Construção e aplicação de uma sequência didática para o ensino de trigonometria usando software geogebra

The present study aims to analyze the potentialities and limitations of GeoGebra software on what concerns trigonometry s teaching and learning processes. Taking the present resources of public school from the state of Rio Grande do Norte, the research intends to answer the following question: Could we use the current conditions of public school and the Geogebra software to optimize the trigonometry s learning and teaching processes situation? . To make it a possible to answer the question above, a module of investigative activities was created and applied. The methodological intervention was made among second year High School students from a public school in Natal, RN. The theoretical reference of Mathematics Didactics was taken was a base, adopting the conceptions of Borba and Penteado (2001), Valente (1999) and Zulatto (2002, 2007) about the use of Information Technology (IT) on Mathematics classrooms. In order to create the investigative activities helped us to understand how the students make their constructions and their visual perception through the process of dragging images on the computer screen. Furthermore, the activities done with the GeoGebra software s resources facilitate the resolution of trigonometry situations

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

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

Formação continuada de professores que ensinam matemática: o papel do ábaco na ressignificação da prática pedagógica

The present dissertation performs a study about abacus part on the continuous education of Elementary School s Mathematic teachers on what concerns the basic operations of addition and subtraction with (re)unification by using the manipulative and/or informatical abacus. Therefore, the research intends to answer the following question: How does a teacher reframe the pedagogical practice while teaching the Decimal Numeral System and the conventional operations of addition and subtraction with (re)unification through manipulative and informatical abacus? In order to do so, we rely ourselves on the Guy Brousseau s Theory of Didactic Situations (TDS) from 1996 that affirms the necessity to trace a way in accordance with the teaching situations that lead the student s learning; and on the work of Pierre Lévy (1993), in which the poles of communication oral, written and virtual create three ways of communication through which the learning process happens. The methodology of this paper was based on the Strategic Research-Action of Franco (2005). The didactic sequence was elaborated in accordance with TDS and used the manipulative and informatical abacus as didactic resource. With the application of the didactic sequence, it was verified that the continued formation of Elementary School s teachers concerning the operations of addition and subtraction on the initial years/levels is pertinent once it has been observed some difficulties of the teachers concerning this mathematical subject. Besides, the analysis of the didactic sequence has allowed one to realize that teachers had some difficulties concerning the numeric representation with order zero, the resolution of operations of addition and subtraction using the manipulative and informatical abacus and the realization of (re)unification on the subtraction with meaning. These observations has been discussed with the teachers and, after that, it has been done some didactic-methodological routings of the operations of addition and subtraction with re(unification) that contributes with the teaching and learning process.

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

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

O uso da abordagem CTSA para o ensino de energia tendo o desenvolvimento sustentável como eixo temático

In recent decades, humanity has become increasingly concerned with environmental problems. Proofs of this are increasing initiatives in civil society organizations, private institutions and government actions, either local, state or national actions to promote environmental protection. The goal of this research is to contribute to the formation of citizens more aware of their responsibilities to sustainable development issues, simultaneously to their learning of physics in the secondary school. Thus, we have designed a research project that aims to evaluate the effectiveness of the adoption of the concept of sustainable development as a central theme in physics classes in high school. From this goal, we designed, implemented and evaluate lesson plans that aim not only to construct and apply the concept of energy, but also to understand their transformations and conservation law, as well as their processes of production, distribution and consume in the context of physical laws in which it is involved. Then, it was deliberately provided to students, during classes, to read, interpret and produce texts, by this way being able to think and start to have a critical view of the world around him, as well as absorb the energy concept and understand his occurrence in phenomena of nature and in technologies. The approach used for this was that constraining science, technology, society and environment - STSE. This teaching methodology has been applied in the IFRN Ipanguaçu campus, for students of two classes of first year of high school integrated course in agroecology and in technical computing. The survey results show the effectiveness of both methods with respect to the viewpoints of students in relation to the guidelines of sustainable development and the learning of physics content proposed. It is hoped with this dissertation to contribute to the formation of future men and women as citizens environmentally friendly, but also as a source of inspiration for teachers who wish to foster in its students such a critical position about civic education, from their classes

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Uma sequência didática a partir da temática terremotos com ênfase em CTS

Throughout its history the population of the region of Mato Grande, which includes the city of João Câmara, in Rio Grande do Norte, was subject to earthquakes. These events are caused by a geological fault, known as fault Samambaia. In the 1980s there was an intensification of this phenomenon culminating in an earthquake 5.1 on the Richter scale in the early hours of November 30, 1986, causing researchers from Brazil and other countries to shift to the region to conduct research in Seismology. During this period there was a strong interaction between scientists and local people. With the aim of studying how people experienced that moment that marked the history of the city of João Câmara, from interviews with some individuals who witnessed the incident, is that this research was developed. Taking as a theoretical approach to Science, Technology and Society (STS), aimed to thus carry the theme in a systematic way to the classroom, promoting ways to help teachers with the scientific training and guidance to students in case of occurrence of earthquakes

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

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