The primary concern in today's educational system is the rate of progress students achieve in the classroom. Research has shown token reinforcement programs to be an effective method of increasing rate of work in the classroom; however, token economies are time consuming and do not meet the needs of all classroom situations. The purpose of this study was to test the effectiveness of the use of free time as a reinforcer in increasing rate of speed in working arithmetic problems and peer acceptance (how well an individual is accepted by his peers). The data indicated that free time as a positive reinforcer did increase the rate of speed in working arithmetic problems correctly; however, it did not affect peer acceptance.

The Selmer varieties of a hyperbolic curve X over ℚ are refinements of the Selmer group arising from replacing the Tate module of the Jacobian with higher quotients of the unipotent étale fundamental group. It is hoped that these refinements carry extra arithmetic information. In particular the nonabelian Chabauty method developed by Kim uses the Selmer variety to give a new method to find the set X(ℚ). This thesis studies certain local and global properties of the Selmer varieties associated to finite dimensional quotients of the unipotent fundamental group of a curve over ℚ. We develop new methods to prove finiteness of the intersection of the Selmer varieties with the set of local points (and hence of the set of rational points) and new methods to implement this explicitly, giving the first examples of explicit nonabelian Chabauty theory for rational points on projective curves.

Este trabajo estudia las condiciones sociales e institucionales que marcaron el inicio de la Didáctica de las Matemáticas como contenido de enseñanza y se describen las características que adoptó en esta primera época. Se centra en la aritmética y la cuestión central del estudio es: ¿Cómo se preparaba a los futuros maestros para enseñar aritmética en la escuela, desde la creación de las Escuelas Normales, durante el segundo tercio del siglo XIX? Esa formación se adquiría por una triple vía: las clases de aritmética en las Escuelas Normales, los estudios sobre Metodología de la aritmética que se impartían en una asignatura pedagógica y las prácticas en las escuelas primarias anejas a las Normales. Es un trabajo sobre la Historia de las disciplinas escolares, particularizada al caso de la aritmética en una institución naciente: las Escuelas Normales. Su temática y los métodos de análisis utilizados le confieren un carácter interdisciplinar. / The primary goal of this thesis is to study the social and institutional conditions that influenced the early stages of the art of teaching mathematics in Spain. It is focused on arithmetic and the main question of the study is: How were teachers prepared for teaching arithmetic in school since the creation of the Escuelas Normales, during the second third of the 19th Century? That training was provided in three ways: the arithmetic lessons imparted in the Escuelas Normales, the studies on arithmetic methodology imparted during a pedagogy subject, and a traineeship in one of the primary schools that were adjacent to the Escuelas Normales. This work is about history of school subjects, and in particular arithmetic in the then just born Spanish institution of the Escuelas Normales. Its subject and analysis methods make it an interdisciplinary research.

This work has as study object the Parker charters, school materials focused on discipline arithmetic. The research aims to investigate the movement of such materials that have contributed to the modernization of the teaching of this discipline. The time frame begins in 1912, year of the new organization of primary education in Sergipe, and the final milestone is the year 1953, referred to the dating of the latest report of the education inspector found. To prepare this study, I adopted the evidentiary paradigm in order to dialogue with bibliographic and documentary sources: laws, decrees, messages, educational programs, magazines, in addition to Parker works. Also articulated the evidence located to the concepts of school culture (FELGUEIRAS, 2010b), culture school material (FELGUEIRAS, 2010b), school materials (CARVALHO, 2011), school discipline (Chervel, 1990) and circulation (CHARTIER, 1990), to elucidate this aspect of school material culture in Sergipe, in the fields of history of mathematics education and the history of school subjects. / A presente dissertação tem como objeto de estudo as Cartas de Parker, materiais escolares voltados à disciplina Aritmética. A pesquisa tem como objetivo principal investigar a circulação desses materiais que contribuíram para modernização do ensino dessa disciplina. O recorte temporal inicia em 1912, ano da nova organização do ensino primário em Sergipe, e o marco final é o ano de 1953, ano a que se refere a datação do último relatório do inspetor de ensino encontrado. Para a elaboração deste estudo, adotei o paradigma indiciário, a fim de dialogar com as fontes bibliográficas e documentais: leis, decretos, mensagens, programas de ensino, revistas, além das obras de Parker. Também articulei os indícios localizados aos conceitos de cultura escolar (FELGUEIRAS, 2010b), cultura material escolar (FELGUEIRAS, 2010b), materiais escolares (CARVALHO, 2011), disciplina escolar (CHERVEL, 1990) e circulação (CHARTIER, 1990), visando elucidar esse aspecto da cultura material escolar em Sergipe, nos campos da história da educação matemática e da história das disciplinas escolares.