La enseñanza y aprendizaje de la trigonometría a partir de prácticas matemáticas que fundamentan la relación entre trigonometría y música

Abstract

The present degree work entitled "Teaching and learning of Trigonometry from mathematical practices that support the relationship between Trigonometry and Music" is presented within the framework of the teaching-learning process for sinusoidal and periodic functions, understanding that in the teaching of school mathematics, the use of trigonometry directly affects the formalization of mathematics for university cycles; as stated by Aray, Guerrero, Montenegro and Navarrete (2020), who affirm that a superficial learning of trigonometry generates a series of incidents in the learning of calculus at the university level. That is why the intention of this work is to design a teaching-learning instrument that promotes significant knowledge of sinusoidal functions as the basis for the study of formal trigonometry. In order to develop an instrument for the teaching-learning of sinusoidal and periodic functions, it is necessary to carry out an analysis of the mathematical practices that support the relationship between mathematics and music, specifically, in the study of sound as periodic phenomenon; For this, a socio-epistemological approach is proposed that will allow the identification of the actions and elements included in the mathematical practices carried out by different mathematicians throughout history, up to the Fourier trigonometric series approach, reaching a level of formalization for the trigonometry.