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Ekdahl, Anna-Lena
Publications (10 of 17) Show all publications
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
Ekdahl, A.-L., Björklund, C. & Runesson Kempe, U. (2018). Finger Patterns as means to experience numbers' part-part-whole relations. In: E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Ed.), Proceedings of the 42nd Conference of the International Group for Psychology of Mathematics education: . Paper presented at PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, 2018, Umeå, Sweden (pp. 42-42). Umeå: PME, 5
Open this publication in new window or tab >>Finger Patterns as means to experience numbers' part-part-whole relations
2018 (English)In: 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, Oral presentation with published abstract (Other academic)
Place, publisher, year, edition, pages
Umeå: PME, 2018
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-41363 (URN)
Conference
PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, 2018, Umeå, Sweden
Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2019-02-21Bibliographically approved
Ekdahl, A.-L. & Lindgren, H. (2018). Gemensamt fokus på förskolebarns taluppfattning och aritmetiska förmågor: Ett samverkansprojekt där teori och praktik flätas samman. In: : . Paper presented at Forskningsbaserad undervisning - Teori och praktik i samverkan, Högskolan för lärande och kommunikation och Jönköpings kommun, 13 november, Jönköping..
Open this publication in new window or tab >>Gemensamt fokus på förskolebarns taluppfattning och aritmetiska förmågor: Ett samverkansprojekt där teori och praktik flätas samman
2018 (Swedish)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [sv]

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

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

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

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

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

National Category
Educational Sciences
Identifiers
urn:nbn:se:hj:diva-42093 (URN)
Conference
Forskningsbaserad undervisning - Teori och praktik i samverkan, Högskolan för lärande och kommunikation och Jönköpings kommun, 13 november, Jönköping.
Available from: 2018-11-20 Created: 2018-11-20 Last updated: 2019-02-21Bibliographically approved
Björklund, C., Alkhede, M., Kullberg, A., Reis, M., Marton, F., Ekdahl, A.-L. & Runesson Kempe, U. (2018). Teaching finger patterns for arithmetic development to preschoolers. 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 >>Teaching finger patterns for arithmetic development to preschoolers
Show others...
2018 (English)Conference paper, Published 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.

National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42220 (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., Venkat, H., Runesson Kempe, U. & Askew, M. (2018). Weaving in connections: Studying changes in early grades additive relations teaching. South African Journal of Childhood Education, 8(1), Article ID a540.
Open this publication in new window or tab >>Weaving in connections: Studying changes in early grades additive relations teaching
2018 (English)In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 8, no 1, article id a540Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
University of Johannesburg, 2018
Keywords
Connections; Example space; Additive relations; Primary mathematics; Part-part-whole teaching; Missing number problem teaching; Changes in teaching; Variation theory; South Africa
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-39015 (URN)10.4102/sajce.v8i1.540 (DOI)000430807400001 ()HLKPUFIS (Local ID)HLKPUFIS (Archive number)HLKPUFIS (OAI)
Available from: 2018-03-16 Created: 2018-03-16 Last updated: 2019-11-25Bibliographically approved
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