| 1. |
- Nyman, Rimma, Doktor, et al.
(author)
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Rika lösningar på rika problem : Tornet
- 2018
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In: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 45:4, s. 35-40
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Journal article (pop. science, debate, etc.)
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| 2. |
- Nyman, Rimma, et al.
(author)
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Rika lösningar på rika problem : att dela smörgåsar
- 2016
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In: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 199:3, s. 21-24
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Journal article (pop. science, debate, etc.)abstract
- I tre artiklar med början i denna vill vi ta upp erfarenheter från att ha arbetat med rika matematiska problem. Först ut är vår beskrivning av hur vi engagerade lärare, lärarstudenter och deras elever i problemet Att dela smörgåsar.
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| 3. |
- Nyman, Rimma, et al.
(author)
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Rika lösningar på rika problem : att välja glasskulor
- 2018
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In: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 45:1, s. 9-12
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Journal article (pop. science, debate, etc.)abstract
- I en serie av tre artiklar tar vi upp erfarenheter från arbete med rika matematiska problem. I den förra artikeln presenterade vi problemet Att dela smörgåsar. I denna andra del har vi valt en enkel variant av ett klassiskt kombinatorikproblem i en elevnära kontext. Vi har samlat in lösningar från elever i årskurs 2–3 och synliggör olika uttrycksformer.
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| 4. |
- Nyman, Rimma, 1983, et al.
(author)
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To set an example: shifts in awareness when working with Venn diagrams
- 2018
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In: Matematikdidaktiska forskningsseminariet MADIF-11. - : Svensk förening för MatematikDidaktisk Forskning - SMDF. ; , s. 223-223
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Conference paper (other academic/artistic)abstract
- Venn diagrams and basic set theory can serve as a tool for pre-service teachers to grasp complex networks of mathematical concepts, such as different quad-rilaterals (Moyer & Bolyard, 2003). Basic set theoretic concepts carry intui-tive meanings (Bagni, 2006), and Venn diagrams where the interior of closed plane curves represent sets, are simple and non-controversial, even for children (Freudenthal, 1969). Previous research is inconclusive regarding the benefit of Venn diagrams (Moyer and Bolyard, 2003). As a reoccurring part of a mathematics course in the primary teacher educa-tion, two lectures and associated workshops have introduced basic set theo-retical concepts and Venn diagrams to the pre-service teacher. The discovery of objects belonging to several sets seemed unproblematic in the first work-shop, the understanding of intersection became an obstacle when working with numerical problems. We conclude that working with properties of objects is not enough to under-stand set intersection. In order to support their future students’ mathematical development, pre-service teachers need to be aware of their awareness when working with problems (awareness-in-action), but also of this awareness in turn (awareness-in-discipline) (Mason, 2011).
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| 5. |
- Säfström, Anna Ida, Doktor, 1984-
(author)
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A competency framework for analysis of mathematical practice
- 2013
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In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. - Kiel : IPN, Leibniz Institute for Science and Mathematics Education. - 9783890882901 - 3890882900 ; , s. 129-136
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Conference paper (peer-reviewed)
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| 6. |
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| 7. |
- Säfström, Anna Ida, Doktor, 1984-, et al.
(author)
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Embodied fractions : Conceptual difficulties in the light of grounding metaphors
- 2018
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In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. - Umeå : PME. - 9789176019061 ; , s. 287-287
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Conference paper (peer-reviewed)abstract
- Fractions and rational numbers are known to be hard to both teach and learn, as there are many conceptual difficulties concerning fractions. For example, pupils may interpret the entirety of a picture as the whole (Mack, 1990), or seeing a part as a fourth as long as the whole is divided in four parts, regardless of the size of the parts (Ball, 2007). A recent study has revealed additional difficulties: Seeing fractions as divisions may hinder pupils to recognise one of the parts as ¼, and claim that it is the partition that is ¼. The role of numerator and denominator can be mixed up, or the denominator may be seen as the remaining parts, resulting in a picture of 2 fifths to be named 2/3. Pupils can also claim that a fraction has a specific representation, for example that it should be the upper right fourth of a circle that should be shaded, in order for the picture to represent one fourth. One possible reason for misconceptions is stereotypical or restricted use of representations of rational numbers, especially area models (Zhang, Clements & Ellerton, 2015). However, if the number line is introduced, there is a risk that the difficulties are transferred to the new representation. In the recent study, some pupils saw the number line as a whole, and place one half at the centre, regardless of the part of the line visible.In this study, we relate conceptual difficulties concerning fractions to Lakoff and Núñez (2000) four grounding metaphors for numbers, by analysing the underlying metaphors of visual models used by pupils when the difficulties manifest. The results give implications for the introduction of fractions in the early years of elementary school. Our poster will present how misconceptions can manifest in area models and on the number line, how these misconceptions are related to the metaphor implicitly used in the models, and suggested activities where metaphors aid the understanding of fractions.
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| 8. |
- Säfström, Anna Ida, Doktor, 1984-, et al.
(author)
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Implementing alternative models for introducing multiplication
- 2019
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In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education. - : European Society for Research in Mathematics Education. - 9789073346758 ; , s. 4447-4454
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Conference paper (peer-reviewed)abstract
- The research literature provides plenty of examples of epistemological analyses of multiplication and descriptions of the complexity of the conceptual field of multiplication. Nevertheless, multiplication is often introduced as repeated addition, although decades of research have identified this pedagogical choice as leading to persistent problems in students’ conceptualisation of multiplication. In this paper, we describe a teaching design that aims to implement theoretical and empirical research results regarding multiplication in classroom practice. Within our design, models in the form of iconic representations serve as a means for creating patterns that make multiplicative invariants and structures visible. The teaching we have designed is currently tested in a mid-scale randomized controlled trial and in a large-scale professional development project.
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| 9. |
- Säfström, Anna Ida, Doktor, 1984-
(author)
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Preschoolers exercising mathematical competencies
- 2018
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In: Nordisk matematikkdidaktikk, NOMAD. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 23:1, s. 5-27
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Journal article (peer-reviewed)abstract
- The mathematical ideas that emerge in children’s free and guided play can be both complex and sophisticated, and if they are linked to formal mathematics, they can be a powerful basis for mathematical development. To form such links, one needs knowledge of how children use and express these ideas. This is especially true in the intersection of arithmetic and geometry, where the intermingling of numerical and spatial concepts and skills is not yet fully understood. This study aims to gain understanding of children’s mathematical practices by describing the interplay of key mathematical ideas, and more specifically how young children exercise mathematical competencies in the intersection of early arithmetic and geometry. The results show that children can use spatial representations when reasoning about numbers, and that they are able to connect spatial and numerical structures. Furthermore, it is shown that children not only use and invent effective procedures, but also are able to explain, justify and evaluate such procedures.
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| 10. |
- Säfström, Anna Ida, Doktor, 1984-, et al.
(author)
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Problem solving as a learning activity : an initial theoretical model
- 2020
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Conference paper (peer-reviewed)abstract
- Problem solving has been considered the gold standard of mathematical activity. It is a goal of mathematics education that students become problem solvers, and it is suggested that problem solving is a superior method for learning mathematics. However, the arguments supporting the claim that problem solving leads to better learning are often vague. In specific studies, problem solving often constitutes mere one part of a compound design, making it difficult to determine the specific contribution of problem solving. The aim of this paper is to develop an initial theoretical model for problem solving as a learning activity, based on existing frameworks and previous research. Suggestions for how this model could be empirically tested are also discussed.
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