Geometrical representations in the learningof two-variable functions

摘要

This study is part of a project concerned with the analysis of how students workwith two-variable functions. This is of fundamental importance given the role ofmultivariable functions in mathematics and its applications. The portion of the project wereport here concentrates on investigating the relationship between students' notion ofsubsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions. APOS theory and Duval's theory of semiotic representations are used astheoretical framework. Nine students, who had taken a multivariable calculus course, wereinterviewed. Results show that students' understanding can be related to the structure oftheir schema for R3 and to their flexibility in the use of different representations.