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Description
Phantom Sun is a ten-minute piece in three sections, and is composed for flute, clarinet in b-flat, violin, cello, and percussion. The three-part structure for this work is a representation of the atmospheric phenomenon after which the composition is named. A phantom sun, also called a parhelion or sundog, is a weather-related phenomenon caused by the horizontal refraction of sunlight in the upper atmosphere. This refraction creates the illusion of three suns above the horizon, and is often accompanied by a bright halo called the circumzenithal arc. The halo is caused by light bending at 22° as it passes through hexagonal ice crystals. Consequently, the numbers six and 22 are important figures, and have been encoded into this piece in various ways.
The first section, marked “With concentrated intensity,” is characterized by the juxtaposition of tonal ambiguity and tonal affirmation, as well as the use of polymetric counterpoint (often 7/8 against 4/4 or 7/8 against 3/4). The middle section, marked “Crystalline,” provides contrast in its use of unmetered sections and independent tempos. The refraction of light is represented in this movement by a 22-note row based on a hexachord (B-flat, F, C, G, A, E) introduced in measure 164 of the first section. The third section, marked “With frenetic energy,” begins without pause on an arresting entrance of the drums playing an additive rhythmic pattern. This pattern (5+7+9+1) amounts to 22 eighth-note pulses and informs much of the motivic and structural considerations for the remainder of the piece.
The first section, marked “With concentrated intensity,” is characterized by the juxtaposition of tonal ambiguity and tonal affirmation, as well as the use of polymetric counterpoint (often 7/8 against 4/4 or 7/8 against 3/4). The middle section, marked “Crystalline,” provides contrast in its use of unmetered sections and independent tempos. The refraction of light is represented in this movement by a 22-note row based on a hexachord (B-flat, F, C, G, A, E) introduced in measure 164 of the first section. The third section, marked “With frenetic energy,” begins without pause on an arresting entrance of the drums playing an additive rhythmic pattern. This pattern (5+7+9+1) amounts to 22 eighth-note pulses and informs much of the motivic and structural considerations for the remainder of the piece.
ContributorsMitton, Stephen LeRoy (Author) / DeMars, James (Thesis advisor) / Norton, Kay (Committee member) / Rogers, Rodney (Committee member) / Arizona State University (Publisher)
Created2017
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
ContributorsHsu, Gabrielle (Performer) / Kierum, Caitlin (Performer) / Song, Yiqian (Performer) / Fox, Matt (Performer) / Lougheed, Julia (Performer) / Jones, Evelyn (Performer) / Miller, Isaac (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-14
ContributorsMoonitz, Olivia (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-13
ContributorsAnderle, Jeff (Performer) / Wegehaupt, David (Performer) / Bennett, Joshua (Performer) / Clements, Katrina (Performer) / Dominguez, Vincent (Performer) / Druesedow, Libby (Performer) / Englert, Patrick (Performer) / Liang, Jack (Performer) / Moonitz, Olivia (Performer) / Ruth, Jeremy (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-09
ContributorsNeidermayer, Tyler (Performer) / Karam, Andrea Luque (Performer) / White, Jonathan (Performer) / Manka, Andrew (Performer) / Chaston, Aubrey (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-31
ContributorsSpring, Robert (Performer) / Gardner, Joshua (Performer) / Buck, Elizabeth (Performer) / Schuring, Martin (Performer) / Micklich, Albie (Performer) / Ericson, John Q. (John Quincy), 1962- (Performer) / Smith, J. B., 1957- (Performer) / Ryan, Russell (Contributor) / ASU Library. Music Library (Publisher)
Created2018-09-16
ContributorsZhu, Shuang (Performer) / Spring, Robert (Performer) / Zhang, Aihua (Performer) / Skinner, Wesley (Performer) / Jiang, Zhou (Performer) / ASU Library. Music Library (Publisher)
Created2018-09-09
ContributorsSadownik, Stephanie (Performer) / Di Russo, Michelle (Conductor) / ASU Library. Music Library (Publisher)
Created2018-04-08