mathematical ideas and principles associated with a structural approach to additive relations.

    Looking at the articles and the re-analysis, the results suggest that, for learning, it matters which representations are offered to the children. Some representations seem to facilitate the discernment of the parts and whole, and their relations. The results suggest that it matters which examples are offered. A systematic sequence of examples has the potential to bring to the fore relations between different part-whole examples, which offer the children opportunity to learn mathematical principles such as commutativity. Furthermore, the results indicate that what is made possible to learn about additive part-whole relations is associated with what aspects are opened up as dimensions of variation (Marton, 2015). Foremost, though, the results reveal the importance of making connections to highlight number relations and key features associated with the structural approach to additive relations. The results suggest that how variation is offered, and whether and how the teacher explicitly (verbally and gesturally) draws attention to relations, ideas and aspects, is crucial for the learning of additive part-whole relations. Moreover, through the separate articles and the re-analysis, the outcomes indicate that the structural approach to additive part-whole relations and conjectures from variation theory are possible to implement in different contexts and for different ages of children.

  • 18.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Björklund, C.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Finger Patterns as means to experience numbers' part-part-whole relations2018In: Proceedings of the 42nd Conference of the International Group for Psychology of Mathematics education / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, Vol. 5, p. 42-42Conference paper (Other academic)
  • 19.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Björklund, Camilla
    Göteborgs universitet.
    ”10-masken” och förskolebarns lärande i målstyrda processer2018Conference paper (Other (popular science, discussion, etc.))
    Abstract [sv]

    I forskningsprojektet FASETT (VR-UVK 2014-1791) undersöker vi 5-åringars taluppfattning och aritmetikfärdigheter och möjligheterna att genom målorienterade processer stötta barn i att utveckla framgångsrika strategier för aritmetisk problemlösning. I två kommuner har vi tillsammans med förskollärare prövat ut aktiviteter i syfte att utveckla särskilda förmågor som förmodas vara nödvändiga för framgångsrik problemlösning i aritmetik, såsom att urskilja tals del-helhets-struktur, fingertal samt representationer av tal. Barnens (N= 65) taluppfattning och hur deras förskollärare arbetat med förmågorna på ett systematiskt sätt presenteras i föreläsningen, med tyngdpunkt på vad som görs möjligt att lära i aktiviteterna och effekter för barnens utveckling av talförståelse och aritmetikfärdigheter. Aktiviteter som prövats ut i projektet är teoretiskt grundade i Variationsteorin (Marton, 2015). I projektet uppmuntrar vi användning av fingrarna som redskap för att strukturera tal och operera med tal. Flera av aktiviteterna påminner om bekanta lekar och spel från förskolan, till exempel tärningsspel, ”10-masken” och enklare räknesagor. I föreläsningen presenterar vi en fördjupad analys av aktiviteten ”10-masken”, hur förskollärarna iscensatt aktiviteten på olika sätt och vilken betydelse det har haft för barnens lärandemöjligheter. ”10-masken” består av ett snöre med tio pärlor, där ett antal pärlor göms i handen och resten förblir synliga. Uppgiften är att ta reda på hur många pärlor som är gömda. Detta är inte en ny aktivitet i förskolan. Däremot, indikerar vår analys, spelar det roll hur en aktivitet med så många matematiska idéer introduceras och tas om hand av förskolläraren i mötet med barnen. Baserat på resultatet kan vi se att ”10-masken” erbjuder en potential av viktiga matematiska idéer, som är av stor pedagogisk betydelse för barns matematiklärande, men det spelar en avgörande roll hur förskolläraren gör i aktiviteten.

  • 20.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Björklund, Camilla
    Gothenburg University.
    A structural approach to the ten first natural numbers: Pre-school teachers’ different ways of handling the artefact; ‘snake-game’.2017Conference paper (Refereed)
  • 21.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Björklund, Camilla
    University of Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Teaching to change ways of experiencing numbers – An intervention program for arithmetic learning in preschool2019In: Proceedings of the 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education: Volume 2: Research Reports (A-K) / [ed] Mellony Graven, Hamsa Venkat, Anthony A. Essien & Pamela Vale, Pretoria, South Africa: PME , 2019, p. 209-216Conference paper (Refereed)
    Abstract [en]

    This paper reports on an eight months long intervention program with eight five-year-olds in Swedish preschool. Four main activities were designed to enable the children to discern part-part-whole relations of the first ten numbers. The aim of this paper is to present how progress in children’s arithmetical skills are associated with the activities they have encountered in the intervention program. Learning outcomes based on pre-, post- and delayed interviews show that the participating children made distinct progress in the way they experience numbers, with long-term effects on their arithmetic skills. In this paper we discuss the analysis of what was taught and what was learnt incommensurable terms.

  • 22.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Kullberg, Angelika
    University of Gothenburg, Sweden.
    Different learning possibilities in preschool mathematics from the same task2018Conference paper (Refereed)
    Abstract [en]

    In this paper one specific task in a series of tasks focusing on part-part-whole relations of the ten first natural numbers and finger patterns for structure number relations, is presented and discussed. The tasks were designed, planned and enacted in an intervention program conducted in Swedish preschool during an eight-month period. In the program nine preschool teachers worked in close collaboration with the research team in planning how to enact tasks with their 5-year-old children, in an iterative process. The specific task, called the ‘snake game’, consists of five or ten beads on a string, some of the beads where to be hidden and the children would find out the hidden part by using structured finger patterns. The task was designed in accordance with the variation theory assumptions that certain aspects need to be discerned as dimensions of variations. The aim of the paper is to examine which dimensions of variations that were opened up by the teachers and what was made possible for the children to learn from the enactment of the ‘snake game task’. The data set includes 67 video observations from the teacher’s enactment of the task. The results suggest that what seems to be a ‘non-complex task’ (five/ ten beads on a string) offers rich mathematical experiences and has potential to bring fore important aspects of numbers and number relations. However, depending on which dimensions of variations that were opened up reveals different learning possibilities.

  • 23.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lindgren, Helen
    Högskolan i Borås.
    Gemensamt fokus på förskolebarns taluppfattning och aritmetiska förmågor: Ett samverkansprojekt där teori och praktik flätas samman2018Conference paper (Refereed)
    Abstract [sv]

    I forskningsprojektet FASETT[1] flätas teori och praktik samman. Projektet syftar till att generera kunskap om barns tidiga taluppfattning, utifrån delvis andra perspektiv än de dominerande inom fältet, och se hur en pedagogisk verksamhet i samverkan med forskare kan bidra till barns utveckling av aritmetikfärdigheter.

    I projektet arbetade nio förskollärare och 65 femåringar på fem förskolenheter i ett tätt samarbete med en grupp forskare under en åttamånadersperiod. Deltagarna träffades kontinuerligt, diskuterade och fördjupade sig i aritmetiken med fokus på aktiviteter gällande de tio första talens del-del-helhetsrelationer. Aktiviteterna var till viss del välkända, men bearbetade utifrån tidigare forskningsresultat och variationsteorin (Neuman, 1987; Marton, 2015). Utgångspunkten och reflektionerna vid gruppträffarna var intervjuer av barnens olika sätt att uppfatta tal och lösa enklare aritmetikproblem samt lärarnas iscensättande av de planerade aktiviteterna. Genom att gemensamt diskutera de filmade aktiviteterna kunde aktiviteterna förfinas och förskollärarnas didaktik utvecklas för att möta barnens behov. 

    Pågående analyser visar att designen av projektet möjliggjort för förskollärare och forskare att i kollaboration implementera ett alternativt teoretiskt underbyggt sätt att utveckla barns taluppfattning och förmåga att   lösa enklare aritmetikproblem genom att exempelvis använda sig av fingrarna som redskap för att strukturera talrelationer och inte enbart räkna ’ett till ett’.

    Analysen av de barnintervjuer som gjordes innan aktiviteterna introduceras och de barnintervjuer som gjordes efter forskningsprojektets slut visar att förskollärarnas målorienterade processer med största sannolikhet haft effekter på barnens aritmetiska förmågor. De preliminära resultaten indikerar att valet av att fokusera på ett fåtal aktiviteter möjliggjorde för en djupare reflektion kring teoretiska antaganden och vad barn behöver få syn på för att lära sig om tal och talrelationer.

    [1] ”Förmågan Att Sinnligt Erfara de Tio första Talen som nödvändig grund för aritmetiska färdigheter”, finansierat av Vetenskapsrådet 2015-2018

  • 24.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lundberg, Birgitta
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Keerekes, Klara
    Matematik i förskoleklassen VA-MER: Ett samverkansprojekt mellan Vaggeryds kommun och Mathematics Education Research2019Conference paper (Other academic)
    Abstract [sv]

    De senaste åren har en rad förändringar gällande förskoleklassen genomförts. Den 1 juli 2016 fick förskoleklassen en egen del i läroplanen och från och med läsåret 2018/19 blev förskoleklassen obligatorisk och omfattas nu av skolplikten. Det förändrade uppdraget i förskoleklassen samt det obligatoriska kartläggningsmaterialet, har ökat lärares behov av att möta uppdraget. Kartläggningsmaterialet i matematiskt tänkande ska hjälpa lärare att tidigt identifiera elever som visar en indikation på att inte nå de kunskapskrav som sen ska uppnås i årskurs 3 i grundskolan. Däremot saknas direkta implikationer för undervisning som stimulerar alla elevers möjlighet att utveckla sina förmågor i matematik.

    I ett nystartat samverkansprojekt mellan Vaggeryds kommun och Högskolan för Lärande och Kommunikation kommer kommunens alla lärare i förskoleklass att arbeta tillsammans med forskare tillhörande forskargruppen i matematik (MER-gruppen), i syfte att stärka likvärdighet i utbildningen inom Vaggeryd kommun.

    Syftet med projektet är att se hur en pedagogisk verksamhet i samverkan med forskare kan bidra till att lärarna:

    • utvecklar förmågan att diskutera ämnesinnehåll i matematikundervisningen,
    • utvecklar förmågan att utifrån kartläggningsmaterialet diskutera didaktiska implikationerna för undervisning,
    • gemensamt bygger ett fundament i matematikundervisningen, med stöd av aktuell forskning, i syfte att utveckla alla elevers förmågor i matematik.

    Erfarenheter från ett nyligen avslutat forskningsprojekt där lärare och forskare i tätt samarbete genomförde och reflekterade över undervisningsaktiviteter, visar att detta verkade vara en framgångsrik modell för att utveckla undervisning. Därför väljs ett liknande upplägg i detta samverkansprojekt.

    I den inledande fasen av projektet träffas lärargruppen och forskarna en gång per månad. Träffarna förläggs på kommunens skolor. De påbörjade samtalen mellan deltagarna i samverkansprojektet visar att det finns ett stort behov av att diskutera matematikundervisning och att utveckla ett målinriktat arbete som främjar alla elevers möjligheter att lära matematik.

  • 25.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, South Africa.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, South Africa.
    Weaving in connections: Studying changes in early grades additive relations teaching2018In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 8, no 1, article id a540Article in journal (Refereed)
    Abstract [en]

    In this article, we present aspects of teaching that draw attention to connections – both within and between examples – in order to explore the potential objects of learning that are brought into being in the classroom space and thus what is made available to learn. Our focus is on exploring differences in teaching over time, in the context of learning study style development activity of additive relation problems in three Grade 3 classes in South Africa. In a context where highly-localised and fragmented instruction has been noted, this study reports on the nature and extent of changes in connections in instruction over time. The application of a coding framework focused on simultaneity and connections in teaching points to a richer range of structural relationships within examples, and more connecting work between examples in the second year in comparison to the first year.

  • 26.
    Gegerfelt, Gideon
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Johansson, Alexander
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Surfplattor - ett kompletterande verktyg i matematikundervisningen: En litteraturstudie om surfplattors användning i matematikundervisningen för att utveckla elevers kunskaper i aritmetik2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 27.
    Gradin, Lovisa
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lennartsson, Emilia
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Eye-tracking och elevers lärande i matematik: En litteraturstudie2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med den här studien är att sammanställa och problematisera forskning kring hur eye-tracking som metod kan användas för att synliggöra elevers förståelse för matematik. Eye-tracking är en metod där människors ögonrörelser studeras för att undersöka den visuella uppmärksamheten utifrån fixeringar och sackader. En eye-tracker är en apparat som används för att mäta ögonrörelser.  Studiernas undersökningar utgår från en hypotes om att det finns ett samband mellan ögonrörelser och kognitiva processer. Sammanställningen har sitt ursprung i en litteraturstudie där artiklar har funnits genom sökningar i olika databaser. Tolv vetenskapliga studier valdes ut baserat på inklusions- och exklusionskriterier, och analyserades i detalj. Dessa studier pekar på att eye-tracking kan visa skillnader mellan vilka strategier eleverna använder, skillnader mellan hög- och lågpresterande elever samt skillnader i kognitiv belastning. Studierna visar också att det finns flera möjligheter med eye-tracking som metod men lyfter också fram begränsningar. En möjlighet är att eye-tracking i vissa fall är mer objektiv än andra metoder och en annan är att eye-tracking kan visa strategier som eleven själv inte kan verbalisera. Begränsningar är att den kognitiva uppmärksamheten inte alltid stämmer överens med deltagarens visuella fokus samt att resultatet kan vara svårt att urskilja vid emotionella reaktioner.  Eye-tracking jämförs ofta med olika sorters intervjuer och flera studier förespråkar att kombinera eye-tracking med andra metoder för att samla in kompletterande data. I slutet av texten lyfts de etiska dilemman fram som kan uppstå vid eye-tracking.

  • 28.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Albinsson, Malin
    Järfälla barn- och elevhälsa, Järfälla kommun, och Department of Special Education, Stockholm University.
    A phenomenographic analysis of students’ use of base-ten material2020Conference paper (Refereed)
    Abstract [en]

    Previous research indicates that manipulatives, like base-ten blocks, not necessarily strengthen students’ understanding of numerical place-value and the decimal numeral system. This study takes its starting point in the hypothesis that to create functional teaching situations with base-ten blocks, it is necessary to first know students’ prior understanding of such manipulatives. Therefore, here we present a phenomenographic analysis of students’ understanding how such manipulative material can be used to represent multidigit numbers. The data was collected from individual interviews with 58 students in grade 1 (6-7 years old).We identify six qualitatively different categories of students’ understanding, and, based on these, suggest implications for the design of teaching situations.

  • 29.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Papadopoulos, I.
    Pairing numbers: An unconventional way of evaluating arithmetic expressions2019Conference paper (Refereed)
  • 30.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Papadopoulos, Ioannis
    Aristotle University, Thessaloniki, Greece.
    The impact of number pairing on students' ideas on how to evaluate numerical expressions2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 238-238Conference paper (Refereed)
  • 31.
    Gunnarsson, Robert
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Håkansson, Per
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Vasaskolan, Skövde.
    Identifying what is critical for learning ‘rate if change’: Experiences from a learning study in Sweden2019In: Theory and practice of lesson study in mathematics: An international perspective / [ed] R. Huang, A. Takahashi & J. P. da Ponte, Cham: Springer, 2019, p. 441-456Chapter in book (Refereed)
    Abstract [en]

    Learning study is an adapted version of lesson study developed in Hong Kong and Sweden. It has commonalities with lesson study but is framed within a specific pedagogical learning theory – variation theory. Central in variation theory is the object of learning and what is critical for students’ learning. Hence, as with lesson study, it is a collective and iterative work where teachers explore how they can make the object of learning available to students, but what characterises learning study is the use of a specific learning theory. In this process, special attention is paid to the critical aspects of the object of learning. We argue that to identify the aspects that are critical, the aspects need to be verified and refined in classrooms. In this chapter, we demonstrate how teachers gain knowledge about such critical aspects. Particularly, we show how these critical aspects cannot be extracted only from the mathematical content or the students pre-understanding alone, but evolve during the learning study cycles. For this we use a learning study about the mathematical topic of rate of change in grade 9 in Sweden as an illustration. We describe how an analysis of how students solved tasks in pre- and post-test and during the lessons, as well as how the mathematical content was presented in lessons, helped the teachers identify what was critical for learning to understand and express the rate of change for a dynamic situation.

  • 32.
    Hansson, Henrik
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Learning Study.
    Keyfactors to promote a sustainable culture of an adaptive form of Lesson/Learning study in Sweden and what the keyfactors implies to leadership2017Conference paper (Other academic)
  • 33.
    Hyltén, Ola
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Läromedels varierande innehåll och möjlighet till lärande: En läromedelsgranskning om växande geometriska mönster för årskurs 62019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this study, the purpose is to analyze how growing geometric patterns occur in mathematics textbooks. The study proceeds from the variation theory and its conceptual apparatus. Therefore, the main focus is how the contextual variation occur in mathematics textbooks. It will also be an analyze of other variation parts, in order to see how contextual parts and other variation parts affects students’ opportunities of learning.  

    The study proceeds from a qualitative method where a content analysis is used in the analysis of mathematics textbooks. In the analysis, four different teaching materials are chosen, all from sixth grade. These gave the opportunity to find many different variations in the mathematics textbooks.

    The analysis of mathematics textbooks led to following result. Analyzing contextual variation parts and other variation parts, showed a great variation in all the mathematics textbooks. However, variation differed in how it occurred and how it gave opportunities for students to learn. 

    Based on the analysis, the results from it can supply how variation were used in the mathematics textbooks. To use the mathematics textbooks as single resources is an opportunity for teachers. On the contrary, it is important that the teaching uses a content with variation in order to develop students’ knowledge.

  • 34.
    Håkansson, Per
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Vasaskolan, Skövde.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Frågan är vad frågan gör – olika frågeställningars betydelse för hur elever uttrycker och använder förändringstakt i matematik2018In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 6, no 2, p. 44-62Article in journal (Refereed)
    Abstract [en]

    The aim of this study is to compare the impact of different phrasings of questions as of how students relate and express relations between different quantities in student tasks concerning rate of change. Through a qualitative analysis we compare how students in ninth grade (age 15) respond to two different framings of questions, concerning how fast the volume of fluid in two medicine bags change. The analysis indicates that a comparing question (”which changes fastest?”) can open up a wide outcome space, in which we could observe five qualitatively distinct ways of solving the task. Furthermore, a question that requests a value (“how fast does it change?”) seem to encourage students to make multiplicative comparisons, which is close to the mathematical meaning of rate of change. Finally, we discuss the potential of each question for pointing to different aspects of rate of change, and how they could be used by teachers for different purposes in teaching situations.

  • 35.
    Håkansson, Per
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    KEY ASPECTS OF EXPRESSING THE RATE OF CHANGE IN LOWER SECONDARY SCHOOL MATHEMATICS2017Conference paper (Refereed)
  • 36.
    Håkansson, Per
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Vasaskolan, Skövde.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    What is critical in order to learn the average rate of change?2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 55-55Conference paper (Refereed)
  • 37.
    Jansson, Malin
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Karlsson, Lisa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Elever förståelse av kommutativitet: En litteraturstudie om elevers förståelse och användning av kommutativitet2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Det finns olika områden inom matematik som är extra viktiga att elever behärskar. Aritmetik, som ofta definieras som räknelära, är ett sådant område och inom aritmetiken återfinns räknesätten: addition, subtraktion, multiplikation och division samt deras egenskaper. En av dessa egenskaper om återfinns i räknesätten addition och multiplikation, är kommutativitet. Syftet med litteraturstudien är att kartlägga vad vetenskapliga studier visar om elevers förståelse av kommutativitet som en matematisk egenskap. Syftet besvaras genom följande frågor: Vilken förståelse av kommutativitet har elever innan de fått formell undervisning om det, vilken betydelse har undervisningens form för elevernas förståelse av kommutativitet samt vilken roll har ordet kommutativitet för elevernas förståelse för begreppet kommutativitet. Resultatet har visat på att det krävs undervisning om kommutativitet i multiplikation, men inte i addition samt att undervisningens form faktiskt har betydelse för elevers förståelse. Trots att kommutativitet nämns i läromedel i tidiga årskurser har det framkommit att ordet kommutativitet inte har någon påverkan på elevens begreppsmässiga förståelse och behöver alltså inte kunna ordet för att tillämpa egenskapen.

    De publikationer som samlats in består främst av vetenskapliga artiklar, men även av en svensk doktorsavhandling. Litteraturen har kvalitetsbedömts och valts ut med hjälp av inklusionskriterier som nämns i litteraturstudien.

  • 38.
    Johansson, Tom
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Att urskilja det kritiska: En variationsteoretisk studie om undervisning med växande geometriska mönster2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Teaching of growing geometrical patterns should be seen as a bridge between arithmetic and algebraic thinking, that through giving the students tasks that enables generalization of arithmetic expressions. Swedish students’ results show that they perform better arithmetically than algebraically therefore, the aim of this study is to ascertain which aspects that are critical to students’ development from an arithmetic thinking to an algebraic thinking.

    This study is a learning study where a lesson was planned and performed in three different classes in grade 5 and 6. The lessons included a pre-test and a posttest to further validate the study and the tests, combined with the lessons, contributed to the result of the study. When planning and analyzing the lessons the theory that was applied was variation theory which focuses on what is learned, what learning that takes place and what can be improved to further the learning.

    The result of this study shows that it can be critical for students to discern regularities in growing geometrical patterns and also to separate regularity from proportionality. Furthermore, the study found another critical aspect which is to discern the meaning of letters within mathematics. The result also reveals two variation patterns which enables discerning of aspects that appear critical for students.

    When teaching about growing geometrical patterns there are several aspects teachers need to make possible for students to discern. Through utilization of variation patterns that are well prepared and thought through these aspects can be visualized and consequently auxiliary advance students understanding for algebra.

  • 39.
    Karlsson, Rebecca
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Kollberg, Olivia
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Fingrar som verktyg i matematiken under de tidiga skolåren: En litteraturstudie om fingeranvändningens för- och nackdelar2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna litteraturstudie belyser vi olika forskares syn gällande fingeranvändningen i matematiken. Syftet med studien var att få en bild av vad forskning lyfter fram om fingeranvändning i matematikundervisningen samt användningens konsekvenser. I studien framkommer både för- och nackdelar med fingeranvändningen gällande elevers talförståelse och aritmetik. Vid datainsamlingen användes databaserna ERIC, MathEduc, Google Scholar, SwePub och Primo för att få fram vetenskapliga publikationer.  För att få fram relevanta publikationer som berör vårt område använde vi oss av inkluderings- och exkluderingskriterier. I resultatdelen jämförs, analyseras och kopplas de olika publikationerna samman. Studien resulterade i att vi fann att fingeranvändningen kan vara både fördelaktig och begränsande. En ståndpunkt som kommit fram genom studien är att fokus ska ligga på hur fingrarna används eftersom det finns både mer och mindre effektiva tillvägagångssätt. Några fördelar som har framkommit är att fingrarna kan ses som ett konkret material samtidigt som det utvecklar del och helhetsrelationer. Fingrarna kan även vara begränsande eftersom de blir otillräckliga när talen överstiger tio och förlorar därmed sin funktion. Forskare är oense om fingeranvändningen har en positiv eller negativ inverkan för elevers matematiska utveckling.

  • 40.
    Klingberg, Ellen
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Andersson, Madeleine
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Gester - ett verktyg i matematikundervisning: En litteraturstudie2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Litteraturstudiens syfte är att genom didaktisk forskning beskriva gesters roll för matematiklärande. För att besvara syftet har två frågeställningar tagits fram: På vilka sätt kan gester användas i matematikundervisning? Hur kan gester hjälpa elever att utveckla förståelse för matematik? 

    Litteraturstudien är genomförd med hjälp av en litteraturanalys av tio vetenskapliga artiklar som sållats fram i en systematisk databassökning. 

    Studierna visar att gester används på olika sätt i klassrummet. Resultatet tyder på att elever tar till sig kunskap oavsett om instruktioner med gester sker av lärare i ett klassrum, är videoinspelade eller förmedlas med avatarer. Flera av studierna förespråkar att använda gester vid inlärning men att urskilja olika gester och använda dem medvetet.

    Slutsatsen är att använda gester kan vara fördelaktigt vid lärande. Gester garanterar dock inte lärande utan behöver sättas i ett sammanhang där det kompletterar talet. 

  • 41.
    Kullberg, Angelika
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Björklund, Camilla
    Department of Education, Communication and Learning, University of Gothenburg, Gothenburg, Sweden.
    Brkovic, Irma
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816Article in journal (Refereed)
    Abstract [en]

    In this paper, we report how 5-year-olds’ arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children’s ways of experiencing numbers’ part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report is based on an analysis of assessments with 103 children (intervention group n = 65 and control group n = 38) before and after the intervention and a follow-up assessment 1 year after the intervention. Our findings show that the learning outcomes of the intervention group were significantly higher compared to those of the control group after the intervention and that differences between the groups remained even 1 year after the intervention. In particular, the results show that children participating in the intervention group learned to recognize and use part-part-whole relations in novel arithmetic tasks.

  • 42. Kullberg, Angelika
    et al.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Reis, Maria
    Learning to see numbers as parts and whole in preschool.2017Conference paper (Refereed)
  • 43.
    Kullberg, Angelika
    et al.
    University of Gothenburg, Sweden.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Reis, Maria
    University of Gothenburg, Sweden.
    Björklund, Camilla
    University of Gothenburg, Sweden.
    Preschool children’s understanding of numbers shown in a partitioning task2019In: Proceedings of the 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education: Volume 4: Oral Communications and Poster Presentations / [ed] Mellony Graven, Hamsa Venkat, Anthony A. Essien & Pamela Vale, Pretoria, South Africa: PME , 2019, p. 59-59Conference paper (Refereed)
    Abstract [en]

    Children’s ways of handling numbers in arithmetic tasks has been studied extensively, providing us with insights about strategies for solving tasks and development of arithmetic skills (Carpenter & Moser, 1982). Children’s ability to decompose numbers is one important part of development, since the ability allows children to apply different strategies when solving tasks (Hunting, 2003). Children’s different ways of encountering numbers in simple tasks may give a comprehensive understanding of the challenges in learning to use numbers in proficient ways. When experiencing part-part-whole relations of numbers, the child needs to consider the parts and the whole simultaneously. This paper reports on an analysis of 103 individual interviews with 5-year-old children on two occasions during their last year in preschool in Sweden. We report on the analysis of one particular task illustrating children’s experience of numbers when partitioning seven hidden marbles into two parts. The specific research question was: What different ways of experiencing numbers by 5-year-old children were exposed in a partitioning task?

    Variation theory (Marton, 2015) was used to analyse children’s ways of experiencing numbers and what aspects were critical to discern in order to solve the task. Variation theory emanates from more than thirty years of phenomenographic research, investigating different ways in which the same phenomena can be experienced. We found that children experienced numbers in six different ways: as number words, as names, as extents, as countables, as structure, or as known number facts. Our study shows that those ways of experiencing numbers that are foregrounding the cardinal, ordinal and the parts and whole simultaneously end up in plausible answers and the children initiate ways to handle the task in powerful ways. Consequently, if the children experience either the cardinal (e.g. numbers as extent) or the ordinal (e.g. numbers as names) they are not able to decompose the whole and thereby solve the task.

    References

    Carpenter, T. P., & Moser, J. M. (1982). The development of addition and subtraction problem-solving skills. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective. Hillsdale, NY: Lawrence Erlbaum.

    Hunting, R. P. (2003). Part-whole number knowledge in preschool children. Journal of Mathematical Behavior, 22(3), 217-235.

    Marton, F. (2015). Necessary conditions of learning. New York: Routledge.

  • 44.
    Kullberg, Angelika
    et al.
    University of Gothenburg, Sweden.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. University of the Witwatersrand, South Africa.
    Marton, Ference
    University of Gothenburg, Sweden.
    What is made possible to learn when using the variation theory of learning in teaching mathematics?2017In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 49, no 4, p. 559-569Article in journal (Refereed)
    Abstract [en]

    The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theory has been used to analyze teaching and students’ learning in classrooms. In mathematics education, variation theory has also been used to explore variation in sets of instructional examples. For example, it has been reported how teachers, by using variation and invariance within and between examples, can help learners to engage with mathematical structure. In this paper, we describe the variation theory of learning, its underlying principles, and how it might be appropriated by teachers. We illustrate this by an analysis of one teacher’s teaching before and after he participated in three lesson studies based on variation theory. Both the theory and the empirical illustration focus on ‘what is made possible to learn’ in different learning situations. We show that in the two analyzed lessons, different things were made possible to learn.

  • 45.
    Lidberg, Lovisa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lärarkunskaper inom programmering i matematikundervisningen.: En kvalitativ intervjustudie som synliggör lärares kunskaper inom programmering i årskurs 1-3.2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Programming is a relatively new element in the school, which teachers should work with. My perception is that teachers have mixed reactions about programming and its content. Therefore, this study was conducted with the aim of creating an understanding of teachers’ knowledge in programming in mathematics teaching in grade 1-3. Three questions were used to achieve the aim of this study, they are: what knowledge and competence do teachers in mathematics have in programming, what knowledge do teachers have of the subject matter in the curriculum in relation to programming, and how teachers work with the content programming in mathematics teaching.

    The study is an interview study that has been used to gather information about the teachers' knowledge in programming. In total, five teachers were interviewed, of whom 4 worked in grades 1-3 and one in grade 4. The theoretical framework MKT were used to collect the data, interview and for the analysis of the data. The result has shown that it is a benefit if the teachers know words and concepts that are used in programming and how different programming tools works. Furthermore, the results shows how the teachers' worked with programming and how it can be used in teaching mathematics.

  • 46.
    Lindeberg, Ludvig
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Växande geometriska mönster i skolan: En studie om undervisningsmetoder, svårigheter och utveckling.2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This study investigates how teachers work with growing geometric patterns, with a focus on students aged 10-12 in the west of Sweden. Specifically, it uncovers what methods teachers use and the difficulties they experience when teaching growing geometrical patterns, as well as outlining how they believe teaching in this subject can be developed. 

    Teaching growing geometrical patterns is part of the Swedish curriculum, because it is seen as a pathway to algebra. Current research says that there are two main theories on teaching growing geometrical pattern, hierarchically or dynamically. This study takes a qualitative approach to investigate these theories further. It uses phenomenology as a theoretical framework, as a way to understand the complex phenomenon of teaching. Semi-structured interviews were conducted with four primary school teachers in Sweden. The data gained from these interviews was analysed multiple times using the hermeneutical spiral, to ensure scientific rigour. The findings demonstrate that teachers prefer using hands on methods when teaching growing geometrical patterns to students, such as a method called the “math machine” and using real objects to create patterns. However, they experience difficulties when instructing students how to turn the pattern into a formula, as students often find this progression difficult to grasp. Additionally, the teachers explained that study material has a big impact on how much time teaching growing geometrical patterns is allocated in the classroom, as most of them will only teach this topic if it is covered in the textbook. For the teaching to improve, teachers need more resources regarding how to teach growing geometrical patterns, particularly when it comes to developing formula, and the teaching of the topic needs to be further promoted by the Swedish National Agency for Education.

  • 47.
    Mellroth, Elisabet
    et al.
    Karlstad University, Department of Mathematics and Computer Science, Sweden.
    Boesen, Jesper
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Noticing mathematical potential – A proposal for guiding teachers2019In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education / [ed] Uffe Thomas Jankvist, Marja van den Heuvel-Panhuizen & Michiel Veldhuis, European Society for Research in Mathematics Education, 2019, p. 3688-3695Conference paper (Refereed)
    Abstract [en]

    It has been shown to be problematic for teachers to use Krutetskii´s definition of mathematical abilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize what teachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problemsolving process to some of the abilities defined by Krutetskii. The results give clear descriptions of what teachers can observe in pupils’ mathematical activities to notice their mathematical potential. We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and to generalize can be observed. To be able to notice MHAPs, teachers need research-based support on how and what to observe in their pupils. Our proposed guide needs to be tested and validated to explore if it will help teachers to notice MHAPs s and subsequently support their learning.

  • 48.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Learning to see distinctions through learning studies: Critical aspects as an example of pedagogical content knowledge2019In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 8, no 3, p. 196-211Article in journal (Refereed)
    Abstract [en]

    Purpose

    The purpose of this paper is to identify changes in teacher’s pedagogical content knowledge (PCK) as a result of their participation in two learning studies in mathematics.

    Design/methodology/approach

    A group of four mathematics teachers and the researcher of this paper explored two objects of learning related to division with decimal numbers and the straight-line equation in a learning study (LS) project over the course of one year. The data used consist of eight video-recorded lessons, four written student tests, eight student interviews and 14 recorded team meetings. The analysis was based on the variation theory principle about learning (Marton, 2015) and on ontological assumptions within the phenomenographic approach (Marton, 1981).

    Findings

    It was found that teachers’ PCK was changed and refined through the LS process in terms of differences in ways of understanding and discussing critical aspects related to each object of learning. In the paper, the terms “presumed critical aspects” and “explored critical aspects” are used to illustrate this difference. Furthermore, the concepts are viewed in relation to three subdomains of PCK: knowledge of content and curriculum (KCC), knowledge of content and students (KCS) and knowledge of content and teaching (KCT).

    Originality/value

    Bringing out the difference between “presumed critical aspect” and “explored critical aspects” advances the view that critical aspects are dynamic and emergent in practice – in the interaction between teaching and student learning. The research exposes “explored critical aspects” as a specific form of PCK in which KCC, KCS and KCT are intertwined.

  • 49.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Utmaningar i ämnesdidaktiskt kollegium2018Conference paper (Refereed)
  • 50.
    Mårtensson, Pernilla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Keerekes, Klara
    Att designa och förändra matematikuppgifter i learning study—en modell för att utveckla lärarstudenters yrkeskompetens2019Conference paper (Other academic)
    Abstract [sv]

    I den här studien har vi undersökt på vilka sätt 41 grundlärarstudenter, med inriktning mot årskurs 4‒6, designade och förändrade matematikuppgifter för att utveckla kunskap om undervisning och skolelevers lärande av specifika ämnesinnehåll. Under höstterminen 2018 deltog lärarstudenterna i en fem-veckors matematikdidaktikkurs inom ramen för grundlärarprogrammet på Högskolan för lärande och kommunikation, Jönköping University. Kursen är till stor del uppbyggd utifrån learning study‒konceptet (Marton & Pang, 2003), vilket kort kan beskrivas som ett kollegialt, iterativt och intervenerande utvecklingsarbete med inslag av ämnesdidaktiskforskning (Runesson Kempe, 2016). I den aktuella kursen innebar detta bland annat att arbetet utgick från studenternas egna frågor om undervisning och lärande men i samråd med lärare från kursens samverkansskolor. Samverkan med skolor i regionen är en avgörande faktor för kursen eftersom det möjliggör för studenterna att undersöka elevers förståelse av något ämnesinnehåll och utifrån det forma och genomföra undervisning. Vidare var studenterna i kursen indelade i grupper (3‒4 studenter per grupp), i vilka man systematiskt planerade, genomförde och analyserade undervisning i två cykler. I detta arbete användes ämnesdidaktisk forskning och variationsteorin (Marton & Pang, 2003) som redskap för att komma åt vad skoleleverna behöver få syn på för att utveckla kunskap i förhållande till specifika ämnesinnehåll. Studiens data samlades in under kursen och består av lärarstudenternas skriftliga reflektioner om de uppgifter som de designade och prövade i lektionerna och om hur och varför dessa förändrades eller borde förändras. Syftet med studien är att identifiera och beskriva de olika sätt lärarstudenterna förändrade matematikuppgifterna utifrån ett variationsteoretiskt perspektiv. I presentationen visas några sådana exempel.

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