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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.

Since the time of Pythagoras, philosophers, educators, and researchers have theorized that connections exist between music and mathematics. While there is little doubt that engaging in musical or mathematical activities stimulates brain activity at high levels and that increased student involvement fosters a greater learning environment, several questions remain to determine if musical stimulation actually improves mathematic performance. This study took a qualitative approach that allowed 24 high school students to express their direct experiences with music and mathematics, as well as their perceptions of how the two fields are related. Participants were divided into four equal groups based on school music participation and level of mathematic achievement, as determined by their performance on the Texas Assessment of Knowledge and Skills (TAKS). Students participated in a series of three interviews addressing their experiences in both music and mathematics, and took the Multiple Intelligences Developmental Assessment Scales (MIDAS). TAKS data and MIDAS information were triangulated with interview findings. Using a multiple intelligence lens, this study addressed the following questions: (a) How do students perceive themselves as musicians and mathematicians? (b) What experiences do students have in the fields of music and mathematics? (c) Where do students perceive themselves continuing in the fields of music and mathematics? and (d) How do students perceive the fields of music and mathematics relating to each other? Contrary to most existing literature, the students who perceived a connection between the two fields saw mathematics driving a deeper understanding of the musical element of rhythm. Not surprisingly, students with rich backgrounds in music and mathematics had a higher perception of the importance of those fields. Further, it became readily apparent that test data often played a minimal role in shaping student perceptions of themselves in the field of mathematics. Finally, it became apparent from listening to the experiences of high school students, there are many growth areas for schools in order to meet the needs of their students.

Verbindungen zwischen Musik und Mathematik aus naturwissenschaftlicher, musiktheoretischer und pädagogischer Perspektive und deren did.-meth. Möglichkeiten im Unterricht der Grundschule

Univerzita Karlova v Praze / Pedagogická fakulta / Katedra výtvarné výchovy // Charles University in Prague / Faculty of Education / The Department of Fine Art Education Netradiční výrazové prostředky a techniky Matematické principy v komparaci netradičního výtvarného a hudebního díla UnconventionalMeansofexpressionandtechniques Mathematical principles in comparing unconventional visual and musical art Klára Effenbergerová Výtvarná výchova - pedagogika Prezenční studium, 5. ročník Datum dokončení: květen 2011 Vedoucí práce: Doc. PhDr. Jaroslav Bláha, Ph.D. Abstract The thesis deals with a comparative analysis of a project called Poéme électronique in the Philips Pavilion (1958), while an emphasis is put on its mathematical background and broader interdisciplinal contexts. Particular attention is devoted to grand oldman Iannis Xenakis. The thesis tries to interpret the phenomenon of Electronic poetry, which we understand as an effort to design a multimedia "Gesamtkunstwerk". This brings the necessitate of the multi-specialized synthetic approach in searching of a relationship between the kinds of arts, and the analysis of interactions of individual project components.