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Ekdahl, Anna-Lena
##### Publications (10 of 32) Show all publications
Ekdahl, A.-L. (2023). 6-year-olds’ different ways of reasoning about a larger collection of items. In: EARLI 2023: Book of abstracts. Paper presented at The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece (pp. 125-125).
Open this publication in new window or tab >>6-year-olds’ different ways of reasoning about a larger collection of items
2023 (English)In: EARLI 2023: Book of abstracts, 2023, p. 125-125Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

Children develop an understanding of numbers by, for instance, counting items in smaller or larger sets. When a larger set is placed in a regular arrangement (for example, in rows) subitizing or counting can be used to quantify a subset, and thereby determine the size of the larger set. It becomes more challenging when the items are placed in an irregular arrangement. The aim of this study is to answer the question: How do 6-year-olds estimate and reason about how to determine a quantity of a larger set in an irregular arrangement? In this study, 130 Swedish 6-year-olds were asked: How many cubes do you think there are on the tray? How could you find out? looking at a tray with 47 randomly arranged wooden cubes. In the analysis, students’ answers were summarized. Codes, inductively sprung from the data, were used to describe students’ reasoning. The analysis shows that around half of the students made a reasonable estimation of the number of cubes. In 2/3 of the observations, single-unit counting was in focus in students’ reasoning when determining the size of the set of cubes. Whereas in 1/3 of the observations, decomposing the whole collection into subsets, either of the same size (e.g., groups of five) or different size, was in focus in their reasoning. Hence, the study reveals different ways in which 6-years-olds reason about estimating or determining the size of an uncountable set. Based on this, implications for how to teach quantification and estimation are discussed.

##### Keywords
Early Childhood Education, Mathematics/Numeracy, Primary Education, Reasoning
##### National Category
Pedagogy Mathematics
##### Identifiers
urn:nbn:se:hj:diva-62857 (URN)
##### Conference
The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece
Available from: 2023-11-07 Created: 2023-11-07 Last updated: 2023-11-07Bibliographically approved
Elofsson, J. & Ekdahl, A.-L. (2023). Supporting or restricting mathematical communication and reasoning in teaching 6-year olds. In: EARLI 2023: Book of abstracts. Paper presented at The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece (pp. 446-446).
Open this publication in new window or tab >>Supporting or restricting mathematical communication and reasoning in teaching 6-year olds
2023 (English)In: EARLI 2023: Book of abstracts, 2023, p. 446-446Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

Communication and reasoning in mathematics is described as important for student learning. Hence, teachers have a central role to invite students to engage in reasoning and collective problem solving. One common way to promote this is for the teacher to ask questions. However, there is limited knowledge of how teachers make use of the input provided by students on the asked questions in their mathematics teaching to support further learning and mathematical inquiry. In the present study, we investigated qualitative differences in how preschool class teachers responded to and incorporated 6-year old students’ input in teaching about numbers and arithmetic. The data gathered for analysis consisted of fieldnotes collected through observations of 145 mathematics teaching episodes in 95 classes. To make it possible to map the qualitative different ways teachers responded to and incorporated students’ input in their teaching, the Mediating Primary Mathematics framework was used as an analytical tool. The results show that teachers responded to and incorporated student input in different ways in their teaching. In almost 2/3 of the teaching episodes, teachers stopped at only briefly confirming the input given as right or wrong, or just gave generally encouraging responses to the student. In just under 1/3 of the teaching episodes, teachers took advantage of and incorporated student input in their teaching to advance and verify their mathematical reasoning. This highlights that teachers may develop their ways of responding to and elaborating on students’ input in teaching, which could improve students’ opportunities for learning mathematics.

##### Keywords
Early Childhood Education, Mathematics/Numeracy, Primary Education, Teaching/Instructional Strategies
##### National Category
Pedagogy Mathematics
##### Identifiers
urn:nbn:se:hj:diva-62858 (URN)
##### Conference
The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece
Available from: 2023-11-07 Created: 2023-11-07 Last updated: 2023-11-07Bibliographically approved
Kullberg, A. & Ekdahl, A.-L. (2023). To see the yet unseen – “critical aspects” as a key to developing teaching and students’ learning. In: EARLI 2023: Book of abstracts. Paper presented at The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece (pp. 269-270).
Open this publication in new window or tab >>To see the yet unseen – “critical aspects” as a key to developing teaching and students’ learning
2023 (English)In: EARLI 2023: Book of abstracts, 2023, p. 269-270Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

The aim of the symposium is to present and discuss the notion of “critical aspects” as a key concept for developing teaching and thus students’ learning. The concept “critical aspects” is central to phenomenography and variation theory, pinpointing what aspects students need to discern in order to develop their understanding of the object of learning in focus for the teaching. In four different presentations, with a focus on different age groups and subjects, the notion of critical aspects is discussed. In the first presentation the authors discuss how critical aspects can be used by teachers in primary school as a point of departure in mathematics teaching – in tasks as well as activities. In the second presentation the authors discuss how teachers can help kindergarteners to discern critical aspects through reading a picture book. In the third presentation the author presents a study focusing on primary teachers’ understanding of “growth mindset” and how critical aspects of this concept can be used as a foundation to inform teacher education. The final presentation discusses how teachers and teacher students understand the notion of critical aspects and what needs to be focused upon in teacher training in order for teachers/teacher students to grasp this concept in a qualified way. The symposium has scientific relevance as it opens up for different perspectives of a central concept in phenomenography and variation theory. It also has educational relevance, as the notion of critical aspects can be understood as foundational for developing teaching.

##### Keywords
Attitudes and Beliefs, Conceptual Change, Early Childhood Education, Instructional Design, Mathematics/Numeracy, Mindsets, Primary Education, Qualitative Methods, Reading, Synergies between Learning / Teaching and Research, Teacher Professional Development, Teaching Approaches, Teaching/Instructional Strategies, Writing/Literacy
##### National Category
Pedagogy Didactics
##### Identifiers
urn:nbn:se:hj:diva-62852 (URN)
##### Conference
The 20th Biennial EARLI Conference for Research on Learning and Instruction, 22-26 August 2023, Thessaloniki, Greece
##### Note

Invited Symposium.

Available from: 2023-11-07 Created: 2023-11-07 Last updated: 2023-11-07Bibliographically approved
Björklund, C., Ekdahl, A.-L., Kullberg, A. & Reis, M. (2022). Preschoolers’ ways of experiencing numbers. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 84-110
Open this publication in new window or tab >>Preschoolers’ ways of experiencing numbers
2022 (English)In: LUMAT: International Journal on Math, Science and Technology Education, E-ISSN 2323-7112, Vol. 10, no 2, p. 84-110Article in journal (Refereed) Published
##### Abstract [en]

In this paper we direct attention to 5–6-year-olds’ learning of arithmetic skills through a thorough analysis of changes in the children’s ways of encountering and experiencing numbers. The foundation for our approach is phenomenographic, in that our object of analysis is differences in children’s ways of completing an arithmetic task, which are considered to be expressions of their ways of experiencing numbers and what is possible to do with numbers. A qualitative analysis of 103 children’s ways of encountering the task gives an outcome space of varying ways of experiencing numbers. This is further analyzed through the lens of variation theory of learning, explaining why differences occur and how observed changes over a prolonged period of time can shed light on how children learn the meaning of numbers, allowing them to solve arithmetic problems. The results show how observed changes are liberating new and powerful problem-solving strategies. Emanating from empirical research, the results of our study contribute to the theoretical understanding of young children’s learning of arithmetic skills, taking the starting point in the child’s lived experiences rather than cognitive processes. This approach to interpreting learning, we suggest, has pedagogical implications concerning what is fundamental to teach children for their further development in mathematics.

##### Place, publisher, year, edition, pages
University of Helsinki, 2022
##### Keywords
arithmetic, numbers, phenomenography, preschoolers, variation theory
##### National Category
Mathematics Learning
##### Identifiers
urn:nbn:se:hj:diva-58160 (URN)10.31129/LUMAT.10.2.1685 (DOI)2-s2.0-85135212675 (Scopus ID)POA;;824558 (Local ID)POA;;824558 (Archive number)POA;;824558 (OAI)
##### Funder
Swedish Research Council, 721-2014-1791 Available from: 2022-08-10 Created: 2022-08-10 Last updated: 2022-09-02Bibliographically approved
Ekdahl, A.-L. & Andersson, A. (2022). SATSA - ett projekt om undervisning av tal och räknande i förskoleklass. In: : . Paper presented at Forskningsbaserad undervisning – teori och praktik i samverkan, Högskolan för lärande och kommunikation, Jönköping University, 9 november 2022.
Open this publication in new window or tab >>SATSA - ett projekt om undervisning av tal och räknande i förskoleklass
2022 (Swedish)Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [sv]

Ur abstraktet: SATSA står för Strukturell Ansats i undervisning Som grund för hållbart Aritmetik lärande och är ett projekt finansierat av Vetenskapsrådet. I SATSA riktas uppmärksamheten mot kvaliteten i undervisning i förskoleklass (6-åringar) med avseende på hur tal, antal och räknestrategier behandlas som innehåll för lärande.

##### National Category
Didactics Mathematics
##### Identifiers
urn:nbn:se:hj:diva-58849 (URN)
##### Conference
Forskningsbaserad undervisning – teori och praktik i samverkan, Högskolan för lärande och kommunikation, Jönköping University, 9 november 2022
Available from: 2022-11-10 Created: 2022-11-10 Last updated: 2022-11-10Bibliographically approved
Elofsson, J., Ekdahl, A.-L. & Björklund, C. (2022). Teachers incorporating 6-yearolds’ input in mathematics teaching. In: C. Fernández, S. Llinares, Á. Gutiérrez & N. Planas (Ed.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education: Volume 4, research reports (Si-Z), oral communications, poster presentations. Paper presented at 45th Conference of the International Group for the Psychology of Mathematics Education, Alicante, Spain, July 18-23, 2022 (pp. 203). Psychology in Mathematics Education (PME), Vol. 4
Open this publication in new window or tab >>Teachers incorporating 6-yearolds’ input in mathematics teaching
2022 (English)In: Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education: Volume 4, research reports (Si-Z), oral communications, poster presentations / [ed] C. Fernández, S. Llinares, Á. Gutiérrez & N. Planas, Psychology in Mathematics Education (PME) , 2022, Vol. Vol. 4, p. 203-Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

The potential for student mathematics learning lies both in the teacher ability to ask questions and to follow up and incorporate student input into the teaching of a specific content (Murata, 2015). Swedish students are expected to engage in reasoning and collective problem solving in highly communicative teaching practice. To improve these learning situations, it is important to understand how teachers are making use of student input in teaching. In this study we seek to map and understand how teachers in preschool classes respond to and incorporate student input in mathematics teaching.

This paper reports on findings from a study focusing on mathematics teaching in preschool classes in Sweden (6-yearolds). The data consist of 145 observations (from 95 individual teachers) of mathematics teaching relating to whole numbers. The data for analysis consist of fieldnotes and was collected during fall 2021. The MPM-framework “Mediating Primary Mathematics” (Venkat & Askew, 2018) was used as an analytical tool to identify the ways teachers in preschool classes respond to and incorporate student input in their mathematics teaching. Following the four levels in the framework, the results show that in 61,4% of the observations, teachers give students very little opportunity to contribute with input beyond short responses, merely confirming or giving generally encouraging responses to the student. This is to becompared to 29,7% of the observations, where teachers take advantage of student input by incorporating these into the teaching situation to advance or verify students’ mathematical reasoning. In the third largest group (8.3 % of the observations), the teachers pulled back or made no evaluation of the student input. Only in one case (0.7% of the observations), the teacher took advantage of the student input and both advanced and explained it further to support learner progression.

The results raise questions about how teachers’ ways of responding to and elaborating on students’ input might influence students’ opportunities for learning about numbers. In particular, when teachers advance, verify, and explain student input, significant connections and justifications for solution methods are highlighted.

##### Place, publisher, year, edition, pages
Psychology in Mathematics Education (PME), 2022
##### Series
Proceedings of the International Group for the Psychology of Mathematics Education, E-ISSN 0771-100X
##### National Category
Pedagogy Mathematics
##### Identifiers
urn:nbn:se:hj:diva-58569 (URN)978-84-1302-178-2 (ISBN)
##### Conference
45th Conference of the International Group for the Psychology of Mathematics Education, Alicante, Spain, July 18-23, 2022
Available from: 2022-10-03 Created: 2022-10-03 Last updated: 2022-10-03Bibliographically approved
Kerekes, K. & Ekdahl, A.-L. (2022). VA MER 2.0 – Forskningsbaserad matematikundervisning i förskoleklass och årskurs 1. In: : . Paper presented at Forskningsbaserad undervisning – teori och praktik i samverkan, Högskolan för lärande och kommunikation, Jönköping University, 9 november 2022.
Open this publication in new window or tab >>VA MER 2.0 – Forskningsbaserad matematikundervisning i förskoleklass och årskurs 1
2022 (Swedish)Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [sv]

Ur abstraktet: Sedan 2019 har forskningsgruppen i matematik, vid Högskolan för Lärande och Kommunikation, Jönköping University, ett väl upparbetat samarbete med Vaggeryds kommun. Forskare och kommunens lektor har under tre år utarbetat ett hållbart samverkansavtal (ULF) där utveckling av matematikundervisning i förskoleklass stått i fokus. I det så kallade VA-MER projektet har forskare tillsammans med lärare i förskoleklass i en iterativ process utvecklat och systematiskt utprövat ett antal vetenskapligt förankrade undervisningsaktiviteter som ska främja elevers taluppfattning och problemlösningsförmåga. Det har resulterat i ett antal dokumenterade undervisningsaktiviteter som är tänkta att fortsättningsvis vara ett stöd i matematikundervisningen för såväl verksamma som nyanställda lärare i kommunens förskoleklasser. En fråga som har väckts under projektets gång är hur de grundläggande matematiska idéer ska förvaltas och utvecklas i årskurs 1.

##### National Category
Didactics Mathematics
##### Identifiers
urn:nbn:se:hj:diva-58848 (URN)
##### Conference
Forskningsbaserad undervisning – teori och praktik i samverkan, Högskolan för lärande och kommunikation, Jönköping University, 9 november 2022
Available from: 2022-11-10 Created: 2022-11-10 Last updated: 2022-11-10Bibliographically approved
Ekdahl, A.-L. & Bengtson Carlström, H. (2021). Bygga broar mellan praktik och akademi - ett hållbart ULF-avtal. In: : . Paper presented at Forskningsbaserad undervisning – teori och praktik i samverkan, Jönköping University, 9 november 2021.
Open this publication in new window or tab >>Bygga broar mellan praktik och akademi - ett hållbart ULF-avtal
2021 (Swedish)Conference paper, Oral presentation with published abstract (Other academic)
##### Abstract [sv]

Ett utvecklingsprojekt startades 2019 på initiativ av Vaggeryds kommun. Då kommunens lektor under en längre tid har varit knuten till den praktiknära forskningsmiljön PUF och forskargruppen i matematik, vid Högskolan för Lärande och Kommunikation, och det beviljades ULF-medel från Göteborgsnoden, startades projektet VA–MER? Vid uppstarten formulerades syfte och mål för projekten utifrån kommunens behov. Målet med projektet var bland annat att genom kollegialt lärande och med stöd av forskare gemensamt bygga ett fundament i matematikundervisningen i förskoleklass med stöd av aktuell forskning, i syfte att utveckla elevers taluppfattning.

Projektet följer ett forskningsbaserat upplägg. Alla lärare som deltar i projektet planerar och prövar undervisningsaktiviteter. Därefter reflekterar de över dessa tillsammans med kollegor och lärosätets forskare/ lärare. Projektet går nu in på sitt tredje läsår. Syftet med projektet har delvis reviderats. Utifrån förra läsårets utvärdering och elevresultat har en övergripande forskningsfråga formulerats, liksom frågor kopplade till lokala behov på respektive enhet. Ett ännu större fokus läggs nu på elevers lärande och på hur undervisning möjliggör för alla elever att utveckla sin förmåga att resonera om tal.

I nuläget deltar två lärare/forskare från Högskolan för lärarande och kommunikation och tolv lärare i förskoleklass (från sju enheter). Några lärare har avslutat sin medverkan av naturliga skäl, medan andra lärare har tillkommit. Lärarna och forskarna träffas kontinuerligt, för att planera och diskutera matematikundervisning tillsammans. Deltagarnas olika erfarenheter av att ha undervisat i förskoleklass, den geografiska spridningen i kommunen, mixen av små och stora enheter, samt lärosätets lärare med forskning inom området och lång erfarenhet av undervisning utgör en god grund för skolutveckling.

Unikt med projektet är att alla kommunens lärare i förskoleklass deltar. Samordnare är kommunens lektor i matematikdidaktik, som har 20% av sin tjänst för arbete med bland annat skolutveckling och för att vara en länk mellan akademin och skolan. Hon har även det organisatoriska ansvaret och samverkar kontinuerligt med forskare, rektorer och verksamhetschef. Det finns täta kontaktvägar när problem uppstår.

Ur ett huvudmannaperspektiv är en kontinuerlig och systematisk fortbildning, grundat på analyser av mål, styrdokument och elevers måluppfyllelse samt aktuell forskning avgörande för att utveckla undervisning. Vi tror att VA–MER? kan stärka likvärdigheten i Vaggeryd kommuns förskoleklassverksamhet samt förskoleklassens pedagogiska uppdrag, vilket i sin tur kommer attbidra till elevernas högre måluppfyllelse.

Lärosätets upplevelse av VA–MER? är att det tar tid att bygga relationer mellan lärare och lärare och forskare för att kunna se varandra som resurser och föra diskussioner på lika villkor. Utifrån ett lärosätesperspektiv ställs man inför utmaningar att få modellen att fungera, stötta de som är ensamma på sin enhet, få alla att våga pröva nya aktiviteter, filma och utmana de som deltagit under två läsår till att utveckla sin undervisning ytterligare.

Vi tänker att framgångsfaktorer för projektet VA MER är: långsiktigheten, - förändring tar tid, likvärdigheten - alla kommunens enheter deltar, den goda framförhållningen - tid för träffar schemaläggs i läsårsplaneringen, avgränsningen – matematik och fokus på taluppfattning samt att projektidén är väl känd - projektet är allas angelägenhet (verksamhetschefens, utvecklingsledarens, rektorernas och lärarnas och lärosätets).

Bron mellan Vaggeryds kommun och Högskolan för Lärande och Kommunikation där ULF-projekt bedrivs har blivit mer stabil. Samarbetet fortsätter att utvecklas beroende av den täta kontakt som finns etablerat mellan lärosätets forskningsmiljö, lektor och verksamhetschef i samverkande kommun.

I konferenspresentationen delges erfarenheter från projektet utifrån såväl ett huvudmanna- som från ett lärosätesperspektiv.

##### National Category
Educational Sciences
##### Identifiers
urn:nbn:se:hj:diva-55938 (URN)
##### Conference
Forskningsbaserad undervisning – teori och praktik i samverkan, Jönköping University, 9 november 2021
Available from: 2022-02-23 Created: 2022-02-23 Last updated: 2022-02-23Bibliographically approved
Ekdahl, A.-L. (2021). Different learning possibilities from the same activity: Swedish preschool teachers’ enactment of a number relation activity. Scandinavian Journal of Educational Research, 65(4), 601-614
Open this publication in new window or tab >>Different learning possibilities from the same activity: Swedish preschool teachers’ enactment of a number relation activity
2021 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 65, no 4, p. 601-614Article in journal (Refereed) Published
##### 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, 2021
##### 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)HOA;;1372633 (Local ID)HOA;;1372633 (Archive number)HOA;;1372633 (OAI)
Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2021-12-13Bibliographically approved
Ekdahl, A.-L., Nord, M. & Kullberg, A. (2021). Different opportunities to learn subtraction bridging through ten in grade 1. In: EARLI2021 Book of abstracts: . Paper presented at 19th Biennial EARLI Conference, 23-27 August 2021 (pp. 36-36).
Open this publication in new window or tab >>Different opportunities to learn subtraction bridging through ten in grade 1
2021 (English)In: EARLI2021 Book of abstracts, 2021, p. 36-36Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

Teaching addition and subtraction using 10 as a benchmark is seen as a powerful strategy for advancing pupils’ learning of arithmetic skills when solving tasks like 13-5. Using 10 as a benchmark for solving the task entails for example that the pupils need to be aware of that 5 can be partitioned into 3 and 2, and that the task may be solved in two steps, 13-3=10, and 10-2=8. In this study two lessons in two grade 1 classes, taught by different teachers, are analyzed on a finegrained level. Our aim is to exemplify and discuss how 10 as a benchmark is used in teaching subtraction bridging through ten and what that may imply for pupils’ learning. Our research question is; What different opportunities to learn ‘10 as a benchmark’ are offered in two lessons of subtraction in the number range of 1 to 20? Variation theory (Marton, 2015) is the theoretical framework used for analysis. The analysis shows how different opportunities to learn subtraction bridging through ten are offered in the lessons by the aspects of the content brought to the fore for the pupils to experience.

##### Keywords
Mathematics, Numeracy, Phenomenography, Primary Education
Didactics
##### Identifiers
urn:nbn:se:hj:diva-54889 (URN)
##### Conference
19th Biennial EARLI Conference, 23-27 August 2021
##### Note

The conference was held online.

Available from: 2021-10-18 Created: 2021-10-18 Last updated: 2022-12-13Bibliographically approved

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