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- Björklund, Camilla, 1977, et al.
(författare)
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Implementing a structural approach in preschool number activities. Principles of an intervention program reflected in learning
- 2021
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Ingår i: Mathematical Thinking and Learning. - : Informa UK Limited. - 1098-6065 .- 1532-7833. ; 23:1, s. 72-94
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Björklund, Camilla, 1977, et al.
(författare)
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Preschool class students’ discernment of number structure in a spatial pattern.
- 2024
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Ingår i: In Häggström, J., Kilhamn, C., Mattsson, L., Palmér, H., Perez, M., Pettersson. K., Röj-Lindberg, A.-S. & Teledahl, A. (Eds.), Mediating mathematics. Proceedings of MADIF14 (pp. 85–96).. - : SMDF.
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Konferensbidrag (refereegranskat)
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| 6. |
- Björklund, Camilla, 1977, et al.
(författare)
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Preschoolers’ ways of experiencing numbers
- 2022
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Ingår i: LUMAT. - : University of Helsinki. - 2323-7112. ; 10:2, s. 84-110
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Björklund, Camilla, et al.
(författare)
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Teaching finger patterns for arithmetic development to preschoolers
- 2018
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 8. |
- Björklund, Camilla, 1977, et al.
(författare)
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Teaching finger patterns for arithmetic development to preschoolers
- 2018
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Ingår i: Proceedings of MADIF 11The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, January 23–24, 2018. - Borås, Sweden : Stema Specialtryck AB. - 1651-3274. - 9789198402421
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Konferensbidrag (refereegranskat)
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| 9. |
- Ekdahl, Anna-Lena, et al.
(författare)
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”10-masken” och förskolebarns lärande i målstyrda processer
- 2018
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Konferensbidrag (populärvet., debatt m.m.)abstract
- 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.
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| 10. |
- Ekdahl, Anna-Lena
(författare)
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6-year-olds’ different ways of reasoning about a larger collection of items
- 2023
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Ingår i: EARLI 2023. ; , s. 125-125
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Konferensbidrag (refereegranskat)abstract
- 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.
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