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Hur ser man bråk?: en studie om visuella representationer av bråk
Kristianstad University, Faculty of Education.
Kristianstad University, Faculty of Education.
2019 (Swedish)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesisAlternative title
How do you see fractions? : a study about visual representations of fractions (English)
Abstract [sv]

I denna studie undersöker vi matematiklärares olika synsätt utifrån deras erfarenheter kring visuella representationer och aspekter av bråk. Lärare intervjuades om en uppsättning problem som deras elever fick lösa, vilka var de metoderna som användes. Vi undersöker därav även om det finns några samband mellan klassresultaten och matematiklärarnas olika synsätt. Tre olika teorier användes som ramverk vid både metodövervägandet och analysen; Fyra utvecklingsstadier vid inlärning med representationer, fem aspekter av bråk och pedagogical content knowledge. Resultaten visar att det finns likheter och skillnader i deltagande lärares synsätt. Några likheter var att alla deltagande lärare finner visuella representationer att vara ett användbart hjälpmedel vid utveckling av elevers förståelse samt att de alla uttrycker en större bekantskap med aspekten del-helhet jämfört med de övriga aspekterna. Några skillnader mellan lärarnas synsätt var att de har olika inställningar till huruvida bråk uppfattas som svårt för eleverna men också i vilken utsträckning visuella representationer ska användas i årskurs 9. Vid analys av klassresultaten finner vi några samband där eleverna har svårare för uppgifter med areamodeller som inte är indelade i lika stora delar, uppgifter med tallinjer och uppgifter där eleverna ska uttrycka sig med ord. Lärarnas kommentarer till detta är att eleverna saknar förståelse för den matematik som ska användas och att eleverna på så sätt använder en felaktig metod. Lärarna kommenterar även att vissa uppgifter i studien kräver en större begreppsförståelse vilket påverkar elevernas resultat på uppgifterna.

Abstract [en]

In this study we examine mathematics teacher’s verity in their reasoning and their different perspectives about visual representations and sub-constructs of fractions. Teachers were interviewed about task that their students solved, which were the methods used in this study. Therefor we also examine if there are any correlations between the teacher’s different perspectives of visual representations and the classes results on fraction tasks. The study was based on three theoretical frameworks; Four stages through the use of representations, five sub-constructs of fraction and pedagogical content knowledge. The methodological consideration and analysis were based on these theories. The result showed that there were some similarities and differences in the teacher’s reasoning. A similarity was that all participated teachers found visual representations as a helpful tool when teaching fractions for student’s conceptual understanding. Another similarity was that all teachers were more familiar with the part-whole sub-construct than the other subconstructs of fraction. Some differences in the teacher’s reasoning were if they found fraction difficult or not for the students and in which extent visual representation should be used in the ninth grade. When the class results were analyzed some connections were found. Student have difficulties with tasks where area models are not equaled partitioned, with tasks related to number lines and to tasks were the students must change from a visual to a textual representation. According to the teachers comments these difficulties accurse due to that the students lacks a curtain mathematical understanding that is required when solving these tasks. This leads to the use of an inaccurate method. The teacher’s also comments that some tasks in this study requires a higher conceptual understanding which affects the classes’ results.

Place, publisher, year, edition, pages
2019. , p. 97
Keywords [en]
Fraction, Visual representations, Representations, Five sub-constructs of fraction, Teachers perspectives, Teachers reasoning, Conceptual understanding
Keywords [sv]
Bråk, visuella representationer, representationsformer, fem aspekter av bråk, lärares synsätt, lärares resonemang, begreppsförståelse
National Category
Didactics Mathematics Learning Pedagogy Pedagogical Work
Identifiers
URN: urn:nbn:se:hkr:diva-18963OAI: oai:DiVA.org:hkr-18963DiVA, id: diva2:1281611
Educational program
Teacher Education
Supervisors
Examiners
Available from: 2019-01-23 Created: 2019-01-22 Last updated: 2019-01-23Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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