| 1. |
- Al-Murani, Thabit, et al.
(författare)
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Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England
- 2019
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Ingår i: Research in Mathematics Education. - : Informa UK Limited. - 1479-4802 .- 1754-0178. ; 21:1, s. 6-24
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Tidskriftsartikel (refereegranskat)abstract
- We demonstrate the power of Variation Theory as an analytical tool used to understand the underlying conceptual structure of mathematics lessons taught by English primary school teachers. We study excerpts of three lessons that are posted on a professional website. We show how lesson analysis using variation allows us to focus on what is made available to be learnt in the lesson excerpts. We identify some differences in their use of dimensions of variation and the associated ranges of change and discuss how suitable patterns of variation and invariance might differ according to the nature of the learning focus. We reflect on the value of our analytical approach.
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| 2. |
- Berggren, Johannes
(författare)
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An important part of the whole : The role of metaphors in the teaching and learning of mathematics
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This study aims to investigate the role of metaphor in the teaching and learning of mathematics. Two different studies help to fulfil this aim.The first study involves a configurative literature review of empirical mathematics education research where two interpretations of the metaphor concept are applied: conceptual metaphor and extraneous metaphor, with the purpose of distinguishing patterns in metaphor concept use. The analysis found explicit, vague, or absent theoretical definitions of the metaphor concept as well as several metaphor examples, and generated three categories of concept use: 1) Conceptual metaphor, 2) Extraneous metaphor, and 3) Potentially conceptual/extraneous. The review stresses the need for a theoretical and empirical distinction between different types of metaphors, to sharpen the analytical tools available to researchers and, by extension, to more clearly highlight the specific function of metaphor in teachers’ classroom work.The second study examines the presence of three conceptual metaphors as the basis for rational numbers as fractions in Swedish textbooks for years 1–3 and which aspects of fractions are distinguished in the student responses required in these books. The results are related to process-object theory (Sfard, 1991), intending to discern the different degrees of reification of the mathematical objects that hypothetically have the opportunity to develop with the help of these metaphors. The results show, in three of the book series, an abundance of labelling exercises related to the metaphor Arithmetic is object construction, mainly with images of geometric shapes. One book series reversely introduces fractions with The measuring stick metaphor and Arithmetic is motion along a path, with representations of number lines in focus. All in all, there is a significant variation between the textbooks, which could have consequences for instruction.This thesis shows the importance of theoretically distinguishing conceptual metaphor from extraneous metaphor, and of understanding their different roles in a teaching and learning context. The thesis also shows how the conceptual metaphors underlying the mathematical concepts describe different aspects of these concepts and that several conceptual metaphors need to be taken into account, together with a consideration of different degrees of reification of the mathematical objects. In addition, the thesis shows that metaphors, as they are understood in Conceptual metaphor theory, point to similar conceptual and discursive processes that can be found in Sfard’s (1991, 2008) more established theories on mathematical conceptualisation.
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| 3. |
- Bråting, Kajsa, Docent, 1975-, et al.
(författare)
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Exemplifying different methodological approaches of analysing textbooks in mathematics
- 2022
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Ingår i: The relation between mathematics education research and teachers' professional development. - Göteborg : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 1651-3274. - 9789198402452 ; 16, s. 125-129, s. 125-129
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Konferensbidrag (refereegranskat)abstract
- In this symposium, we will discuss different ways of analysing mathematics textbooks from a methodological point of view. The discussion will be based on examples from five separate ongoing analyses of Swedish textbooks divided into two methodological approaches; one where analysis is conducted within an established theoretical framework, and one where analytical tools are constructed through combining aspects of different theories. The symposium will be held at the conference MADIF-13.
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| 4. |
- Bråting, Kajsa, 1975-, et al.
(författare)
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Exploring the intersection of algebraic and computational thinking
- 2021
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Ingår i: Mathematical Thinking and Learning. - : Informa UK Limited. - 1098-6065 .- 1532-7833. ; 23:2, s. 170-185
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Tidskriftsartikel (refereegranskat)abstract
- This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of programming activities suggested for school mathematics are discussed in detail. We argue that although the semiotic representations of programming languages are similar to algebraic notation the meanings of several concepts in these two domains differ. In a learning perspective these differences must be taken into account, especially considering that students have to convert between registers with both overlapping and specific meanings.
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| 5. |
- Bråting, Kajsa, et al.
(författare)
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Inledning
- 2021
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Ingår i: Programmering i skolmatematiken - möjligheter och utmaningar. - Uppsala : Studentlitteratur AB. ; , s. 17-24
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Bokkapitel (refereegranskat)
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| 6. |
- Bråting, Kajsa, 1975-, et al.
(författare)
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Integrating programming in Swedish school mathematics : description of a research project
- 2020
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Ingår i: Sustainable mathematics education in a digitalized World. - 9789198402445 ; , s. 101-110
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Konferensbidrag (refereegranskat)abstract
- This paper describes a new research project investigating the implementation of programming in Swedish school mathematics, specifically in relation to algebra learning. Based on Chevallard’s framework of transposition of knowledge, we investigate what types of activities and systems of representations are introduced and argued for as programming makes its way into mathematics teaching, and what these may entail.Tentative results reveal syntactic and semantic differences between programming and algebra that may cause problems for students. Interviews with teachers show that they seek inspiration and activities from social media and internet rather than textbooks and other published teaching material.
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| 7. |
- Bråting, Kajsa, 1975, et al.
(författare)
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Integrating programming in Swedish school mathematics: description of a research project
- 2021
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Ingår i: Y. Liljekvist, L. Björklund Boistrup, J. Häggström, L. Mattsson, O. Olande, H. Palmér (Eds.), Sustainable mathematics education in a digitalized world. Proceedings of MADIF12. - : SMDF. - 1651-3274. - 9789198402445
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Konferensbidrag (refereegranskat)abstract
- This paper describes a new research project investigating the implementation of programming in Swedish school mathematics, specifically in relation to algebra learning. Based on Chevallard’s framework of transposition of knowledge, the project investigates what types of activities and systems of representations are introduced and argued for as programming makes its way into mathematics teaching, and what these may entail. Tentative results reveal syntactic and semantic differences between programming and algebra that may cause problems for students. Interviews with teachers show that they seek inspiration and activities from social media and internet rather than textbooks and other published teaching material.
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| 8. |
- Bråting, Kajsa, Docent, 1975-, et al.
(författare)
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Mathematical competencies and programming : The Swedish case
- 2023
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Ingår i: Mathematical competencies in the digital era. - Cham : Springer. - 9783031101403 - 9783031101410 ; , s. 293-310
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Bokkapitel (refereegranskat)abstract
- In this chapter, we consider opportunities and challenges of integrating programming in school mathematics by looking closer at the Swedish case. Especially, we aim to unpack how the integration of programming in mathematics can affect students’ opportunities to develop mathematical competencies. Three examples taken from a Swedish research project are described and discussed in detail. In the first example, we focus on differences regarding syntax and semantics in programming and mathematics, relevant in a learning perspective. In the second and third examples, we highlight the teachers’ views of how programming may enhance the traditional learning of school mathematics, and describes one particular lesson where students solve pattern problems in Python. Each example is discussed in relation to different mathematical competencies.
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| 9. |
- Bråting, Kajsa, 1975, et al.
(författare)
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Programming and mathematical competencies: the case of Sweden
- 2022
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Ingår i: U.T. Jankvist & E. Geraniou (red.), Mathematical Competencies in the Digital Era from a Networking of Theories Point of View. - : Springer. - 9783031101403 ; , s. 293-310
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Bokkapitel (refereegranskat)abstract
- The aim of this chapter is to gain knowledge about how the Swedish way of implementing programming affects students’ opportunities to develop mathematical competencies.
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| 10. |
- Bråting, Kajsa, et al.
(författare)
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Syntax och semantik i programmering och matematik
- 2021
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Ingår i: Programmering i skolmatematiken - möjligheter och utmaningar. - : Studentlitteratur AB. ; , s. 57-70
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Bokkapitel (refereegranskat)abstract
- Det här kapitlet jämför programmering och matematik ur ett språkligt och begreppsligt perspektiv. Genom att betrakta ett programmeringsspråk som en ny form av matematisk representation menar författarna att elevers erfarenhet av programmering kommer att påverka deras förståelse av matematiska begrepp. Eftersom programmeirng i den svenska matematikkursplanen för grundskolan har skrivits in som en del av det centrala innehållet i algebra, undersöker författarna specifikt begreppen variabel och funktion, samt användningen av algebraiska symboler, framförallt likhetstecknet. Två undervisningsexempel analyseras i detalj, ett program i Scratch och ett program i JavaScript. Författarna argumenterar för att lärare behvöer känna till närr symboler har olika betydelser i programmering respektive matematik, och hurbetydelsen av matematiska begrepp, såsom variable och funktion, får delvis andra innebörder i programmering.
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