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<p>Proofs are notoriously difficult. While the challenges students face when working on proofs are well-documented, more research is needed on what students do when working on proofs, especially in the context of linear algebra. My research focuses on student work on proofs in linear algebra through the lens of Tall's worlds of mathematics: the embodied world, the symbolic world, and the formal world. The embodied world consists of graphs, diagrams, and their properties. The symbolic world contains operations, formulas, and calculations. The formal world consists of axioms, formal definitions, and formal proofs. I conducted task-based interviews with linear algebra students in which they determined if given proofs were valid and then constructed their own proofs for different statements. In different interviews, I encouraged participants to use different worlds of mathematics. Through this study, I hoped to gain some understanding of how approaches to proof constructions and validations within the different worlds of mathematics affect students' personal proof constructions and validations. I also sought to understand what participants viewed as challenging or helpful about each world of mathematics with regards to proofs.</p> <p><br></p> <p>I found that participants often chose a world of mathematics based on the given topic rather than their preferred world or my encouragement to use a given world. Encouraging participants to use the embodied world resulted in their using generic examples. Encouraging participants to use the symbolic or formal worlds had little effect, likely due to participants' views of the symbolic and formal worlds which differed from my views of the symbolic and formal worlds. Participants said the embodied world was helpful for developing understanding, but felt limited by its specificity. A challenge of the symbolic world was the level of precision needed and the large number of variables. Participants viewed the formal world as helpful for proofs and its generality, but logic was a challenge. Reflecting on the study, participants said that the three-world framework was helpful for organizing their thoughts when working on problems.</p>

[pt] Este trabalho investiga a história que Leibniz acrescenta à narrativa do humanista italiano Laurent Valla, transformando-a de uma anedota a respeito da liberdade humana diante presciência e vontade divinas em um estudo sobre a natureza da criação. Na história, os infinitos mundos possíveis são apresentados a Teodoro, em sonho, por Palas Atena, filha de Júpiter. O que ele vê pelos cômodos do palácio são infinitas histórias alternativas ao destino infeliz de Sexto Tarquínio, filho do último dos reis da monarquia romana. Esses mundos possíveis estão organizados em ordem decrescente de perfeição, sendo que o mais rico em variedade se encontra no alto da pirâmide, que é a forma geométrica a que Leibniz identifica o lugar em que Deus delibera sobre o melhor. Este trabalho percorre a estrutura da pirâmide para compreender o que Teodoro vê em cada cômodo e o que garante a própria divisória entre os cômodos. Nesse trajeto, verifica-se que um dos cálculos envolvidos na arquitetura da pirâmide é a dissemelhança entre a parte e o todo no melhor dos mundos. Sexto participa da variedade do mundo existente com seu infortúnio. No interior de um dos cômodos, Teodoro é introduzido aos problemas da análise infinita ao folhear o livro dos destinos. Por fim, este trabalho mostra que a natureza distópica da pirâmide não se restringe às histórias alternativas que Teodoro encontra em cada cômodo, mas há também outros mundos no interior do próprio mundo existente. O mundo mais perfeito se distingue por conter mais variedade que os demais, o que faz dele um mundo denso. É possível transitar pela densidade desse mundo através das distopias, ora entendidas como uma imitação da estrutura da lei do contínuo, ora consideradas como um suporte corporal que permite percorrer, alternadamente, os mundos fenomênicos. / [en] This thesis investigates the story that Leibniz adds to the narrative of the Italian humanist Laurent Valla, transforming it from an anecdote about human freedom in face of divine foreknowledge and will in a study about the nature of creation. In the story, the infinite possible worlds are presented to Theodorus in a dream by Pallas Athena, daughter of Jupiter. What he sees through the rooms of the palace are infinite alternative stories to the unfortunate fate of Sextus Tarquinius, son of the last king of the Roman monarchy. These possible worlds are organized in descending order of perfection, so that the richest in variety is at the top of the pyramid, which is the geometric form to which Leibniz identifies the place where God deliberates on the best. This work traverses the structure of the pyramid to understand what Theodore sees in each room and what ensures the very partition between the rooms. On this route, it is verified that one of the calculations involved in the architecture of the pyramid is the dissimilarity between the part and the whole in the best of the worlds. Sextus participates in the variety of the existing world with its misfortune. Inside one of the rooms, Theodorus is introduced to the problems of infinite analysis by leafing through the book of fates. Finally, this work shows that the dystopic nature of the pyramid is not restricted to the alternative stories that Theodorus finds in each room, but there are also other worlds within the existing world itself. The most perfect world stands out for containing more variety than the others, which makes it a dense world. It is possible to transit through the density of this world through dystopias, understood firstly as an imitation of the structure of the law of the continuum and, secondly, as a bodily support that allows one to traverse, alternately, the phenomenal worlds.

By their very nature, physical classrooms limit the external resources that are readily available to teachers and students. However, many educators desire to expand the student's learning environment to include outside resources (Partnership for 21st Century Skills, 2009; NCSS, 2010; U.S. Dept. of Education, 2004). Much of this desire is due to the influence of constructivism; however, many teachers are without the knowledge and resources to implement a Constructivist Learning Environment (CLE) (Diem, 1999; Mason et al., 2000; Swan and Hofer, 2008). Therefore, how to create a suitable community-driven learning environment that allows classroom teachers to utilize resources outside their immediate location is a problem faced by many of today's educators. Past research has identified five key attributes any CLE must incorporate: embedded within realistic and authentic environments, allow for communication and collaboration among and between students, teachers and mentors, allow for multiple perspectives and views to be seen and shared, promote a student's self-awareness and self-reflection, and allow the learner to be autonomous (Jonassen, 1994; Driscoll, 2005). When considering this list against technological affordances, the one technology that appears capable of fulfilling these requirements is virtual worlds (Kemp and Haycock, 2008). Designed as a developmental research study, this research validates the use of virtual worlds as a development tool when building a CLE within the K-12 environment. / Ph. D.

Previous research has found that users' interactions with others in online environments are often guided by the same rules and stereotypes we apply in our everyday lives. However, fewer studies have used virtual worlds as an experimental setting for the systematic examination of how avatar appearance and offline identity affect the outcome of users' actual interactions. This online field experiment measured the effect of avatar attractiveness, avatar gender, purported user gender, and favor size on the rate at which users received help across 2,300 separate user interactions. In addition, the main study's avatar gender, purported user gender, and favor size manipulations were replicated with a human avatar condition with 761 participants to examine whether trends for these factors' effects were similar with human avatars. In the main study, attractive avatars generally received more help than less attractive avatars. However, purported female users were helped less frequently than purported male users when represented by avatars that were either male or less attractive. Trends in the human avatar condition were similar to those observed in the main study. Implications for avatar-mediated communication and the persistence of sex roles in virtual environments are discussed. / Master of Arts

En este trabajo presentamos un análisis sobre la colaboración cientifica de la psicologia social y de la personalidad, configurada desde el Journal of Personality and Social Psychology (JPSP), desde su inicio en 1965, hasta el año 2000. Lo realizamos desde una doble perspectiva: un análisis cuantitativo bibliométrico y un análisis histórico descriptivo. Además, presentamos un análisis de la colaboración institucional y los colegios invisibles desde la teoria "Small Worlds". Desde la psicologia social y de la personalidad, analizamos las teorías y los autores más significativos para su desarrollo histórico en disciplinas cientificas, y las áreas más relevantes por las que discurren. Desde una perspectiva bibliométrica, se analizan las variables habituales para un estudio bibliométrico. Para el análisis de colaboración, nos basamos en el modelo "Small Worlds". Comprobamos que puede ser un instrumento muy útil para analizar la concentración en redes sociales" y en este caso, la colaboración cientifica. / In this research we present an analysis concerning the scientific collaboration of social and personality psychology, shaped from the Journal of Personality and Social Psychology (JPSP) since its beginning in 1965 until the year 2000. We made it from a double prospective: a bibliometric cuantitative analysis and a descriptive historical analysis of social and personality psychology. Moreover, we present an analysis of the insti tutional cooperation and the invisible colleges of the "Small Worlds" theory. We analyse the most significative theories and authors to its historical development in some scientific subjects and the most important areas in which they are developed. From a bibliometric prospective, usual options to make a bibliometric research are studied.

This thesis explores economic aspects of virtual worlds by focusing on a specific massively multiplayer online role-playing game, RuneScape. In particular, it examines the similarities and differences between the virtual economics and real world economics, the economic understanding of RuneScape players and the possibility of using virtual worlds as a laboratory for testing economic behavior and theory. This thesis uses a versatile methodology that includes texts, direct observation, self-reports, and other reports to investigate the research questions. Virtual economics in general and RuneScape in specific are understudied so far and this study fills a gap in the literature. The unique contributions of this thesis are: a comprehensive survey that reveals player perceptions of economics, a new equation useful for modeling money supply, and a new use of faucet-drain economy in massively multiplayer online games. The results indicate that virtual economics of RuneScape partially reflects real world economics, player perceptions of virtual and real world economy are surprisingly complex, and virtual worlds can be used to study real world economics. Game developers, players, economists, educators, researchers, and individuals who are interested in massively multiplayer online games and economy in general can benefit from this study.

(in English) This thesis deals with space in Japanese science fiction literature in 1960s. The aim is to find out specificity of japanese space in works with apocalyptic endings. Theoretical part deals with concept of possible worlds, various approaches to space and above all with theory of fictional worlds, which I use as main methodology of this thesis. Practical part is topoanalysis and comparison of three selected literary works: Inter Ice Age 4 (Dai yon kanpyōki 第四間氷期, 1959) by Abe Kōbō 安部公房 (1924-1993), Ten Billion Days and One Hundred Billion Nights (Hyaku oku no hiru to sen oku no yoru百億の昼と千億の夜, 1967) by Mitsuse Ryū 光瀬竜 (1928-1999) and Japan Sinks (Nihon chinbotsu 日本沈没) by Komatsu Sakyō 小松左京 (1931-2011). In topoanalysis I focus primarily on island position of Japan and role of the ocean.

En prenant comme point de départ l'interprétation de l'épopée homérique par Erich Auerbach, ce mémoire se consacre à la notion d'immersion fictionnelle, non sous son versant psychologique de phénomène contingent de la conscience imageante, mais sous son versant imaginaire, en tant que mythe sociétal d'immédiateté déterminant des stratégies esthétiques et médiatiques concrètes, que j'articule autour des poétiques contemporaines de construction de mondes (world building). L'enjeu est de saisir les répercussions esthétiques de ce fantasme d'une représentation qui occulterait à la fois sa médiateté et le réel-sensible, à une époque où la transfictionnalité et la transmédiaticité s'élèvent tranquillement comme modes narratifs dominants de notre culture occidentale contemporaine. Avec cette conviction que le terme d'immersion doit être replacé dans le cadre de ses effets, le premier chapitre s'affairera à démêler quelques difficultés théoriques que pose la notion en la problématisant sous l'égide des questions ontologiques de vérité et de la position phénoménologique de Sartre sur l'imaginaire. Tout en posant les outils théoriques nécessaires aux analyses subséquentes, le deuxième chapitre approfondit cette problématisation en empruntant aux théories modales des mondes possibles un cadre conceptuel opératoire, qui amènera, notamment grâce au concept formalisé de «~monde~», à concevoir la fiction comme un mouvement de distanciation. Appuyé par la lecture du roman tolkienien, le troisième chapitre tourne le fantasme d'immersion du côté d'une pulsion encyclopédique de complétude, concrétisée par des stratégies textuelles d'accumulation informationnelle et de virtualisation de données diégétiques laissées en suspens -- effets d'actualité que je qualifie d'extra-narratifs en les présentant en contraste des principes prescriptifs du \emph{muthos} aristotélicien formant une chaîne causale téléologique fondée sur une loi d'économie narrative. Le quatrième et dernier chapitre, articulé autour de la notion encore trop peu étudiée de canonicité, observe les poétiques de construction de mondes telles qu'elles se désamorcent elles-mêmes, dans le contexte des univers partagés, en engendrant des incohérences logiques donnant lieu à la tenue d'un discours auctorial-éditorial régissant les vérités fictionnelles comme moyen de maintenir l'immersivité de la représentation. L'analyse générique des comic-books de superhéros et une enquête sur la gestion éditoriale de l'univers de Star Wars permettront d'identifier les multiples modalités de délimitation de la frontière entre canon et apocryphe. En conclusion, je reviens brièvement sur la notion d'immersion, ainsi exemplifiée, en la resémiotisant comme une médiation compétitive de mise en présence de l'être. / Starting from Erich Auerbach's interpretation of the Homeric epic, this master's dissertation studies the notion of fictional immersion, not in its psychological aspect of a contingent phenomena of human consciousness, but rather in its collective imaginary sense, as a societal myth of immediacy generating concrete aesthetic and media strategies that I investigate from the standpoint of contemporary poetics of world building. The objective is to apprehend the aesthetic repercussions of this desire for a mediation that would conceal both the real and its own mediacy, in a time where transfictionality and transmedia storytelling are becoming more and more the dominant narrative modes of our contemporary western culture. Under the conviction that immersion must be looked at as a set of cultural strategies, the first chapter unravels some theorical difficulties bounded to the term by problematizing it towards ontological questions of truth and Sartre's phenomenological stance on the imaginary. While laying a necessary theorical toolset for subsequent analyses, the second chapter examines these problems by borrowing to possible worlds modal theories a set of working concepts, which will lead to the assumption that fiction is a movement of distanciation, notably with the aide of the formal concept of ``world''. Through a reading of the tolkienian novel, the third chapter directs the desire for immersion towards an encyclopedic impulsion for completeness, embodied by textual strategies such as informational proliferation and allusion to virtual diegetic data -- strategies leaving an impression of the actual that I describe as extra-narrative in contrast to Aristote's \emph{muthos} forming a teological causal chain based on a principle of an unitary narrative. The fourth and final chapter, articulated around the still too little studied notion of canonicity, observes poetics of world building as they neutralize themselves, particularly with shared universes, by generating logical inconsistencies giving birth to authorial and editorial discourses stating fictional truths as a way of maintaining the mediation's immersivity. The analysis of the superhero comics genre and an inquiry of the editorial management of the Star Wars universe will exemplify the multiple modalities of this delimitation between the canon and the apocryphal. As a conclusion, I briefly come back to the notion of immersion itself by redescribing it as a competitive mediation of presence.