Sequências de Fibonacci e a Razão Áurea - aplicações no ensino básico

This thesis aims to present a study of the Fibonacci sequence, initiated from a simple problem of rabbits breeding and the Golden Ratio, which originated from a geometrical construction, for applications in basic education. The main idea of the thesis is to present historical records of the occurrence of these concepts in nature and science and their influence on social, cultural and scientific environments. Also, it will be presented the identification and the characterization of the basic properties of these concepts and howthe connection between them occurs,and mainly, their intriguing consequences. It is also shown some activities emphasizing geometric constructions, links to other mathematics areas, curiosities related to these concepts and the analysis of questions present in vestibular (SAT-Scholastic Aptitude Test) and Enem(national high school Exam) in order to show the importance of these themes in basic education, constituting an excellent opportunity to awaken the students to new points of view in the field of science and life, from the presented subject and to promote new ways of thinking mathematics as a transformative science of society.

Concepções de licenciandas em pedagogia sobre o ensino de ciências nos ciclos I e II da educação básica

O conteúdo de ciências no Ensino Fundamental dos ciclos I e II é ministrado por um professor polivalente com formação em Pedagogia. Sua formação deve possibilitar uma visão global do fenômeno educativo, o que implica a construção de conhecimentos múltiplos e contextualizados, porém com pouco aprofundamento. Este trabalho objetiva identificar as opiniões e dificuldades de licenciandos de Pedagogia a respeito dos conteúdos de Ciências nos dois primeiros ciclos do Ensino Fundamental, mediado por dois questionamentos: Com relação aos conteúdos de ciências ministrados no I e II ciclos, você os considera fácil ou difícil? Sendo solicitado que justificasse sua resposta; De acordo com seus conhecimentos sobre ciências, cite as principais dificuldades que você teria (tem/teve) em ensinar ciências nos ciclos I e II. Participaram do estudo 29 licenciandas da turma de Ensino das Ciências Naturais II do Curso de Pedagogia da Universidade Federal do Rio Grande do Norte. Com relação ao questionamento referente à consideração dos conteúdos de ciências, 52% das licenciandas consideraram fácil, 31% difícil e 17% não responderam a questão. Foram identificadas três categorias de respostas: processo de elaboração do planejamento (20,5% fácil e 20,5% difícil), nível de conhecimento dos alunos (7% fácil e 0% difícil) e natureza dos conteúdos abordados (14% fácil e 10,5% difícil). Foram classificadas três categorias distintas em relação às dificuldades em ensinar ciências: natureza dos conteúdos abordados (50%), aspectos metodológicos (25%), e conhecimento básico (25%). A análise dos resultados revelou que a principal dificuldade das licenciandas em Pedagogia quanto à aplicabilidade do ensino de ciências nos primeiros ciclos do Ensino Fundamental esta diretamente relacionada à falta de conhecimento básico destes conteúdos, que somente foram estudados por elas no Ensino Básico, indicando a necessidade de incorporação de abordagens de conteúdos de ciências no currículo do curso de Pedagogia.

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Uma análise do ensino de Geografia utilizando as representações cartográficas no 2º ciclo nas escolas públicas de Natal - RN

Análisis de Ensino de la geografía usando las representaciones cartográficas en el ciclo 2º en las escuelas públicas de Navidad - RN, en la vista de la relación teo'rico-pra'ctica dividida en dos, en cuanto a la aplicabilidad verdadera de estos recursos en la educación de la geografía. Este análisis entiende una revisión bibliográfica, a la luz de teorías y de conceptos en el proceso de la educación y de aprender de la geografía y el uso de los recursos de los geocartográficos el largo de historia. El objetivo para caracterizar pertenecer al espacio de la escuela, a la escuela en la comunidad, a la educación de la geografía y al uso de los recursos cartográficos, la importancia de los recursos didácticos como ayudas de los metodológicos en la educación de la geografía, la dirección de señalar soluciones para mejorar las lecciones en Ensino básico, y comtemplaba preguntas primordiales relativas a los profesores prácticos; para la comprensión, mientras que profesional de la educación, la lucha para la valuación de la enseñanza y la educación pública; para la importancia social de la mejora de la formación de profesores de la educación básica, en el ejercicio completo de las actividades de enseñanza, y para el acceso a las fuentes y a los espacios de la investigación donde ejercemos la función del profesor del formador en el Instituto de Educación Superior Presidente Kennedy IFESP

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

Concepções de licenciandas em pedagogia sobre o ensino de ciências nos ciclos I e II da educação básica

O conteúdo de ciências no Ensino Fundamental dos ciclos I e II é ministrado por um professor polivalente com formação em Pedagogia. Sua formação deve possibilitar uma visão global do fenômeno educativo, o que implica a construção de conhecimentos múltiplos e contextualizados, porém com pouco aprofundamento. Este trabalho objetiva identificar as opiniões e dificuldades de licenciandos de Pedagogia a respeito dos conteúdos de Ciências nos dois primeiros ciclos do Ensino Fundamental, mediado por dois questionamentos: Com relação aos conteúdos de ciências ministrados no I e II ciclos, você os considera fácil ou difícil? Sendo solicitado que justificasse sua resposta; De acordo com seus conhecimentos sobre ciências, cite as principais dificuldades que você teria (tem/teve) em ensinar ciências nos ciclos I e II. Participaram do estudo 29 licenciandas da turma de Ensino das Ciências Naturais II do Curso de Pedagogia da Universidade Federal do Rio Grande do Norte. Com relação ao questionamento referente à consideração dos conteúdos de ciências, 52% das licenciandas consideraram fácil, 31% difícil e 17% não responderam a questão. Foram identificadas três categorias de respostas: processo de elaboração do planejamento (20,5% fácil e 20,5% difícil), nível de conhecimento dos alunos (7% fácil e 0% difícil) e natureza dos conteúdos abordados (14% fácil e 10,5% difícil). Foram classificadas três categorias distintas em relação às dificuldades em ensinar ciências: natureza dos conteúdos abordados (50%), aspectos metodológicos (25%), e conhecimento básico (25%). A análise dos resultados revelou que a principal dificuldade das licenciandas em Pedagogia quanto à aplicabilidade do ensino de ciências nos primeiros ciclos do Ensino Fundamental esta diretamente relacionada à falta de conhecimento básico destes conteúdos, que somente foram estudados por elas no Ensino Básico, indicando a necessidade de incorporação de abordagens de conteúdos de ciências no currículo do curso de Pedagogia.