Elementos de la heurística de Arquímedes identificados en estudiantes de grado noveno en la comparación de magnitudes

Abstract

The research work developed within the framework of the Master's Degree in Education of the Universidad Distrital Francisco José de Caldas is presented. It was developed in the second semester of 2016, with twelve ninth grade students, the main interest of this degree work was to recognize if students approached a model of thought spontaneously, from the design and application of a sequence of six activities that incorporated elements of Archimedes' heuristics, in the comparison of magnitudes supported by physical experimentation and dynamic geometry. The methodology in which this work was framed was in qualitative research from Denzin & Lincoln (1994). As a result of the research, identification and description of students' heuristics was achieved where it was possible to demonstrate approximations to the elements of Archimedes heuristics in the comparison of magnitudes, relating the actions of students within five strategies that were highlighted in the development of activities. Finally, it could be concluded that the design and implementation of the sequence of activities was structured from two elements of Archimedes heuristics, the mechanical hypotheses and the compositional hypotheses, the former placing emphasis on experimentation from notions and propositions of static that appeared spontaneously in the implementation of activities. The second ones allowed the students to put into play the composition of areas by strings or parallel lines under some elements of euclidean geometry.