Thesis (MMus (Music))--University of Stellenbosch, 2009. / The relationship between music and mathematics has been subjected to debate for centuries. There are two schools of thought with the one viewpoint holding that the relationship between mathematics, which is conceived as an abstract and cold discipline, compared to music, which is rich with emotion, must be very limited. Arguments for this view draws, for example, on recent research which indicates that musical talent is not inherently linked to mathematical capability. On the other pole of the debate is the belief that although music and mathematics contribute to different parts of society, there is a very important inter-relationship between the two fields. Of great interest to the latter is the Greek composer Iannis Xenakis whose musical aesthetics incorporates this philosophy. As composer, Xenakis used mathematical theories as basis for his musical works. He not only incorporated well known mathematical principles such as the Golden Section into his compositions but went further and, for instance, utilized Boolean Algebra, Probability theory and Stochastic processes in his music. His composition method based on these mathematical principles became known under the term Stochastic music and forms the focus of this thesis. The research project concentrates on the early part of Xenakis’ life in order to provide insight into the development of his composition methods. The mathematical principles at the centre of his stochastic compositions receive specific rationalisation. In doing so, the most significant probability distributions (Linear, Exponential, Poisson and Normal distribution) are defined in terms of their properties and Xenakis’ use of them. The application of these distributions is considered by looking at the early works Metastaseis (in which Xenakis confronted most of his musical problems and which formed the basis for his musical style) and Achorripsis (where he fully developed their implementation). An in-depth examination of the construction of Achorripsis is performed while scrutinizing Xenakis’ calculations. Specific attention is drawn to alterations and adjustments made to the calculations. His implementation of them into the final score is furthermore examined and it is shown where he deviated between the calculations and score. The thesis concludes by considering the extent and significance of the adjustments made by the composer in the name of artistic freedom.

This literature review looks into the effects of integrating music in mathematics teaching andhow it influences the problem solving ability. A systematic search for scientific articles was madeto investigate the research area. All together 13 scientific articles were chosen, which presentedvarious ways to integrate music in mathematics teaching and which had found different resultsin their studies. Generally, the articles presented positive effects of integrating music inmathematics teaching to develop students’ problem solving ability and mathematical learning.Similarities and differences between the presented articles were compared in the results of thisstudy, which showed common features in the characters of music and mathematics. In this study,problem solving is used in a wide definition which includes arithmetic, communication,reasoning and mathematical concepts

Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Abstract This study examines the potential for music education to enhance children's mathematical achievement and understanding. Psychological and neuroscientific research on the relationship between music and mathematics has grown considerably in recent years. Much of this, however, has been laboratory-based, short-term or small-scale research. The present study contributes to the literature by focusing on specific musical and mathematical elements, working principally through the medium of singing and setting the study in five primary schools over a full school year. Nearly 200 children aged seven to eight years, in six school classes, experienced structured weekly music lessons, congruent with English National Curriculum objectives for music but with specific foci. The quasi-experimental design employed two independent variable categories: musical focus (form, pitch relationships or rhythm) and mathematical teaching emphasis (implicit or explicit). In all other respects, lesson content was kept as constant as possible. Pretests and posttests in standardised behavioural measures of musical, spatial and mathematical thinking were administered to all children. Statistical analyses (two-way mixed ANOVAs) of student scores in these tests reveal positive significant gains in most comparisons over normative progress in mathematics for all musical emphases and both pedagogical conditions with slightly greater effects in the mathematically explicit lessons. This investigation addresses concerns that UK and US governments' quests for higher standards in mathematics typically result in impoverished curricula with limited access to the arts. In showing that active musical engagement over time can improve mathematical achievement, as hypothesised, this work adds to a growing body of research suggesting that policy-makers and educationalists should reconsider curriculum balance.

This dissertation examines elementary teacher candidates' perceptions of hip-hop culture and utilizing hip-hop pedagogy in a mathematics classroom. This study demonstrates how elements of hip-hop may be integrated into an elementary mathematics methods course to develop pedagogical knowledge that challenges teacher candidates to explore the benefits of utilizing hip-hop as a tool in the classroom. This study contributes to the growing body of research that investigates the use of hip-hop pedagogy in educator preparatory programs. Participants in this study were teacher candidates at a large university in Texas enrolled in the final year of their educator preparatory program. This research shows that as a result of integrating hip-hop pedagogy in the mathematics methods course, teacher candidates had increased knowledge and more positive perceptions of hip-hop culture, and they demonstrated a greater willingness to integrate hip-hop pedagogy in their future classrooms.

The work deals with the possibility of interconnecting the teaching of mathematics with music. The theoretical part focuses on the relationship between mathematics and music, student motivation, the theory of multiple intelligence and also on whether music can contribute to the development of mathematical thinking. The practical part delivers five lesson preparations, where the main topic is music education and several other ways to use music education in another mathematical topic. KEYWORDS Music in mathematics, rhythm in mathematics, musical instruments in mathematics, motivation, word problems, equations, intersubject relations, Gardner's theory of multiple intelligence.