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Hur elever resonerar om kommutativitet i numeriska uttryck
Jönköping University, School of Education and Communication. Jönköpings Länstrafik.
2018 (Swedish)Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesisAlternative title
How students reason about commutativity in numerical expressions (English)
Abstract [sv]

Ett av grundskolans uppdrag är att elever ska utveckla kunskap om de fyra räknesättens olika egenskaper. En sådan egenskap är kommutativitet för räknesättet addition, vilket innebär att termers rumsliga placering inte har betydelse för summan. Inom kunskapsområdet aritmetik och algebra är kunskap om den kommutativa egenskapen av vikt. I denna studie intervjuades tio elever i årskurs 2. Intervjuerna var semistrukturerade, vilket bland annat innebar att en intervjuguide följdes. Syftet var att kvalitativt beskriva hur elever resonerar kring operationer med tydlig kommutativitet genom att också använda operationer utan kommutativa egenskaper. Analysen visar att eleverna kan fokusera på olika aspekter av kommutativitet, de kan fokusera på summan, på termerna eller på operationen. Studien visar också att det förekommer elever som övergeneraliserar den kommutativa egenskapen till att gälla vid uttryck med subtraktion.

Abstract [en]

According to the curriculum, students in elementary school should develop their understanding of the different properties of addition, subtraction, multiplication and division. One property is commutativity for addition. Which means that the terms’ spatial position does not change the sum. A solid understanding of the commutative property is of importance in arithmetic but also in algebra. This qualitative study is based on interviews with ten students in second grade. The purpose of the study is to investigate how students reason when they meet sequences with commutative and non-commutative expressions. The result is that students tend to describe commutativity by focusing on either the sum, the terms or the operation. Students in the study also overgeneralize the commutative property to expression with subtraction.

Place, publisher, year, edition, pages
2018. , p. 38
Keywords [en]
mathematics, commutativity, calculating
Keywords [sv]
matematik, kommutativitet, numeriska beräkningar, numeriska uttryck
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-40122ISRN: JU-HLK-JU-2-20180564OAI: oai:DiVA.org:hj-40122DiVA, id: diva2:1216520
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Available from: 2018-06-21 Created: 2018-06-11 Last updated: 2018-06-21Bibliographically approved

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