O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Pedagogia etnomatemática : ações e reflexões em matemática do Ensino Fundamental com um grupo sócio cultural específico

mongst the trends in Mathematics Education, which have as their object a more significant and criticallearning, is the Ethnomathematics. This field of knowledge, still very recent amongst us, besides analyzing an externalist history of the sciences in a search for a relationship between the development of the scientific disciplines and the socio-cultural context, goes beyond this externalism, for it also approaches the intimate relationships betwe_n cognition and culture. In fact, the Ethnomathematics proposes an alternative epistemological approach associated with a wider historiography. It struggles to understand the reality and come to the pedagogical action by means of a cognitive approach with strong cultural basis. But the difficulty of inserting the Ethnomathematics into the educational context is met by resistance from some mathematics educators who seem indifferent to the influence of the culture on the understanding of the mathematics ideas. It was with such concerns in mind that I started this paper that had as object to develop a curricular reorientation pedagogical proposal in mathematics education, at the levei of the 5th grade of the Ensino Fundamental (Elementary School), built from the mathematical knowledge of a vegetable farmers community, 30 km away from the center of Natal/RN, but in accordance with the teaching dimensions of mathematics of the 1 st and 2nd cycles proposed by the Parâmetros Curriculares Nacionais - PCN: Numbers and Operations, Space and Form, Units and Measures, and Information Treatment. To achieve that, I developed pedagogical activities from the mathematical concepts of the vegetable farmers of that community, explained in my dissertation research in the period 2000 through 2002. The pedagogical process was developed from August through Oecember 2007 with 24 students of the 5th Grade of the Ensino Fundamental (Elementary School) of the school of that community. The qualitative analysis of the data was conducted taking into account three categories of students: one made up of students that helped their parents in the work with vegetables. Another one by students whose parents and relatives worked with vegetables, though they did not participate directly of this working process and one third category of students that never worked with vegetables, not to mention their parents, but lived adjacent to that community. From the analyses and results of the data gathered by these three distinct categories of students, I concluded that those students that assisted their parents with the daily work with vegetables solved the problem-situations with understanding, and, sometimes, with enriching contributions to the proposed problems. The other categories of students, in spite of the various field researches to the gardens of that community, before and during the pedagogical activities, did not show the same results as those students/vegetable farmers, but showed interest and motivation in ali activities of the pedagogical process in that period

Não é que eu sei ser professora!: formação continuada e construção do currículo da matemática para o ciclo de alfabetização

Esta dissertação investiga como a prática da formação continuada em Matemática dos professores do Núcleo de Educação da Infância/Colégio de Aplicação (NEI/CAp) tem possibilitado a construção do currículo da Matemática para o ciclo de alfabetização nessa instituição. Assumimos os princípios metodológicos da abordagem qualitativa com ênfase na pesquisa colaborativa. Privilegiamos atividades de formação continuada organizadas em sessões de estudos e reflexões sobre a prática pedagógica que envolveram todos os partícipes. Para a construção dos dados realizamos a escolha de instrumentos e procedimentos metodológicos como a entrevista individual e as sessões reflexivas de videoformação e de estudo. Com a intensão de responder a questão central da pesquisa definimos duas categorias de interpretação: a formação continuada em Matemática dos professores do NEICAp dos anos iniciais do Ensino Fundamental e a construção do currículo da Matemática dos anos iniciais do Ensino Fundamental nesta escola. Constatamos que a prática da formação continuada em Matemática acontece dentro da própria instituição e tem como interesse, além da formação permanente dos seus professores, o desenvolvimento da escola e a aprendizagem dos alunos. Avaliamos que por meio de estudos e reflexões sobre as práticas docentes, análises de propostas pedagógicas de Secretarias de Educação e de outros documentos oficiais do Ministério da Educação, em momentos de formação continuada em contextos vivenciadas pelos professores do NEI/CAp, vem sendo possível construir o currículo desta instituição e, consequentemente, a sua proposta curricular, na qual privilegiamos a área da Matemática

RoboEduc: especificação de um software educacional para ensino da robótica às crianças como uma ferramenta de inclusão digital

Because of social exclusion in Brazil and having as focus the digital inclusion, was started in Federal University of Rio Grande do Norte a project that could talk, at the same time, about concepts of collaborative learning and educational robotics , focused on children digitally excluded. In this context was created a methodology that approaches many subjects as technological elements (e. g. informatics and robotics) and school subjects (e. g. Portuguese, Mathematics, Geography, History), contextualized in everyday situations. We observed educational concepts of collaborative learning and the development of capacities from those students, as group work, logical knowledge and learning ability. This paper proposes an educational software for robotics teaching called RoboEduc, created to be used by children digitally excluded from primary school. Its introduction prioritizes a friendly interface, that makes the concepts of robotics and programming easy and fun to be taught. With this new tool, users without informatics or robotics previous knowledge are able to control a robot, previously set with Lego kits, or even program it to carry some activities out. This paper provides the implementation of the second version of the software. This version presents the control of the robot already used. After were implemented the different levels of programming linked to the many learning levels of the users and their different interfaces and functions. Nowadays, has been implemented the third version, with the improvement of each one of the mentioned stages. In order to validate, prove and test the efficience of the developed methodology to the RoboEduc, were made experiments, through practice of robotics, with children for fourth and fifth grades of primary school at the City School Professor Ascendino de Almeida, in the suburb of Natal (west zone), Rio Grande do Norte. As a preliminary result of the current technology, we verified that the use of robots associated with a well elaborated software can be spread to users that know very little about the subject, without the necessity of previous advanced technology knowledges. Therefore, they showed to be accessible and efficient tools in the process of digital inclusion

Dificuldades no processo ensino aprendizagem de trigonometria por meio de atividades

This study analyses the difficulties that teachers of high school face in the process of the teaching of trigonometry through activities in a construtivist focus. It contains a review of some publications and dissertations related with the study of trigonometry elaborated in the last years by several authors. It resorts to the study of teaching engineering as an instrument used in the research. It also presents a set of activities which will serve as sample to other teachers of mathematics; and points ways for the overcome of the difficulties found

Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Reflexões e contribuições para o ensino de gravitação clássica no nível médio

The subject of Classic Gravitation is part of the actual curriculum for High School in Brazil, and it is taught in the first year of that education level. This master thesis presents a research regarding the subject Classic Gravitation in High School. This research was based in two complementary guidelines of research and action. The first guideline was the analysis of 21 didactic books of physics which are the more frequently used in High School, in the city of Natal/RN. The second guideline, worked after being verified the most common deficiencies presents in the didactic books, was the elaboration, followed by a practical application, of a course suggesting how to approach that subject in the classroom. The Parâmetros Curriculares Nacionais para o Ensino Médio (National Curricular Parameters for High School PCNEM) defend that Classic Gravitation is very important in the student s formation and that its study helps the comprehension of many nature s phenomena. Because of this vision of that subject by the PCNEM, the 21 analyzed books were separated in two groups: the first one, containing 10 books, was edited before the spreading of PCNEM, and the second, with 11 books, after that spreading. Whatever the group to which the didactic books belonged, the great majority of them let that subject in a second plan; two of them even suggesting, in the teacher s orientations, that the subject Gravitation can be suppressed in case of insufficient time . These analyses points that the PCNEM had produced no changes in the conception of the authors that wrote books regarding that subject. To analyze the didactic books, we elaborated a script which was used as an analysis tool, in which we put in evidence the relative importance of the historic and philosophic contextualization of the subject, the quotidian experience of the students and the interdisciplinary approach, among other aspects. It became evident that the didactic books give very little emphasis to historic aspects of the knowledge construction, to the relations with the day-by-day questions and to the interdisciplinary character of the subject Gravitation. It calls attention the non concordance among the authors opinions regarding the necessary previous knowledge or prerequisites the students should fulfill in order to begin to study Gravitation. The course we elaborated was given to a group of teachers as well as to students. In those courses we treated theoretical and practical aspects and emphasized historical questions and the ones which are related to people s daily life. The course for teachers was realized as an extra-mural activity of the UFRN and was given by the author of this thesis at the Escola Estadual Francisco Ivo Cavalcanti (a state public school in Natal/RN). There were 23 teachers present, from several public schools and several fields of knowledge. The thesis supervisor and the master degree s colleagues of the author acted as collaborators , reporting the participants opinions and speeches. The course to the students, on the other hand, had the participation of 300 regular students who belonged to 6 different 1st year classes of the High School Escola Marista de Natal (RN), in which the author acts as a physics teacher. The student s course was realized as part of the regular curriculum activities, in which three classes stood under the responsibility of the author and other three classes in charge of another Marista s teacher, who participated as a collaborator . The teacher s course as well as the students one were given in two stages, with five hours each. The first stage was divided in two moments, the first one focused on the survey of the spontaneous conceptions about gravitation, in which we worked basically with experiments of free throwing and pendulum, and the second one focused in theoretical presentations and quarrels about universe s models. In the second stage of the course we improved the study of Kepler s laws and the Newton s Universal Gravitation law, and we used as motivating tools some practices involving the construction of the solar system in scale. As instruments for evaluating both courses we used questionnaires and reported the speeches with participants opinions, beyond usual written evaluations in the course for the students. The teachers who participated in the course showed very good wills in realizing interdisciplinary practices; nevertheless, according their own speeches, they frequently came across the difficulty of how to do . From the experience we had in both courses, we conclude that the approach we propose hear to the teaching of the subject Classic Gravitation , supported on the tripod theory, practice and historical and philosophical aspects, is viable and effective. One hopes that this research may contribute in the formation of a opinion, among the teachers, concerning how to approach the subject of Classic Gravitation, and may offer suggestions in order those who want to apply that approach may develop classroom practices aiming to improve the teaching of that subject, which has a singular importance in the formation of High School students

Elaboração e aplicação de uma estratégia de ensino sobre os conceitos de calor e de temperatura

This piece of work has investigated the alternative conceptions shown by students of secondary school, concerned to the concepts of warmth and temperature, aiming the elaboration and application of a learning strategy as of the diagnose risen from the conceptions present in students. The learning strategy was built up by a sequence of activities that involve History of Science and experiments, put in a course that had as a base the proposal of the Group of Redevelopment of Physics Teaching (GREF). We have used as the conductor wire of our research the development of thermo dynamics since the development of the first thermo machines, passing by the Industrial Revolution and the evolution of concepts of warmth and temperature. The learning strategy was applied to a group of second grade of secondary school in a public school in Mossoró (RN). By doing these activities we tried to become the concepts, which are part of thermo dynamics, more meaningful to the students. We have estimated that the application of the strategy has represented some profits to the students of the group, concerning to learning of laws and concepts of thermo dynamics (specifically the concepts of warmth and temperature), as well as what it is referred to the overcoming of its initial conceptions

A Informática como recurso didático para a aprendizagem de Física no ensino médio

The accomplishment of this work was motivated by our concerns, while teacher of Physics discipline, in the medium teaching and in the higher education, where we have been observing a lot of difficulties in the students' acting, to the they try to give pursuit out to their studies of the classroom, because of the lack of appropriate equipments, or even, of a laboratory where they can put in practice the studied contents. The work aims at to build and to test an educational software that it serves as tool auxiliadora in Physics learning in the Medium Teaching, in the area of electricity, with emphasis in the study of the electrodynamic in resistors. The developed software comes as an alternative to the learning problems, putting the computer science as auxiliary tool, because, besides being an alternative in the middle of the technological expansion, endowed with several resources, it stimulates the significant learning, according to David Ausubel's perspective. A software containing a program destined to the applicability of physics contents in the branch of the electricity is presented as an auxiliary tool, where the student can, not just, to review the contents presented at room, as well as for in practice, through a virtual laboratory, some of these contents, besides testing their knowledge through a bank of discursive subjects. The evaluation of the developed software was made submitting him/it to the professionals' of physics area appreciation. Equally, through continuous evaluations, they were made comparisons among the students' of five different groups acting, in the same school, that you/they were used of the program as tool of his auxiliary learning, and the acting of those that didn't use it

A formação inicial do professor de química e o uso das novas tecnologias para o ensino: um olhar através de suas necessidades formativas

La disertación, desarrollada en el Programa de PostGraduación en Enseñanza de las Ciencias Naturales y de la Matemática de la UFRN, estudia las necesidades formativas de licenciandos en Química sobre el uso de las nuevas tecnologías de la información y de las comunicaciones (NTIC), en especial, las relacionadas con la utilización de programas computacionales para la enseñanza de la química. En la actual sociedad del conocimiento, se torna imperativo la eclosión de nuevas formas de aprender y de enseñar, que requieren de nuevas concepciones del trabajo pedagógico. En ese sentido, se exige de los profesores el desarrollo de nuevas habilidades y competencias. El presente trabajo está comprometido con la búsqueda de elementos que puedan nortear los procesos formativos de profesores de química con el objetivo de contribuir con una mejor preparación de la formación inicial, tomando en cuenta sus necesidades de formación. Fue utilizado el cuestionario como instrumento de investigación para diagnosticar y caracterizar las necesidades fomativas, buscando establecer correlaciones entre diferentes variables que cacarterizan el estudio, con el fin de establecer semenazas y discrepancias entre las habilidades docentes en estudio y las necesidades formativas. Los analises de los datos tomo elementos de la estadistica descriptivo e inferencial, con analises multivariados, lo que posibilitó identificar las necesidades formativas. Los resultados muestran ue de forma general los licenciandos evaluan como de bajo, el grado de desarrollo de las habilidades para enseñar usando las NTIC, así como manifiestan sentir necesidades formativas en todas las habilidades referentes a esa esfera del trabajo docente

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Opiniões sobre estágio curricular e prática de ensino na licenciatura em química: o caso do CEFET-PB

The Brazilian legal documents are directing the reformulation of the courses that prepare students to be teachers. Through out the country many institutions look for to fit themselves in such documents. On the other hand, other IES (Superior Education Institutions), when they are setting up such courses they looked for to be adequate to the new public politics. Based on the National Curricular Norms to form teachers for Basic Education, in tertiary level, in 2004 it was created at the CEFET-PB,the Chemistry Course (Licenciatura) to prepare people to be teachers, whose organization. This work presents the results of a research of phenomenological nature that aimed to comprehend the teachers opinions, in the range of discussions about the current politics of formation, particularly related to the CNE/CP 1 and CNE/CP 2/2002 resolutions. This work based on the curricular proposal for the Chemistry Course (Licenciatura), presents the relationship between the probationary period and the teaching practice at the CEFET-PB, in order to contribute for a reflection about these categories to clarify the teachers of the course. It started from the consideration of all changes operated in contemporary society implies changes on teacher's pedagogical practices. It was used tow instruments for the data collection: a questionnaire with open and closed questions and recordable interviews. Nine teachers form the CEFET-PB took apart and four licensed teachers. It was based in a theoretic frame as a support for discussions about the different models of teachers formation. We concluded that the representations of teachers about probationary period the practice on the activity for the teachers formation was strongly anchored in characteristic elements of the formative tendency of a institution that historically acted on a technician formation, and the results pointed to strong signs of attitudes based on a model of the technical rationality

O espaço formativo na escola: um estudo com professoras dos 4º e 5º anos do ensino fundamental.

Es extensa, de parte de los docentes, la discusión sobre la articulación de actividades y estrategias de enseñanza que vengan a proporcionar una participación más activa del alumnado. Sin embargo tal tarea constituye un desafío para muchos profesores ya que, muchas veces, la formación inicial no siempre los prepara para esta perspectiva. Nosotros entendemos que es necesario desarrollar en los maestros una autonomía crítica, tomando la escuela como espacio formativo. El objetivo de este trabajo fue él de incentivar un espacio de discusión y reflexión para profesores en ejercicio de los 4° y 5° años de la Enseñanza Fundamental I. Ese espacio que era orientado para que ellos estudiasen y articulasen, entre otras cosas, el conocimiento disciplinar de Ciencias y la organización y sistematización de actividades de enseñanza que lleven a una participación más activa de los estudiantes. La investigación se realizó en una escuela privada de Natal/RN, que atiende a estudiantes desde la educación infantil hasta la enseñanza secundaria. Se desarrolló en cuatro fases: la 1ª, de familiarización, cuyo objeto de estudio se dio a través de la observación del salón de clase y del análisis de la planificación anual: la 2ª, de identificación de las dificultades de los maestros, teniendo como instrumentos encuestas con preguntas abiertas y elaboración de textos. La 3ª, en la perspectiva de proporcionar una intervención, se usó como instrumentos de investigación, el diario de clase y otras actividades como talleres, cursos y la elaboración de material didáctico. En la 4ª fase, para reconocer los posibles cambios en la práctica docente, ocurrieron nuevas observaciones en el salón de clase, el análisis de las planificaciones. Los datos obtenidos fueron organizados en tablas y clasificados. Los resultados señalan cambios en la práctica de esos profesionales, la introducción de la disciplina de Ciencias en el espacio formativo y el material didáctico elaborado ha sido un subsidio importante para ayudarlos en las clases

Questões objetivas sobre funções das provas de matemática do vestibular da UFRN dos anos de (2001 a 2008): um diagnóstico sobre os erros que os candidatos cometem

La dificultad que los alumnos encuentran en el aprendizaje de matemática viene siendo objeto de investigación por estudiosos en educación matemática, tanto en Brasil como en el exterior. El objetivo de este estudio consiste em investigar las dificuldades en el aprendizado sobre funciones matemáticas y la influencia de las concepciones alternativas a partir de los errores que los candidatos acerca de las cuestiones sobre funciones en la prueba objetiva de matemática del acceso a la universidad de los años de 2001 a 2008. Teniendo como cuestiones de estudio para alcanzar el objetivo propuesto: identificar la relevancia del tema funciones que son contemplados en las pruebas de acceso a la Universidad; asi como cuáles han sido los tipos de funciones más privilegiados y menos privilegiados; analizar si la contextualización de la pregunta y la presencia de elementos no textuales han influenciado en el aumento de tal dificultad; analizar si la representación semiótica agrega mayor exigencia a la pregunta; analizar respecto a la exigencia matemática de la pregunta; analizar lo que se refiere al desempeño de los candidatos para verificar cuál pregunta tuvo mejor desempeño y cuál el peor e identificar los errores más frecuentemente cometidos por los candidatos en esas pruebas. Las reflexiones de los estudiosos como: Radatz (1980), Cury (1994), Socas (1997), Borasi (1997), Franchi e Rincón (2004), Pochulu (2004) presentan las dificultades en el aprendizaje matemático, que aparecen a partir de los errores cometidos por los alumnos, quando estos errores reciben la influencia de las concepciones alternativas. El estudio que se presenta en esta disertación configura un análisis de los errores que los candidatos han cometido en las preguntas objetivas sobre el tema funciones de las pruebas de acceso a la Universidad de los años de 2001 a 2008, a partir de los relatorios de la Comissão Permanente do Vestibular COMPERVE/UFRN. Con la intención de alcanzar los objetivos propuestos para este estudio, fueran sido construidas categorías de análisis. Los resultados encontrados han sido: El tema funciones es el más frecuente entre los demás con (28,1%); el tipo de función priorizada durante esos años ha sido la función logarítmica con (24%); la contextualización de las preguntas exige una mayor comprensión por parte del candidato de lo que las situaciones directas; la caracterización semiótica posee elementos que estructuran esas preguntas que el educando debe saber asociar al texto; la exigencia matemática posibilitó analizar que el procedimiento medio ha sido el más requisitado; el desempeño de los candidatos ha sido en la mayoría bajo (50%); y los principales errores que ellos han cometido han sido de realizar traducciones incorrectas de las expresiones que aparecen en las situaciones-problema; utilizar todos los datos que aparezcan en el problema sin tomar en cuenta si el cálculo realizado responde a la pregunta solicitada; no interpretar coherentemente las informaciones del gráfico; decodificar incorrectamente los valores representados por literales en una recta numérica. Los resultados señalizan la necesidad de una revisión didáctico-metodológicas de la enseñanza de funciones a raíz de las cuales las dificultades en el aprendizaje se han presentado

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher