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Runesson Kempe, UllaORCID iD iconorcid.org/0000-0001-7556-7974
Alternative names
Publications (10 of 89) Show all publications
Kullberg, A., Björklund, C. & Runesson Kempe, U. (2024). Seeing number relations when solving a three-digit subtraction task. Educational Studies in Mathematics
Open this publication in new window or tab >>Seeing number relations when solving a three-digit subtraction task
2024 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816Article in journal (Refereed) Epub ahead of print
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. 

Place, publisher, year, edition, pages
Springer, 2024
Keywords
Decompose, Early arithmetic skills, Number relations, Subtraction, Three-digit subtraction, Variation theory
National Category
Mathematics Learning
Identifiers
urn:nbn:se:hj:diva-63446 (URN)10.1007/s10649-023-10287-0 (DOI)2-s2.0-85182417145 (Scopus ID)HOA;;933707 (Local ID)HOA;;933707 (Archive number)HOA;;933707 (OAI)
Funder
Swedish Institute for Educational Research, 2018-00038
Available from: 2024-01-30 Created: 2024-01-30 Last updated: 2024-01-30
Björklund, C. & Runesson Kempe, U. (2022). Strategies informed by various ways of experiencing number relations in subtraction tasks. Journal of Mathematical Behavior, 67, Article ID 100994.
Open this publication in new window or tab >>Strategies informed by various ways of experiencing number relations in subtraction tasks
2022 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 67, article id 100994Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Elsevier, 2022
Keywords
Arithmetic strategies, Number relations, Semantic structures, Subtraction, Variation theory of learning
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-58065 (URN)10.1016/j.jmathb.2022.100994 (DOI)000831751600003 ()2-s2.0-85134269536 (Scopus ID)HOA;;822946 (Local ID)HOA;;822946 (Archive number)HOA;;822946 (OAI)
Funder
Swedish Institute for Educational Research, 2018–00038
Available from: 2022-07-27 Created: 2022-07-27 Last updated: 2022-08-16Bibliographically approved
Pillay, V., Adler, J. & Runesson Kempe, U. (2022). The sequencing and pairing of examples in the midst of sameness and difference: Opening opportunities to learn. Pythagoras (AMESA), 43(1), Article ID a667.
Open this publication in new window or tab >>The sequencing and pairing of examples in the midst of sameness and difference: Opening opportunities to learn
2022 (English)In: Pythagoras (AMESA), ISSN 1012-2346, E-ISSN 2223-7895, Vol. 43, no 1, article id a667Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
AOSIS, 2022
Keywords
critical aspects of object of learning, learner-generated examples, sequencing, pairing and juxtaposing examples, variation theory
National Category
Learning
Identifiers
urn:nbn:se:hj:diva-59218 (URN)10.4102/pythagoras.v43i1.667 (DOI)000893577700001 ()2-s2.0-85164610187 (Scopus ID)GOA;;850085 (Local ID)GOA;;850085 (Archive number)GOA;;850085 (OAI)
Available from: 2022-12-22 Created: 2022-12-22 Last updated: 2023-08-17Bibliographically approved
Kullberg, A., Runesson Kempe, U., Björklund, C., Nord, M. & Maunula, T. (2021). Afforded and experienced variation. In: The Earli Sig 9 Conference, 10-11 February 2021: Programme. Paper presented at The EARLI SIG 9 Conference, 10-11 February 2021 (pp. 20-20).
Open this publication in new window or tab >>Afforded and experienced variation
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2021 (English)In: The Earli Sig 9 Conference, 10-11 February 2021: Programme, 2021, p. 20-20Conference paper, Oral presentation with published abstract (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.

National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-59135 (URN)
Conference
The EARLI SIG 9 Conference, 10-11 February 2021
Available from: 2022-12-13 Created: 2022-12-13 Last updated: 2022-12-13Bibliographically approved
Björklund, C., Ekdahl, A.-L. & Runesson Kempe, U. (2021). Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning. Mathematical Thinking and Learning, 23(1), 72-94
Open this publication in new window or tab >>Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning
2021 (English)In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 23, no 1, p. 72-94Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Taylor & Francis, 2021
Keywords
Arithmetic skills, early childhood education, intervention, variation theory of learning
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46896 (URN)10.1080/10986065.2020.1756027 (DOI)000532430500001 ()2-s2.0-85084464857 (Scopus ID)HOA (Local ID)HOA (Archive number)HOA (OAI)
Funder
Swedish Research Council, 721-2014-1791
Note

Included in doctoral thesis in manuscript form with the title "Implementing a structural approach in preschool number activities: Effects of an intervention program".

Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2021-01-26Bibliographically approved
Rosenbaum, C., Runesson Kempe, U. & Svensson, A. (2021). Rikta blicken mot texten. Forskning om undervisning och lärande, 9(1), 31-49
Open this publication in new window or tab >>Rikta blicken mot texten
2021 (Swedish)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 9, no 1, p. 31-49Article in journal (Refereed) Published
Abstract [sv]

Inom svensk forskning om läsundervisning har det framhållits att elever redan på mellanstadiet (åk 4-6) behöver utveckla litterär kompetens och få vägledning i hur de kan angripa och bearbeta en text för att utveckla fördjupad läsförståelse. Syftet med föreliggande artikel är att ge ett kunskapsbidrag beträffande hur undervisning som syftar till att utveckla förmågan att dra slutsatser om en skönlitterär huvudpersons karaktärsdrag kan utformas. En specifik litteraturdidaktisk aktivitet som utvecklats inom ramen för en Learning study i årskurs 4 och 5 studerades närmare. Syftet med undervisningen var att eleverna skulle utveckla sin förmåga att dra slutsatser om en huvudpersons karaktärsdrag utifrån en läst text. 15 timmars videoinspelade lektioner, där samma berättelse användes i samtliga cykler, analyserades med utgångspunkt i variationsteori. Analysen visar att de olika cyklerna erbjöd olika lärandemöjligheter beroende på hur läraren gav instruktioner till lärandeaktiviteten, hur uppgiften formulerades och utformades, om texten och huvudpersonens karaktärsdrag kom i fokus och relaterades till varandra samt vilka aspekter som öppnades upp som dimensioner av variation.

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.

Place, publisher, year, edition, pages
Lärarstiftelsen, 2021
Keywords
Variation theory, Learning study, Middle school education, Literature education, Reading comprehension, Literary competence, Inferences, Character traits, inferenser, karaktärsdrag, läsförståelse, learning study, litterär kompetens, litteraturdidaktik, mellanstadieundervisning, variationsteori
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-53682 (URN)POA;;53682 (Local ID)POA;;53682 (Archive number)POA;;53682 (OAI)
Available from: 2021-06-23 Created: 2021-06-23 Last updated: 2022-07-20Bibliographically approved
Kullberg, A., Björklund, C., Brkovic, I. & Runesson Kempe, U. (2020). Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns. Educational Studies in Mathematics, 103(2), 157-172
Open this publication in new window or tab >>Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns
2020 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 103, no 2, p. 157-172Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2020
Keywords
Preschool, Addition, Subtraction, Part-part-whole, Variation theory, Intervention, Arithmetic
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-47075 (URN)10.1007/s10649-019-09927-1 (DOI)000514516300002 ()2-s2.0-85076597141 (Scopus ID)HOA HLK 2020 (Local ID)HOA HLK 2020 (Archive number)HOA HLK 2020 (OAI)
Funder
Swedish Research Council, 721-2014-1791
Note

An earlier draft of the paper was presented at the International Group for the Psychology of Mathematics Education Conference 2018 in Umeå, Sweden.

Available from: 2019-12-13 Created: 2019-12-13 Last updated: 2020-03-05Bibliographically approved
Kullberg, A., Vikström, A. & Runesson, U. (2020). Mechanisms enabling knowledge production in learning study. International Journal for Lesson and Learning Studies, 9(1), 78-91
Open this publication in new window or tab >>Mechanisms enabling knowledge production in learning study
2020 (English)In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 9, no 1, p. 78-91Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Emerald Group Publishing Limited, 2020
Keywords
Learning study, Mathematics, Professional learning communities, Variation theory
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-45535 (URN)10.1108/IJLLS-11-2018-0084 (DOI)000507527000001 ()2-s2.0-85069910623 (Scopus ID)
Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2021-10-09Bibliographically approved
Gunnarsson, R., Runesson, U. & Håkansson, P. (2019). Identifying what is critical for learning ‘rate if change’: Experiences from a learning study in Sweden. In: R. Huang, A. Takahashi & J. P. da Ponte (Ed.), Theory and practice of lesson study in mathematics: An international perspective (pp. 441-456). Cham: Springer
Open this publication in new window or tab >>Identifying what is critical for learning ‘rate if change’: Experiences from a learning study in Sweden
2019 (English)In: 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.

Place, publisher, year, edition, pages
Cham: Springer, 2019
Series
Advances in Mathematics Education, ISSN 1869-4918
Keywords
Learning study; Critical aspects; Rate of change
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42201 (URN)10.1007/978-3-030-04031-4 (DOI)000487363300022 ()978-3-030-04030-7 (ISBN)978-3-030-04031-4 (ISBN)
Available from: 2018-12-03 Created: 2018-12-03 Last updated: 2020-06-05Bibliographically approved
Björklund, C., Kullberg, A. & Runesson Kempe, U. (2019). Structuring versus counting: critical ways of using fingers in subtraction. ZDM - the International Journal on Mathematics Education, 51(1), 13-24
Open this publication in new window or tab >>Structuring versus counting: critical ways of using fingers in subtraction
2019 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 1, p. 13-24Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Part-Whole relations, Preschool, Spontaneous finger use, Structuring numbers, Subtraction, Variation theory
National Category
Learning
Identifiers
urn:nbn:se:hj:diva-42857 (URN)10.1007/s11858-018-0962-0 (DOI)000463647400002 ()2-s2.0-85059835394 (Scopus ID)HOA HLK 2019 (Local ID)HOA HLK 2019 (Archive number)HOA HLK 2019 (OAI)
Available from: 2019-02-04 Created: 2019-02-04 Last updated: 2019-05-08Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0001-7556-7974

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