Fractions and Pythagorean Tuning—An Interdisciplinary Study in Secondary Education

Abstract

Formal education is experiencing a series of reforms that favor the integration of the contents of different areas in the teaching and learning of the different educational stages. The present study examined the use of an interdisciplinary music and mathematics experience in Secondary Education in Galicia (Spain) in the 2016/17 academic year. A descriptive-exploratory design was used, through a Likert questionnaire applied to 197 students with a diagnostic test and a reference test, and a study of multiple cases was carried out in which information was collected through classroom observations. The results show improvements in the understanding of mathematical and musical concepts, and attitudes and procedures so we can argue that the use of interdisciplinary activities have favored the development of teaching-learning opportunities in mathematical and musical training.Mathematics 2019, 7, 1227 2 of 13 attitudes. However, there is no record of studies linking both these disciplines in compulsory secondary education (ESO). The FractionsFractions are present in the most diverse contexts; they form part of the secondary education curriculum and are essential for learning algebra, geometry, and other areas of higher mathematics [7].Research on this construct creates a certain interest because many students consider fractions to be among the most complex mathematical concepts tackled in the early school years. The difficulties stem from a lack of conceptual understanding and procedural fluidity due to the limited use of manipulative teaching materials, visual representations and/or assessment of responses before attempting to use a formal algorithm [8]. The students see fractions as meaningless symbols or look at the numerator and denominator as separate numbers instead of understanding them as a unified whole [9]. In addition, these doubts persist when they arrive at secondary school as they have not understood the concept or have learnt it badly.Perrenoud [10] argues that the reason students do not make adequate progress stems from the lack of teacher competence in teaching math effectively and not being able to apply mathematics to daily life. In this regard, Castro-Rodríguez, Rico and Gómez [11] emphasize that innovative materials and forms of teaching are very important elements as they capture the schoolchildren's attention and allow them to obtain satisfactory results both academically and personally. Therefore, it is necessary for educators to break the monotony in their classrooms, stimulate their students by introducing novel aspects that arouse their interest and present them with approaches that will motivate and provoke a taste for and curiosity about the world of mathematics. Taking this into account, the main objective of our work is to be able to understand fractions significantly and use them in a range of actions, concepts and procedures linked to varied situations, encouraging students to discover them on their own, and as a team, and then to discuss the strengths and weaknesses of each strategy [7].

Enseñanza Interdisciplinaria Música-Matemática: La Guitarra Y Su Rol Protagónico en El Desarrollo Histórico De La Música Occidental

“…Además, de acuerdo con la indagación realizada, son escasas las investigaciones ligadas al uso del temperamento igual que busquen integrar Música y Matemática con fines educativos (e.g. Chao-Fernández et al, 2019).…”

Influence of Musical Learning in the Acquisition of Mathematical Skills in Primary School

“…According to studies, the interdisciplinary approach of teaching music with mathematics positively affects cognitive development and skills related to both disciplines and student's academic results [1,15,16]. Some of the reasons may be that learning is more attractive when the contents are addressed together, which provides emotional security and confidence [17,18].…”

O ritmo dos conjuntos: uma experiência interdisciplinar entre música e matemática

“…No entanto, o uso dessa prática pode ser recompensada por um ambiente agradável harmonizando dimensões tanto físicas como emocionais (María Dorinda Mato-Vázquez et al, 2019, p. 182) desenvolvendo diversas habilidades (An et al, 2019, p. 15) promovendo um maior engajamento com a matemática (An et al, 2014, p. 10). Nesse contexto, verifica-se a relevância da interdisciplinaridade entre a música e a matemática que pode promover o desenvolvimento do aluno de forma ampla (An et al, 2008(An et al, , 2019 produzindo um aprendizado ativo, com ganhos conceituais importantes e pactuados na coletividade (Chao-Fernández et al, 2019;María Dorinda Mato-Vázquez et al, 2019). O presente estudo tem como objetivo avaliar as reações dos alunos ao serem expostos a uma aula interdisciplinar de música e matemática.…”