Do acolhimento ao acompanhamento compartilhado: a construção colaborativa de uma proposta para o estágio curricular no curso de pedagogia

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

O Raciocínio lógico-matemático: classificação e uso em concursos públicos

This study offers an analysis of classification of the main issues of logic and logical thinking found in competitive tendering and math tests, according to their concepts and characteristics, whether involving mathematics, or not. Moreover, a research on the evolutionary historic processes of logic according to three major crises of the foundations of mathematics was conducted. This research helped to define Logic as a science that is quite distinctive from Mathematics. In order to relate the logical and the mathematical thinking, three types of knowledge, according to Piaget, were presented, with the logical-mathematical one being among them. The study also includes an insight on the basic concepts of propositional and predicative logic, which aids in the classification of issues of logical thinking, formal logic or related to algebraic, and geometric or arithmetic knowledge, according to the Venn diagrams. Furthermore, the key problems - that are most frequently found in tests are resolved and classified, as it was previously described. As a result, the classification in question was created and exemplified with eighteen logic problems, duly solved and explained

Cálculo mental e a produção do conhecimento matemático

This text presents the research developed with students of the 5th year of elementary school at a public school in the city of Taubaté-SP, involved in solving problems involving the Mental Calculation. The read authors show that the Mental Calculation is relevant for the production of mathematical knowledge as it favors the autonomy of students, making it the most critical. Official documents that guide educational practices, such as the Parâmetros Curriculares Nacionais also emphasize that working with mental arithmetic should be encouraged as it has the potential to encourage the production of mathematical knowledge by the student. In this research work Completion of course the tasks proposed to students, who constituted the fieldwork to production data, were designed, developed and analyzed in a phenomenological approach. The intention, the research was to understand the perception of students in the face of situations that encourage them to implement appropriate technical and mental calculation procedures. We analyze how students express and realize the strategies for mental calculation in the search for solution to problem situations

A construção da ideia de número na educação infantil

This paper seeks to understand-the process by which the child in kindergarten builds the idea of number. Therefore we developed a qualitative study of phenomenological approach that involved field work in the classroom with children of four and five years. Starting from their real-world contexts, their experiences and using the natural language tasks are designed to help the student to go beyond the already known, analyzing how they thinks and what knowledge they bring their lived experience. By interference carried expanded mathematical ideas acquired. The analysis and interpretation of research data shows that the idea of number is built by children from all kinds of relationships created between objects and the world around them, and the more diverse are these experiences, the greater the understanding opportunities and development of mathematical skills and competencies. It showed also that, in kindergarten, children tread just a few ways to build the idea of number

Regiões de estabilidade no ambiente de um sistema de asteroide triplo

This work was developed from the study by Araujo, R.A.N. et al. Stability regions around the components of the triple system 2001 SN263. (Monthly Notices Of The Royal Astronomical Society, 2012, v. 423(4), 3058-3073 p.) where it was studied the stable and unstable regions system (2001 SN263), which is a triple asteroid system, and these are celestial orbiting our sun. Being close to the Earth is characterized as NEA (Near-Earth Asteroids), asteroids and which periodically approach the Earth's orbit, given that there is great interest in the study and exploitation of these objects, it is the key can carry features that contribute to better understand the process of formation of our solar system. Study the dynamics of bodies that govern those systems proves to be greatly attractive because of the mutual gravitational perturbation of bodies and also by external disturbances. Recently, NEA 2001 SN263 was chosen as a target of Aster mission where a probe is sent for this triple system, appearing therefore the need for obtaining information for characterizing stable regions internal and external to the system, with respect to the effects of radiation pressure. First, this study demonstrated that the integrator used showed satisfactory results of the orbital evolution of bodies in accordance with previous studies and also the characterization of stable and unstable regions brought similar results to the study by Araujo et al. (2012). From these results it was possible to carry out the implementation of the radiation pressure in the system in 2001 SN263, in a region close to the central body, where the simulations were carried out, which brought as a result that the regions before being characterized as stable in unstable true for small particles size from 1 to 5 micrometers. So the next orbital region to the central body and the ... ( Complete abstract click electronic access below)

Uma Proposta de utilização de um software educacional para o ensino de poliedros

This paper presents an educational proposal to use an educational software for the teaching of mathematics, following in the conduct of activities, the main aspects of sociocultural theory of Vygotsky. For this, it chose the Poly educational software, with which were developed teaching and learning activities for the polyhedra content provided in the São Paulo State Mathematics curriculum for the 7th year of elementary school. The objectives of this pedagogical proposal are to stimulate situations of social interaction among students and between students and the teacher, using an educational software as a mediator instrument and present a different way of using digital technology in math classes, aiming production of mathematical knowledge

Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory

Potencial gravitacional lunar

We know that the orbit of a lunar satellite, and consequently its orbital lifetime is mainly inuenced by the gravitational field of the Moon, Earth and Sun. In this text we study the Lunar gravitational potential and its influence on the gravitational field. We adapted a program in order to map the Moon gravitational field. To that end it was necessary to develop a program that allows the simulation and mapping the lunar full potential. Our program was based on the program developed by Hélio Kuga, and adapted to our case (Moon). We used the model proposed by Konopliv et al. 2001, we proposed various degree and order expansions of spherical harmonics that served us to compare and validate our program

A visualização no ensino de geometria com o Geogebra 3D

This research presents an investigation about the relevance of visualization in teaching geometry. Our interest turns to analyzing the use of technology in teaching geometry, seeking to highlight their contribution to learning. The students of today - second decade of the 21st century - require that, each time more, the school move towards the integration of technologies for teaching since tablets, smartphone, netbook, notebook are items present on daily life of most students. Thereby, we investigate, taking the phenomenological orientation, the potential of educational software, especially the Geogebra 3D, directed at teaching math and favoring the work with the geometry viewing. At work we bring some theoretical considerations about the importance of viewing for the geometric learning and the use of technologies. We build an intervention proposal for the classroom of the 7th year of elementary school with tasks aimed at visual exploration and allow the teacher to work the concept of volume of geometric solids

O Ensino de Geometria por meio de atividades investigativas: uma experiência com alunos do primeiro ano do Ensino Médio

This qualitative nature of work was developed with the participation of a group of students enrolled in the first year of high school from a public school of the state of São Paulo, in the city of Taubaté. Their goal was to determine how students deal with geometry tasks in investigative classes. To guide this research was drawn up the following question: As students of the first year of high school express their knowledge of building triangles and quads in classes of investigative activities?. The choice of investigative nature of this activity occurred by enhancing student participation and thus generate a greater chance of it not be guided only by what the teacher wants, but by his own curiosity and using their own tools for this. In the data analysis process stands out the interest generated in students for this type of activity and posture maintained throughout the work, mobilizing their expertise to answer the questions posed

A percepção do professor de Biologia e a sua formação: a Educação Ambiental em questão

O presente artigo apresenta os resultados de uma pesquisa cujo objetivo foi identificar as percepções dos professores de Biologia do município de Piracicaba, SP, e dos alunos concluintes de um curso de licenciatura em Ciências Biológicas em relação à presença da Educação Ambiental em sua formação inicial, a fim de discutir a inserção da temática na universidade em geral e, especificamente, na licenciatura em Ciências Biológicas. Os resultados indicam que o professor de Biologia ainda necessita de uma formação mais crítica em relação à educação ambiental e que, numa perspectiva complexa, essa formação necessita ser tratada de forma mais rigorosa na universidade e nas licenciaturas em Ciências Biológicas para que os profissionais formados possam atuar, efetivamente, na formação cidadã para uma sociedade mais sustentável.

Abordando o ensino de óptica através da construção de telescópios

A proposta deste trabalho é a construção artesanal de um telescópio refletor do tipo Newtoniano relacionando conteúdos abordados na disciplina de óptica, como a formação de imagens em lentes e espelhos, aberrações esféricas e cromáticas, interferência e difração, com cada fase do processo de construção. Com o aparelho construído é possível abordar a fotografia lunar e planetária com alta resolução e sua utilização por alunos do curso de Licenciatura em Física já demonstra ser um grande incentivo à contemplação do céu e à compreensão de muitos fenômenos físicos, com ocorrências de eclipses, formação das marés, estações do ano, etc, que geralmente são pouco abordados nas escolas de Ensino Fundamental e Médio. de acordo com diagnóstico realizado pelos alunos de graduação em algumas escolas do município de Bauru, verificou-se que a única abordagem de astronomia é apenas em relação ao sistema solar, especificamente órbitas planetárias, nas disciplinas de Física ou Geografia. Além do telescópio, a utilização de animações produzidas por alunos de graduação também pode ser considerada como uma ferramenta eficiente no ensino de astronomia, principalmente para alunos de Ensino Fundamental.

Teoria da Formação e Avaliação no currículo de Educação Física

Having as reference the curricular proposals that composed the new directives for Formation of Professors for the Basic Education, Full Licence in Brazil, it was aimed to analyze in the pedagogic project of a Physical Education Licence course, the professional profile proposed, the conceptual orientation adopted (curriculum model) as well the evaluation proposed in the curriculum. These results obtained from the descriptive study have contemplated documental source and content analysis approach, utilizing as basis for discussion of the results the formation theory. Among the most significant data it was established that, the presented professor profile must consider an Academic, Technological, Practical and Socio-Reconstructionist orientation, detaching during the evaluation process a high skill level in Academic Orientation, as well remarking that the evaluation is presented as a great gap in the pedagogic project.

Oscilador harmônico amortecido e séries infinitas

Neste trabalho discute-se um arranjo experimental bastante simples e de baixo custo, cujo objetivo consiste em se exemplificar de forma concreta a aplicação de técnicas matemáticas envolvendo solução por séries infinitas destinadas ao estudo de determinado fenômeno físico. Esta prática desenvolvida e direcionada aos alunos de um curso de Graduação em Matemática, consiste basicamente de um estudo quantitativo relacionado ao comportamento oscilatório amortecido de um sistema constituído por uma massa acoplada a uma mola. Os resultados experimentais corroboraram muito bem a teoria fenomenológica e possibilitam a determinação numérica de uma constante física normalmente considerada desprezível, mencionada de passagem nos livros textos. Um fato de destaque deste trabalho referente ao fenômeno ondulatório estudado, ilimitado no tempo, mas limitado no espaço, é o de permitir uma boa discussão com os estudantes sobre o conceito de limite matemático.

A temática ambiental e as diferentes compreensões dos professores de física em formação inicial

Procuramos identificar as concepções dos licenciandos de física em relação à temática ambiental, bem como analisamos as propostas por eles elaboradas e os obstáculos que se lhes apresentam quando decidem tratar alguns aspectos da problemática ambiental em suas atividades de ensino. Os dados foram coletados a partir do desenvolvimento de algumas atividades na disciplina de Prática de Ensino oferecida a alunos concluintes de um curso de Licenciatura em Física de uma universidade pública no estado de São Paulo. Os dados evidenciam que as concepções que os licenciandos elaboram sobre a temática ambiental podem tornar-se obstáculos para a incorporação desses aspectos em suas propostas de ensino. da mesma forma, não há, por parte dos licenciandos, uma compreensão mais ampla quanto ao significado da temática ambiental, quanto às implicações do movimento ambientalista para as práticas culturais e pedagógicas e possibilidades de exploração de temas ambientais associados a propostas de ensino de física.