Using the onto-semiotic approach to identify and analyzemathematical meaning when transiting between differentcoordinate systems in a multivariate context

摘要

The main objective of this paper is to apply the onto-semiotic approach to analyzethe mathematical concept of different coordinate systems, as well as some situations anduniversity students' actions related to these coordinate systems. The identification of objectsthat emerge from the mathematical activity and a first intent to describe an epistemic networkthat relates to this activity were carried out. Multivariate calculus students' responses toquestions involving single and multivariate functions in polar, cylindrical, and sphericalcoordinates were used to classify semiotic functions that relate the different mathematicalobjects.