In this paper I present a theoretical analysis (genetic decomposition) of the cognitive constructions for the concept of infinite Riemann sums following Piaget\'s model of epistemology. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my continual observations of students in the process of learning. Based on this analysis I plan to suggest instructional procedures that motivate the mental activities described in the proposed genetic decomposition. In a later study, I plan to present empirical data in the form of informal interviews with students at different stages of learning. The analysis of those interviews may suggest a review of my initial genetic decomposition.

This experiment was designed to determine which assessment method: continuous assessment (in the form of daily in-class quizzes), cumulative assessment (in the form of online homework), or project-based learning, best predicts student learning (dependent upon posttest grades) in an undergraduate mathematics course. Participants included 117 university-level undergraduate freshmen enrolled in a course titled "Mathematics for Calculus". Initially, a multiple regression model was formulated to model the relationship between the predictor variables (the continuous assessment, cumulative assessment, and project scores) versus the outcome variable (the posttest scores). However, due to the possibility of multicollinearity present between the cumulative assessment predictor variable and the continuous assessment predictor variable, a stepwise regression model was implemented and caused the cumulative assessment predictor variable to be forced out of the resulting model, based on the results of statistical significance and hypothesis testing. The finalized stepwise regression model included continuous assessment scores and project scores as predictor variables of students' posttest scores with a 99% confidence level. Results indicated that ultimately the continuous assessment scores best predicted students' posttest scores.

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Made available in DSpace on 2016-04-27T16:57:52Z (GMT). No. of bitstreams: 1 dissertacao_roberto_cavalcante_santos.pdf: 1068715 bytes, checksum: 3a9427de227cebfaf9b2e468ddbc205a (MD5) Previous issue date: 2005-05-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis is devoted to the study of ifMathematics in the curriculum structure and teachers formationli, included in the Postgraduate Course Studies of the Mathematics Education Program at PUC/SP and is part of the ihFormation of Mathematics Teacherslc Research Project, which gathers a set of investigations that study the processes of initial and continuous formation of Mathematics Teachers in Undergraduate courses and in projects of continuous formation, aiming at identifying changes that have already been implemented, given the current demands of the Brazilian educational system. The focus of this study is to investigate what has been done in regard to the Mathematics curriculum of Elementary Education and how course coordinators understand the articulations between Mathematics curricula learned in Undergraduate courses and the school curriculum programs that will be taught by future teachers. It also investigates where graduate students who have majored in Mathematics stand, as far as their own formation to teach Mathematics is concerned. To carry out this study, we have analyzed other works done in the area of Mathematics teaching related to Undergraduate Mathematics programs, in addition to the local education law in practice. We have also looked into on line school curricula and syllabuses of some leading education institutions, as well as surveys conducted with Mathematics course coordinators and the opinion of last year Mathematics majors on how they see their own education. The results show that it is extremely hard to discuss the approach on the Elementary Education curricula, which future teachers are going to teach, without reviewing contents, in order to set the requirements of the other subjects in the Undergraduate program and by justifying this with the low performance in Mathematics of the students who enroll in Math school. In their turn, the surveyed students show a great concern with their own ability to teach basic contents. We hope this work can contribute to the discussion of alternative proposals regarding the initial formation of Mathematics teachers / O presente trabalho insere-se na linha de pesquisa "Matemática na estrutura curricular e formação de professores", do Programa de Estudos Pós-graduados em Educação Matemática, da PUC/SP e integra o projeto de Pesquisa Formação de Professores de Matemática , que reúne um conjunto de investigações que estudam processos de formação inicial e continuada de professores de Matemática, em cursos de licenciatura e em projetos de formação continuada, buscando identificar mudanças implementadas, face às demandas atuais do sistema educacional brasileiro. Nossa pesquisa tem o objetivo de investigar o que está sendo trabalhado relativamente aos conteúdos matemáticos da Educação Básica e de que modo coordenadores de cursos compreendem as articulações entre os conteúdos matemáticos ensinados na Licenciatura e aqueles que serão futuramente ensinados pelos alunos licenciados. Também investiga como os egressos dos cursos de Licenciatura em Matemática se posicionam frente à sua própria formação para ensinar Matemática. Para realizar este estudo, primeiramente fizemos um levantamento de estudos já realizados na área de Educação Matemática relacionados aos cursos de Licenciatura em Matemática, além da própria legislação educacional em vigor. Em seguida fizemos uma consulta a grades e ementas de algumas instituições formadoras que as disponibilizaram pela Internet, entrevistas com coordenadores de alguns cursos de Licenciatura em Matemática, além de ouvir a análise elaborada pelos alunos do último ano em relação à sua própria formação. Os resultados mostram que existe uma grande dificuldade em discutir a abordagem desses conteúdos da Educação Básica, que o futuro professor ensinará, sem atrelá-la a idéia de revisar conteúdos, para constituir os pré-requisitos das demais disciplinas da Licenciatura e justificando isso pela formação matemática precária dos alunos que ingressam nos cursos de licenciatura. Por sua vez, os alunos egressos entrevistados demonstram grande preocupação com a própria capacidade para ensinar os conteúdos básicos. Esperamos que a pesquisa possa contribuir para a discussão de propostas alternativas referentes à formação inicial dos professores de Matemática

In this paper I present a theoretical analysis (genetic decomposition) of the cognitive constructions for the concept of infinite Riemann sums following Piaget\''s model of epistemology. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my continual observations of students in the process of learning. Based on this analysis I plan to suggest instructional procedures that motivate the mental activities described in the proposed genetic decomposition. In a later study, I plan to present empirical data in the form of informal interviews with students at different stages of learning. The analysis of those interviews may suggest a review of my initial genetic decomposition.

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Made available in DSpace on 2016-04-27T16:58:33Z (GMT). No. of bitstreams: 1 Shirley Ferreira Signorelli.pdf: 4346228 bytes, checksum: a37d23996da101385ce1df722242946c (MD5) Previous issue date: 2007-10-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this investigation was the elaboration and implementation of a virtual environment for a part time distance course for students of the Computer Science and Systems of Information. The students failed in a former discipline that approaches topics of elementary Mathematics. It happened in a particular university in the city of São Paulo. Our focus was on analyzing this environment, the tools and interactions that happened on distance mode, about the content of real function of one variable. The methodology used, design-based research, favored proposing and analyzing the activities about this topic, as well as their reorganization and, the re design of the environment. The Blackboard platform and the used tools were analyzed based on Chaves (2000) criteria, and it seemed efficient as a virtual environment for the learning in our course. However, we leaved some critical and suggestions for future works, mainly about the role of the tools for communication within part time distance courses. The analysis of the students and teacher speeches' was based on the Model of Argumentative Strategy (CASTRO et al, 2004) and allowed to raise some aspects on the understanding of Real Functions of one variable, as they were privileged in the different interactive spaces such as forum, chat, email and daily log. Aspects like the meaning production in Mathematics can be produced due to the authority of a teacher or of another student who is considered good by the classroom peers, or based on everyday language usage or on cultural characteristics. Moreover, we found that besides the students lack of prerequisite elementary mathematics, there is a lack of a culture for on-line courses / Nesta pesquisa objetivamos a elaboração e implementação de um ambiente virtual para um curso semipresencial, para estudantes dos cursos de Bacharelado em Ciência da Computação e Sistemas de Informação de uma instituição particular na cidade de São Paulo, dependentes na disciplina que aborda tópicos de pré-calculo. Nosso foco recaiu na análise do ambiente, da viabilidade das ferramentas e das interações que ocorreram a distância, no que tange o conteúdo de Funções de uma Variável Real. A metodologia utilizada, design research, permitiu propor e analisar as atividades sobre este tópico, incluindo a reestruturação e complementação deste ambiente. A plataforma Blackboard e as ferramentas foram analisadas segundo critérios definidos por Chaves (2000) e se mostraram eficazes como ambiente virtual de aprendizagem atendendo, para nosso curso, os critérios necessários. Entretanto, deixamos algumas críticas e sugestões para trabalhos futuros, principalmente quanto o papel do uso de ferramentas de comunicação em cursos semipresenciais. A análise dos discursos dos alunos e docente baseados no Modelo de Estratégia Argumentativa (CASTRO et al, 2004) permitiu levantar alguns aspectos sobre a compreensão de Funções de uma Variável Real que foram privilegiados nos diferentes espaços interativos como fórum, chat, e-mail e diário de rotina, tais como o fato de que a produção de significados em Matemática pode estar apoiada na autoridade do professor ou alunos bem vistos pela classe, na linguagem cotidiana e no aspecto cultural. Observamos ainda que além da falta de pré-requisitos de matemática básica, ainda há falta de cultura de trabalhos on-line