Enrichment of elementary school symmetry-learning process by using melody transformations
Treść / Zawartość
Mathematics and Music - two dierent aspects of human creativity, seemingly belonging to separate areas: science and humanities. Despite this, there are multiple well-known common elements and analogies between the two. Especially well explored is the use of mathematics in music. The opposite, which is the use of music in mathematics, seems unusual and is rarely discussed, including the educational aspect. This paper proposes an exemplary approach of using music to enrich and facilitate mathematics teaching and provides its initial empirical verification. The research presented in this paper describes an additional model which presents the possibility and efectiveness of using music to teach geometric transformations of the plane (reflection symmetry and point reflection) at 6th-7th elementary music school grade levels (12 - 13 years old students). The research initially confrmed the hypothesis that the analysis of musical themes and their transformations can be used in music schools as a new model of facilitating the mathematical understanding of reflection symmetry and point reflection. After an experimental music theory lesson concerning melody transformations and a presentation of the parallels between geometric transformations and their melodic transformation equivalents, the results of the POST-TEST in mathematics were significantly better than the PRE-TEST results for the entire experimental class. Moreover, the spontaneous transfer of knowledge from music to mathematics, concerning the understanding of point and reflection symmetry, was observed. The new musical model turned out to be a useful artifact to some students. The additional research results concern the awareness of the possibility of knowledge transfer between mathematics and music. The teachers of mathematics and music theory involved with the experimental class have not made use of the possibility of transferring musical knowledge to mathematics before, while elementary-level music school students are aware of some analogies between mathematics and music.