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Weaving in connections: Studying changes in early grades additive relations teaching
Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Praktiknära utbildningsforskning (PUF), Matematikdidaktisk forskning. Wits School of Education, University of the Witwatersrand, South Africa.
Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Praktiknära utbildningsforskning (PUF), Matematikdidaktisk forskning. Wits School of Education, University of the Witwatersrand, South Africa.ORCID-id: 0000-0002-6453-1623
Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Praktiknära utbildningsforskning (PUF), Matematikdidaktisk forskning. Wits School of Education, University of the Witwatersrand, South Africa.ORCID-id: 0000-0001-7556-7974
Wits School of Education, University of the Witwatersrand, South Africa.
2018 (Engelska)Ingår i: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 8, nr 1, artikel-id a540Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

In this article, we present aspects of teaching that draw attention to connections – both within and between examples – in order to explore the potential objects of learning that are brought into being in the classroom space and thus what is made available to learn. Our focus is on exploring differences in teaching over time, in the context of learning study style development activity of additive relation problems in three Grade 3 classes in South Africa. In a context where highly-localised and fragmented instruction has been noted, this study reports on the nature and extent of changes in connections in instruction over time. The application of a coding framework focused on simultaneity and connections in teaching points to a richer range of structural relationships within examples, and more connecting work between examples in the second year in comparison to the first year.

Ort, förlag, år, upplaga, sidor
University of Johannesburg , 2018. Vol. 8, nr 1, artikel-id a540
Nyckelord [en]
Connections; Example space; Additive relations; Primary mathematics; Part-part-whole teaching; Missing number problem teaching; Changes in teaching; Variation theory; South Africa
Nationell ämneskategori
Didaktik
Identifikatorer
URN: urn:nbn:se:hj:diva-39015DOI: 10.4102/sajce.v8i1.540ISI: 000430807400001Lokalt ID: HLKPUFISOAI: oai:DiVA.org:hj-39015DiVA, id: diva2:1191251
Tillgänglig från: 2018-03-16 Skapad: 2018-03-16 Senast uppdaterad: 2019-11-25Bibliografiskt granskad
Ingår i avhandling
1. Teaching for the learning of additive part-whole relations: The power of variation and connections
Öppna denna publikation i ny flik eller fönster >>Teaching for the learning of additive part-whole relations: The power of variation and connections
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Jönköping: Jönköping University, School of Education and Communication, 2019. s. 121
Serie
Dissertation. School of Education and Communication, ISSN 1652-7933 ; 038
Nyckelord
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
Nationell ämneskategori
Didaktik Matematik
Identifikatorer
urn:nbn:se:hj:diva-46899 (URN)978-91-88339-28-7 (ISBN)978-91-88339-29-4 (ISBN)
Disputation
2019-12-13, Hb116, School of Education and Communication, Jönköping, 13:00 (Engelska)
Opponent
Handledare
Tillgänglig från: 2019-11-25 Skapad: 2019-11-25 Senast uppdaterad: 2019-11-25Bibliografiskt granskad

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Ekdahl, Anna-LenaVenkat, HamsaRunesson Kempe, Ulla

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