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Implementing a structural approach in preschool number activities: Principles of an intervention program reflected in learning
Department of Education, Communication and Learning, University of Gothenburg, Gothenburg, Sweden.
Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.ORCID iD: 0000-0001-7556-7974
2020 (English)In: Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

Place, publisher, year, edition, pages
Taylor & Francis, 2020.
Keywords [en]
Arithmetic skills, early childhood education, intervention, variation theory of learning
National Category
Didactics Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-46896DOI: 10.1080/10986065.2020.1756027OAI: oai:DiVA.org:hj-46896DiVA, id: diva2:1372640
Note

Included in doctoral thesis in manuscript form with the title "Implementing a structural approach in preschool number activities: Effects of an intervention program".

Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2020-05-15
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: 2019-11-25Bibliographically approved

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Ekdahl, Anna-LenaRunesson Kempe, Ulla

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