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Ekdahl, A.-L. & Lundberg, B. (2024). Att utveckla undervisning om tal och talrelationer i förskoleklass. Forskning om undervisning och lärande, 12(2), 85-107
Open this publication in new window or tab >>Att utveckla undervisning om tal och talrelationer i förskoleklass
2024 (Swedish)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 12, no 2, p. 85-107Article in journal (Refereed) Published
Abstract [sv]

Syftet med artikeln är att bidra med kunskap om hur en intervention, med fokus på undervisning om tal och talrelationer i förskoleklass, kan utveckla matematikundervisning. I interventionen har en undervisningsutvecklande modell tagits som utgångspunkt, där planering, genomförande och reflektion över undervisning har skett i en cyklisk process tillsammans med kollegor och forskare. Då interventionen sträckte sig över fyra år, gavs möjligheter att identifiera och förändra komponenterna i relation till syfte och kontext. En nyckelkomponent är de reflektionsunderlag som utvecklades och hur de bidrog till reflektion kring undervisning och lärande. De vetenskapligt förankrade aktiviteterna som förfinades är en annan nyckelkomponent. Kunskapsprodukten som har genererats innehåller en undervisningsguide med beprövade och designade undervisningsaktiviteter, med tillhörande reflektioner kring lärares matematikdidaktiska handlingar samt den undervisningsutvecklande modellen.

Abstract [en]

Developing the teaching of numbers and number relations in preschool class

The purpose of this article is to contribute knowledge about how an intervention, focused on teaching numbers and number relations in preschool class, can develop teaching. In the intervention, we employed a practice-oriented model based on planning, teaching, evaluating, and reflecting on teaching in an iterative process, in collaboration with colleagues and researchers. We carried out this intervention over four years, during which we identified key components of the model that were essential for the development of mathematics teaching. We also changed these components based on the purpose and local context. A key component is the reflection documents that were developed and how they contributed to reflection on teaching and learning. Another key component is the research-based activities that we refined. The knowledge product includes a teaching guide with documented and designed teaching activities with reflections on the teacher's enactment of the mathematical activities as well as the teaching model.

Place, publisher, year, edition, pages
Lärarstiftelsen, 2024
Keywords
Mathematics, Preschool class, Teaching development, Knowledge product, Number relations, matematik, förskoleklass, intervention, undervisningsutveckling, kunskapsprodukt, undervisning om talrelationer
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-66254 (URN)10.61998/forskul.v12i2.23896 (DOI)POA;;973111 (Local ID)POA;;973111 (Archive number)POA;;973111 (OAI)
Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Björklund, C., Elofsson, J., Kullberg, A., Ekdahl, A.-L., Runesson Kempe, U. & Alkhede, M. (2024). Förskoleklasselevers användning av talstrukturer. Forskning om undervisning och lärande, 12(2), 31-45
Open this publication in new window or tab >>Förskoleklasselevers användning av talstrukturer
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2024 (English)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 12, no 2, p. 31-45Article in journal (Refereed) Published
Abstract [sv]

I artikeln presenteras och diskuteras förskoleklasselevers förmåga att se och använda talstrukturer för att bestämma antal, samt hur förmågan utvecklas efter att de deltagit i interventioner under ett läsår. Totalt intervjuades 361 elever som deltagit i interventionerna alternativt i vanlig förskoleklassundervisning. Intervjuerna gjordes under tidig hösttermin samt vid förskoleklassårets slut. En specifik uppgift innehållande ett spatialt mönster i intervjumaterialet utgör underlag för att synliggöra hur eleverna erfar och använder talstrukturer, både kvantitativt och kvalitativt. Analysen tar vidare avstamp i en variationsteoretisk syn på lärande, där sättet att erfara ett fenomen, i detta fall tal och strukturer så som de framträder i en figur ordnad i ett spatialt mönster, har betydelse för vad eleven kan göra med tal, till exempel på vilket sätt man kan bestämma antal. Särskilt diskuteras vilka implikationer resultaten har för utvecklingen av matematikundervisning i förskoleklass och elevers fortsatta aritmetiklärande.

Abstract [en]

Developing mathematics education contributing to equity in preschool class

In the article, we present and discuss preschool class students’ ability to see and use number structures to determine number and how this ability develops after participating in interventions during one academic year. A total of 361 students who participated in the interventions or in regular preschool class teaching were interviewed early in the autumn term and at the end of the preschool class year. One task containing a spatial pattern in the interview material forms the basis for identifying how students experience and use number structures, quantitatively and qualitatively. The analysis is further based on a variation theory view of learning, where the way of experiencing a phenomenon, in this case numbers and structures as they appear in a figure arranged in a spatial pattern, has significance for what the student can do with numbers, e.g., how to determine numbers. In particular, implications of the results for developing mathematics teaching in preschool class and students continued arithmetic learning are discussed.

Place, publisher, year, edition, pages
Lärarstiftelsen, 2024
Keywords
Number structures, Interventions, Preschool class, Student interviews, talstrukturer, interventioner, förskoleklass, elevintervjuer
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-66253 (URN)10.61998/forskul.v12i2.23890 (DOI)POA;;973103 (Local ID)POA;;973103 (Archive number)POA;;973103 (OAI)
Funder
Swedish Research Council, 2020-03712
Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Ekdahl, A.-L. & Kerekes, K. (2024). Implementing a French teaching program in a Swedish grade 1 classroom. In: Johan Häggström, Cecilia Kilhamn, Linda Mattsson, Hanna Palmér, Miguel Perez, Kerstin Pettersson, Ann-Sofi Röj-Lindberg & Anna Teledahl (Ed.), Proceedings of MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education Örebro, March 19–20, 2024: . Paper presented at MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education, Örebro, Sweden, March 19–20, 2024 (pp. 152-152). Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF
Open this publication in new window or tab >>Implementing a French teaching program in a Swedish grade 1 classroom
2024 (English)In: Proceedings of MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education Örebro, March 19–20, 2024 / [ed] Johan Häggström, Cecilia Kilhamn, Linda Mattsson, Hanna Palmér, Miguel Perez, Kerstin Pettersson, Ann-Sofi Röj-Lindberg & Anna Teledahl, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2024, p. 152-152Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

In this presentation we share experiences of having implemented a French teaching program in a Swedish grade 1 classroom for the duration of one school year. The French teaching program, Arithmetic and Comprehension at Elementary School (ACE) takes a structural and relational approach to teaching and learning numbers in early grades. The aim of this presentation is to describe the implementation process of the ACE-program in a Swedish context and to discuss how principles of variation theory can develop the program. Following the structure and the principle of the program we found that the program, with small adjustments, is possible to implement in a Swedish grade 1. We suggest that the program may be further developed by adding principles of variation theory.

Place, publisher, year, edition, pages
Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2024
Series
Skrifter från SMDF, E-ISSN 1651-3274 ; 18
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-66257 (URN)978-91-984024-7-6 (ISBN)
Conference
MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education, Örebro, Sweden, March 19–20, 2024
Note

Short communications.

Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Elofsson, J., Runesson Kempe, U., Ekdahl, A.-L. & Björklund, C. (2024). Kartläggning av förskoleklassens matematikundervisning om tal – kvalitativa skillnader och lärandemöjligheter. Forskning om undervisning och lärande, 12(1), 47-68
Open this publication in new window or tab >>Kartläggning av förskoleklassens matematikundervisning om tal – kvalitativa skillnader och lärandemöjligheter
2024 (English)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 12, no 1, p. 47-68Article in journal (Refereed) Published
Abstract [sv]

Under hösten 2021 gjordes en kartläggning av matematikundervisningen i 95 förskoleklasser i syfte att bidra med kunskap om vad kvalitet i undervisning kan innebära och vad elever ges möjligheter att lära om tal, tals egenskaper och dess användning. Analysverktyget "Mediating Primary Mathematics" användes för att identifiera skillnader i undervisningens kvalitet, det vill säga hur ett matematiskt innehåll behandlades och medierades i undervisningen. Resultatet visar på en variation i hur innehållet medieras och därmed vad elever ges möjligheter att lära. Goda undervisningsexempel har observerats, samtidigt som utvecklingsområden identifierats. Artefakter förekommer ofta, men används inte alltid på sätt som synliggör matematiska samband och innebörder. Lösningsmetoder får sällan stå i centrum för undersökning, jämförelse och värdering i undervisningen. Elevinspel bekräftas ofta, samtidigt som det blir tydligt att undervisningen sällan erbjuder utveckling och bearbetning av dessa.

Abstract [en]

Mapping of Preschool Class Mathematics Teaching about Numbers - Qualitative Differences and Learning Opportunities

During the autumn of 2021, an observational study was conducted in 95 Swedish preschool classes with the aim of mapping and describing the quality of teaching. The framework "Mediating Primary Mathematics" was utilized to identify and assess variations in the quality of teaching about numbers, their properties, and usage, that is, how the mathematical content was treated and mediated in the teaching situation. The result revealed variations in how the mathematical content was mediated, which impacted the learning opportunities provided to students. While several examples of high-quality mathematics teaching were observed, areas for improvement were also identified. Artifacts were frequently used in teaching, although their usage did not consistently emphasize mathematical relationships and meanings. Furthermore, teaching rarely emphasized comparison and evaluation of different solution methods. Student contributions were often acknowledged, but it became evident that their input was rarely elaborated upon.

Place, publisher, year, edition, pages
Lärarstiftelsen, 2024
Keywords
Preschool class, Mathematics, Teaching, Quality, Learning opportunities, Numbers, Part-whole relations of numbers, förskoleklass, matematik, undervisning, kvalitet, lärandemöjligheter, tal, tals del-helhetsrelationer
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-66252 (URN)10.61998/forskul.v12i1.22918 (DOI)POA;;973102 (Local ID)POA;;973102 (Archive number)POA;;973102 (OAI)
Funder
Swedish Research Council, 2020-03712
Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Björklund, C., Elofsson, J., Kullberg, A., Ekdahl, A.-L., Runesson Kempe, U. & Alkhede, M. (2024). Preschool class students’ discernment of number structure in a spatial pattern. In: Johan Häggström, Cecilia Kilhamn, Linda Mattsson, Hanna Palmér, Miguel Perez, Kerstin Pettersson, Ann-Sofi Röj-Lindberg & Anna Teledahl (Ed.), Proceedings of MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education Örebro, March 19–20, 2024: . Paper presented at MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education, Örebro, Sweden, March 19–20, 2024 (pp. 85-95). Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF
Open this publication in new window or tab >>Preschool class students’ discernment of number structure in a spatial pattern
Show others...
2024 (English)In: Proceedings of MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education Örebro, March 19–20, 2024 / [ed] Johan Häggström, Cecilia Kilhamn, Linda Mattsson, Hanna Palmér, Miguel Perez, Kerstin Pettersson, Ann-Sofi Röj-Lindberg & Anna Teledahl, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2024, p. 85-95Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we present what 361 preschool class students discern of number structures in a task containing a spatial pattern. The analysis, grounded in the variation theory of learning, focuses on the students’ discernment of composite units as parts of a larger whole. To discern a task as a structure of parts and whole is presumed to be significant for what the student can do with numbers, e.g. to determine the exact number of objects in a spatial pattern. The results reveal four different ways in which students discern structures, each one with implications for the students’ abilities to determine the number of the pattern. The results induce implications for the development of mathematics teaching in preschool classes and also raise further questions for research about students’ arithmetic learning.

Place, publisher, year, edition, pages
Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2024
Series
Skrifter från SMDF, E-ISSN 1651-3274 ; 18
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-66255 (URN)978-91-984024-7-6 (ISBN)
Conference
MADIF 14, The fourteenth research conference of the Swedish Society for Research in Mathematics Education, Örebro, Sweden, March 19–20, 2024
Funder
Swedish Research Council, 2020-03712
Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Ekdahl, A.-L. & Björklund, C. (2024). Teaching number relations with finger patterns when exceeding 10. In: : . Paper presented at The 15th International Congress on Mathematical Education, Sydney, Australia, 7-14 July, 2024.
Open this publication in new window or tab >>Teaching number relations with finger patterns when exceeding 10
2024 (English)Conference paper, Published paper (Refereed)
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-66258 (URN)
Conference
The 15th International Congress on Mathematical Education, Sydney, Australia, 7-14 July, 2024
Available from: 2024-09-20 Created: 2024-09-20 Last updated: 2024-09-20Bibliographically approved
Ekdahl, A.-L., Nord, M. & Kullberg, A. (2024). What matters in teaching for students’ learning opportunities of subtraction in the 1–20 number range?. Scandinavian Journal of Educational Research
Open this publication in new window or tab >>What matters in teaching for students’ learning opportunities of subtraction in the 1–20 number range?
2024 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed) Epub ahead of print
Abstract [en]

Not all students in early grades develop efficient strategies for solving subtraction tasks. In this paper, we examine subtraction teaching in the 1–20 number range. We analyzed two first-grade lessons addressing similar subtraction tasks, using variation theory to identify what aspects of the content were foregrounded in the teaching. The analysis showed that both lessons supported the discernment of aspects of subtraction. However, the learning opportunities differed depending on what aspects the students were enabled to discern, the recurrence and variation of the elicited aspects, and how the teachers made the aspects visible by means of representations. The findings highlight how teaching can make it more likely for students to experience aspects of learning necessary to solve subtraction tasks such as 13–5 = _ . Additionally, the findings show how subtraction can be taught to enhance strategies using number relations that are also useful in higher number ranges.

Place, publisher, year, edition, pages
Taylor & Francis, 2024
Keywords
Subtraction, mathematics teaching, representations, 10 as a benchmark, variation theory, early arithmetic
National Category
Didactics Learning
Identifiers
urn:nbn:se:hj:diva-66534 (URN)10.1080/00313831.2024.2419064 (DOI)001346928200001 ()2-s2.0-85209120574 (Scopus ID)HOA;;66534 (Local ID)HOA;;66534 (Archive number)HOA;;66534 (OAI)
Funder
Swedish Institute for Educational Research, 2018-00038
Available from: 2024-11-06 Created: 2024-11-06 Last updated: 2024-11-29
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: 2024-09-20Bibliographically 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: 2024-09-20Bibliographically 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: 2024-09-20Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-4685-1594

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