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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.
    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. 

  • 3. 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)
  • 4.
    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.

  • 5.
    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. 

  • 6.
    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.

  • 7.
    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)
  • 8.
    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.

  • 9.
    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.

  • 10.
    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)
  • 11.
    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.

  • 12.
    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)
  • 13.
    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.

  • 14.
    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

  • 15.
    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.

  • 16.
    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
  • 17.
    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.

  • 18.
    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)
  • 19.
    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)
  • 20.
    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.

  • 21.
    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)
  • 22.
    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.

  • 23.
    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.

  • 24.
    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)
  • 25.
    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)
  • 26.
    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.

  • 27.
    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.

  • 28.
    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.

  • 29.
    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. 

  • 30. 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)
  • 31.
    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.

  • 32.
    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.

  • 33.
    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.

  • 34.
    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.

  • 35.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Utmaningar i ämnesdidaktiskt kollegium2018Conference paper (Refereed)
  • 36.
    Mårtensson, Pernilla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Hansson, Henrik
    Jönköping University, School of Education and Communication.
    Challenging teachers' ideas about what students need to learn: Teachers' collaborative work in subject didactic groups2018In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 7, no 2, p. 98-110Article in journal (Refereed)
    Abstract [en]

    Purpose

    The purpose of this paper is to contribute to the understanding of the processes that make teachers learn in a collaborative arrangement similar to lesson study (LS) and learning study (LearS). The teachers in this collaboration wanted to enhance teaching and student learning (grades 4-7) about decimal numbers.

    Design/methodology/approach

    The analysis is based on data from five teachers’ collaborative work in an adaptive arrangement of LS and LearS called subject didactic groups. Data consist of eight audio recordings of the teachers’ meetings as well as written and photographic documentation of the meetings. The analysis was carried out through the lens of expansive learning within an activity system (Engeström, 1987). This entailed a focus on contradictions between teachers’ ways of thinking and acting when individually and collaboratively developing their teaching, on the solutions to the conflicts produced by the teachers, and on how these challenged the teachers’ ideas about what the students need to learn.

    Findings

    The authors identified contradictions between formative and summative assessment, exams and stressed students, prevailing norms about teaching and the theoretical tool used for planning and analyzing lessons and student learning, and the local curriculum and time constraints. The solutions to the conflicts were the driving force for developing new and more qualitative knowledge about what the students need to learn.

    Originality/value

    This paper gives explicit examples of contradictions and solutions that can challenge and drive teachers to expand their learning in an adaptive form of LS and LearS suited to daily teaching.

  • 37.
    Pang, M. F.
    et al.
    Faculty of Education, The University of Hong Kong, Hong Kong.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    The Learning study: recent trends and developments2019In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 8, no 3, p. 162-169Article in journal (Refereed)
  • 38.
    Papadopoulos, Ioannis
    et al.
    Aristotle University, Thessaloniki, Greece.
    Gunnarsson, Robert
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    The use of ‘mental’ brackets when calculating arithmetic expressions2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 3 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 451-458Conference paper (Refereed)
  • 39.
    Ramdhany, Viren
    et al.
    University of 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.
    Christiansen, Iben Maj
    Stockholm University, Sweden.
    Dissonance and continuity in the mathematical education and training experiences of pre-service secondary mathematics teachers2018In: African Journal of Research in Mathematics, Science and Technology Education, ISSN 1811-7295, Vol. 22, no 2, p. 186-195Article in journal (Refereed)
    Abstract [en]

    The education and professional development of pre-service mathematics teachers occur across different contexts. Key contexts of mathematics learning and learning to teach are school, university undergraduate mathematics and mathematics teaching-related learning in teacher education courses. International literature suggests that each of these contexts legitimises different views of mathematics teaching and learning. For pre-service teachers traversing these contexts, moves between sites can be experienced in more continuous or more dissonant ways. The disjunctures associated with dissonant experiences lead to openings for value judgments related to the distinctions that are drawn, opening possibilities for a wider range of pedagogic decisions. In this paper, we explore, through interviews with four pre-service teachers in one post-graduate certificate of education (PGCE) course, perceptions of continuity and dissonance across sites related to mathematics and mathematics education, and teaching and learning. Our findings point largely to experiences of continuity between the high school and undergraduate contexts, with the PGCE course recognised as different from these contexts. 

  • 40.
    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.
    Teachers and researchers in collaboration. A possibility to overcome the research-practice gap?2019In: European Journal of Education, ISSN 0141-8211, E-ISSN 1465-3435, Vol. 54, no 2, p. 250-260Article in journal (Refereed)
    Abstract [en]

    Taking as its point of departure the discussion about the disconnection between research and practice, this article presents learning study as a research approach to overcoming this gap. Learning study has commonalities with design research and lesson study, but is a teacher-researcher collaboration where both have a common object of research. Thus, it is research with teachers, rather than on teachers and focuses on constructing knowledge concerning objects of learning as well as teaching-learning relationships. The focus of the research collaboration is professional problems related to the object of learning that teachers encounter in their everyday practice. The process is guided by a theory of learning and pedagogy?the variation theory. The knowledge product of learning study is a theoretical description of what must be learned in order to develop a specific capability. Examples of knowledge contributions from learning study are given and it is suggested that such knowledge can be considered to be public knowledge that can be shared, used and developed by other teachers in other contexts. Furthermore, it is suggested that there are specific features of learning study that make it a research approach that may strengthen connections between research and practice.

    The full text will be freely available from 2021-05-28 00:05
  • 41.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Kullberg, Angelika
    University of Gothenburg, Sweden.
    Learning to Teach with Variation: Experiences from Learning Study in Sweden2017In: Teaching and Learning Mathematics through Variation: Confucian Heritage Meets Western Theories / [ed] Rongjin Huang and Yeping Li, Sense Publishers, 2017, p. 355-374Chapter in book (Other academic)
  • 42.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. University of Witwatersrand, Johannesburg, South Africa.
    Lövström, A.
    Jönköping University, School of Education and Communication.
    Hellquist, Björn
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Beyond the borders of the local: How “instructional products” from learning study can be shared and enhance student learning2018In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 7, no 2, p. 111-123Article in journal (Refereed)
    Abstract [en]

    Purpose: The purpose of this paper is to present how experiences gained from a theory-informed lesson study – learning study (LrS) – in regard to a specific learning goal can be shared and used by other teachers in new contexts.

    Design/methodology/approach: A group of teachers worked together in a cyclic, iterative process of planning, evaluating and revising teaching. The aim was to provide possibilities for grade 2 and 3 students to become familiar with negative numbers. The teacher group came to the conclusion that the students needed to be able to differentiate some aspects of negative numbers. The conjecture was put to the test in a follow-up study (FS) with five new teachers and eight classes. One lesson was taught based on the empirical findings in the LrS.

    Findings: The results suggest that teachers’ collaborative work has possibilities to produce knowledge about critical aspects of learning that can be communicated and adopted in new contexts. The teachers in the FS were able to make sense of the results from LrS and incorporate the critical aspects in their teaching in a way that enhanced students’ learning.

    Originality/value: It is demonstrated that teacher collaboration in LrS can create knowledge that goes beyond the border of the local context. 

  • 43.
    Runesson Kempe, Ulla
    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.
    Lövström, Anna
    Mörbylånga municipality, Mörbylånga, Sweden.
    Theory-informed lesson study as practice based research: identifying what is critical for grade 2 and 3 pupils’ learning of negative numbers2017In: Quadrante, ISSN 0872-3915, Vol. XXVI, no 2, p. 19-42Article in journal (Refereed)
    Abstract [en]

    The aim of the paper is to demonstrate how a theory-informed lesson study can be a form of practice-based research where knowledge is generated within the process of teachers’ actions. Learning study shares features with lesson study, such as the iterative design, the teacher driven approach and with attention to student learning, but is guided by a theoretical framework. The dominant theory has been variation theory. In learning study, the focus is the object of learning and what must be learned to make the object of learning one’s own. A learning study about learning and teaching negative numbers to young pupils (age 8-9) in a Swedish context is used as an example. Our proposal is in resonance with Morris’ and Hiebert’s (2011) suggestion; that lesson study is a system that can generate instructional products that are sharable and open for improvement by other actors. The ‘instructional product’ from learning study is a theoretical description of the object of learning, how it is constituted and can be taught. In the learning study reported, three teachers worked in collaboration to identify the critical aspects for realizing the existence of negative numbers. The critical aspects emerged and were successively specified in the process and as a result of a thorough analysis of data on pupils’ learning and the lessons. 

  • 44.
    Runesson Kempe, Ulla
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Lövström, Anna
    Hellqvist, Björn
    Making distinctions – critical for the learning of the 'existence' of negative numbers? Exploring how 'instructional products' from a theory informed Lesson study can be shared and enhance student learning2017Conference paper (Refereed)
    Abstract [en]

    In this paper, we present how experiences gained from a theory informed Lesson study in regards to a specific learning goal can be shared and used by other teachers in new contexts. A group of teachers worked together in a cyclic, iterative process of planning, evaluating and revising teaching. The aim was to provide possibilities for grade 2 and 3 students to become familiar with negative numbers, thus to extend the number range from N to Z. Based on theoretical tenets about learning and empirical findings in the study the teacher group draw the conclusion that the pupils needed to be able to differentiate some aspects of negative numbers. The conjecture was put to the test in a follow-up study with five new teachers and eight classes. One lesson was taught based on the empirical finding in the Lesson study. When learning gains from pre- to post-test in these classes were compared to those in the Lesson study, similarities were found. It is suggested that accumulate evidence about ‘what must be learned’ across different classroom settings can be gained through a theory informed and goal oriented Lesson study.

  • 45.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Variationsteori som redskap för att analysera lärande och designa undervisning2017In: Undervisningsutvecklande forskning: exemplet learning study / [ed] Ingrid Carlgren, Malmö: Gleerups Utbildning AB, 2017, p. 45-60Chapter in book (Other academic)
  • 46.
    Sidenvik, Emil
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Historiska talsystem och taluppfattning: En studie om hur det egyptiska talsystemet kan användas till att stärka elevers taluppfattning2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna studie undersöks vad som är kritiskt för elever när ett historiskt talsystem ska användas i undervisningen. Syftet med studien är att identifiera kritiska aspekter som elever behöver urskilja för att kunna utveckla sin taluppfattning genom undervisning där det egyptiska talsystemet används. Syftet besvaras med hjälp av två forskningsfrågor; Vilka aspekter är kritiska? Vilka variationsmönster kan synliggöra de kritiska aspekterna?

    Studien baseras på variationsteorin och metoden learning study. Studien har utförts i två klasser i årkurs fyra. Studien består av ett för- och eftertest, samt en lektion som hållits i båda klasserna. Resultatet visar på att det fanns fyra kritiska aspekter för denna elevgrupp. Lektionen innehöll tre olika variationsmönster som resultatet påvisar ha belyst de kritiska aspekterna, eftersom eleverna presterat bättre i samtliga delar som testats. I vissa delar har andelen elever som svarat rätt ökat från 13% till över 50%. I studien dras slutsatsen att användning av historiska talsystem är ett effektivt sätt att utveckla elevers taluppfattning samt att de variationsmönster som använts i denna studie har lyckats belysa de aspekter som var kritiska för eleverna så att de har kunnat urskilja dem.

  • 47.
    Ullergård Pappas, Sofia
    et al.
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Gustafsson, Joanna
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Talsortsräkning – en strategi för huvudräkning och för att förstå tal.2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Enligt TIMSS–studien 2015 presterar elever inom matematikämnet sämre i kategorintaluppfattning och aritmetik än i de övriga kategorierna. Med det som utgångspunkt är syftet med vår litteraturstudie att beskriva hur huvudräkningsstrategin talsortsräkning behandlas inom matematikdidaktisk forskning. Frågeställningarna ”vilka fördelar/nackdelar har strategin talsortsräkning?”, ”när väljer elever talsortsräkning?” och ”vad bör en lärare tänka på när undervisning om strategin planeras och genomförs?”utformades utifrån syftet. För att vidare besvara frågeställningar har vi analyserat ett flertal publikationer. Det analyserade materialet omfattar 9 vetenskapliga tidskriftsartiklar och 2 konferensbidrag. Samtliga publikationer är studier som utförts inom matematikdidaktik och berör huvudräkning. Forskning visar att talsortsräkning kan vara användbar i ett flertal situationer. Det kan vara en god ide att låta elever påbörja undervisning om huvudräkning med strategin talsortsräkning. Strategin används främst av elever med lägre taluppfattning och vid enkla uppgifter och har visat sig mer effektiv att använda vid additionsuppgifter jämfört mot subtraktionsuppgifter. Resultatet visar på ett antal olika nackdelar gällande talsortsräkning. Vid beräkning av subtraktionsuppgifter kan det exempelvis bli nödvändigt att behöva byta räknesätt samt att det finns en risk för att negativa tal kan uppstå. Det har visat sig att en lärares roll och förhållningssätt vid undervisningssammanhang har en stor betydelse för elevers syn och användning av strategier.

  • 48.
    Venkat, Hamsa
    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.
    Askew, Mike
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mediating primary mathematics: theory, concepts, and a framework for studying practice2018In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 97, no 1, p. 71-92Article in journal (Refereed)
    Abstract [en]

    In this paper, we present and discuss a framework for considering the quality of primary teachers’ mediating of primary mathematics within instruction. The “mediating primary mathematics” framework is located in a sociocultural view of instruction as mediational, with mathematical goals focused on structure and generality. It focuses on tasks and example spaces, artifacts, inscriptions, and talk as the key mediators of instruction. Across these mediating strands, we note trajectories from error and a lack of coherence, via coherence localized in particular examples or example spaces, towards building a more generalized coherence beyond the specific example space being worked with. Considering primary mathematics teaching in this way foregrounds the nature of the mathematics that is made available to learn, and we explore the affordances of attending to both coherence and structure/generality. Differences in ways of using the framework when either considering the quality of instruction or working to develop the quality of instruction are taken up in our discussion. 

  • 49.
    Venkat, Hamsa
    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.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Improving multiplicative reasoning in a context of low performance2019In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 1, p. 95-108Article in journal (Refereed)
    Abstract [en]

    In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12–13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention consisting of four lessons, designed with attunement to classroom culture and levels of learning, was implemented. Outcomes based on pre- and post-testing pointed to substantial gains in both schools, leading to interest in understanding the nature and extent of changes in models and calculation approaches in high performance and high gain item clusters. Increases in appropriate setting up of symbolic models of multiplicative situations and in more efficient calculation are discussed. 

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