Students’ realization of the role of contour curves for functions from R2 to R

Περίληψη

The present study consists of three components: a) analysis of the mental images that students construct in their minds through the use of contour curves in order to visualize the graph of a function of two variables in 3, b) investigation of the conceptions of students of how to relate contour curves with some of the methods used to find the limit of a function of two variables, so that they may arrive at a conclusion regarding the existence of the limit of a function in 2 and c) explanation of the type of difficulties that students face and the dynamic transformations that they use through the construction of contour curves during their effort to visualize the graph of a function of two variables in polar coordinate system. To examine the aforementioned components, a field study was implemented with the participation of 75 students. The experimental group, which attended a several variables Analysis course, consisted of second year students in the Department of Mathematics of University of Patras. For data collection, a test on both the thematic axes was set, and interviews with five students were employed. The analysis focuses on ways in which students
use the mental images they create to solve the test tasks. Results that can support prospective studies on the role of contour curves are presented.