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Embodied fractions: Conceptual difficulties in the light of grounding metaphors
Högskolan i Halmstad, Akademin för lärande, humaniora och samhälle, Centrum för lärande, kultur och samhälle (CLKS), Lärande, Profession och Samhällsutveckling.ORCID-id: 0000-0003-4984-6376
Högskolan i Halmstad, Akademin för lärande, humaniora och samhälle, Centrum för lärande, kultur och samhälle (CLKS), Lärande, Profession och Samhällsutveckling.ORCID-id: 0000-0003-2441-1341
2018 (engelsk)Inngår i: 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, s. 287-287Konferansepaper, Poster (with or without abstract) (Fagfellevurdert)
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.

sted, utgiver, år, opplag, sider
Umeå, 2018. Vol. 5, s. 287-287
Emneord [sv]
bråk, representationer, metaforer
HSV kategori
Identifikatorer
URN: urn:nbn:se:hh:diva-37543OAI: oai:DiVA.org:hh-37543DiVA, id: diva2:1232071
Konferanse
42nd Conference of the International Group for the Psychology of Mathematics Education (PME42), July 3-8, 2018, Umeå, Sweden
Tilgjengelig fra: 2018-07-10 Laget: 2018-07-10 Sist oppdatert: 2018-09-20bibliografisk kontrollert

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