Relación entre actividades propuestas por estudiantes para profesor de matemáticas y algunas perspectivas socio epistemológicas asociadas a prácticas matemáticas que han fundamentado los números enteros

Abstract

Throughout time there have been ways of constructing the integer that vary depending on each era and existing culture. Therefore, by recognizing these historical facts, it is possible that mathematics teachers can accompany their students in the construction of the whole number from various perspectives, and thus be able to reflect on other types of alternatives that could be taken in some contexts present actually. In this sense, if these socio-epistemological perspectives are unknown, then it will be a more difficult task (both for the mathematics teacher and for his students) to get to construct the whole number. In this regard, today there are many cases in which the teacher brings to his students the knowledge already constituted, which forces them to have a rote learning, and with this, it is difficult for them to learn to solve daily problems related to the integer number, given that they did not have the opportunity to experience its construction, and therefore, they lack many tools that can help them to analyze if they can associate it with certain contexts, and in what way they can do it. In response to this need, some socio-epistemological perspectives that have based the integer number over time were analyzed, in search of mathematical activities that could be present in many of the situations proposed today by mathematics teachers both in training and in exercise for teaching these numbers. For this reason, eight didactic units of students of the Intensive Practice academic space were analyzed, offered by the curricular project of Bachelor of Mathematics of the Universidad Distrital Francisco José de Caldas in the city of Bogotá, in order to determine how much they are taking into account these perspectives. For this, an analysis model was developed with which it was possible to relate the socio-epistemological perspectives found, with the activities related to the whole number proposed by some undergraduate students in mathematics. In this analysis it was possible to show that most of them did not take into account any socio-epistemological perspective as support for their activities, but it was also found that it is important to do so, since, if these historical facts are recognized, the students will have a better learning about how the integer number could be constructed.