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  • 1.
    Alexandersson, Mikael
    et al.
    Göteborgs universitet.
    Runesson, Ulla
    Göteborgs universitet.
    The tyranny of the temporal dimension: learning about fundamental values through the Internet2006In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 50, no 4, p. 411-427Article in journal (Refereed)
    Abstract [en]

    In this article we report on one of four schools involved in a research project aiming to develop knowledge about the way in which teaching knowledge is conveyed with the help of information and communication technology. A particular interest was issues of fundamental values. Two classes in Grade 9 of Swedish compulsory school were studied, by observations and interviews, when seeking information about international conflicts on the Internet. The results show that most students searched for and collected information with a focus on mainly one dimension: the temporal dimension of the conflict in question. How this focus on chronologically ordered historical events affected the students' ability to develop the capacity for individual standpoints on questions concerning ethics, morals, equality, and democracy by way of studying conflicts is discussed.

  • 2. 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)
  • 3.
    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.

  • 4.
    Björklund, Camilla
    et al.
    Department of Education, Communication and Learning, University of Gothenburg, 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.
    Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning2021In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 23, no 1, p. 72-94Article in journal (Refereed)
    Abstract [en]

    We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The research question is how teaching grounded on a structural approach and designed based on principles of variation theory is reflected in children’s learning of numbers. To answer this, three analyses were conducted, addressing: i) how the children’s ways of experiencing numbers changed after participating in the intervention, ii) how the theoretical ideas were afforded in the intervention program, and iii) synthesizing how the affordance was associated with the children’s arithmetic learning. One group of eight children participating in the intervention program was chosen for thorough analysis. Progression was observed in how the children changed their ways of experiencing numbers during the intervention that allowed them to enact more advanced arithmetic strategies, which was associated with the structural approach in teaching. The results also show how analysis focusing on aspects discerned in learning and aspects afforded in teaching provides a way of describing arithmetic learning with significant implications for teaching practices.

  • 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.
    Björklund, Camilla
    et al.
    University of Gothenburg, Department of Education, Communication and Learning, Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Strategies informed by various ways of experiencing number relations in subtraction tasks2022In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 67, article id 100994Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to develop greater understanding of how the way students experience a task is related to which, and how, number relations are discerned. We study how 42 Grade 1 students solved a word problem in a number range that was new to them: 32–25 = __. The variation theory of learning has informed our analysis, opening for thorough analyses of what constitutes differences in the students’ acts in solving the arithmetic word problem and how they experience the task. Observations of their strategies and ways of reasoning revealed that how the students discern the semantic structure and number relations relates to their ways of encountering the task and consequently their success in solving it. The study offers a complementary approach to understanding arithmetic skills that contribute knowledge as to why some students develop powerful ways of solving arithmetic tasks while others get stuck in cumbersome strategies. 

  • 7.
    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)
  • 8.
    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)
  • 9.
    Chik, Pakey Pui-man
    et al.
    University of Hong Kong.
    Runesson, Ulla
    Göteborgs universitet.
    Learning experience and possibilities: a study on two primary 4 chinese language lessons in Hong Kong2008In: Educational Research Journal, ISSN 1560-8263, Vol. 23, no 1, p. 71-95Article in journal (Other academic)
    Abstract [en]

    In this paper, we explore how learning experience can best be described and relate to the teaching enactment so as to inform teaching practices in specific contexts. Two lessons dealing with the same topic in Primary 4 in Hong Kong schools were videotaped and a post-lesson diagnostic worksheet was given to the students. The aim of the study was to identify differences between the two lessons in what was made possible for learning on the topic, and to relate those differences to students’ perception and outcomes in learning. The data collected were analysed from the theoretical assumption that “variation” in the “object of learning” is essential to creating learning opportunities in the classroom. The results showed a critical difference in the way the teachers handled the object of learning. This was in turn found to have contributed to the opening of different “patterns of variation and invariance” in and thus, different possibilities for learning the object of learning. This difference was also reflected in the students' report of their perception and outcomes in learning.

  • 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. 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.

  • 12.
    Ekdahl, Anna-Lena
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Teachers’ responses to incorrect answers on missing number problems in South Africa2015In: The twenty-third ICMI Study: Primary mathematics study on whole numbers: Proceedings / [ed] Xuhua Sun, Berinderjeet Kaur and Jarmila Novotná, 2015, p. 431-439Conference paper (Refereed)
    Abstract [en]

    This paper examines differences in how three Grade 3 South African teachers responded to students’ incorrect answers in whole class teaching of the part-whole relationship in additive missing number problems. Nine video recorded lessons, taught by three teachers, were analysed, with attention paid to teaching episodes containing incorrect students’ answers. The variation theoretical analyses indicated differences in the ways teachers responded to incorrect answers. We argue that different ways of responding to incorrect answers may provide different learning possibilities.

  • 13.
    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.

  • 14.
    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.

  • 15.
    Hansson Scherman, Marianne
    et al.
    Göteborgs universitet.
    Runesson, UllaGöteborgs universitet.
    Den lärande patienten2009Collection (editor) (Other academic)
  • 16.
    Hansson Scherman, Marianne
    et al.
    Göteborgs universitet.
    Runesson, Ulla
    Göteborgs universitet.
    Som patienten ser det2009In: Den lärande patienten / [ed] Marianne Hansson Scherman, Ulla Runesson, Lund: Studentlitteratur, 2009, p. 87-113Chapter in book (Other academic)
  • 17.
    Kullberg, A.
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Box 300, Gothenburg, 405 30, Sweden.
    Björklund, C.
    Department of Education, Communication and Learning, University of Gothenburg, Box 300, Gothenburg, 405 30, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Practice Based Educational Research, Mathematics Education Research. Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Box 300, Gothenburg, 405 30, Sweden.
    Seeing number relations when solving a three-digit subtraction task2024In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816Article in journal (Refereed)
    Abstract [en]

    The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical aspects and their relations of the object of learning. In this paper, we focus on what number relations students see in a three-digit subtraction task, and how they see them. We analyzed interview data from 55 second-grade students who used decomposition strategies to solve 204 − 193 =. The variation theory of learning was used to analyze what number relations the students experienced and how they experienced them, aiming to explain why they made errors even though they used presumably powerful strategies in their problem-solving. The findings show that students who simultaneously experienced within-number relations and between-number relations when solving the task succeeded in solving it, whereas those who did not do this failed. These findings have importance for understanding what students need to discern in order to be able to solve subtraction tasks in a proficient way. 

  • 18. Kullberg, A
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Exploring teaching and learning of letters in algebra: a report from a Learning study2006In: Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Prague, Czech Republic, July 16-21, 2006). Volume 1 / [ed] Novotna, Jarmila, Moraova, Hana, Kratka, Magdalena, Stehlikova, Nad'a,, 2006Conference paper (Refereed)
  • 19.
    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 patterns2020In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 103, no 2, p. 157-172Article 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.

  • 20. Kullberg, Angelika
    et al.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication. Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Nilsson, Pernilla
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Vikström, Anna
    Learning study and teachers' change of practice2014Conference paper (Refereed)
  • 21.
    Kullberg, Angelika
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research. Göteborgs Universitet.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Exploration and search for the external and internal horizon of the object of learning2013In: Book of Abstracts: 5th Biennial Conference EARLI 2013, 2013, p. 7-8Conference paper (Other academic)
    Abstract [en]

    Within the phenomenographic tradition the object of learning depicts the capability that is to be learned by the learner (Marton &Booth, 1997). The object of learning can be defined by its critical aspects, since they are seen as necessary for the learner to discern in order to learn. The aim of this paper is to discuss the nature of the object of learning by investigating how its meaning can change as it is explored by teachers. We analyzed seven recorded meetings in which four teachers and a researcher discussed the nature of the object of learning while they were planning, analyzing and revising a lesson. We found that the meaning of the critical aspects identified changed for the teachers due to the discussion and analysis of the lessons and thereby the meaning of the object of learning changed also. From at first being defined, they later become refined and specified as the teachers acquired deeper understanding of the object of learning. Distinctions were made to separate out what was of significance for the object of learning and what is not (the objects external horizon). Furthermore, an exploration by the teachers was made of how different aspects relate to each other (the objects internal horizon). The findings indicate that qualitative differences in teachers’ experience of the object of learning emerge through the collaborative investigation.

  • 22.
    Kullberg, Angelika
    et al.
    University of Gothenburg.
    Mårtensson, Pernilla
    University of Gothenburg.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research. University of Gothenburg.
    Exploring teachers' investigation of the object of learning: An analysis of A Learning Study about division2012Conference paper (Refereed)
    Abstract [en]

    This paper investigates how teachers explore the object of learning in a learning study in mathematics. The object of learning depicts the capability that is learned by the learner. For each object of learning there are critical aspects that the learner needs to discern. The aim of the paper is to describe the meanings that the critical aspects have for the teachers at different stages in the learning study process. The study is a part of a lager study in Sweden investigating teachers’ learning from learning studies (LGK-project). In this paper we report on the analysis of seven collaborative meetings, with four teachers and a researcher, from the point of view of how the critical aspects and object of learning are discussed using the framework of variation theory. The object of learning was that students in the 7th grade would understand that in a division, with a denominator between 0 and 1, the quotient becomes larger than the numerator. The study shows that the meaning of the critical aspects, identified by the teachers, changes for the teachers due to the discussion and analysis of the lessons. From at first being defined, they later become refined and more explicit as the teachers get deeper understanding of the object of learning. Furthermore, student learning is enhanced, most likely, by the changes made in the teaching due to the teachers’ deeper understanding of the object of learning.

  • 23.
    Kullberg, Angelika
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Göteborg, Sweden.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    What is to be learned? Teachers' collective inquiry into the object of learning2016In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 60, no 3, p. 309-322Article in journal (Refereed)
    Abstract [en]

    Within the phenomenographic research tradition, the object of learning depicts the capability that is to be learned by the learner. It has been argued that the object of learning cannot be fully known in advance since what is to be learned depends on the learners as well as on the content taught. The object of learning and its nature needs to be explored. In this paper, we analyze how a group of teachers collaboratively investigated an object of learning when they planned, enacted, analysed, and revised a mathematical task. We describe distinctions made by the group in the inquiry into teaching and learning, and how delimitations and distinctions made transformed the teaching and meaning of the object of learning.

  • 24.
    Kullberg, Angelika
    et al.
    University of Gothenburg, Sweden.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Practice Based Educational Research, Mathematics Education Research.
    Björklund, Camilla
    University of Gothenburg, Sweden.
    Nord, Maria
    University of Gothenburg, Sweden.
    Maunula, Tuula
    University of Gothenburg, Sweden.
    Afforded and experienced variation2021In: The Earli Sig 9 Conference, 10-11 February 2021: Programme, 2021, p. 20-20Conference paper (Refereed)
    Abstract [en]

    The use of variation theory as a tool for designing lessons has been widely applied and received a lot of attention e.g. in mathematics education. More limited attention has been given to the use of variation theory as a means to analyze teaching and learning. This theoretical paper addresses the connection between the afforded and experienced variation when analyzing teaching and learning with a variation theory framework. Variation theory is in this case used as a tool for analyzing the relationship between teaching and learning, exploring the enacted, and lived object of learning. The connection between what is afforded in teaching and what students learn, can in this way be described in commensurable terms. With examples from a study about students’ learning of number relations in mathematics in first grade, we highlight this connection by illustrating differences identified in the teachers enactment of the same task, and what the students’ learned.

  • 25. Kullberg, Angelika
    et al.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Examples with variation. Teachers’ choice and use of mathematical examples2015Conference paper (Refereed)
  • 26.
    Kullberg, Angelika
    et al.
    Göteborgs universitet.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Learning about the numerator and denominator in teacher-designed lessons2013In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 25, no 4, p. 547-567Article in journal (Refereed)
    Abstract [en]

    This study concerns pupils’ experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils’ understanding of operations such as b/c of a in lessons where the teachers were aware of some pupils’ difficulties beforehand and what needed special attention. Five classes were involved in the study and 10 video-recorded lessons and written pre- and post-tests were analysed. Even though the lessons were designed for learning how to operate with both unit and non-unit fractions, we found that more pupils could solve items with unit fractions than with non-unit fractions. We found that few pupils in this study had difficulties with equal partitioning. Instead, it seemed difficult for some pupils to understand the role of the numerator and denominator and to differentiate between the amount of parts and the amount of objects in each part, and some pupils did not differentiate between the numbers of units and the amount of objects within a unit. This study identified some critical aspects that the pupils need to discern in order to learn how to operate with unit and non-unit fractions of a discrete quantity.

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  • 27. Kullberg, Angelika
    et al.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Teacher learning reflected in practice – a case study of six mathematics teachers’ teaching2014Conference paper (Refereed)
  • 28. Kullberg, Angelika
    et al.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Using simultaneity, variation and invariance to handle the content: Changes in teachers’ teaching of the same topic in mathematics after participation in learning studies2013In: Lesson and learning study as teacher reserach. The World Association of Lesson studies international conference programme book, 2013, p. -81Conference paper (Other academic)
  • 29.
    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.

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  • 30.
    Kullberg, Angelika
    et al.
    University of Gothenburg.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Marton, Ference
    University of Gothenburg.
    Vikström, Anna
    Luleå University of Technology.
    Nilsson, Pernilla
    Halmstad University.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Häggström, Johan
    University of Gothenburg.
    Teaching one thing at a time or several things together?: Teachers changing their way of handling the object of learning by being engaged in a theory-based professional learning community in mathematics and science2016In: Teachers and Teaching: theory and practice, ISSN 1354-0602, E-ISSN 1470-1278, Vol. 22, no 6Article in journal (Refereed)
    Abstract [en]

    Twelve lower secondary schoolteachers in mathematics and science were asked to teach a topic of their choice during a lesson that was video-recorded. We were able to analyse 10 of the cases and we found that all of them were similar in one respect: concepts and principles were introduced one at a time, each one followed by examples of the concept or principle in question, apparently to highlight its essential meaning. All the teachers participated in three modified lesson studies with three cycles in four different groups during three semesters. The modified lesson studies were built on a theoretical idea supported by a large number of recent studies. The theory states that new meanings (of concepts and principles, for instance) are learned through engaging with instances of contrasting concepts and principles. The core idea is that new meanings derive from differences, not from sameness. After the three modified lesson studies, the teachers were asked to once again teach the same topic as in the recorded lessons before the lesson studies. The new lessons were also recorded and the analysis showed that there was one thing in common in all cases: all of the 10 teachers dealt with the relevant concepts and principles in relation to each other (i.e. simultaneously) and not one at a time. By thus bringing out the differences between them, their meaning was made possible to grasp for the students. The study lends support to the conjecture that the modified lesson study is a powerful tool for enabling teachers to structure the content of their teaching in accordance with a principle that is more powerful in making learning possible, even if this contradicts their taken-for-granted practice.

  • 31.
    Kullberg, Angelika
    et al.
    Göteborgs universitet.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Changes in teaching equations with one unknown after participating in learning studies2013In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education: Vol. 5 / [ed] Anke Lindmeier, Aiso Heinze, 2013Conference paper (Refereed)
  • 32.
    Kullberg, Angelika
    et al.
    University of Gothenbourg.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Different possibilities to learn from the same task2014In: PNA, ISSN 1886-1350, E-ISSN 1887-3987, Vol. 8, no 4, p. 139-150Article in journal (Refereed)
    Abstract [en]

    In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessonsin the 8thgrade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator less than 1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task wasused in the lessons, the way it was enacted provided different possibilities to learn.

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  • 33.
    Kullberg, Angelika
    et al.
    University of Gothenburg.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Mårtensson, Pernilla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    The same task? - different learning possibilities2013In: Task Design in Mathematics Education. Proceedings of ICMI Study 22 / [ed] Claire Margolinas, 2013, p. 609-616Conference paper (Refereed)
    Abstract [en]

    In this chapter we focus on variation of the design and the implementation of a specific task during three mathematics lesson in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator <1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task wasused in the lessons the way it was enacted provided different possibilities to learn.

  • 34.
    Kullberg, Angelika
    et al.
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Gothenburg, Sweden.
    Vikström, Anna
    Department of Arts, Communication and Education, Luleå University of Technology, Luleå, Sweden.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Mechanisms enabling knowledge production in learning study2020In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 9, no 1, p. 78-91Article in journal (Refereed)
    Abstract [en]

    Purpose: The purpose of this paper is to add to the discussion about practitioner research in schools – by addressing mechanisms and systematic strategies based on theory in a research model, which enables the creation of knowledge products that enhance student learning and are sharable between teachers.

    Design/methodology/approach: The research question is the following: Can a specific form of teachers’ research produce practice-based knowledge relevant beyond the borders of the local school context? This question is addressed through empirical examples from previously published papers on learning studies in natural sciences, mathematics and language.

    Findings: This paper promotes the view that teachers in learning studies can create practical public knowledge relevant beyond their local context. The authors suggest that learning studies and variation theory can offer teachers mechanisms to create such public knowledge.

    Originality/value: The paper proposes that teachers’ collaboration in professional learning communities, as in a learning study, not only has the capacity to increase students’ and teachers’ learning, but it can also be used to create practical public knowledge. 

  • 35. Liljestrand, Johan
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Interaction, organisation, tasks and possibilities for Learning about mathematical  relationships: A Swedish classroom compared with a US classroom2006In: Making connections: comparing mathematics classrooms around the world / [ed] David Clarke, Jonas Emanuelsson, Eva Jablonka, Ida Ah Chee Mok, Rotterdam: Sense Publishers, 2006, p. 165-184Chapter in book (Other academic)
  • 36. Liljestrand, Johan
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Supporting learning: individualisation and everyday mathematics as learning supporters in the Swedish classroom2004Conference paper (Other academic)
  • 37. Liljestrand, Johan
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Supporting learning: on teacher and student interaction when learning about functions and graphs – a comparative perspective2004Conference paper (Other academic)
  • 38. Ling, Lo Mun
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Teachers' learning from learning studies: an example of teaching and learning fractions in primary four2007In: Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education PME31, Seoul, Korea, July 8-13, 2007. Vol. 1 / [ed] Jeong Ho-Woo, Hee-Chan Lew, Kyo-Sik Park, Dong-Yeop Seo, 2007, p. 157-162Conference paper (Refereed)
  • 39. Marton, F
    et al.
    Runesson, Ulla
    Göteborgs universitet.
    Are critical feature of the object of learning in Hong Kong, also critical in Sweden?2009Conference paper (Other academic)
  • 40.
    Marton, Ference
    et al.
    University of Gothenburg.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    The idea and practice of learning study2015In: Realising learning: Teachers' professional development through lesson study and learning study / [ed] Keith Wood and Saratha Sithamparam, London: Routledge, 2015, p. 103-121Chapter in book (Refereed)
  • 41.
    Marton, Ference
    et al.
    Göteborgs universitet.
    Runesson, Ulla
    Göteborgs universitet.
    Tsui, Amy B. M.
    University of Hong Kong.
    The space of learning2004In: Classroom discourse and the space of learning / [ed] Ference Marton, Amy B.M. Tsui, Mahwah, N.J.: Lawrence Erlbaum Associates, 2004, p. 3-36Chapter in book (Other academic)
  • 42.
    Mårtensson, Pernilla
    et al.
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Runesson, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Exploring and finding what must be learned about the constants in a linear function.: Teachers' inquiry into their own practice2014In: Conference abstracts: Becoming reflective educators and professionals of learning., 2014Conference paper (Refereed)
  • 43.
    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)
  • 44.
    Pillay, Vasen
    et al.
    Univ Witwatersrand, Fac Humanities, Sch Educ, Johannesburg, South Africa..
    Adler, Jill
    Univ Witwatersrand, Fac Humanities, Sch Educ, Johannesburg, South Africa..
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Practice Based Educational Research, Mathematics Education Research. Univ Witwatersrand, Fac Humanities, Sch Educ, Johannesburg, South Africa..
    The sequencing and pairing of examples in the midst of sameness and difference: Opening opportunities to learn2022In: Pythagoras (AMESA), ISSN 1012-2346, E-ISSN 2223-7895, Vol. 43, no 1, article id a667Article in journal (Refereed)
    Abstract [en]

    The teaching of mathematics cannot be thought of without considering the use of examples. The examples that teachers use during a lesson and how they mediate the example set is critical to what opportunities for learning are opened up during the lesson. In this article, we explore how a teacher mediates an example set with focus particularly on what is varied and what remains the same. The case that we draw on is taken from a larger learning study conducted in Grade 10 mathematics classes and the lesson that is used in this article was the last lesson in the learning study cycle. We use variation theory, specifically how the sequencing, pairing and juxtaposing of examples provides learners with opportunities to discern the critical aspect of the object of learning. We analyse the teacher's mediation of the example set on a micro level, as this enables us to illuminate and develop our argument, while simultaneously offering a detailed example of mathematics teaching. We argue that it is the systematic and deliberate structuring of variation within an example set in the midst of invariance coupled with the teacher's mediation of both planned and learner-generated examples that is critical for opening opportunities to learn.

  • 45.
    Rosenbaum, Cecilia
    et al.
    Jönköping University, School of Education and Communication.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witsvatersrand, Johannesburg, Sydafrika.
    Svensson, Anette
    Jönköping University, School of Education and Communication, HLK, Learning Practices inside and outside School (LPS). Jönköping University, School of Education and Communication, HLK, Communication, Culture and Diversity (CCD).
    Rikta blicken mot texten2021In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 9, no 1, p. 31-49Article in journal (Refereed)
    Abstract [en]

    In Swedish research on reading instruction, it has been emphasized that students already in middle school (grades 4-6) need to develop literary competence and receive guidance on how they can process a text in order to develop in-depth reading comprehension. The aim of the article is to contribute with knowledge regarding how teaching that aims to develop the ability to draw conclusions about a fictional protagonist’s character traits can be designed. A specific activity focusing literature education that was developed within the framework of a Learning study in grades 4 and 5 was studied in more detail. The purpose of the teaching unit was that the students would develop their abilities to draw conclusions about a protagonist’s character traits in a fictional text. 15 hours of video-recorded lessons, where the same story was used in all cycles, were analyzed using variation theory. The analysis shows that the different cycles offered different learning opportunities depending on how the teacher gave instructions to the learning activity, how the task was formulated and designed, if the text and the protagonist’s character traits came into focus and related to each other, and which aspects were opened up as dimensions of variation.

  • 46.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Learning study – en ämnesdidaktisk och praktikutvecklande forskningsansats2016In: Skolnära forskningsmetoder / [ed] Elsie Anderberg, Lund: Studentlitteratur AB, 2016, p. 63-88Chapter in book (Other (popular science, discussion, etc.))
  • 47.
    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.

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  • 48.
    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)
  • 49.
    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. 

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  • 50.
    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. 

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