This study looks at the use of integrated mathematics and music lessons at the high school level. Four lessons were taught by the researcher in both a research and a control class to determine how mathematically motivated music instruction affects students understanding of operations of functions, composition of functions, inverse functions and domain and range. A pretest-posttest was used to determine the effect of these lessons and a questionnaire was used to identify differences between groups and to help determine the effect of musical applications of mathematics on students’ mathematical perceptions, self-efficacy and grit. The pretest-posttest included both a standard mathematics section and a section involving non-musical applications. A gain score approach using independent sample t tests was used to determine the impact of the integrated instruction. The research group demonstrated significantly greater gains both overall and on the applications portion of the exam. Additional qualitative analysis was done to determine how the posttests differed between groups. Three major differences were identified: the research group used function notation more frequently than the control group, the control group demonstrated confusion between composition of functions and inverse functions while the research group did not and the research group showed more mathematical work for the applications portion of the exam than the control group. Qualitative analysis was also done to identify trends in the questionnaire data. Among the major differences between groups was the increased willingness to work with mathematical applications in the future by the research group compared to the control group. The integrated instruction led to comparable and in some cases significantly better mathematics outcomes than the control group and led students to an increased willingness to work with mathematical applications both on the posttest and moving forward.

Thesis (M.S.)--Central Connecticut State University, 2008. / Thesis advisors: S. Louise Gould, Philip P. Halloran, Shelley Jones. " ... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 21-22). Also available via the World Wide Web.

The study examines the role of music in the lives and work of 20th century mathematicians within the framework of understanding the contribution of affect to mathematical thinking. The current study focuses on understanding affect and mathematical identity in the contexts of the personal, familial, communal and artistic domains, with a particular focus on musical communities. The study draws on published and archival documents and uses a multiple case study approach in analyzing six mathematicians. The study applies the constant comparative method to identify common themes across cases. The study finds that the ways the subjects are involved in music is personal, familial, communal and social, connecting them to communities of other mathematicians. The results further show that the subjects connect their involvement in music with their mathematical practices through 1) characterizing the mathematician as an artist and mathematics as an art, in particular the art of music; 2) prioritizing aesthetic criteria in their practices of mathematics; and 3) comparing themselves and other mathematicians to musicians. The results show that there is a close connection between subjects’ mathematical and musical identities. I identify eight affective elements that mathematicians display in their work in mathematics, and propose an organization of these affective elements around a view of mathematics as an art, with a particular focus on the art of music. This organization of affective elements related to mathematical thinking around the view of mathematics as an art has implications for the teaching and learning of mathematics.

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.