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

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

O erro produzido pelo aluno no contexto pedagógico: uma luz ou uma pedra no meio do caminho?

Student’s mistakes as viewed in a didactic and pedagogical perspective are a phenomenon inevitably observed in any context in which formal teaching-andlearning processes are taking place. Researchers have shown that such mistakes are viewed most of the times as undesirable and often as a consequence of lack of attention or poor commitment on the part of the student and rarely considered didactically useful. The object of our reflections in this work is exactly those mistakes, which are born in the entrails of the teaching-and-learning processes. It is our understanding that a mistake constitutes a tool which mediates knowledge and may therefore become a strong ally of the instructor’s actions in her/his teaching tasks and thus should be taken into the teacher’s best consideration. Understanding a mistake as so, we postulate that the teacher must face it as a possibility to be exploited rather than as a negative occurrence. Such an attitude on the part of the teacher would undoubtedly render profitable didactic situations. To deepen the understanding of our aim, we took a case study on the perception of senior college students in the program of Mathematics at UFRN in the year 2009, 2nd term. The reason of this choice is the fact that Mathematics is the field presenting traditionally the poorest records in terms of school grades. In this work we put forth data associated to ENEM1 , to the UFRN Vestibular2 and the undergraduate courses on Mathematics. The theoretical matrixes supporting our reflections in this thesis follow the ideas proposed by Castorina (1988); Davis e Espósito (1990); Aquino (1997); Luckesi (2006); Cury (1994; 2008); Pinto (2000); Torre (2007). To carry out the study, we applied a semi-structured questionnaire containing 14 questions, out of which 10 were open questions. The questions were methodologically based on the Thematic Analysis – One of the techniques for Content Analysis schemed by Bardin (1977) – and it was also used the computer program Modalisa 6.0 (A software designed by faculties the University of Paris VIII). The results indicate that most of the teachers training instructors in their pedagogical practice view the mistakes made by their students only as a guide for grading and, in this procedure, the student is frequently labeled as guilty. Conclusive analyses, therefore, signal to the necessity of orienting the teachers training instructors in the sense of building a new theoretical contemplation of the students’ mistakes and their pedagogical potentialities and so making those professionals perceive the importance of such mistakes, since they reveal gaps in the process of learning and provide valuable avenues for the teaching procedures.