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Translation av funktionsgrafer med dynamiska matematikprogram: En fallstudie av gymnasieelevers undersökande arbetssätt med GeoGebra
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (Swedish)Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesisAlternative title
Translation of Function Graphs with Dynamic Mathematics Software : A Case Study About Upper Secondary School Students Exploratory Work with GeoGebra (English)
Abstract [sv]

I denna studie analyserades potentialen av ett dynamiskt matematikprogram när elever arbetar med translation av funktionsgrafer och använder ett undersökande arbetssätt. I studien användes det dynamiska matematikprogrammet GeoGebra. Åtta elever i åldern 16–17 år arbetade parvis med en sextio minuter lång workshop, innehållande uppgifter som behandlade translation av funktioner på formen 𝑓(𝑥+𝑑)+𝑐, där konstanterna 𝑑 och 𝑐 varierades med GeoGebra. Skärm- och ljudinspelning gjordes på elevernas datorer och samlades in för analys. Därtill samlades också elevernas skriftliga svar på uppgifterna i workshopen in. Ett urval av data gjordes: tre av de fyra inspelningarna valdes ut att analyseras och därtill begränsades transkribering till 5 av 9 uppgifter i workshopen. Analysen gjordes inom det teoretiska ramverket semiotisk mediering (Bartolini Bussi & Mariotti, 2008). Genom systematisk kodning skapades 90 koder som sedan genom axial kodning arbetades fram till 4 centrala teman: eleverna uttrycker att 𝑐 är detsamma som 𝑚-värde; eleverna refererar till att 𝑐 och 𝑑 flyttar grafen, utan att specificera riktning; eleverna anger riktning grafen flyttar för positiva 𝑐 och 𝑑 och eleverna talar om att 𝑑 gör så att det blir nya 𝑥-värden. Resultatet av studien visar att det finns en potential med dynamiska matematikprogram att ge en ingång för elever att tolka innebörden av translation, men en utmaning eleverna möter i arbetet är att förstå den bakomliggande matematiken. Resultatet visar även att eleverna gjorde beskrivningar av translation men inte förklaringar och att det speciellt var svårt att försöka förklara varför olika värden konstanten 𝑑 påverkar grafen som den gör. Det identifierades också att två grupper tolkade konstanten 𝑐 som 𝑚-värde (det vill säga hänvisar till 𝑦=𝑘𝑥+𝑚) vilket hävdas visa ett möjligt utvecklingsbehov av teorin om semiotisk mediering.

Abstract [en]

In this study the potential that resides in a dynamic mathematics software to support students’ work with translation of function graphs when they work exploratory was analysed. In the study the dynamic mathematics software GeoGebra was used. Eight students in the age 16-17 worked in pairs in a sixty-minute-long workshop that was comprised of tasks that deals with the translation of functions of the form 𝑓(𝑥+𝑑)+𝑐, where the constants 𝑑 and 𝑐 were varied using GeoGebra. Data was collected in the form of screen and audio recordings made using the computers of the students. The students written answers were also collected. A selection of the collected data was made and analysed: three of the four recordings were chosen for analysis and these were furthermore limited to be only transcribed for 5 of the 9 tasks in the workshop. The analysis was made using the theory of semiotic mediation (Bartolini Bussi & Mariotti, 2008). Systematic coding resulted in 90 codes which then through axial coding produced 4 central themes: the students express that 𝑐 is the same as 𝑚 (as in 𝑦=𝑘𝑥+𝑚); the students refer to 𝑐 and 𝑑 as moving the graph, without specifying direction; the students specify the direction the graph moves for positive 𝑐 and 𝑑 and the students talk about 𝑑 making new 𝑥-values. The result of the study shows that there is a potential with dynamic mathematics software to promote students’ creation of meaning of translation, but a challenge students encounter is to understand the underlying mathematics. The results also show that students made descriptions of translation but did not provide explanations, and that they especially had difficulties to explain why varying values of the constant 𝑑 affects the graph the way it does. In addition, the study also identified that two groups interpreted the constant 𝑐 as the same as 𝑚 in the linear equation 𝑦=𝑘𝑥+𝑚, which here claims to show a possible need to elaborate the theory of semiotic mediation.)

Place, publisher, year, edition, pages
2018. , p. 32
Keywords [sv]
Artefakter, dynamiska matematikprogram, funktioner, GeoGebra, matematikundervisning, semiotisk mediering, translation, undersökande arbetssätt
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-149623ISRN: LiU-LÄR-MA-A--2018/4--SEOAI: oai:DiVA.org:liu-149623DiVA, id: diva2:1232304
Subject / course
Mathematics
Educational program
Programme for Teacher Education, Linköping
Supervisors
Examiners
Available from: 2018-07-11 Created: 2018-07-11 Last updated: 2018-07-11Bibliographically approved

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