15,808 research outputs found

    Students’ Development of Geometric Reasoning About the Derivative of Complex-Valued Functions

    Get PDF
    The purpose of this study was to explore the nature of students’ reasoning about the derivative of a complex-valued function, and to study ways in which they developed this reasoning while working with Geometer’s Sketchpad (GSP). The participants in this study were four students from one undergraduate complex analysis class. The development of participants’ reasoning about the derivative of a complex-valued function was captured via video-recording and screen-capture software in a four-day interview sequence consisting of a two-hour-long interview each day. This reasoning was interpreted through the theoretical perspective of embodied cognition. The findings indicated that students manifested embodied reasoning through gesture and speech, through algebraic and geometric inscriptions, and through interaction with the physical environment and the virtual environment provided by GSP. The findings further indicated that students needed to advance their geometric reasoning about the derivative of a complex-valued function in three essential ways in order to reason geometrically about the derivative as a local linear approximation. First, with help from gesture and speech, they recognized that they did not know how to characterize a linear complex-valued function. Second, with help from algebraic and geometric inscriptions, they reasoned that a linear complex-valued function f(z) rotates and dilates every circle by the same amounts Arg(f^\u27 (z)) and |f^\u27 (z)|, respectively. Finally, through embodied reasoning in both the virtual and physical environments, students recognized the need to focus on how a complex-valued function rotates and dilates small circles only. These findings suggest that one approach to improving student learning about the derivative of a complex-valued function is to highlight these three geometric aspects of the derivative, and to offer students opportunities to reason about this geometry in embodied ways listed above

    The composer as technologist : an investigation into compositional process

    Get PDF
    This work presents an investigation into compositional process. This is undertaken where a study of musical gesture, certain areas of cognitive musicology, computer vision technologies and object-orientated programming, provide the basis for a composer (author) to assume the role of a technologist and acquire knowledge and skills to that end. In particular, it focuses on the application and development of a video gesture recognition heuristic to the compositional problems posed. The result is the creation of an interactive musical work with score for violin and electronics that supports the research findings. In addition, the investigative approach into developing technology to solve musical problems that explores practical composition and aesthetic challenges is detailed

    Teaching for progression: speaking and listening

    Get PDF

    /Offscreen/

    Full text link
    Master of Fine Arts (MFA)Art and DesignUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/156111/1/DeepBlue_Fitzgerald_2018_MFA_Thesis.pd

    Gesture in Karnatak Music: Pedagogy and Musical Structure in South India

    Get PDF
    This thesis presents an examination of gesture in Karnatak music, the art music of South India. The topic is approached from two perspectives; the first considers Karnatak music structure from a gestural perspective, looking both at the music itself and at the gestures that create it, while the second enquires into the role played by physical gesture in vocal pedagogy. The broader aims of the thesis are to provide insight into the musical structure of the Karnatak style, and to contribute to wider discourses on connections between music and movement. An interdisciplinary approach to the research is taken, drawing on theories and methods from the fields of ethnomusicology, embodied music cognition, and gesture studies. The first part of the thesis opens with a discussion of differences between practical and theoretical conceptions of the Karnatak style. I argue for the significance in practice of svara-gamaka units and longer motifs formed of chains of such units, and also consider the gestural qualities of certain motifs and their contribution to bhāva (mood). Subsequently, I present a joint musical and motoric analysis of a section of Karnatak violin performance, seeking to elucidate the dynamic processes that form the style. The second part of the thesis enquires into the role played by hand gestures produced by teachers and students in vocal lessons, looking at what is indexed by the gestures and how such indexing contributes to the pedagogic process. This part of the thesis also considers how gestures contribute to the formation and maintenance of common ground between teacher and student. The final chapter brings the two strands of this thesis together to discuss the connections that exist between musical and physical gesture in Karnatak music

    Spectators’ aesthetic experiences of sound and movement in dance performance

    Get PDF
    In this paper we present a study of spectators’ aesthetic experiences of sound and movement in live dance performance. A multidisciplinary team comprising a choreographer, neuroscientists and qualitative researchers investigated the effects of different sound scores on dance spectators. What would be the impact of auditory stimulation on kinesthetic experience and/or aesthetic appreciation of the dance? What would be the effect of removing music altogether, so that spectators watched dance while hearing only the performers’ breathing and footfalls? We investigated audience experience through qualitative research, using post-performance focus groups, while a separately conducted functional brain imaging (fMRI) study measured the synchrony in brain activity across spectators when they watched dance with sound or breathing only. When audiences watched dance accompanied by music the fMRI data revealed evidence of greater intersubject synchronisation in a brain region consistent with complex auditory processing. The audience research found that some spectators derived pleasure from finding convergences between two complex stimuli (dance and music). The removal of music and the resulting audibility of the performers’ breathing had a significant impact on spectators’ aesthetic experience. The fMRI analysis showed increased synchronisation among observers, suggesting greater influence of the body when interpreting the dance stimuli. The audience research found evidence of similar corporeally focused experience. The paper discusses possible connections between the findings of our different approaches, and considers the implications of this study for interdisciplinary research collaborations between arts and sciences

    Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding

    Get PDF
    In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)
    • 

    corecore