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Different learning possibilities from the same activity: Swedish preschool teachers’ enactment of a number relation activity
Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.ORCID iD: 0000-0002-4685-1594
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. Vol. 65, no 4, p. 601-614
Keywords [en]
Variation theory, mathematical activity, in-service preschool teachers, early numbers, part-whole relationship, part-whole relations, finger patterns
National Category
Didactics Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-46895DOI: 10.1080/00313831.2020.1739131ISI: 000523149300001Scopus ID: 2-s2.0-85082747980Local ID: HOA;;1372633OAI: oai:DiVA.org:hj-46895DiVA, id: diva2:1372633
Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2024-09-20Bibliographically approved
In thesis
1. Teaching for the learning of additive part-whole relations: The power of variation and connections
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: 2024-09-20Bibliographically approved

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Ekdahl, Anna-Lena

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