Browsing by Author "Dr. Ronald Fulp, Committee Member"

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    Kindergarten Teachers' Mathematics Teaching Cycle: Attending to Issues of Culture and Student Understanding
    (2008-12-04) Edgington, Cynthia Page; Dr. Allison McCulloch, Committee Chair; Dr. Hollylynne Lee, Committee Member; Dr. Patricia Marshall, Committee Member; Dr. Ronald Fulp, Committee Member
    The purpose of this study is to examine the mathematics teaching cycle of two kindergarten teachers who took part in a professional development project that promoted culturally relevant pedagogy and teaching mathematics for understanding. The study aims to address the lack of research with respect to how teaching mathematics for understanding and attending to students’ cultural backgrounds can effectively be incorporated into teachers’ lesson planning practices. The present study also examines if and how the teachers’ enacted math lessons are consistent with the ideologies associated with culturally relevant pedagogy and teaching for understanding. The participants for this study were two kindergarten teachers in North Carolina who participated for one year in a three-year professional development project called Nurturing Mathematics Dreamkeepers. The data consisted of a lesson planning interview, a lesson planning observation, video-taped math lessons, and a post-lesson reflective session. The conceptual framework for this study considers Simon’s (1995) mathematics teaching cycle as a way to describe the planning and teaching process. Within the mathematics teaching cycle, Ladson-Billings’ (1995a) tenets of culturally relevant pedagogy and Hiebert, et al.’s (1997) dimensions of classrooms that support teaching for understanding are both used as a lens to examine the participants’ teaching cycles. The findings from this study suggest that the teachers attend to many things during their lesson planning, including the learning objective, classroom activities and their students’ backgrounds. Some aspects of their enacted lessons were consistent with the ideologies associated with culturally relevant pedagogy and teaching for understanding. The teachers exhibited high academic expectations for all students and provided contexts that are meaningful for their students. Although the teachers encouraged their students to develop their own strategies for solving problems, they did not value all of the strategies suggested by their students. Overall, some aspects of CRP and teaching for understanding were evident in the teachers’ lesson planning observation and in their enacted lessons. If a goal of mathematics instruction is to increase student understanding in a learning environment that is accessible to all students and where academic success is experienced by all students, the mathematics education community can learn from studies such as this how to make this goal a reality.
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    On Geometric Control Design for Holonomic and Nonholonomic Mechanical Systems
    (2007-07-17) Osborne, Jason; Dr. Larry Norris, Committee Member; Dr. Dmitry Zenkov, Committee Chair; Dr. Ronald Fulp, Committee Member; Dr. Stephen Campbell, Committee Member
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    Use of Integral Signature and Hausdorff Distance in Planar Curve Matching
    (2009-12-02) Iwancio, Kathleen Marie; Dr. Pierre Gremaud, Committee Member; Dr. Ronald Fulp, Committee Member; Dr. Irina Kogan, Committee Chair; Dr. Karen Hollebrands, Committee Member
    Curve matching is an important problem in computer image processing and image recognition. In particular, the problem of identifying curves that are equivalent under a geometric transformation arises in a variety of applications. Two curves in $mathbb{R}^2$ are called congruent if they are equivalent under the action of the Euclidean group, i.e. if one curve can be mapped to the other by a combination of rotations, reflections, and translations. In theory, one can identify congruent curves by using differential invariants, such as infinitesimal arc-length and curvature. The practical use of differential invariants is problematic, however, due to their high sensitivity to noise and small perturbations. Other types of invariants that are less sensitive to perturbations were proposed in literature, but are much less studied than classical differential invariants. In this thesis we provide a detailed study of matching algorithms for planar curves based on Euclidean integral invariant signatures. Several types of local and global signatures are considered. We examine numerical approximations of signatures, sensitivity to perturbation, dependence on parametrization and a choice of initial point, and effects of the symmetries of the original image on signatures. Furthermore, we use Hausdorff distance between signatures to define a distance between congruence classes of curves.