Geometrical representations in the learning of two-variable functions |
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Authors: | Maria Trigueros and Rafael Martínez-Planell |
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Institution: | (1) Departamento de Matem?tica, Universidad de Puerto Rico en Mayag?ez, Mayag?ez, 00680, Puerto Rico;(2) Depto. de Matem?ticas, Instituto Tecnol?gico Aut?nomo de M?xico, R?o Hondo #1, Tizap?n, San Angel, M?xico DF, 01000, M?xico |
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Abstract: | 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 two-variable functions. APOS theory and Duval’s theory of semiotic representations 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 R3 and to their flexibility in the use of different representations. |
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Keywords: | |
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