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Teaching for the learning of additive part-whole relations: The power of variation and connections
Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
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 [en]
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: urn:nbn:se:hj:diva-46899ISBN: 978-91-88339-28-7 (print)ISBN: 978-91-88339-29-4 (electronic)OAI: oai:DiVA.org:hj-46899DiVA, id: diva2:1372663
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
List of papers
1. Coding teaching for simultaneity and connections: Examining teachers’ part-whole additive relations instruction
Open this publication in new window or tab >>Coding teaching for simultaneity and connections: Examining teachers’ part-whole additive relations instruction
2016 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 93, no 3, p. 293-313Article in journal (Refereed) Published
Abstract [en]

In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations instruction were developed. Teachers’ use of multiple representations within an example, attention to part-whole relations within examples, and relations between multiple examples were identified, with teachers’ linking actions in speech or gestures pointing to connections between these. In this article, the coding framework is detailed and exemplified in the context of a structural approach to part-whole teaching in six South African grade 3 lessons. The coding framework enabled us to see fine-grained differences in teachers’ handling of part-whole relations related to simultaneity of, and connections between, representations and examples as well as within examples. We went on to explore the associations between the simultaneity and connections seen through the coding framework in sections of teaching and students’ responses on worksheets following each teaching section.

Keywords
Additive relations, Coding framework, Connections, Primary mathematics, Simultaneity, South Africa, Variation theory
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-31993 (URN)10.1007/s10649-016-9700-0 (DOI)2-s2.0-84965019191 (Scopus ID)HLKSkolnäraIS (Local ID)HLKSkolnäraIS (Archive number)HLKSkolnäraIS (OAI)
Available from: 2016-10-17 Created: 2016-10-17 Last updated: 2019-11-25Bibliographically approved
2. Weaving in connections: Studying changes in early grades additive relations teaching
Open this publication in new window or tab >>Weaving in connections: Studying changes in early grades additive relations teaching
2018 (English)In: South African Journal of Childhood Education, ISSN 2223-7674, E-ISSN 2223-7682, Vol. 8, no 1, article id a540Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
University of Johannesburg, 2018
Keywords
Connections; Example space; Additive relations; Primary mathematics; Part-part-whole teaching; Missing number problem teaching; Changes in teaching; Variation theory; South Africa
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-39015 (URN)10.4102/sajce.v8i1.540 (DOI)000430807400001 ()HLKPUFIS (Local ID)HLKPUFIS (Archive number)HLKPUFIS (OAI)
Available from: 2018-03-16 Created: 2018-03-16 Last updated: 2019-11-25Bibliographically approved
3. Different learning possibilities from the same activity - Swedish preschool teachers’ enactment of a number relation activity
Open this publication in new window or tab >>Different learning possibilities from the same activity - Swedish preschool teachers’ enactment of a number relation activity
(English)Manuscript (preprint) (Other academic)
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46895 (URN)
Note

In review.

Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2019-11-25
4. Implementing a structural approach in preschool number activities: Effects of an intervention program
Open this publication in new window or tab >>Implementing a structural approach in preschool number activities: Effects of an intervention program
(English)Manuscript (preprint) (Other academic)
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-46896 (URN)
Note

In review.

Available from: 2019-11-25 Created: 2019-11-25 Last updated: 2019-11-25

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Ekdahl, Anna-Lena

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89101112131411 of 32
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