The construction of formulas: an articulation between geometry and algebra

Abstract

The objective of this article is to perform out a theoretical reflection on two Activities of Study and Research -AEI, which focus on the construction of formulas for the calculation of volume measurements. The first deals with a formula to calculate the volume measure of a regular tetrahedron constructed from a cube and the second deals with a formula to calculate the volume measure of an octahedron obtained by truncating a regular tetrahedron. The reflection was made from an articulation between geometry and algebra from the apprehensions of a figure, in terms of Records of Semiotic Representation and of the four phases of the algebraic modeling process. The movement of geometric constructions, carried out in GeoGebra, together with natural language, allow the development of apprehensions of figures, the perception of relationships between parts of the figures and the consequent algebraic representation of the formulas sought.