Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

A Compreensão da idéia do número racional e suas operações na EJA: uma forma de inclusão em sala de aula

The awareness of the difficulty which pupils, in general have in understanding the concept and operations with Rational numbers, it made to develop this study which searches to collaborate for such understanding. Our intuition was to do with that the pupils of the Education of Young and Adults, with difficulty in understanding the Rational numbers, feel included in the learning-teaching process of mathematics. It deals with a classroom research in a qualitative approach with analysis of the activities resolved for a group of pupils in classroom of a municipal school of Natal. For us elaborate such activities we accomplished the survey difficulties and obstacles that the pupils experience, when inserted in the learning-teaching process of the Rational numbers. The results indicate that the sequence of activities applied in classroom collaborated so that the pupils to overcome some impediments in the learning of this numbers

Física no cotidiano: da cozinha para a sala de aula relato de uma experiência didática no município de Limoeiro do Norte (CE)

Brazilian high school teaching has passing through important changes. Based on current legislation and other official documents this research focus on the notion of contextualization, discussing the possibilities of a Physics teaching contextualized at a kitchen environment. Given the difficulties presented by students in establishing the relation between the contents discussed in classroom and their own daily lives, we propose the elaboration and application of a didactic unity. This started after the analyses of an initial questionnaire answered by the students. The didactic unity was elaborated based on an earlier proposal made by GREF (Physics Teaching Reelaboration Group) for a Thermal Physics course, and involved situations on students daily lives, in particular, those activities tried to relate formal contents discussed in classrooms to the kitchen environment. The didactic unity was applied to a public high school classroom at Limoeiro do Norte (CE). After evaluation of this experience it is possible to state that contextualization is a challenge that shall be faced, so that students may have a more critical look at physics, understanding that this subject is of relevance to all of us and is present in all world around us

Aplicações das atividades estruturadas de Skemp para a construção do conhecimento matemático

The present study constitutes a discussion about the application of Structured Activities to the construction of the mathematical knowledge, proposed by Richard Skemp. The discussion is based on the research that the author carried out in a public school of the state education chain buy using procedures of the research-action. It investigates the possibility of adoption of the proposal of Skemp in a new reality. It utilizes explanations from several theorists to understand the necessity and, at the same time, to enhance the efficiency of the referred activities in first grades of elementary school when students have their first mathematics teachings. It emphasizes the important rule of the teacher, as mediator to the mental constructions of the child. It presents considerations about the results achieved by the research, noticing the possibility of adoption of the studied proposal even though it is necessary an adjustment of the procedures to appropriate didactic-pedagogic requirements to the educational reality in which this project was done

As quatro operações básicas: uma compreensão dos procedimentos algorítmicos

The current research had as main objective to analyze the possibility of knowledge elaboration/re-elaboration about ideas and algorithmic procedures related to basic operations by pupils of the 6th degree fundamental teaching in a significant learning process. This way the study had as basis a methodological intervention developed in a 6th degree class of a Fundamental Teaching Municipal School in the city of João Pessoa, PB. The research had as central steps the application of pre-tests (1 and 2); the execution of semi-structured interviews with the pupils involved in the theme deep studies; the elaboration and development of teaching activities, having as referential the significant learning and the application of a pre-test. The data collected in the pre-tests (1 and 2) showed a low level of the pupils comprehension about the contents related to the four operations. The answers to the post-test questions were analyzed mainly from the qualitative point of view based on the mathematic concepts comprehension theory proposed by Skemp (1980) having as complementary subsidy data collected through interviews. The analysis of the results obtained in the post-test showed that the major part of pupils reached a relational comprehension about the ideas and algorithmic procedures related to addition, subtraction, multiplication, and division. Such results showed us that the application of a teaching methodology that privileges the content comprehension, considering the pupils previous knowledge and the reflection about the action along the activities proposed, made possible the elaboration or re-elaboration of knowledge by pupils regarding to contents adopted as theme for our research

Controvérsias sobre a natureza da luz: uma aplicação didática

Researches in the field of Science Teaching have shown, in recent decades, that students from high school level have difficulties in understanding basic concepts of science, in general, and physics, in particular. The specific literature indicates, as a priority for a scientific education of better quality, a more structured understanding about science. This work proposes the introduction of elements of History and Philosophy of Science in high school as an aid to learning the concepts of optics, in general, and of aspects concerning the nature of science, specifically. Making use of historical episodes regarding the controversy on the nature of light, especially during the seventeenth and eighteenth centuries, as well as clippings of the history of optics in relation to the development of models that explain the process of vision, we formulated a teaching unit and implemented it on two night high school classes of a public school in the city of Parnamirim (RN). The unit involved, primarily, the reading of three historical texts containing written questions followed by a collective debate ("moot"). The results indicated some difficulties in overcoming the misconceptions related to the process of vision and the nature of light. Nevertheless, we believe that the teaching unit has succeeded in relation to the learning of most students, both in relation to a better understanding of science as well as concepts of optics

A utilização de espaços de educação não formal por professores de biologia de Natal-RN

La práctica educativa en espacios no formales es un recurso didáctico catalizador de motivación e interese, tanto para alumnos como para los profesores. El crecimiento de los espacios no formales coincide con los cambios recientes en el mundo en los campos sociales, políticos, económicos y culturales. Como una de las consecuencias de esos cambios, tenemos el crecimiento de otras instancias difusoras de conocimientos rompiendo, así, la hegemonía de la escuela. De esa forma, en este trabajo busqué investigar la frecuencia y las formas de utilización de los espacios de educación no formal por profesores de biología, de la enseñanza media, de la Ciudad de Natal (RN). Procuré también, identificar cuales son los espacios de educación no-formal que son utilizados; describir los recursos y las acciones desarrolladas en eses espacios; identificar la existencia o no de interese y la importancia que atribuyen a los espacios para la enseñanza de biología, además de divulgar los espacios utilizados como recursos didácticos. Para alcanzar estos objetivos fueron hechas observaciones de los espacios, aplicados cuestionarios y realizadas entrevistas con los profesores que realizan actividades junto a tales instituciones. Para el análisis de los datos se utilizó tanto el abordaje cuantitativo como cualitativa. Nos basamos en referenciales teóricos de autores que buscan establecer las relaciones entre diferentes modalidades de educación para mejor comprender lo que es la educación no-formal y su trayectoria histórica. Constaté que los profesores utilizan los espacios de educación no-formales, aun la cantidad de visitas al año sea reducida, en virtud de varias dificultades por ellos apuntadas, tales como el transporte, la falta de recursos financieros y de apoyo para viabilizar la visita, entre otros. Verifiqué también que los profesores demostraron un alto interese por los espacios no-formales y apuntaron como principales justificativas para considerarlos importantes para la enseñanza de la biología la posibilidad de establecer conexiones entre la teoría y la practica, además de la complementariedad

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

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

A desistência de alunos na licenciatura em física no Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN): causas e sugestões para o combate

This dissertation proposes studying the issue of withdrawal undergraduate in physics at the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte (IFRN) and collaborate with suggestions for dealing with this problem. The first chapter begins with an overview of two significant problems in the Brazilian educational system: the high dropout rates in degrees in physics and the lack of teachers with specific training in this science. Then, we discuss the relevance of this research to the area of physics teaching, as well as justify its completion as part of a professional master's degree. After, we present a proper definition for the term withdrawal, which is based on the existing problem in the IFRN. And, in the same chapter, we explicitly the focus, the objectives and the methodological aspects of this work. The results obtained in our investigation are presented in next four chapters. In the second chapter of this dissertation, we present: a brief history of the creation of IFRN degree in physics, the functioning of this course and the foundation of classrooms 2004.2 and 2006.1. We also show a kind of map of the withdrawal of the groups investigated (the dropout rate was 84.4% in both groups) and an analysis of the relationship between the curricula of each of them and the number of dropouts. In the third chapter, we display a descriptive statistics of the students which dropout and found that the largest dropout occurred with students who are women, married, parents of one kid; workers, joined with a minimum age of 23 years and completed high school at least 6 years. Then in the fourth chapter, we reveal and discuss the students' reports on the causes of their dropout. From the data presented, we can say that the answer to the question "What was the main reason for your dropout?" Is mainly in personal injury claims: another option for upper-level course and lack of time to devote to the course. In the fifth chapter, we show the results related to teacher s opinions about the phenomenon in question. We detected three main causes for the abandonment, according to teachers: the lack of dedication, the lack of interest and lack of integration in the course. In the sixth and final chapter, we discuss the results and present our conclusion and the proposed report - the product of this dissertation, presented as Annex. This report contains mainly suggestions for curricular and institutional actions that can contribute to reducing the dropout degree in Physics in the IFRN. The main actions suggested are: implementation of the curriculum in disciplines, implementation of programs or actions to combat this poor content of basic training, implementation of specific programs or actions for the student worker, and dissemination of IFRN degree in physics in schools through seminars or workshops

Abordagem de temas em saúde pública por meio de atividades lúdicas com professoras da educação infantil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Atividades estruturais de equações polinomiais numa abordagem histórica por meio de e-book

The present study investigates how the inter-relationship of the content of polynomial equations works with structured activities and with the history of mathematics through a sequence of activities presented in an e-book, so that the result of this research will proceed will result in a didactic and pedagogic proposal for the teaching of polynomial equations in a historical approach via the reported e-book. Therefore, we have considered in theoretical and methodological assumptions of the History of Mathematics, in structured activities and new technologies with an emphasis on e-book tool. We used as a methodological approach the qualitative research, as our research object adjusts to the objectives of this research mode. As methodological instruments, we used the e-book as a synthesis tool of the sequence of activities to be evaluated, while the questionnaires, semi-structured interviews and participant observation were designed to register and analyze the evaluation made by the research, participants in the structured activities. The processing and analysis of data collected though the questionnaires were organized, classified and quantified in summary tables to facilitate visualization, interpretation, understanding, and analysis of these data. As for participant observation was used to contribute to the qualitative analysis of the quantified data. The interviews were synthetically transcribed and qualitatively analyzed. The analysis ratified our research objectives and contributed to improve, approve and indicate the use of e-book for the teaching of polynomial equations. Thus, we consider that this educational product will bring significant contributions to the teaching of mathematical content, in Basic Education

Física do meio ambiente: desafios de uma disciplina focada na formação de habilidades gerais

A disciplina Física do Meio Ambiente (FMA) foi criada em 1976 no Departamento de Física Teórica e Experimental da UFRN e, atualmente, faz parte da estrutura curricular do curso de Licenciatura em Física da UFRN e é de caráter obrigatório. Tal caráter se justifica, dentre outros motivos, pelo fato de que esta disciplina representa uma boa oportunidade dos licenciandos estudarem de que forma a Física pode contribuir para a compreensão de fenômenos relativos ao nosso Meio Ambiente, sejam eles relacionados às atividades humanas ou aos fenômenos naturais propriamente ditos e que, de uma forma ou de outra, afeta a sociedade. O nosso trabalho de pesquisa teve como objetivo principal elaborar um novo programa de ensino para a disciplina de Física do Meio Ambiente adequado às necessidades da educação científica para o século XXI. A pesquisa foi conduzida inicialmente com um levantamento histórico da disciplina desde sua origem no Departamento de Física ate os dias atuais, analise dos Projetos Pedagógicos do curso de Licenciatura em Física da UFRN, revisão bibliográfica sobre as definições de competências e habilidades em um contexto de ensino e segundo o pensamento de vanguarda nesse campo de pesquisa, acompanhamento do curso durante um semestre através de aulas observacionais, aplicação de questionário para a coleta de dados e análise de alguns livros didáticos de Física do Ensino Médio. A partir do perfil ou modelo profissional para o licenciado em Física da UFRN definimos os objetivos gerais para a disciplina de FMA em termos de habilidades gerais relacionadas com as atividades que um futuro professor de Física irá desempenhar no seu dia a dia. O nosso programa de ensino foi pensado no sentido de introduzir conteúdos de didática específica ao longo da disciplina, isto é, familiarizar os professores em formação com investigação e inovação didáticas voltadas para o ensino de temas que envolvam a conexão entre Física e Meio Ambiente. Como resultado de nossa pesquisa foi proposto um novo Programa de Ensino para FMA que pode ser útil aos futuros professores desta disciplina e foi elaborado segundo uma metodologia de organização científica do processo ensino

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