Subitizing, a quick apprehension of the numerosity of a small set of items, is inconsistently utilized by preschool educators to support early number understandings (Sarama & Clements, 2009). The purpose of this qualitative study is to investigate the relationship between children’s number understanding and subitizing activity. Sarama and Clements (2009) consider students’ subitizing activity as shifting from reliance upon perceptual processes to conceptual processes. Hypothesized mental actions carried into subitizing activity by children have not yet been empirically investigated (Sarama & Clements, 2009). Drawing upon Piaget’s (1968/1970) three mother structures of mathematical thinking, the theoretical implications of this study consider expanding the scope of Piaget’s (1968/1970) definition of topological thinking structures to include patterned orientations. Increasing the scope of this definition would allow for the investigation of the development of topological thinking structures and subitizing activity. An 11-week teaching experiment was conducted with six preschool aged children in order to analyze student engagement with subitizing tasks (Steffe & Ulrich, in press). To infer what perceptual and conceptual processes students relied upon when subitizing, tasks were designed to either assess or provoke cognitive changes. Analysis of interactions between students and the teacher-researcher informed this teacher-researcher of cognitive changes relative to each student’s thinking structure. Results indicated that students rely upon the space between items, symmetrical aspects of items, and color of items when perceptually subitizing. Seven different types of subitizing activity were documented and used to more explicitly describe student reliance upon perceptual or conceptual processes. Conceptual subitizing activity was redefined in this study, as depending upon mental reversibility and sophisticated number schemes. Students capable of conceptual subitizing were also able to conserve number. Students capable of conserving number were not always capable of conceptual subitizing. The symmetrical aspects of an item’s arrangement elicited students’ attention towards subgroups and transitioning students’ perceptual subitizing to conceptual subitizing. Combinations of counting and subitizing activity explained students’ reliance upon serial and classification thinking structures when transitioning from perceptual subitizing to conceptual subitizing. Implications of this study suggest effectively designed subitizing activity can both assess students’ number understandings, and appropriately differentiate preschool curriculum. / Ph. D.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo deste trabalho à desenvolver a teoria bÃsica de esquemas e mostrar que duas variedades projetivas birracionalmente equivalentes e nÃo-singulares sobre um corpo algebricamente fechado possuem um mesmo gÃnero geomÃtrico. Um resultado relacionado permite determinar se uma hipersuperfÃcie nÃo-singular de grau d em um espaÃo projetivo Pn à uma variedade nÃo-racional. / This work aims to develop basic scheme theory and show that two projective, non-singular and birationally equivalent varieties over an algebraically closed field have same geometric genus. A related result allows to check whether a non-singular hipersurface of degree d in a projective space Pn is a non-rational variety.

La présente thèse a pour objet l'étude de l'appropriation de nouvelles pratiques au sein des organisations. Cette problématique est abordée par le prisme des processus psychologiques développementaux, cognitifs et sociaux en jeu dans le développement des compétences des acteurs. Notre réflexion théorique nous amène à présenter les travaux précurseurs lewiniens, quelques modèles significatifs du changement organisationnel et de l'apprentissage organisationnel, puis un modèle d'analyse des compétences permettant de décrire les schèmes d'activité des acteurs en matière d'invariants opératoires (i.e., ce qui est tenu pour vrai ou pertinent) et de règles d'action (i.e., actions effectrices sur l'environnement). La mise en place d'une série d'études expérimentales nous permet de conclure que le développement des compétences individuelles et collectives est facilité lorsque le dispositif d'apprentissage permet aux acteurs d'associer la conceptualisation des invariants opératoires à la production des règles d'action. Ces résultats sont expliqués principalement au regard du concept piagétien de prise de conscience. Les contributions et limites de la thèse sont finalement discutées. / This thesis focuses on the appropriation of new practices within organizations. This topic is analyzed through the lens of the developmental, cognitive and social psychological processes involved in the development of stakeholders' competencies. Our theoretical discussion presents the Lewinian approach to change management, several significant organizational change and organizational learning models, as well as a model of competencies analysis that breaks down stakeholder's activity schemes into operational invariants (i.e., what is held for true or relevant) and action rules (i.e., actions effecting the environment). A series of experimental studies reveals that the development of individual and collective competencies is facilitated when the learning material allows stakeholders to link the conceptualization of operational invariants to the production of action rules. These results are mostly explained in terms of the Piagetian concept of awareness. The contributions and limits of the thesis are finally discusse

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This study examines the party-controlled communication of the five most important political parties in the North West Province of South Africa during the 1999 general elections. The main assumption is that political parties in developing democracies have a normative obligation to do more than canvas for votes during an election campaign. Political parties should also be instrumental through their communication in fostering a democratic political culture. Central to this argument is the notion that a typical marketing approach is not suitable for an election campaign in a developing democracy. In accordance with the participatory approach to development, it is thus proposed that the two-way symmetrical model for public relations (as proposed by James Grunig) is a more appropriate approach to election campaigns. Especially relevant for this study is the two-way symmetrical model's emphasis on interaction and the establishment of long tern relationships with target publics. Through an extensive qualitative analysis of all relevant material (party manifests, newspaper advertisements, radio advertisements, pamphlets, posters and web pages), it was found that South African political parties placed much less emphasis on the "image" of the party or its leader compared to their American counterparts. However, that did not imply that the substance of the message was emphasised adequately. On the contrary, the political parties participating in the elections in the North-West province generally failed the normative criteria of informing voters and identifying democratic values adequately. Furthermore it was found that the cognitive and emotional campaign messages were not fully integrated. While the focus was on typical election issues (emotional message), these issues were not explained and contextualised within a developing democracy to the full extend (cognitive message). Therefore the emotional message was not utilised to focus the voter's attention on policy issues and democratic values. In conclusion it is argued that political parties should do much more than merely canvas for votes. They should also empower voters by informing them on their policy issues and highlighting democratic values in society. Only then the new South African democracy will be sustainable. / Thesis (Ph.D. (Communication Studies))--North-West University, Potchefstroom Campus, 2004.

This study examines the party-controlled communication of the five most important political parties in the North West Province of South Africa during the 1999 general elections. The main assumption is that political parties in developing democracies have a normative obligation to do more than canvas for votes during an election campaign. Political parties should also be instrumental through their communication in fostering a democratic political culture. Central to this argument is the notion that a typical marketing approach is not suitable for an election campaign in a developing democracy. In accordance with the participatory approach to development, it is thus proposed that the two-way symmetrical model for public relations (as proposed by James Grunig) is a more appropriate approach to election campaigns. Especially relevant for this study is the two-way symmetrical model's emphasis on interaction and the establishment of long tern relationships with target publics. Through an extensive qualitative analysis of all relevant material (party manifests, newspaper advertisements, radio advertisements, pamphlets, posters and web pages), it was found that South African political parties placed much less emphasis on the "image" of the party or its leader compared to their American counterparts. However, that did not imply that the substance of the message was emphasised adequately. On the contrary, the political parties participating in the elections in the North-West province generally failed the normative criteria of informing voters and identifying democratic values adequately. Furthermore it was found that the cognitive and emotional campaign messages were not fully integrated. While the focus was on typical election issues (emotional message), these issues were not explained and contextualised within a developing democracy to the full extend (cognitive message). Therefore the emotional message was not utilised to focus the voter's attention on policy issues and democratic values. In conclusion it is argued that political parties should do much more than merely canvas for votes. They should also empower voters by informing them on their policy issues and highlighting democratic values in society. Only then the new South African democracy will be sustainable. / Thesis (Ph.D. (Communication Studies))--North-West University, Potchefstroom Campus, 2004.

The study of algebraic varieties originates from the study of smooth manifolds. One of the focal points is the theory of differential forms and de Rham cohomology. It’s algebraic counterparts are given by algebraic cycles and Chow groups. Linearizing and taking the pseudo-abelian envelope of the category of smooth projective varieties, one obtains the category of pure motives. In this thesis, we concentrate on studying the pure Chow motives of Severi-Brauer varieties. This has been a subject of intensive investigation for the past twenty years, with major contributions done by Karpenko, [Kar1], [Kar2], [Kar3], [Kar4]; Panin, [Pan1], [Pan2]; Brosnan, [Bro1], [Bro2]; Chernousov, Merkurjev, [Che1], [Che2]; Petrov, Semenov, Zainoulline, [Pet]; Calmès, [Cal]; Nikolenko, [Nik]; Nenashev, [Nen]; Smirnov, [Smi]; Auel, [Aue]; Krashen, [Kra]; and others. The main theorem of the thesis, presented in sections 4.3 and 4.4, extends the result of Zainoulline et al. in the paper [Cal] by providing new examples of motivic decompositions of generalized Severi-Brauer varieties.