Elaboração e aplicação de uma sequência de atividades para o ensino da trigonometria numa abordagem histórica

The present work aims to report the construction of a workbook for teaching trigonometry focusing the possible mix between the historical approach to the teaching of mathematics and the professional master´s degree. For this, considerations about the history of mathematics as a teaching methodology, the education of the math teacher who will teach trigonometry and also about the course of elaboration and experimentation of the activities in the workbook were made (using the methodological strategy of action research). Finally, the workbook for the teaching of trigonometry in a historical approach is presented as an example of the above mentioned mix between the history of mathematics, mathematical school content and the professional master´s degree

Ensino de matemática pelo rádio (1950 1970): uma história falada e um documentário didático

This study aimed to describe and analyze aspects of the historical course of teaching Mathematics by Radio Experiences in Rio Grande do Norte, between the decades from 1950 to 1970 in order to organize a documentary (CD-ROM) containing information about Mathematics studied by Radio who have experienced it. In this, we use qualitative research. We seek support in the theoretical framework of cultural history and memory researchers as Certeau (1998), Chartier (1990), Le Goff (2008), Thompson (2002) and Peter Burke (2004). Moreover, we take the elements of oral history. We focus on the teaching of literacy and the primary of the Radio schools in two rural communities - Logradouro and Catolé - who are currently part of the city of Lagoa Salgada (RN) and, with respect to the Junior High School, we stopped in the Course of Madureza at Radio. We used as written sources, especially the documents found in the General Archives of the Archdiocese of Natal (RN) and the employees assigned by the participants of the survey. Our sources come from the oral testimonies of pupils and monitors Lagoa Salgada City, teachers, broadcasters and technicians of Rural Support Service (SAR) Natal (RN). In this study, we identify the geometry Cubação social practices of Lagoa Salgada students. Also identified in the research material, the Global Method with the pedagogy of Paulo Freire, that guided the production of lessons in literacy and primary courses. Content in Mathematics, we find traces of the trend-Empirical activist. In the course of Madureza, there was a tendency formal technique Fiorentini (1995). Finally, as a result of this study, organize and present a documentary (CD-ROM), along with the analysis of this study, containing the history of Mathematics teaching by Radio, from the speech of those who experienced Radio, emphasizing the methodology teaching developed in class, that serves as a reference material for students, professors and researchers.

Um hipermídia sobre fases da lua para o ensino de astronomia a distância

The interdisciplinary nature of Astronomy makes it a field of great potential to explore various scientific concepts. However, studies show a great lack of understanding of fundamental subjects, including models that explain phenomena that mark everyday life, like the phases of the moon. Particularly in the context of distance education, learning of such models can be favored by the use of technologies of information and communication. Among other possibilities, we highlight the importance of digital materials that motivate and expand the forms of representation available about phenomena and models. It is also important, however, that these materials promote the explicitation of student's conceptions, as well as interaction with the most central aspects of the astronomical model for the phenomenon. In this dissertation we present a hypermedia module aimed at learning about the phases of the moon, drawn from an investigation on the difficulties with the subject during an Astronomy course for teaching training at undergraduate level at UFRN. The tests of three semesters of course were analyzed, taking into account also the alternative conceptions reported in the literature in astronomy education. The product makes use of small texts, questions, images and interactive animations. Emphasizes questions about the illumination of the Moon and other bodies, and their relationship to the sun, the perception from different angles of objects illuminated by a single source, the cause of the alternation between day and night, the identification of Moon's orbit around the Earth and the occurrence of the phases as a result of the position of observing it, and the perception of time involved in the phenomenon. The module incorporated considerations obtained from interviews with students in two poles where its given presential support for students of the course, and subjects from different pedagogical contexts. The final form of the material was used in a real situation of learning, as supplementary material for the final test of the discipline. The material was analyzed by 7 students and 4 tutors, among 56 users, in the period in question. Most students considered that the so called "Lunar Module" made a difference in their learning, the animations were considered the most prominent aspect, the images were indicated as stimulating and enlightening, and the text informative and enjoyable. The analysis of learning of these students, observing their responses to issues raised at the last evaluation, suggested gains in key aspects relating to the understanding of the phases, but also indicates more persistent difficulties. The work leads us to conclude that it is important to seek contributions for the training of science teachers making use of new technologies, with attention to the treatment of computer as a complementary resource. The interviews that preceded the use of the module, and the way student has sought the module if with questions and/or previous conflicts - established great difference in the effective contribution of the material, indicating that it should be used with the mediation of teacher or tutor, or via strategies that cause interactions between students. It is desirable that these interactions are associated with the recovery of memories of the subjects about previous observations and models, as well as the stimulus to new observations of phenomena

A leitura como instrumento facilitador da compreensão matemática

This research builds on a qualitative approach and proposes action research to develop, implement and evaluate a strategy grounded in the teaching of geometry reading from different text types, in order to enhance the understanding of mathematical concepts by students in the 6th grade of elementary school. The teaching of mathematics, strengthened by a reading practice that fosters a greater understanding of science, because it would contribute to the expansion of vocabulary, acquire a higher level of reasoning, interpretation and understanding, providing opportunities thus a greater contextualization of the student, making out the role of mere spectator to the builder of mathematical knowledge. As a methodological course comply with the following steps: selecting a field of intervention school, the class-subject (6 years of elementary school) and teacher-collaborator. Then there was a diagnostic activity involving the content of geometry - geometric solids, flat regions and contours - with the class chosen, and it was found, in addition to the unknown geometry, a great difficulty to contextualize it. From the analysis of the answers given by students, was drawn up and applied three interventional activities developed from various text (legends, poems, articles, artwork) for the purpose of leading the student to realize, through reading these texts, the discussions generated from these questions and activities proposed by the present mathematics in context, thus getting a better understanding and interaction with this discipline as hostility by most students. It was found from the intervention, the student had a greater ability to understand concepts, internalize information and use of geometry is more consistent and conscientious, and above all, learning math more enjoyable

Uma sequencia didática para o ensino da resolução da equação do 2. grau : adequação para o uso com professores

The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher

Recorte dos produtos educacionais em história no ensino da matemática e em didática da matemática a partir das dissertações e teses defendidas no brasil entre 1990-2010

This work has the main purpose of conducting a survey of educational products present in dissertations and doctoral theses focused on the use of history in mathematics teaching and Didactics of mathematics with a French foundation produced in graduate programs in the strict sense of the Brazil between 1990 and 2010, the areas of Education, Mathematics Education, school of Natural Sciences and Mathematics and related areas, according to the research proposal of Mendes (2010). Our interest was to select the products that present concrete proposals for educational activities that can be used in the classroom of Basic Education and Training of Teachers of Mathematics. The research was implemented through a bibliographic study documents the Bank of dissertations and theses from CAPES, libraries and archives of some Postgraduate programs in the country who focus their studies on the subject object of this research, besides the Brazilian Digital Library Theses and Dissertations (BDBTD). From this survey we selected works that present educational products materialized in blocks of activities based on the use of teaching history of mathematics to the classroom as well as the sequence of activities based on the Teaching of Mathematics. In possession of material, produce a CD-ROM containing the selected activities, in order to help support the work of teachers regarding the use of these activities, as a supplementary material to textbooks in their math classes

Linguagem matemática: uma proposta de ensino e avaliação da compreensão leitora dos objetos da matemática

This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

Trabalhos prático-experimentais no ensino da biologia: Uma análise dos livros didáticos de Biologia aprovados no PNLD/2012

El trabajo práctico experimental en la educación en Ciencias y en el contexto de la enseñanza de la Biología es un objetivo clave. Teniendo en cuenta la influencia de los libros de texto en la actividad profesional de docentes, interesado en este estudio para caracterizar la orientación de este tipo de materiales, para el trabajo práctico experimental y el uso de la medición en esta actividad. Para ello analizaron las ocho colecciones de libros de Biología aprobado en PNLD en 2012. La investigación es de naturaleza descriptiva e interpretativa y de recogida de datos ha sido elegida por el método de análisis de contenido (BARDIN, 2002). El análisis de los trabajos práctico experimentales buscó caracterizar su naturaleza epistemológica, concepción de la ciencia implícita, conceptual, tipología, contenido conceptual de Biología utilizado, cuántos implican medidas, y cómo se utiliza en este contexto según el procedimiento general para medir propuesto por Núñez y Silva (2008). Los trabajo práctico experimental ha sugerido una epistemología de la enseñanza conceptual, carácter racionalista en su mayoría y dominada por las actividades del tipo de ejercicio práctico, a necesidad de medir está presente en una minoría de estos y se se utiliza el procedimiento general de medición de forma parcial e implícito en la mayoría de los trabajos prático experimentales. Por lo tanto, proponemos en este actividades de estudio a desarrollar una guía de análisis de los trabajo práctico experimentales propuesto en los libros de texto de Biología

O ensino por problemas nos livros de química: uma análise do conteúdo estrutura atômica

La enseñanza de problemas se ha investigado en la didáctica de las ciencias naturales como un medio importante para desarrollar el aprendizaje de los conocimientos científicos y la formación de competencias básicas. Dada la importancia de los libros de texto para la enseñanza de la ciencia, con el fin de verificar el enfoque de la enseñanza con problemas en los libros de química, se procedió a una investigación realizada en las obras aprobadas en PNLD 2012, basado en el método de Análisis de Contenido. Se analizó el contenido de la estructura atómica, como marco teórico la perspectiva de la enseñanza problémica, basada en el materialismo histórico y dialéctico. Metodológicamente la investigación presenta un carácter cualitativo. Los resultados del análisis de contenido corroboraron la cuestiones de estudio iniciales relacionadas con la explicación centrándose en los problemas, lo que permitió inferir la elaboración de una Unidad Didactica basada en los métodos problémicos para la enseñanza de los modelos atómicos por la exposición problémica, la conversación heurística y la busca parcial, como forma de aproximar los estudiantes a la naturaleza de las ciencias naturales y contribuir al desarrollo de actitudes positivas en el aprendizaje de la química

Uma proposta de ensino para o nível fundamental a partir das concepções sobre insetos

O presente trabalho consiste em uma investigação acerca das concepções de estudantes sobre o que é um inseto. Partiu-se do pressuposto de que os alunos expressam concepções errôneas no momento de identificar os representantes do táxon Insecta e que isso é consequência das experiências do cotidiano e de erros conceituais oriundos da formação escolar incorreta. Os objetivos deste trabalho foram investigar sobre concepções alternativas acerca dos insetos com alunos do ensino fundamental II e propor situações para promoção de uma aprendizagem mais ativa. Os dados para analise foram coletados em três turmas de escolas diferentes: uma escola em Nova Parnamirim, da rede privada, e duas da rede pública municipal de ensino: uma do município de Natal/RN e a outra do município de Parnamirim/RN. Utilizou-se como instrumento um questionário aplicado em duas fases. Na primeira etapa foram feitas três questões abertas e duas fechadas. Na segunda, aplicaram-se mais três questões. Nesta oportunidade foram apresentados aos alunos uma lista com imagens de insetos e animais considerados não insetos. Os resultados dos questionários mostraram que os alunos apresentaram na sua maioria, 62%, sentimentos negativos sobre os insetos, expressos por palavras depreciativas, entre elas: nojentos, feios, asquerosos, perigosos, sendo estes mais da metade dos alunos da amostra. Sentimentos positivos representaram 20%: fazem bem ao homem, Deus criou, são bons, são bonitos, e 18% apresentaram neutralidade nessas categorias. Outro resultado apresentado foi que 82% generalizaram os animais artrópodes como sendo insetos. Como forma de resolver problemas relacionados as concepções uma unidade didática foi aplicada em uma das escolas envolvidas na pesquisa, validando assim um instrumento pedagógico que incluiu atividade lúdica constituída de um jogo de tabuleiro proporcionador de uma vivência de aprendizagem focada em conceitos científicos sobre os insetos fáceis de serem apreendidos

Matemática Védica no ensino das quatro operações

This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

A etnomatemática em uma cerâmica da região do Seridó/RN

This work has as objective to describe mathematical knowledge used as tools in the manufacture and marketing of tiles of red ceramic by potters of the Currais Novos village/ RN, located 250 km from the capital of Rio Grande do Norte. For us to reach our objective, we rely on conceptions ambrosianas of Ethnomatematics, besides of the qualitative research in an ethnographic approach. In the empirical part of the research, that went it accomplishes in the period from 2009 to 2012 in the Currais Novos Village, we support the following tools for data collection, semi-structured interviews, field diary, photographs, audio recordings and participant observations. In the analysis of the collected data, we can conclude that there are mathematical knowledge in the management of manufacture and marketing of tiles, often different from the academic mathematics, mainly in the wood cube, on cube of the clays, in the handler with the measures time, the count method , in the arrangement of tiles, in the preparation of the ceramic mass and sale of tiles. Theses knowledge were described and analyzed in the light of the theoretical Ethnomatematics, also supported in official documents, such as Parameters Nacional Curriculares. The analyzes of these knowledge generated subsidies for elaboration of an educational product - a proposal of didactic sequence destined to the Teaching of Mathematics in Elementary and Middle levels for the community schools and region, this proposal is in the Appendix to this work

Obras complementares: um elo entre a leitura e os conteúdos matemáticos

The Federal Government through its Plans and Programs invests in various policies intended to achieve the main goal of the millennium, provide basic education for all. Among them, we highlight in this paper The National Textbook Program, with emphasis on Complementary Works. These works are presented through different genres, such as poems, poetry, short stories, parables, novels, literature, educational materials etc.. providing a range of possible teaching work. However, little is known about the levels of education of teachers as intended. Based on the discussions and studies in this direction, sparked concerns us in the process of teaching and learning in math classes. This made us pay attention to a possibility of study where reading could be included in this process. In this sense, the present study aims at investigating the potential of conceptual and didactic use of Complementary Works on developing the skills of reading and writing mathematics of the first three years of elementary school, and from there, propose a courseware with guidelines for use of these works by teachers of 1st to 3rd year of elementary school. For this, we outline the issues of reading and understanding of mathematical interests as those of our study. In this sense, the proposal was built from the bibliographic works that address the contributions of reading for learning mathematical content, like Machado (2001), Nacarato (2009); Dantas (2011), Smole and Diniz ( 2001). As a result, we created the Guidance for the use of Complementary Works for Teachers to Teach Mathematics with a view to support the practice of teachers and future teachers who teach mathematics. Supported the use of Complementary Works, especially those distributed in public schools by the National Textbook - PNLD and have mathematical content, this guide is intended to present some of the possible use of this feature in math classes. (Education Observatory - Capes / INEP. Ed. 038-2010. TELL Research Group - UFRN - PPGED / PPGEL / PPGECNM - PROPESQ)

História da ciência como estratégia didática no ensino médio: um breve olhar de conteúdos da óptica

From a critique of aspects of the current teaching of physics, we propose in this paper an investigation into the conceptions of Nature of Science (NOS) submitted by students from the high school level, as well as the inclusion of discussions about some elements of NOS, through the History and Philosophy of Science, understanding them as facilitating strategy for more effective learning of Physics and, more specifically, the contents of optics. Based on the historical period corresponding to Greek antiquity to the mid-nineteenth century, built and applied a teaching unit to a high school class at the Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN) Ipanguaçu campus. Our teaching unit involved the reading and interpretation of texts with historical content, observation and assembling five experimental activities, among other activities. Data analysis occurred through questionnaires investigative applied before and after the completion of the teaching unit, as well as questionnaires for content present in the texts. Although not significant, the results indicated that the application of the teaching unit allowed the (re) construction of some conceptions about NOS targets students present in our work, and contribute to a better learning content and greater optical science approach and its nature