Discurso Matemático Escolar: un estudio en el concepto de Pendiente

Abstract

Our research offers an overview of the difficulties that students encounter as they go from mid school to the mayor in Industrial Engineering at the Tecnologico de Estudios Superiores de Cuautitlán Izcalli, in relation to the conceptualization and use of the Slope. There is some research preceding our study, which in different ways introduces the concept of Slope through a didactic type of discourse, a didactic analysis or through a cognitive type of analysis. Analyzing the School Mathematical Discourse in school texts, we find that the concept of Slope is given in three moments: In Analytical Geometry it is characterized as the “cocient of differences”, in Trigonometry it is handled as “the tangent of an angle of inclination” and in pre-calculus texts it is the result of finding the “formula for the prediction of the slope.” In scholar works we encounter a discourse of: Geometric style, descriptive, analytical or through methods to trace or determine of tangents. These do not help the teacher to show procedures. It rather helps to show the students the building of knowledge from different ideas or points of view. Diverse presentations taken from text books and scholar works facilitate through their discourse, the opportunity of clarifying the difference among the concepts of static slope and dynamic slope. From the previous, we consider as a hypothesis that “The current model of teaching does not allow the formulation of a variational tangent.” Applying a probe to students through a sequence it was found in them an ideology, derived from the School Mathematical Discourse, for the concept of slope, acquired from their pre-calculus courses in the present model of teaching (basically about static slope) results which coincide with our research problem. That is, The school mathematical discourse does not facilitate the construction of the notion of Slope, which is necessary to understand elementary concepts of calculus.