Thesis (Ph. D.)--University of Chicago, Department of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.

As the main vehicle through which the majority of the population comes to understand the world around them, the media has the power to dominate public opinion, reinforce traditional notions and introduce new ideologies. With regards to gender, the media’s role is two-prong: it pathologizes and highlights gender deviance, and simultaneous reinforces culturally constructed gender norms. The current study examines media representations of Mary Winkler, a Tennessee woman who shot her minister husband to death in 2006. Winkler’s role as the wife of a religious and community leader implies high morality, sexual demureness, nurturance and obedience. Because Winkler’s involvement in the shooting death of her husband severely conflict with these social and gender role expectations, this work examines how Winkler’s social position affect media depictions of her criminality, and the implications of these depictions on society’s perception of gender, religion, and crime. To answer these questions, 97 newspapers articles produced between April 9th, 2007 (the first day of Winkler’s trial) and August 15, 2007 (the date of Winkler’s release on parole) were analyzed using content analysis methodology. The study results show that Winkler’s adherence to feminine norms was highly influential in her construction as a sympathetic figure and her receipt of a lesser conviction of voluntary manslaughter. / text

We study contact representations of graphs in the plane and in 3D space, where vertices are represented by polygons or polyhedra and each edge is represented by a common boundary between two polygons or polyhedra. In the weighted version of the problem, we find contact representations with the additional restriction that the areas for the polygons or the volumes for the polyhedra realize some pre-specified value for the vertices. We address different variants of the problem depending on the types of polygons or polyhedra (convex or non-convex, axis-aligned or not), types of contacts (proper contacts with common boundaries of non-zero lengths in 2D or non-zero areas in 3D or improper contacts where common boundaries of zero lengths or areas are allowed), and whether holes are allowed in the representation or not. In the plane we mainly focus on the weighted version of the problem. We find optimal (in terms of polygonal complexity) contact representations for planar graphs (both for axis-aligned and non-axis-aligned polygons) and some subclasses of planar graphs. With non-axis-aligned polygons we show that non-convex polygons with 4 sides are sometimes necessary and always sufficient for proportional contact representation of a planar graph, when point contacts are allowed; otherwise for proper contacts 7-sided polygons are sometimes necessary and always sufficient. We give a linear-time algorithm in each case to compute the optimal representation. We also give quadratic-time algorithms to construct optimal proportional contact representations for (2, 0)-sparse graphs (with triangles for improper contacts and with convex quadrilaterals for proper contacts). For maximal outerplanar graphs proportional contact representation with triangles can also be computed in linear time. In case only axis-aligned polygons are used, we show that 8 sides are sometimes necessary and always sufficient for a planar graph. While we do not have a polynomial-time algorithm to construct such a representation, we give a linear-time algorithm to compute representation with 10-sided axis-aligned polygons. We also give linear-time construction algorithms for optimal proportional contact representations with 8-sided polygons for planar 3-trees and Hamiltonian maximal planar graphs, and with rectangles for maximal outerplanar graphs. For contact representation with 3D polyhedra, we consider both the weighted and the unweighted variants of the problem for both planar and non-planar graphs and have some preliminary results. We find several subclasses of planar graphs that have contact representations using cubes or proportional boxes. We also consider (improper) contact representations using tetrahedra, and show that planar graphs, complete bipartite and tripartite graphs, and complete graphs with at most 10 vertices have contact representations with tetrahedra. We also addressed variants of this problem using only unit regular tetrahedra or considering contacts only between apices of the tetrahedra or using both restrictions.

This study explores how aggregate representations of student-contributed content were used in whole-class discussions to scaffold scientific inquiry in two middle school science classrooms. Working together as a knowledge community, students contribute scaffolded observations concerning HelioRoom and WallCology, room-sized “Embedded Phenomena” simulations, using tablet computers. These observations are collected and represented in aggregate form, and are the focus of teacher-led whole-class discussions. This thesis examines the efficacy of these aggregate designs for advancing students’ and teachers’ engagement in and understanding of the object of scientific inquiry, their usefulness for constructing relational models, and the interaction patterns that arise from their use. Findings suggest that aggregate representations of binary relationships that use tallies are well-suited for learning activities that have directed outcomes, such as constructing a relationship network. Aggregate representations that highlight gaps in data, and areas of agreement and disagreement in the data can be effective tools fostering productive discourse in classrooms.

This study explores how aggregate representations of student-contributed content were used in whole-class discussions to scaffold scientific inquiry in two middle school science classrooms. Working together as a knowledge community, students contribute scaffolded observations concerning HelioRoom and WallCology, room-sized “Embedded Phenomena” simulations, using tablet computers. These observations are collected and represented in aggregate form, and are the focus of teacher-led whole-class discussions. This thesis examines the efficacy of these aggregate designs for advancing students’ and teachers’ engagement in and understanding of the object of scientific inquiry, their usefulness for constructing relational models, and the interaction patterns that arise from their use. Findings suggest that aggregate representations of binary relationships that use tallies are well-suited for learning activities that have directed outcomes, such as constructing a relationship network. Aggregate representations that highlight gaps in data, and areas of agreement and disagreement in the data can be effective tools fostering productive discourse in classrooms.

No description available.

The purpose of this thesis is to discuss the rôle of certain types of quiver which appear in the modular representation theory of finite groups. It is our concern to study two different types of quiver. First of all we construct the ordinary quiver of certain blocks of defect 2 of the symmetric group, and then apply our results to the alternating group and to the theory of partitions. Secondly, we consider connected components of the stable Auslander-Reiten quiver of certain groups G with normal subgroup N. The main interest lies in comparing the tree class of components of N-modules, with the tree class of components of these modules induced up to G.

Developmental dyslexia is widely believed to be caused either mainly or in part by an impairment of phonological representations. Although this hypothesis predicts that individuals with dyslexia should show deficits in tasks which require the use of implicit phonological knowledge, this has not yet been directly tested, as the evidence cited in support of this hypothesis usually comes from metalinguistic tasks which demand explicit awareness of phonological units. Additionally, since the ability to perform metalinguistic tasks which involve phonological segments can be enhanced by an individual’s competence in alphabetic literacy, the possibility remains that phonological skills may have been inadequately isolated from the influences of literacy acquisition in many cases. The study reported in this thesis investigated both the representations and the metalinguistic skills of a group of adults with a history of developmental dyslexia, examining areas of phonology which do and do not have orthographic counterparts. To isolate phonological skills from orthographic skills, the representations of conventional segmental contrasts (e.g. /k/ vs /g/) were compared with the representation of suprasegmental contrasts (as seen in minimal pairs such as ′toy factory and toy ′factory), which have no orthographic counterpart. Basic metalinguistic skills were tested by means of a phonological awareness task targeting both segmental and suprasegmental units, and phonological manipulation skills were tested using a Pig Latin task and a Spoonerism task, where participants were required to manipulate both segmental and suprasegmental units (e.g. extracting the segment /b/ from consonant clusters and the main stress from SWW or WSW stress patterns). The results showed that although the performance of the dyslexic group was weaker than that of the control group when tasks required the manipulation of either the segmental or suprasegmental components of words, no evidence was found for a deficit in the tasks which drew on implicit representations or basic metalinguistic skills. These findings suggest that the phonological deficit in dyslexia may be restricted to the ability to manipulate phonological units rather than in the representation of them per se.

This thesis presents a methodology for, and a case study of, the transformation of a social representation. The basis of the thesis is derived from an understanding of representations as a complex, dynamic, pluralistic phenomena that both exist in time and draw their form and meaning from past and present knowledge(s). We are guided by an interest in understanding how one might study a social representation that is already an entrenched social phenomena and how one might go about studying such an entity in a systematic fashion over time. We devised a method through which data can be aggregated over a bound, measurable unit of time and analyzed systematically into core and peripheral systems, allowing for the study of transformation of representation of long duration. Our methodology thus embeds social representations in particular historical, temporal moments in order to assess the structural formation of the representation. To assess the applicability of our methodology, we undertook a study of the social representation of physicians in televised medical dramas. The case of the physician was selected because of their existence as a known social phenomenon of long-duration with a prominent, continuous social presence. In our exploration of this case, we sought to answer two questions. The first asks, ‘what is the social representation of the physician as presented in televised medical dramas’, while the second queries is ‘if and how this social representation has changed over time’. We present thus not only the identification and transformation of a representation, that of the physician, but we also offer a methodology with which to do so. Our methodology demonstrates that exploring representations in the past as a way to study the transformation of social representation has potential to generate new knowledge about old things. While the study of newly emerging phenomena presents an ideal time to study social representations, the study of older representations offers the opportunity to better understand how knowledge is created, changed, and re-created.

No description available.