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Understanding how students learn, that is, how they recognize, process, and internalize new information, is vital to any teacher’s success. Although many theories exist in this field, I have selected three strong theories to initiate a discussion that I see as suggestive of a new, cohesive theory that represents a synthesis of all three. For the purposes of this report, I have selected the theories of constructivism and social constructivism from Piaget and Vygotsky, Bronfenbrenner’s Ecological Systems theory, and Chaos theory as the basis for my proposed model. In the report, these three theories are deconstructed, and various components of each are then synthesized to suggest a comprehensive model. It is my intent that my proposed model be helpful to teachers in designing and tailoring instruction for their students. By understanding the relationships and inter-relationships of the child to the various systems that affect him/her, the teacher can better engage all students toward a successful outcome. / text

This thesis details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, indicating the onset of chaotic motion. These results are compared to simulation results, which suggest chaotic motion through the appearance of strange attractors in the Poincaré maps. Additionally, evidence of the WPP system experiencing both types of chaos simultaneously was found, resulting in a merger of two distinct types of strange attractor. / Master of Science / This report details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This system can be used to investigate what are known as local and global bifurcations. A local bifurcation occurs when the single equilibrium state (corresponding to the pendulum hanging straight down) when spun at low speeds, bifurcates into three equilibria when the spin rate is increased beyond a certain value. The global bifurcations occur when the system experiences sinusoidal forcing near certain equilibrium conditions. The resulting chaotic oscillations are investigated using Melnikov’s method, which determines when the sinusoidal forcing results in chaotic motion. This chaotic motion comes in two types, which cause the system to behave in different ways. Melnikov’s method, and results from a simulation were used to determine the parameter values in which the pendulum experiences each type of chaos. It was seen that at certain parameter values, the WPP experiences both types of chaos, supporting the observation that these types of chaos are not necessarily independent of each other, but can merge and interact.

The desire to develop a holistic framework for knowing and modelling in human enterprises is not new. Methodologies, such as Systems Dynamics, Soft Systems and the Viable Systems Model all claim a holistic perspective. Each of these approaches emphasises the interrelatedness of `things', rather than the `things' themselves. Thus, they avoid the possible fragmentation that can occur when elements within a situation are treated as if they exist independently. Unfortunately, the systems approaches flounder because they fail to reconcile knowledge with the path that brings it into being, or to satisfactorily deal with the concepts of order or communication in language. The Thesis, therefore, provides a greater clarification of these issues, in the light of enactive cognitive science, chaos theory and contemporary theories on dialogue. As a result, a new framework is presented, for knowing and modelling in human enterprises, that is based on our `new' understanding of holism. The organisational context of the Thesis is provided by two generic models, both developed by the author (a model of Duopoly Competition and a model of Chaos Control ), together with a case study of the Danish hearing aid manufacturer Oticon. The Thesis concludes by presenting various insights arising from our new frame of reference and reflecting on their challenges for organisations.

ABSTRACT What is visual art making, the artistic creative process, and how does it work? These questions fuelled an investigation at first theoretical, then incorporating an empirical study centered on attaining understanding relating to the elements and dynamics involved in making visual art. The resultant study aims to offer an approach to gaining comprehensive understanding of the artistic creative process, an understanding that may inform art teaching practice, so that art teachers may better understand the related dynamics of their pedagogical processes. Historically the artistic creative process has been accepted as one consisting of different sequential stages of development. This view however, is evolving due to the growing understanding of interrelated dynamics of life processes offered by, for example, neurological studies of the brain. New thinking links earlier philosophical and psychological ideas presented by such thinkers as James (1894) and Dewey (1934), to the work of Baars (1999), Brown (2000), Ellis (1999), Zeki (2000), in offering a deeper understanding of the natural human creative process. The reflective aspect of the artistic creative process is thus related to the way that we process information every minute of our lives; essentially it is the way we progress through life, minute by minute, learning and evolving, affirming self through finding meaning. Study of current theory relating to the processes of the brain inevitably incorporates modern thinking that revolves around dynamic processes. Originating in thermodynamics, Chaos Theory has travelled far from physics to become incorporated into a broad spectrum of disciplines. It offers a common language that relates to the dynamics of human nature, and as such is totally applicable to areas of learning and human interaction. Here used metaphorically, Chaos Theory serves to elucidate interactive aspects of the discipline of art making, with much to offer an understanding of the artistic creative process as it describes exactly the same process of change and growth through experience. A metaphorical use of the language of Chaos Theory provides visual art making with a means of sharing ideas with other academic disciplines that also constantly deal with the dynamics of the human condition, found for example in the close connections between the methods of exploration of both artists and scientists. In studying the phenomenon of ‘scale’ the physicist Feigenbaum commented on the connections between perceptions of artists and those of scientists, pointing to the way in which their perceptions and analysis of things coincide (Gleick, 1987). The visual analysis evident in the work of Turner or Ruskin reflects the same process of detailed conceptual exploration of material collected by the senses as that of a student of any field of scientific exploration. Chaos Theory is important also in that it provides a language accessible by varying levels of expertise, whether at a simple metaphorical or a more sophisticated level. This work charts these dimensions because “The challenge is to reverse the disconnectedness of the present world and to develop a curriculum that is not based on separateness of knowledge from life and being, but upon their inherent unity and integration” (Lovat and Smith, 1995, p.248). / PhD Doctorate

Sand is an appropriate material to embody and make visible the impulses which may pass through the moving hand and also permeate the universe. Its ability to absorb impressions means it can take on the full range of material states, solid, liquid or vapour, and allows it to speak with the rhythmic language the whole of nature itself uses. Developing a language of forms which more closely speaks this rhythmic language of nature requires an intimate knowledge of the processes of nature. Sand experiments undertaken show the formation a rich array of dazzling patterns. Chaos theory explains this self organizing capacity, and reveals the depth of interdependence of systems within nature. The aspect of self-similarity is also of central significance in appreciating how nature looks and function, and thus how it might be imaged. Drawings from nature were developed using sand as a parameter, starting with the single grain and translating the dynamism of moving sand into mark. Field trips involved looking for waves and repeated lines in nature, and observing how marks form in nature. Chaos theory provides a ground to bring together different spheres of knowledge ?? science, theology and art. It reveals the peculiarities of a material??s behaviour as being of critical importance in the mechanism of evolution. It also provides fresh insight into an incarnational Christian theological perspective, and the relational dynamic within the Trinity. The unity of far and near is also reflected in chaos theory in the self similarity of images. Romantic artists Turner and Van Gogh both engage in the search for a visual language of transcendence through nature using the use of the themes of chaos and order, with an emphasis on physicality and movement. Contemporary artists Goldsworthy, Blanchflower and Kirkeby ground their work in knowledge of material. Changes from solid and rigid to shifting and open show in the development of my work. The immediacy and dynamism of mark making in drawing and staining, ripping and sanding in painting gives process and materiality greater weight. The significance of relationality has reinforced the integrity of horizontal and vertical as expressed in nature and allowed for flexible repositioning of the image within a grid

This paper explores the interrelationships among corporate culture, capital structure, firm performance, and fiduciary duties. Chaos theory, nonlinear dynamics, complex systems theory, and socio-cultural studies of firms’ organizational ecosystems, and enabling infrastructure suggest that the BCE rule is: (i) a superior fiduciary principle to shareholder primacy; and (ii) more likely to enhance firm value in proportion to the importance of intangible assets in its production process. The existence of “epistatic costs” rooted in the non-linear negative feedback effects of perverse agency theory-driven cost cutting is hypothesized. A theoretical model is developed to empirically test for the existence of epistatic costs and optimal levels of organizational tension or “slack.” Broader implications of the model for fiduciary rules, financing decisions, and the current posture of Canadian securities regulation in the takeover context are explored.

This paper explores the interrelationships among corporate culture, capital structure, firm performance, and fiduciary duties. Chaos theory, nonlinear dynamics, complex systems theory, and socio-cultural studies of firms’ organizational ecosystems, and enabling infrastructure suggest that the BCE rule is: (i) a superior fiduciary principle to shareholder primacy; and (ii) more likely to enhance firm value in proportion to the importance of intangible assets in its production process. The existence of “epistatic costs” rooted in the non-linear negative feedback effects of perverse agency theory-driven cost cutting is hypothesized. A theoretical model is developed to empirically test for the existence of epistatic costs and optimal levels of organizational tension or “slack.” Broader implications of the model for fiduciary rules, financing decisions, and the current posture of Canadian securities regulation in the takeover context are explored.