Aspectos estruturais e históricos que relacionam a música e a matemática: uma abordagem interdisciplinar para a aplicação de médias, progressões e logaritmos, no ensino médio

Abstract

This work investigated the relations between mathematics and music, from basic levels, such as the relation between the length of a string and the means, to the relations with exponentials and logarithms. For such, we used the history of music and of mathematics to interact with the teacher and the student in an accessible and curious manner with the intent to awaken the interest for learning the subject and/or even deepening it, aiding in the teaching and learning of these two knowledge areas. In Chapter 1, we present the justifications which lead to producing this work, pointing its objectives. In Chapter 2, as a manner of introducing the subject to the student, and especially to the teacher, we present the relations between music and mathematics. In this chapter, the focus in music becomes necessary so that people lay to this area may become familiar with the musical terms, forms and concepts. Still in this exposition, the mathematical concepts are presented to the readers. In Chapter 3, we present a short historical of logarithms which will serve as support for activity 4 in addition to the understanding of the use of this area in mathematics in organizing occidental contemporary music. In Chapters 4 and 5, supported mainly by Howard Gardner and Ivani Fazenda‟s books, we intend to show that the central idea of this work is theoretically justified in either relation between musical intelligences and logic-mathematical or in the need to modernize the didactics and interdisciplinarity in teaching mathematics. Thus, in Chapter 6, we present activities (workshops) which may be developed with High School students, and with a few adaptations for Grade School – final grades, which should propitiate the expansion of the students view for these two knowledge areas and its relations. These activities involve theoretical and practical exercises in a dynamic, investigative and challenging manner; and, for being contextualized, become interesting and useful.