Music Learning and Mathematics Achievement: a Real-World Study in English Primary Schools

Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Supervisor: Dr Linda Hargreaves This final thesis is submitted for the degree of Doctor of Philosophy. Faculty of Education University of Cambridge October 2018 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. Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Acknowledgements I am deeply grateful to Dr Linda Hargreaves for her enduring patience throughout my extended doctoral process, her continued support in my work, and her wisdom in shaping my academic development here at Cambridge. Her knowledge, insight and kindness have made a profound impact on my work and progress, enabling me to complete this journey despite many obstacles. I would also like to thank my advisors Dr Dénes Szücs and Dr Michelle Ellefson for their ideas and challenges regarding my research at the beginning of my PhD studies and for my examiners, Professor Susan Hallam and Professor Tim Rowland, for their conscientious and thoughtful advice at the completion of my studies. I have appreciation for Emma Rixon at the Faculty of Education, who is always helpful and kind. Additionally, I would like to thank my family and friends who have supported me morally along the way, such as Terumi Ishiguro, Justine Piontek, Yoko Oshima, Wendy Klein and Angelina Vetere. I have been encouraged daily by the writings of Nichiren Daishonin and Daisaku Ikeda, who are wonderful examples and mentors in living a profound life of care. I have deepest gratitude for my best friend and husband, Eddie Sanders. He encourages me to go for my dreams, including this one. I love him and thank him for his forbearance, love and continual emotional support. This thesis is dedicated in memoriam to my mother and father, who had similar dreams but were unable to fulfil them, and to my daughter Sky Marie Sanders, who is always in my heart. 2 Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Statement of Authorship and Authenticity This thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the preface and specified in the text. It is not substantially the same as any that I have submitted, or, is being concurrently submitted for a degree or diploma or other qualification at the University of Cambridge or any other university or similar institution except as declared in the preface and specified in the text. I further state that no substantial part of my thesis has already been submitted, or, is being concurrently submitted for any such degree, diploma or other qualification at the University of Cambridge or any other university or similar institution. I hereby declare that the sources of which I have availed myself have been stated in the body of the report and in the bibliography and that the rest of the work is my own. This following report, exclusive of the bibliography, does not exceed 80,000 words in length. Specifically, with exclusions, it is: 78,396. 3 Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Preface The inspiration for this research has autobiographical and professional origins. These are summarised here to explain the motivations that drive this work and to confirm my qualifications to have carried out the intervention. I believe that music in the schools is valuable for its own sake, yet also for its potential to enhance one’s life as well as other abilities such as mathematical achievement. I also believe in the value of scientific enquiry. I have appreciated science since childhood and won a “young scientist” award at age 12 after monitoring and analysing the effects of differing environmental vibrations on plant growth. Yet perhaps we are all scientists in a sense, as we create and revise our own theories throughout life. In secondary school, I became absorbed in mathematics and represented my school in contests across the region. At the same time, I was playing Chopin and singing Mozart. I had always wondered whether my musical training helped to bring out mathematical abilities or did I just happen to love both? What is the connection between the two disciplines and cognitive domains? My goal in this study was to answer those questions. Both disciplines fully engaged me and I frequently seemed to have experienced what Csikszentmihalyi (1988) calls “flow,” the mental state of immersion in which an optimum balance of challenge and enjoyment is present. Therefore, I began my undergraduate studies double-majoring in music and mathematics. The pattern-making and creative problem-solving elements I enjoyed in musical composition exist in mathematics as well. Therefore, I found a similar satisfaction in my work as a composer that I felt in my work as a mathematician. I believe that every melody, harmony and rhythm has spatial relevance and numerical value. All of the pieces in my honours thesis opera at Columbia University were composed with a mathematical foundation in combination with creativity and heart; it later won the ASCAP Classical Music Award. At the same time, I became fascinated with the function of the brain after doing well in a neuroscience-based psychology class at Columbia University and continued studies in that area as well. I had been teaching composition, piano and voice while working on my baccalaureate and was continually interested in what was going on in my students’ brains as they composed or learned technique and repertoire. While teaching young children (aged four-six) music notation in New York, I noticed that they could learn the counterintuitive method of writing rhythms (less is of a longer duration, e.g., take away a stem then it is doubled) more effectively through expressing it with their bodies. Therefore, I 4 Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools created different moves for each type of rhythm note and called it the rhythm dance. While saying “quarter, quarter, quarter, quarter” we would take one step per quarter note, then while stretching out the steps to a duration twice as long spatially and temporally, we would say “half note, half note,” then we would drop to the floor on the whole note, and shout “whole 2 3 4” while sitting the full duration. The mathematics pedagogy of Milan Hejný and colleagues (2009) at the Faculty of Education at Charles University is reminiscent of this method of physicalizing knowledge through acting out the concept. For example, the understanding of order numbering, addition and subtraction could be enhanced with five-six-year-olds by taking steps forwards and backwards with his “Walk Environment” methodology. I also briefly taught mathematics in a primary school. This occurred by chance, while I was a teacher’s assistant over 15 years ago. Each day, the students played kickball during a break. The teacher had a rule whereby students who were “in trouble” for any reason, including talking out of turn, would have to stay in the classroom and do homework instead. It was my task to watch them during this time. I offered to help them with their homework and the students quickly realized that I explained the mysterious workings of mathematics for them very clearly. They were learning long division and most had difficulty understanding the teacher, who went rather quickly when putting equations on the blackboard, only briefly noting the steps. I helped each of them individually, as each had a different way of understanding (or misunderstanding) the concepts and processes. Quite soon thereafter, the word must have spread, because students started to “misbehave” on purpose so that they could stay inside and discover the joy of long division and other mathematical adventures with Mrs Sanders. This experience convinced me that I wanted to pursue an education degree at the post- graduate level, so I entered a master’s program in education at Columbia University. I soon became a research associate at the Center for Arts Education Research at CU Teachers College and continued while working on both of my master’s degrees there.

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