Razonamiento asociado a la proporcionalidad entre áreas en correspondencia con el modelo educativo de van Hiele en estudiantes de grado séptimo

Abstract

This investigation it tries to identify the level of reasoning with regard to the proportional relations that they present the students in correspondence with the Educational Model of VAN HIELE on in students of the seventh grade, of the Educational Institution Luis Eduardo Arias Reinel located in urban zone of Barbosa - Antioquia – Colombia. In this grade, according to the institutional curriculum organized from the basic standards of competences in mathematics proportionality is a fundamental concept that originates from geometric relationships and is taught at this level of study The students realized a questionnaire of opened questions constructed in correspondence with the Model. To identify the level of reasoning that every student possesses in relation to the concept of proportionality between areas of flat figures. This qualitative investigation was approached from a study of cases, analyzing three students of the grade and of which the geometric visualization allowed them to exhibit a reasoning that places them in a level of agreement with their answers. As a result of the study, it is possible to identify the level of reasoning, thanks to the construction of descriptors and the sequence of activities, which can be extended to other studies and other concepts to facilitate the understanding of how students reason.