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Säfström, Anna IdaORCID iD iconorcid.org/0000-0003-4984-6376
Publications (7 of 7) Show all publications
Säfström, A. I. & Nagy, C. (2018). Embodied fractions: Conceptual difficulties in the light of grounding metaphors. In: Ewa Bergqvist, Magnus Österholm, Carina Granberg & Lovisa Sumpter (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at 42nd Conference of the International Group for the Psychology of Mathematics Education (PME42), July 3-8, 2018, Umeå, Sweden (pp. 287-287). Umeå, 5
Open this publication in new window or tab >>Embodied fractions: Conceptual difficulties in the light of grounding metaphors
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg & Lovisa Sumpter, Umeå, 2018, Vol. 5, p. 287-287Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Umeå: , 2018
Keywords
bråk, representationer, metaforer
National Category
Didactics
Identifiers
urn:nbn:se:hh:diva-37543 (URN)
Conference
42nd Conference of the International Group for the Psychology of Mathematics Education (PME42), July 3-8, 2018, Umeå, Sweden
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2018-09-20Bibliographically approved
Säfström, A. I. (2018). Preschoolers exercising mathematical competencies. Nordisk matematikkdidaktikk, 23(1), 5-27
Open this publication in new window or tab >>Preschoolers exercising mathematical competencies
2018 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 23, no 1, p. 5-27Article in journal (Refereed) Published
Abstract [en]

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 geometryThe 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.

Place, publisher, year, edition, pages
Göteborg: Nationellt centrum för matematikutbildning (NCM), 2018
National Category
Didactics
Identifiers
urn:nbn:se:hh:diva-36554 (URN)
Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-04-19Bibliographically approved
Nyman, R., Säfström, A. I. & Taflin, E. (2018). Rika lösningar på rika problem – att välja glasskulor. Nämnaren : tidskrift för matematikundervisning, 45(1), 9-12
Open this publication in new window or tab >>Rika lösningar på rika problem – att välja glasskulor
2018 (Swedish)In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 45, no 1, p. 9-12Article in journal (Other (popular science, discussion, etc.)) Published
Abstract [sv]

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.

Place, publisher, year, edition, pages
Göteborg: Nationellt centrum för matematikutbildning (NCM), 2018
National Category
Educational Sciences
Identifiers
urn:nbn:se:hh:diva-36407 (URN)
Available from: 2018-03-11 Created: 2018-03-11 Last updated: 2018-03-12Bibliographically approved
Säfström, A. I. (2017). Progression i högre utbildning. Högre Utbildning, 7(1), 56-75
Open this publication in new window or tab >>Progression i högre utbildning
2017 (Swedish)In: Högre Utbildning, ISSN 2000-7558, E-ISSN 2000-7558, Vol. 7, no 1, p. 56-75Article in journal (Refereed) Published
Abstract [sv]

Syftet med denna studie är att undersöka innebörden och användningen av ordet progressioninom högre utbildning. För att ta reda på i vilka betydelser ordet progression används, och huranvändningen av ordet har förändrats över tid, genomförs här en systematisk begreppsanalysav vetenskapliga texter, statliga styrdokument och texter hämtade från svenska lärosätens hemsidor.Som utgångspunkt för analysen särskiljs progression i dess klassiska betydelse och progressionsom en kvalitet i utbildning, undervisning och läromedel. Resultatet av analysen visaratt ordet progression används i allt högre utsträckning, men ofta med oklar betydelse. Detframkom också att det har skett en förskjutning mot användning av ordet progression somkvalitet hos utbildning. En definition av utbildningsprogression föreslås, och konsekvenser förhögre utbildning diskuteras. ©2017 Anna Ida Säfström

Place, publisher, year, edition, pages
Oslo: Nordic Open Access Scholarly Publishing (NOASP), 2017
Keywords
progression, högre utbildning, systematisk begreppsanalys
National Category
Educational Sciences
Identifiers
urn:nbn:se:hh:diva-35084 (URN)10.23865/hu.v7.955 (DOI)
Available from: 2017-09-29 Created: 2017-09-29 Last updated: 2017-10-02Bibliographically approved
Nyman, R., Säfström, A. I. & Taflin, E. (2016). Rika lösningar på rika problem: att dela smörgåsar. Nämnaren : tidskrift för matematikundervisning, 199(3), 21-24
Open this publication in new window or tab >>Rika lösningar på rika problem: att dela smörgåsar
2016 (Swedish)In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 199, no 3, p. 21-24Article in journal (Other (popular science, discussion, etc.)) Published
Place, publisher, year, edition, pages
Göteborg: Nationellt centrum för matematikutbildning (NCM), 2016
Keywords
Rika problem, bråk, proportionalitet
National Category
Social Sciences
Identifiers
urn:nbn:se:hh:diva-32383 (URN)
Available from: 2016-11-10 Created: 2016-11-10 Last updated: 2017-11-29Bibliographically approved
Säfström, A. I. (2013). A competency framework for analysis of mathematical practice. In: Anke M. Lindemeier, Aiso Heinze (Ed.), "Mathematics learning across the life span": proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (PME 37), Kiel, Germany, July 28-August 02, 2013: Vol. 4. Paper presented at 37th Annual Conference of the International Group for the Psychology of Mathematics Education, "Mathematics learning across the life span" (PME 37), Kiel, Germany, July 28-August 2, 2013 (pp. 4-129-4-136). Kiel: IPN, Leibniz Institute for Science and Mathematics Education
Open this publication in new window or tab >>A competency framework for analysis of mathematical practice
2013 (English)In: "Mathematics learning across the life span": proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (PME 37), Kiel, Germany, July 28-August 02, 2013: Vol. 4 / [ed] Anke M. Lindemeier, Aiso Heinze, Kiel: IPN, Leibniz Institute for Science and Mathematics Education , 2013, p. 4-129-4-136Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Kiel: IPN, Leibniz Institute for Science and Mathematics Education, 2013
National Category
Didactics
Identifiers
urn:nbn:se:hh:diva-25399 (URN)978-3-89088-290-1 (ISBN)3890882900 (ISBN)
Conference
37th Annual Conference of the International Group for the Psychology of Mathematics Education, "Mathematics learning across the life span" (PME 37), Kiel, Germany, July 28-August 2, 2013
Available from: 2014-05-22 Created: 2014-05-22 Last updated: 2015-12-11Bibliographically approved
Säfström, A. I. (2012). Describing Mathematical Competencies Among Young Children. In: G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula-Sormunen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero & K. Wæge (Ed.), Proceedings of NORMA 11: The Sixth Nordic Conference on Mathematics Education in Reykjavík, May 11.-14. 2011. Paper presented at The Sixth Nordic Conference on Mathematics Education (NORMA 11), Reykjavík, Iceland, May 11-14, 2011 (pp. 710-710). Reykjavík: University of Iceland Press
Open this publication in new window or tab >>Describing Mathematical Competencies Among Young Children
2012 (English)In: Proceedings of NORMA 11: The Sixth Nordic Conference on Mathematics Education in Reykjavík, May 11.-14. 2011 / [ed] G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula-Sormunen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero & K. Wæge, Reykjavík: University of Iceland Press, 2012, p. 710-710Conference paper, Oral presentation with published abstract (Refereed)
Place, publisher, year, edition, pages
Reykjavík: University of Iceland Press, 2012
National Category
Didactics
Identifiers
urn:nbn:se:hh:diva-25400 (URN)978-9979-54-965-9 (ISBN)
Conference
The Sixth Nordic Conference on Mathematics Education (NORMA 11), Reykjavík, Iceland, May 11-14, 2011
Available from: 2014-05-22 Created: 2014-05-22 Last updated: 2015-10-12Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4984-6376

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