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"F av x är väl egentligen y?": En studie om gymnasieelevers förståelse för funktionsbegreppet och dess representationer
Linnaeus University, Faculty of Technology, Department of Mathematics Education.
2013 (Swedish)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [sv]

Syftet med denna undersökning har varit att studera gymnasieelevers förståelse för funktionsbegreppet.Den teoretiska utgångspunkten har varit att studera elevernas förmåga att växla mellanolika representationsformer och studera deras förståelse för relationen mellan de olika representationerna.Elevernas förmåga att resonera har också varit en väsentlig del och därför har forskningenkring matematiskt resonemang också varit en viktig del i arbetet. För att nå ett resultat har treklasser på gymnasiet fått skriva ett test konstruerat för att svara mot uppsatsens syfte. Utövertestet intervjuades tre av eleverna för att det skulle finnas möjlighet att fånga elevernas förmågaatt resonera. Resultatet kom att visa att vissa elever har svårt att utföra växlingar mellan vissaolika representationer, men mellan andra är det betydligt enklare. Det framkom att eleverna varskolade i ett algoritmiskt tänkande, och att eleverna hade svårt att resonera fritt och kreativt kringfunktionsbegreppet, samt att eleverna hade svårt att skilja de närliggande begreppen ekvation ochfunktion.

Abstract [en]

The aim with this thesis has been to study Swedish high school students’ comprehension for theconcept of a function. The theoretical starting point has been to study the students’ ability tochange between different forms of representations of a function and study their comprehensionfor the relation between the different representations. The students’ ability to use mathematicalreasoning has also been a crucial part for the thesis, and therefore research on mathematicalreasoning has also been an important part. Three high school classes were given a test, whichsought to test their ability to change between different forms of representation. In addition to thetest three students were interviewed, so that the students’ ability to reason would be possible toanalyze. The results came to show that some students have difficulties to change between someof the representations but between others it’s far easier for them. The results also showed thatthe students were trained in algorithmically thinking, and that it was difficult to reason creativelyabout the concept of a function. The students also had trouble separating a function from therelated concept of equations.

Place, publisher, year, edition, pages
2013. , 60 p.
Series
LÄRARUTBILDNINGEN
Keyword [en]
functions, concept of a function, representations, conceptual knowledge, mathematical reasoning
Keyword [sv]
funktioner, funktionsbegreppet, representationsformer, strukturell kunskap, procedurell kunskap, matematiskt resonemang
National Category
Didactics
Identifiers
URN: urn:nbn:se:lnu:diva-26715OAI: oai:DiVA.org:lnu-26715DiVA: diva2:629790
Subject / course
Didactics of Mathematics
Educational program
Lärarprogrammet, inriktning mot verksamhet i grundskolans senare år och gymnasiet
Supervisors
Examiners
Available from: 2013-06-19 Created: 2013-06-17 Last updated: 2013-06-19Bibliographically approved

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