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Description
The end of the nineteenth century was an exhilarating and revolutionary era for the flute. This period is the Second Golden Age of the flute, when players and teachers associated with the Paris Conservatory developed what would be considered the birth of the modern flute school. In addition, the founding in 1871 of the Société Nationale de Musique by Camille Saint-Saëns (1835-1921) and Romain Bussine (1830-1899) made possible the promotion of contemporary French composers. The founding of the Société des Instruments à Vent by Paul Taffanel (1844-1908) in 1879 also invigorated a new era of chamber music for wind instruments. Within this groundbreaking environment, Mélanie Hélène Bonis (pen name Mel Bonis) entered the Paris Conservatory in 1876, under the tutelage of César Franck (1822-1890). Many flutists are dismayed by the scarcity of repertoire for the instrument in the Romantic and post-Romantic traditions; they make up for this absence by borrowing the violin sonatas of Gabriel Fauré (1845-1924) and Franck. The flute and piano works of Mel Bonis help to fill this void with music composed originally for flute. Bonis was a prolific composer with over 300 works to her credit, but her works for flute and piano have not been researched or professionally recorded in the United States before the present study. Although virtually unknown today in the American flute community, Bonis's music received much acclaim from her contemporaries and deserves a prominent place in the flutist's repertoire. After a brief biographical introduction, this document examines Mel Bonis's musical style and describes in detail her six works for flute and piano while also offering performance suggestions.
ContributorsDaum, Jenna Elyse (Author) / Buck, Elizabeth (Thesis advisor) / Holbrook, Amy (Committee member) / Micklich, Albie (Committee member) / Schuring, Martin (Committee member) / Norton, Kay (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet vector calculus, calculus on manifolds, linear algebra, and differential equations all rest upon the idea of functions of two (or more) variables. This dissertation contributes to understanding productive ways of thinking that can support students in thinking about functions of two or more variables as they describe complex systems with multiple variables interacting. This dissertation focuses on modeling the way of thinking of four students who participated in a specific instructional sequence designed to explore the limits of their ways of thinking and in turn, develop a robust model that could explain, describe, and predict students' actions relative to specific tasks. The data was collected using a teaching experiment methodology, and the tasks within the teaching experiment leveraged quantitative reasoning and covariation as foundations of students developing a coherent understanding of two-variable functions and their rates of change. The findings of this study indicated that I could characterize students' ways of thinking about two-variable functions by focusing on their use of novice and/or expert shape thinking, and the students' ways of thinking about rate of change by focusing on their quantitative reasoning. The findings suggested that quantitative and covariational reasoning were foundational to a student's ability to generalize their understanding of a single-variable function to two or more variables, and their conception of rate of change to rate of change at a point in space. These results created a need to better understand how experts in the field, such as mathematicians and mathematics educators, thinking about multivariable functions and their rates of change.
ContributorsWeber, Eric David (Author) / Thompson, Patrick (Thesis advisor) / Middleton, James (Committee member) / Carlson, Marilyn (Committee member) / Saldanha, Luis (Committee member) / Milner, Fabio (Committee member) / Van de Sande, Carla (Committee member) / Arizona State University (Publisher)
Created2012
Description
This is a report of a study that investigated the thinking of a high-achieving precalculus student when responding to tasks that required him to define linear formulas to relate covarying quantities. Two interviews were conducted for analysis. A team of us in the mathematics education department at Arizona State University initially identified mental actions that we conjectured were needed for constructing meaningful linear formulas. This guided the development of tasks for the sequence of clinical interviews with one high-performing precalculus student. Analysis of the interview data revealed that in instances when the subject engaged in meaning making that led to him imagining and identifying the relevant quantities and how they change together, he was able to give accurate definitions of variables and was usually able to define a formula to relate the two quantities of interest. However, we found that the student sometimes had difficulty imagining how the two quantities of interest were changing together. At other times he exhibited a weak understanding of the operation of subtraction and the idea of constant rate of change. He did not appear to conceptualize subtraction as a quantitative comparison. His inability to conceptualize a constant rate of change as a proportional relationship between the changes in two quantities also presented an obstacle in his developing a meaningful formula that relied on this understanding. The results further stress the need to develop a student's ability to engage in mental operations that involve covarying quantities and a more robust understanding of constant rate of change since these abilities and understanding are critical for student success in future courses in mathematics.
ContributorsKlinger, Tana Paige (Author) / Carlson, Marilyn (Thesis director) / Thompson, Pat (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
ABSTRACT Many musicians, both amateur and professional alike, are continuously seeking to expand and explore their performance literature and repertory. Introducing new works into the standard repertory is an exciting endeavor for any active musician. Establishing connections, commissioning new works, and collaborating on performances can all work together toward the acceptance and success of a composer's music within an instrument community. For the flute, one such composer is Daniel Dorff (b. 1956). Dorff, a Philadelphia-based composer, has written for symphony orchestra, clarinet, contrabassoon, and others; however, his award-winning works for flute and piccolo are earning him much recognition. He has written works for such illustrious flutists as Mimi Stillman, Walfrid Kujala, and Gary Schocker; his flute works have been recorded by Laurel Zucker, Pamela Youngblood and Lois Bliss Herbine; and his pieces have been performed and premiered at each of the National Flute Association Conventions from 2004 to 2009. Despite this success, little has been written about Dorff's life, compositional style, and contributions to the flute repertory. In order to further promote the flute works of Daniel Dorff, the primary focus of this study is the creation of a compact disc recording of Dorff's most prominent works for flute: April Whirlwind, 9 Walks Down 7th Avenue, both for flute and piano, and Nocturne Caprice for solo flute. In support of this recording, the study also provides biographical information regarding Daniel Dorff, discusses his compositional methods and ideology, and presents background information, description, and performance notes for each piece. Interviews with Daniel Dorff regarding biographical and compositional details serve as the primary source for this document. Suggestions for the performance of the three flute works were gathered through interviews with prominent flutists who have studied and performed Dorff's pieces. Additional performance suggestions for Nocturne Caprice were gathered through a coaching session between the author and the composer. This project is meant to promote the flute works of Daniel Dorff and to help establish their role in the standard flute repertory.
ContributorsRich, Angela Marie (Contributor) / Novak, Gail (Pianist) (Performer) / Buck, Elizabeth Y (Thesis advisor) / Hill, Gary W. (Committee member) / Holbrook, Amy (Committee member) / Schuring, Martin (Committee member) / Arizona State University (Publisher)
Created2010
Description
The ideas of measurement and measurement comparisons (e.g., fractions, ratios, quotients) are introduced to students in elementary school. However, studies report that students of all ages have difficulty comparing two quantities in terms of their relative size. Students often understand fractions such as 3/7 as part-whole relationships or “three out of seven.” These limited conceptions have been documented to have implications for understanding the quotient as a measure of relative size and when learning other foundational ideas in mathematics (e.g., rate of change). Many scholars have identified students’ ability to conceptualize the relative size of two quantities values as important for learning specific ideas such as constant rate of change, exponential growth, and derivative. However, few researchers have focused on students’ ways of thinking about multiplicatively comparing two quantities’ values as they vary together across select topics in precalculus. Relative size reasoning is a way of thinking one has developed when conceptualizing the comparison of two quantities’ values multiplicatively, as their values vary in tandem. This document reviews literature related to relative size reasoning and presents a conceptual analysis that leverages this research in describing what I mean by a relative size comparison and what it means to engage in relative size reasoning. I further illustrate the role of relative size reasoning in understanding rate of change, multiplicative growth, rational functions, and what a graph’s concavity conveys about how two quantities’ values vary together.
This study reports on three beginning calculus students’ ways of thinking as they completed tasks designed to elicit students’ relative size reasoning. The data revealed 4 ways of conceptualizing the idea of quotient and highlights the affordances of conceptualizing a quotient as a measure of the relative size of two quantities’ values. The study also reports data from investigating the validity of a collection of multiple-choice items designed to assess students’ relative size reasoning (RSR) abilities. Analysis of this data provided insights for refining the questions and answer choices for these assessment items.
ContributorsLock, Kayla Ashley (Author) / Carlson, Marilyn (Thesis advisor) / Apkarian, Naneh (Thesis advisor) / Strom, April (Committee member) / Byerley, Cameron (Committee member) / Roh, Kyeong-Hah (Committee member) / Arizona State University (Publisher)
Created2023
Description
This dissertation reports three studies about what it means for teachers and students to reason with frames of reference: to conceptualize a reference frame, to coordinate multiple frames of reference, and to combine multiple frames of reference. Each paper expands on the previous one to illustrate and utilize the construct of frame of reference. The first paper is a theory paper that introduces the mental actions involved in reasoning with frames of reference. The concept of frames of reference, though commonly used in mathematics and physics, is not described cognitively in any literature. The paper offers a theoretical model of mental actions involved in conceptualizing a frame of reference. Additionally, it posits mental actions that are necessary for a student to reason with multiple frames of reference. It also extends the theory of quantitative reasoning with the construct of a ‘framed quantity’. The second paper investigates how two introductory calculus students who participated in teaching experiments reasoned about changes (variations). The data was analyzed to see to what extent each student conceptualized the variations within a conceptualized frame of reference as described in the first paper. The study found that the extent to which each student conceptualized, coordinated, and combined reference frames significantly affected his ability to reason productively about variations and to make sense of his own answers. The paper ends by analyzing 123 calculus students’ written responses to one of the tasks to build hypotheses about how calculus students reason about variations within frames of reference. The third paper reports how U.S. and Korean secondary mathematics teachers reason with frame of reference on open-response items. An assessment with five frame of reference tasks was given to 539 teachers in the US and Korea, and the responses were coded with rubrics intended to categorize responses by the extent to which they demonstrated conceptualized and coordinated frames of reference. The results show that the theory in the first study is useful in analyzing teachers’ reasoning with frames of reference, and that the items and rubrics function as useful tools in investigating teachers’ meanings for quantities within a frame of reference.
ContributorsJoshua, Surani Ashanthi (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn (Committee member) / Roh, Kyeong Hah (Committee member) / Middleton, James (Committee member) / Culbertson, Robert (Committee member) / Arizona State University (Publisher)
Created2019