Geometrical representations in the learning of two-variable functions

Maria Trigueros, Rafael Martínez-Planell
2009 Educational Studies in Mathematics  
This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report here concentrates on investigating the relationship between students' notion of subsets of Cartesian three-dimensional space and the understanding of graphs of twovariable functions. APOS theory and Duval's theory of semiotic
more » ... s are used as theoretical framework. Nine students, who had taken a multivariable calculus course, were interviewed. Results show that students' understanding can be related to the structure of their schema for R 3 and to their flexibility in the use of different representations. The notion of a multivariable function is fundamental in mathematics and its applications. Research on this subject, however, is scarce. There are many studies that deal with the general idea of a function; however, few make use of the particularities of multivariable functions to explicitly study how students build their understanding about them. While reviewing the literature, we could not find theory-based research studies probing student understanding of this notion. This lack of research findings limits the understanding of how students learn the main ideas involved in the study of multivariable calculus. The purpose of this study is to contribute to filling this gap in the literature. In this paper, we focus on the analysis of some geometrical factors that are related to students' notion of function of two variables.
doi:10.1007/s10649-009-9201-5 fatcat:26n2olvxovggxktcqodiedwk3m