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

Abstract

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.