A matemática das notas musicais: música como ferramenta didática para o ensino de razões e proporções no 9º ano do ensino fundamental

Abstract

This research investigates the contributions of integrating Music and Mathematics to the teaching of ratios and proportions in the ninth grade of Elementary School. The study arose from the observation of recurring difficulties experienced by students in understanding rational numbers, ratios, and proportionality, which are fundamental concepts in mathematics learning. In view of this context, the research was guided by the following question: how can the integration of Music and Mathematics contribute to the teaching of ratios and proportions in a ninth-grade Elementary School class? The general objective was to investigate how this integration could contribute to the teaching of these concepts in the context under investigation. Specifically, the study sought to identify the students’ prior knowledge, analyze the strategies and written work developed during the activities, and examine evidence of learning and the participants’ perceptions after the intervention. Grounded in the contributions of Abdounur (2003), D’Ambrósio (2001), Fazenda (2002), Vygotsky (1998), and Vergnaud (1996), the investigation was designed as a qualitative, descriptive case study conducted with a class of 12 students from a public school in the municipality of Barras, in the state of Piauí, Brazil. As an intervention, an interdisciplinary didactic sequence was designed and implemented, integrating mathematical and musical concepts through the use of a guitar, a keyboard, and a tubophone built from PVC pipes. The proposal explored relationships among sound frequency, the length of vibrating strings, chord formation, and direct and inverse proportionality, allowing students to investigate mathematical concepts in observable situations. Data were produced through a pre-test, practice questionnaires, written work, activity records, a post-test, and a perception questionnaire. The results indicated advances in the understanding of ratios and proportions, with improved performance in situations involving direct and inverse proportionality, as well as evidence of interest and engagement during the activities. The data also suggested that the use of music contributed to the contextualization of mathematical content and enabled connections among school knowledge, physical phenomena, and the participants’ cultural experiences. As an Educational Product, a teaching guide was developed containing workshops and activities aimed at exploring ratios and proportions through musical elements, intended for Basic Education teachers.