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Grafisk och algebraisk representation: Gymnasieelevers förståelse av linjära funktioner
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0001-5571-3524
2016 (Swedish)Licentiate thesis, monograph (Other academic)Alternative title
Graphic and Algebraic Representation : Upper Secondary Students’ Understanding of Linear Functions (English)
##### Abstract [en]

This thesis concerns upper secondary students’ understanding of algebraic and graphic representation of linear functions. Components of the students’ concept images, so-called ‘concept elements’, were studied as a way to capture their understanding. Four aspects affect the graphical view of a linear function, namely the parameter k, the parameter m, the scale of the coordinate axes and the domain of the function. Concerning the scale of the coordinate axis, there is a need to distinguish between two kinds of slope. When the scale of x-axis is changed, the k-value of the function, the so-called analytic slope, is constant but the visual slope changes. The tasks were designed so that three aspects were held constant in each task and one was varied. The study is qualitative and consists of two sub- studies. In the first, six students worked with two tasks involving the parameters k and m in the dynamic software GeoGebra. In the second, eight students were interviewed about a task concerning functions with different domains. Both studies also involved a task concerning the aspect of slope in a non-homogeneous coordinate system (a system with different scales on the axes). The results indicate three main findings: Firstly, students displayed difficulties in distinguishing between analytic and visual slope. Secondly, the word ‘start value’ can lead to conceptual problems when there is no visible intercept between the graphical representation of the function and the y-axis. Thirdly, the students displayed almost no concept elements in relation to the domain of a function.

##### Abstract [sv]

Denna licentiatuppsats behandlar gymnasieelevers förståelse av linjära funktioners algebraiska och grafiska representation. Delar av elevers begreppsbilder, kallade begreppselement, har studerats som en metod att fånga deras förståelse. Fyra aspekter påverkar den grafiska representationen av en linjär funktionens algebraiska representation . Dessa aspekter är: parametern k, parametern m, skalan på koordinatsystemets axlar och funktionens definitionsmängd. Studien är kvalitativ och består av två delstudier. I första delen arbetade tre par elever med uppgifter som rör parametrarna k och m. I andra delen intervjuades åtta elever om uppgifter som behandlar linjära funktioner med olika definitionsmängder. Båda delstudierna innehöll en uppgift som berör aspekten lutning i ett inhomogent koordinatsystem (ett system med olika skalor på axlarna). När skalan på x-axeln förändras är funktionens k-värde, så kallad analytisk lutning, konstant medan den visuella lutningen förändras.

Studiens viktigaste resultat: 1) Elever visar svårigheter att särskilja analytisk och visuell lutning. 2) Ordet startvärde kan leda till konceptuella problem när synlig skärningspunkt på y-axeln saknas. 3) Eleverna visade i stort sett inte några begreppselement i relation till definitionsmängd.

##### Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2016. , 102 p.
##### Series
Karlstad University Studies, ISSN 1403-8099 ; 2016:27
##### Keyword [en]
mathematics education, linear function, graphic representation, scale, concept image
##### National Category
Other Mathematics Didactics
Mathematics
##### Identifiers
ISBN: 978-91-7063-705-6 (print)OAI: oai:DiVA.org:kau-41777DiVA: diva2:921715
##### Presentation
2016-06-02, 13:00 (Swedish)
##### Supervisors
Available from: 2016-05-12 Created: 2016-04-20 Last updated: 2016-05-12Bibliographically approved

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Cite
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