Cambios de concepciones sobre la fracción en estudiantes del espacio de formación didáctica de la aritmética II de licenciatura en matemáticas de la Universidad Distrital Francisco José de Caldas

Abstract

The research work focuses on investigating and analyzing the changes of conceptions about the fraction in students of the training space Didáctica de la Aritmética II of the Licenciatura en Matemáticas of the Universidad Distrital Francisco José de Caldas. The conceptions about fraction at the beginning of the course are partial, which represents a problem of understanding as to what a fraction is, then, the training space has among its objectives to resignify the concepts of fraction with which the students arrive and from there interest arises to analyze the changes of conception that are presented. The research methodology is qualitative with a hermetic approach, where three data collection instruments are used: essay and problem situation applied at the beginning and end of the course, and semi-structured interview in the final phase. The information collected is analyzed based on the theoretical framework proposed by Llinares and Sánchez (1997) who propose four interpretations of the fraction: part-whole and measure, ratio, quotient and operator, concluding that the conception changes are categorized into two, the first is an expansion in the fraction interpretations and the second is a deepening in one more fraction interpretations, these changes are directly related to the change of conception in the treatment of the fraction in a problem situation, since the strategies were diversified taking into account the different contexts in which the fraction appears. Finally, regarding the causes of the changes in conception, which were determined from the interview, it is concluded that there are three: argumentation, representation, and the role of the teacher.