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- Genre: Academic theses
Description
Yannis Constantinidis was the last of the handful of composers referred to collectively as the Greek National School. The members of this group strove to create a distinctive national style for Greece, founded upon a synthesis of Western compositional idioms with melodic, rhyhmic, and modal features of their local folk traditions. Constantinidis particularly looked to the folk melodies of his native Asia Minor and the nearby Dodecanese Islands. His musical output includes operettas, musical comedies, orchestral works, chamber and vocal music, and much piano music, all of which draws upon folk repertories for thematic material. The present essay examines how he incorporates this thematic material in his piano compositions, written between 1943 and 1971, with a special focus on the 22 Songs and Dances from the Dodecanese. In general, Constantinidis's pianistic style is expressed through miniature pieces in which the folk tunes are presented mostly intact, but embedded in accompaniment based in early twentieth-century modal harmony. Following the dictates of the founding members of the Greek National School, Manolis Kalomiris and Georgios Lambelet, the modal basis of his harmonic vocabulary is firmly rooted in the characteristics of the most common modes of Greek folk music. A close study of his 22 Songs and Dances from the Dodecanese not only offers a valuable insight into his harmonic imagination, but also demonstrates how he subtly adapts his source melodies. This work also reveals his care in creating a musical expression of the words of the original folk songs, even in purely instrumental compositon.
ContributorsSavvidou, Dina (Author) / Hamilton, Robert (Thesis advisor) / Little, Bliss (Committee member) / Meir, Baruch (Committee member) / Thompson, Janice M (Committee member) / Arizona State University (Publisher)
Created2011
Description
This paper describes six representative works by twentieth-century Chinese composers: Jian-Zhong Wang, Er-Yao Lin, Yi-Qiang Sun, Pei-Xun Chen, Ying-Hai Li, and Yi Chen, which are recorded by the author on the CD. The six pieces selected for the CD all exemplify traits of Nationalism, with or without Western influences. Of the six works on the CD, two are transcriptions of the Han Chinese folk-like songs, one is a composition in the style of the Uyghur folk music, two are transcriptions of traditional Chinese instrumental music dating back to the eighteenth century, and one is an original composition in a contemporary style using folk materials. Two of the composers, who studied in the United States, were strongly influenced by Western compositional style. The other four, who did not study abroad, retained traditional Chinese style in their compositions. The pianistic level of difficulty in these six pieces varies from intermediate to advanced level. This paper includes biographical information for the six composers, background information on the compositions, and a brief analysis of each work. The author was exposed to these six pieces growing up, always believing that they are beautiful and deserve to be appreciated. When the author came to the United States for her studies, she realized that Chinese compositions, including these six pieces, were not sufficiently known to her peers. This recording and paper are offered in the hopes of promoting a wider familiarity with Chinese music and culture.
ContributorsLuo, Yali, D.M.A (Author) / Hamilton, Robert (Thesis advisor) / Campbell, Andrew (Committee member) / Pagano, Caio (Committee member) / Cosand, Walter (Committee member) / Rogers, Rodney (Committee member) / Arizona State University (Publisher)
Created2012
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
The purpose of this project was to examine the lives and solo piano works of four members of the early generation of female composers in Taiwan. These four women were born between 1950 and 1960, began to appear on the Taiwanese musical scene after 1980, and were still active as composers at the time of this study. They include Fan-Ling Su (b. 1955), Hwei-Lee Chang (b. 1956), Shyh-Ji Pan-Chew (b. 1957), and Kwang-I Ying (b. 1960). Detailed biographical information on the four composers is presented and discussed. In addition, the musical form and features of all solo piano works at all levels by the four composers are analyzed, and the musical characteristics of each composer's work are discussed. The biography of a fifth composer, Wei-Ho Dai (b. 1950), is also discussed but is placed in the Appendices because her piano music could not be located. This research paper is presented in six chapters: (1) Prologue; the life and music of (2) Fan-Ling Su, (3) Hwei-Lee Chang, (4) Shyh-Ji Pan-Chew, and (5) Kwang-I Ying; and (6) Conclusion. The Prologue provides an overview of the development of Western classical music in Taiwan, a review of extant literature on the selected composers and their music, and the development of piano music in Taiwan. The Conclusion is comprised of comparisons of the four composers' music, including their personal interests and preferences as exhibited in their music. For example, all of the composers have used atonality in their music. Two of the composers, Fan-Ling Su and Kwang-I Ying, openly apply Chinese elements in their piano works, while Hwei-Lee Chang tries to avoid direct use of the Chinese pentatonic scale. The piano works of Hwei-Lee Chang and Shyh-Ji Pan-Chew are chromatic and atonal, and show an economical usage of material. Biographical information on Wei-Ho Dai and an overview of Taiwanese history are presented in the Appendices.
ContributorsWang, Jinding (Author) / Pagano, Caio (Thesis advisor) / Campbell, Andrew (Committee member) / Humphreys, Jere T. (Committee member) / Meyer-Thompson, Janice (Committee member) / Norton, Kay (Committee member) / Arizona State University (Publisher)
Created2011
Description
Researchers have documented the importance of seeing a graph as an emergent trace of how two quantities’ values vary simultaneously in order to reason about the graph in terms of quantitative relationships. If a student does not see a graph as a representation of how quantities change together then the student is limited to reasoning about perceptual features of the shape of the graph.
This dissertation reports results of an investigation into the ways of thinking that support and inhibit students from constructing and reasoning about graphs in terms of covarying quantities. I collected data by engaging three university precalculus students in asynchronous teaching experiments. I designed the instructional sequence to support students in making three constructions: first imagine representing quantities’ magnitudes along the axes, then simultaneously represent these magnitudes with a correspondence point in the plane, and finally anticipate tracking the correspondence point to track how the two quantities’ attributes change simultaneously.
Findings from this investigation provide insights into how students come to engage in covariational reasoning and re-present their imagery in their graphing actions. The data presented here suggests that it is nontrivial for students to coordinate their images of two varying quantities. This is significant because without a way to coordinate two quantities’ variation the student is limited to engaging in static shape thinking.
I describe three types of imagery: a correspondence point, Tinker Bell and her pixie dust, and an actor taking baby steps, that supported students in developing ways to coordinate quantities’ variation. I discuss the figurative aspects of the students’ coordination in order to account for the difficulties students had (1) constructing a multiplicative object that persisted under variation, (2) reconstructing their acts of covariation in other graphing tasks, and (3) generalizing these acts of covariation to reason about formulas in terms of covarying quantities.
This dissertation reports results of an investigation into the ways of thinking that support and inhibit students from constructing and reasoning about graphs in terms of covarying quantities. I collected data by engaging three university precalculus students in asynchronous teaching experiments. I designed the instructional sequence to support students in making three constructions: first imagine representing quantities’ magnitudes along the axes, then simultaneously represent these magnitudes with a correspondence point in the plane, and finally anticipate tracking the correspondence point to track how the two quantities’ attributes change simultaneously.
Findings from this investigation provide insights into how students come to engage in covariational reasoning and re-present their imagery in their graphing actions. The data presented here suggests that it is nontrivial for students to coordinate their images of two varying quantities. This is significant because without a way to coordinate two quantities’ variation the student is limited to engaging in static shape thinking.
I describe three types of imagery: a correspondence point, Tinker Bell and her pixie dust, and an actor taking baby steps, that supported students in developing ways to coordinate quantities’ variation. I discuss the figurative aspects of the students’ coordination in order to account for the difficulties students had (1) constructing a multiplicative object that persisted under variation, (2) reconstructing their acts of covariation in other graphing tasks, and (3) generalizing these acts of covariation to reason about formulas in terms of covarying quantities.
ContributorsFrank, Kristin Marianna (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn P (Thesis advisor) / Milner, Fabio (Committee member) / Roh, Kyeong Hah (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2017
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