# Grafisk och algebraisk representation : Gymnasieelevers förståelse av linjära funktioner

Sammanfattning: 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.

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