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

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

O Ensino de medidas e grandezas através de uma abordagem investigatória

This work relates our experience in an investigative practice in the classroom, carried out in State School Jorge Fernandes , located in Natal - RN, having as objective to validate the applying of a education module about Measures and Largenesses in Primary Teaching. We used the constructivist approach; using to Richard s Skemp (1980) theory in order to explicit the students learning according to their comprehension levels. Initially, we carry out an exploratory research to check the participant s previous knowledge. Then, we developed an intervention to validate an education module, structured from needs pointed out from results of the initial research, analyzing the students advances through the final evaluation, displaying growth stages of group front to the knowledge about the matter approached. Finally, we presented our reflections about our experience; putting forward suggestions of the teachers activities, aiming at contributing to the improvement of their practices in classroom during the approach of subject for us investigated

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

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.

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

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

História da matemática na formação do professor: dificuldades e sugestões

This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Luís de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation

Avaliação de Interações entre Professor e Alunos na Educação Matemática: ensino e aprendizagem de recursos pedagógicos

The aim of this paper is to discuss the teachers' need, as autonomous professionals, to evaluate their own pratice. Considering that Descriptive Functional Analysis (DFA) may be a pedagogical method for analysis, implementation, and change of teachers' mathematics teaching practices, the objective of the present research was to teach repertoires compatible with DFA to two mathematics teachers in elementary schools of São Paulo state. When teachers are responsible for evaluation and self evaluation, they recognize themselves as fundamental agents of transformation in education.

Interface entre história da matemática e ensino: uma atividade desenvolvida com base num documento do século XVI

Este artigo propõe a construção de uma interface entre história e ensino de matemática a partir de um diálogo entre historiadores e educadores da matemática. Para tanto, consideramos aspectos epistemológicos e metodológicos ligados à história da matemática, pautada em tendências historiográficas atuais, juntamente com a metodologia baseada no movimento lógico-histórico. A interface contemplou o movimento do pensamento na formação dos conceitos e o contexto no qual tais conceitos foram desenvolvidos, de modo a conduzir à reflexão sobre o processo histórico da construção do conhecimento para a elaboração de atividade didática. Esta atividade teve por base um documento do século XVI dedicado à construção e uso de instrumentos matemáticos, e sua elaboração levou em consideração uma intencionalidade e um plano de ação que viabilizaram o seu desenvolvimento. A organização do ensino articulou as conexões internas e externas trazidas pela análise do documento e a forma do pensamento do desenvolvimento do conceito.

As diferentes “personalidades” do número racional trabalhadas através da resolução de problemas

We address the different "personalities" of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number - rational point, quotient, fraction, ratio, and operator - are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different "personalities" of the rational number. In general, these "personalities" are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these "personalities", the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics.

O ensino de matemática nos cursos de ciências biológicas: uma proposta de conteúdos adequados

Pós-graduação em Educação para a Ciência - FC

Etnomatemática e economia solidária: o caso de um grupo de fabricação de sabão caseiro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A compreensão de matemática em um ambiente online de formação de professores

Pós-graduação em Educação para a Ciência - FC

As contribuições do software Graphmatica na construção do conhecimento matemático de função

Pós-graduação em Educação para a Ciência - FC