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Ekdahl, Anna-Lena
Publications (10 of 19) Show all publications
Ekdahl, A.-L. (2020). Different learning possibilities from the same activity: Swedish preschool teachers’ enactment of a number relation activity. Scandinavian Journal of Educational Research
Open this publication in new window or tab >>Different learning possibilities from the same activity: Swedish preschool teachers’ enactment of a number relation activity
2020 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed) Epub ahead of print
Abstract [en]

In this paper, differences in the implementation of a number activity called the snake game are studied. Nine Swedish preschool teachers worked in collaboration with a research team, enacting the same activity with their groups of 5-year-old children over a 3-month period. Variation theory forms the basis for the analysis of 67 videorecorded enactments. The results suggest that an activity such as the snake game can bring various aspects of numbers to the fore through differences in enactment. The activity became mathematically richer when the teacher compared children’s different finger patterns and used systematically varied examples of number relations. This study’s results contribute knowledge about characteristics of teaching that foregrounds numbers’ part-whole relations.

Place, publisher, year, edition, pages
Taylor & Francis, 2020
Keywords
Variation theory, mathematical activity, in-service preschool teachers, early numbers, part-whole relationship, part-whole relations, finger patterns
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46895 (URN)10.1080/00313831.2020.1739131 (DOI)000523149300001 ()2-s2.0-85082747980 (Scopus ID)GOA HLK 2020 (Local ID)GOA HLK 2020 (Archive number)GOA HLK 2020 (OAI)
Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2020-05-15
Björklund, C., Ekdahl, A.-L. & Runesson Kempe, U. (2020). Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning.
Open this publication in new window or tab >>Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning
2020 (English)In: Article in journal (Refereed) Epub ahead of print
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, 2020
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)
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: 2020-05-15
Mårtensson, P., Ekdahl, A.-L. & Keerekes, K. (2019). Att designa och förändra matematikuppgifter i learning study—en modell för att utveckla lärarstudenters yrkeskompetens. In: : . Paper presented at Forskningsbaserad undervisning - praktik och teori i samverkan.
Open this publication in new window or tab >>Att designa och förändra matematikuppgifter i learning study—en modell för att utveckla lärarstudenters yrkeskompetens
2019 (Swedish)Conference paper, Oral presentation with published abstract (Other academic)
Abstract [sv]

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

Keywords
matematik uppgifter, lärarstudenter, learning study, variationsteori
National Category
Educational Sciences
Identifiers
urn:nbn:se:hj:diva-47337 (URN)
Conference
Forskningsbaserad undervisning - praktik och teori i samverkan
Available from: 2020-01-13 Created: 2020-01-13 Last updated: 2020-01-15Bibliographically approved
Ekdahl, A.-L., Lundberg, B. & Keerekes, K. (2019). Matematik i förskoleklassen VA-MER: Ett samverkansprojekt mellan Vaggeryds kommun och Mathematics Education Research. In: : . Paper presented at Forskningsbaserad undervisning - praktik och teori i samverkan, 12 november 2019, Jönköping, Sverige.
Open this publication in new window or tab >>Matematik i förskoleklassen VA-MER: Ett samverkansprojekt mellan Vaggeryds kommun och Mathematics Education Research
2019 (Swedish)Conference paper, Oral presentation with published abstract (Other academic)
Abstract [sv]

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

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

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

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

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

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

National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-47405 (URN)
Conference
Forskningsbaserad undervisning - praktik och teori i samverkan, 12 november 2019, Jönköping, Sverige
Available from: 2020-01-15 Created: 2020-01-15 Last updated: 2020-01-15Bibliographically approved
Kullberg, A., Ekdahl, A.-L., Reis, M. & Björklund, C. (2019). Preschool children’s understanding of numbers shown in a partitioning task. In: Mellony Graven, Hamsa Venkat, Anthony A. Essien & Pamela Vale (Ed.), Proceedings of the 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education: Volume 4: Oral Communications and Poster Presentations. Paper presented at 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7 – 12 July 2019 (pp. 59-59). Pretoria, South Africa: PME
Open this publication in new window or tab >>Preschool children’s understanding of numbers shown in a partitioning task
2019 (English)In: Proceedings of the 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education: Volume 4: Oral Communications and Poster Presentations / [ed] Mellony Graven, Hamsa Venkat, Anthony A. Essien & Pamela Vale, Pretoria, South Africa: PME , 2019, p. 59-59Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

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

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

References

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

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

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

Place, publisher, year, edition, pages
Pretoria, South Africa: PME, 2019
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46514 (URN)978-0-6398215-6-6 (ISBN)978-0-6398215-7-3 (ISBN)
Conference
43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7 – 12 July 2019
Available from: 2019-10-10 Created: 2019-10-10 Last updated: 2019-10-10Bibliographically approved
Ekdahl, A.-L. (2019). Teaching for the learning of additive part-whole relations: The power of variation and connections. (Doctoral dissertation). Jönköping: Jönköping University, School of Education and Communication
Open this publication in new window or tab >>Teaching for the learning of additive part-whole relations: The power of variation and connections
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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

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

Place, publisher, year, edition, pages
Jönköping: Jönköping University, School of Education and Communication, 2019. p. 121
Series
Doktorsavhandlingar från Högskolan för lärande och kommunikation, ISSN 1652-7933 ; 038
Keywords
variation, variation theory, connections in teaching, making connections, early numbers, teaching and learning additive relations, part-whole relation, part-whole relations of numbers, intervention study
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46899 (URN)978-91-88339-28-7 (ISBN)978-91-88339-29-4 (ISBN)
Public defence
2019-12-13, Hb116, School of Education and Communication, Jönköping, 13:00 (English)
Opponent
Supervisors
Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2019-11-25Bibliographically approved
Ekdahl, A.-L., Björklund, C. & Runesson Kempe, U. (2019). Teaching to change ways of experiencing numbers – An intervention program for arithmetic learning in preschool. In: Mellony Graven, Hamsa Venkat, Anthony A. Essien & Pamela Vale (Ed.), Proceedings of the 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education: Volume 2: Research Reports (A-K). Paper presented at 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7 – 12 July 2019 (pp. 209-216). Pretoria, South Africa: PME
Open this publication in new window or tab >>Teaching to change ways of experiencing numbers – An intervention program for arithmetic learning in preschool
2019 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
Pretoria, South Africa: PME, 2019
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46513 (URN)978-0-6398215-2-8 (ISBN)978-0-6398215-3-5 (ISBN)
Conference
43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7 – 12 July 2019
Available from: 2019-10-10 Created: 2019-10-10 Last updated: 2019-10-10Bibliographically approved
Ekdahl, A.-L. & Björklund, C. (2018). ”10-masken” och förskolebarns lärande i målstyrda processer. In: : . Paper presented at Matematikbiennalen, Karlstad, 25-26 januari, 2018.
Open this publication in new window or tab >>”10-masken” och förskolebarns lärande i målstyrda processer
2018 (Swedish)Conference paper, Oral presentation only (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.

National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42221 (URN)
Conference
Matematikbiennalen, Karlstad, 25-26 januari, 2018
Available from: 2018-12-06 Created: 2018-12-06 Last updated: 2018-12-06Bibliographically approved
Ekdahl, A.-L. (2018). Differences in pre-school teachers' ways of handling a part-part-whole activity. In: : . Paper presented at Madif 11, The 11th Swedish Mathematics Education Research Seminar, Karlstad, Sweden, 23-24 January, 2018.
Open this publication in new window or tab >>Differences in pre-school teachers' ways of handling a part-part-whole activity
2018 (English)Conference paper, Published 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.

National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42218 (URN)
Conference
Madif 11, The 11th Swedish Mathematics Education Research Seminar, Karlstad, Sweden, 23-24 January, 2018
Available from: 2018-12-06 Created: 2018-12-06 Last updated: 2018-12-06Bibliographically approved
Ekdahl, A.-L. & Kullberg, A. (2018). Different learning possibilities in preschool mathematics from the same task. In: : . Paper presented at European Association for Research on Learning and Instruction (EARLI), SIG 9 Conference 2018, 16-18 September, 2018, Birmingham, UK.
Open this publication in new window or tab >>Different learning possibilities in preschool mathematics from the same task
2018 (English)Conference paper, Oral presentation with published abstract (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.

National Category
Educational Sciences Mathematics
Identifiers
urn:nbn:se:hj:diva-42081 (URN)
Conference
European Association for Research on Learning and Instruction (EARLI), SIG 9 Conference 2018, 16-18 September, 2018, Birmingham, UK
Available from: 2018-11-20 Created: 2018-11-20 Last updated: 2019-02-21Bibliographically approved
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