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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 [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.)

2018. , p. 32
##### Keywords [sv]
Artefakter, dynamiska matematikprogram, funktioner, GeoGebra, matematikundervisning, semiotisk mediering, translation, undersökande arbetssätt
Mathematics
##### Identifiers
ISRN: LiU-LÄR-MA-A--2018/4--SEOAI: oai:DiVA.org:liu-149623DiVA, id: diva2:1232304
Mathematics
##### Educational program
Teacher Education
##### Examiners
Available from: 2018-07-11 Created: 2018-07-11 Last updated: 2018-08-07Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 2028 kBChecksum SHA-512
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Type fulltextMimetype application/pdf
##### By organisation
Mathematics and Applied MathematicsFaculty of Science & Engineering
Mathematics

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Cite
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