Mathematical modelling practices and dimensions of learning in geometry

Abstract

This article reports part of the doctoral research carried out in Brazil in 2018, whose scope is to investigate how the learning of geometry happens in mathematical modeling practices. A theoretical model, proposing six different dimensions of geometric learning in modeling practices, is initially presented and discussed. The data of this research, obtained through the development of modeling practices with two classes of elementary school students, allowed to analyze how students learn to use the geometric concept of centroid to determine the average center of a population. This phenomenological analysis concludes that the learning of the concept of centroid occurs through the acquisition of a stratification, in which this concept shows itself with the following meanings: (i) average position of a geometric shape; (ii) point located on a flat figure in such a way that any straight line that passes through it divides that figure into two regions of the same area; (iii) an object's equilibrium point; (iv) center of masses given by the weighted average of the spatial distribution of these masses; (v) weighted average center of spatial dispersion of individuals. This article concludes that this stratification can be interpreted as a generalization / metaphor structure, so that learning the concept of centroid, in modeling practice, can be understood as the acquisition of this structure, namely, the acquisition of a metaphor linguistic-visual that makes it possible to investigate and extract information about space