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

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

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

Conjuntos numéricos

In this work, we present a text on the Sets Numerical using the human social needs as a tool for construction new numbers. This material is intended to present a text that reconciles the correct teaching of mathmatics and clarity needed for a good learning

Função quadrática

In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Uma ferramenta didática para ajudar na fixação dos conceitos introdutórios de análise combinatória

Humans, as well as some animals are born gifted with the ability to perceive quantities. The needs that came from the evolution of societies and technological resources make the the optimization of such counting methods necessary. Although necessary and useful, there are a lot of diculties in the teaching of such methods.In order to broaden the range of available tools to teach Combinatorial Analysis, a owchart is presented in this work with the goal of helping the students to x the initial concepts of such subject via pratical exercises

Calculando distância em geometria espacial usando material manipulável como recurso didático

This work presents a proposal for introducing the teaching of Geometry Space study attempts to demonstrate that the use of manipulatives as a teaching resource can be an alternative learning facilitator for fixing the primitive concepts of geometry, the postulates and theorems, position relationships between points, lines and planes and calculating distances. The development makes use of a sequence of activities aimed at ensuring that students can build a more systematic learning and these are divided into four steps

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Função Afifim: Teoria e aplicações

In this work we present a proposal to contribute to the teaching and learning of affine function in the first year of high school having as prerequisite mathematical knowledge of basic education. The proposal focuses on some properties, special cases and applications of affine functions in order to show the importance of the demonstrations while awaken student interest by showing how this function is important to solve everyday problems

Área e volume da esfera

In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

O erro produzido pelo aluno no contexto pedagógico: uma luz ou uma pedra no meio do caminho?

Student’s mistakes as viewed in a didactic and pedagogical perspective are a phenomenon inevitably observed in any context in which formal teaching-andlearning processes are taking place. Researchers have shown that such mistakes are viewed most of the times as undesirable and often as a consequence of lack of attention or poor commitment on the part of the student and rarely considered didactically useful. The object of our reflections in this work is exactly those mistakes, which are born in the entrails of the teaching-and-learning processes. It is our understanding that a mistake constitutes a tool which mediates knowledge and may therefore become a strong ally of the instructor’s actions in her/his teaching tasks and thus should be taken into the teacher’s best consideration. Understanding a mistake as so, we postulate that the teacher must face it as a possibility to be exploited rather than as a negative occurrence. Such an attitude on the part of the teacher would undoubtedly render profitable didactic situations. To deepen the understanding of our aim, we took a case study on the perception of senior college students in the program of Mathematics at UFRN in the year 2009, 2nd term. The reason of this choice is the fact that Mathematics is the field presenting traditionally the poorest records in terms of school grades. In this work we put forth data associated to ENEM1 , to the UFRN Vestibular2 and the undergraduate courses on Mathematics. The theoretical matrixes supporting our reflections in this thesis follow the ideas proposed by Castorina (1988); Davis e Espósito (1990); Aquino (1997); Luckesi (2006); Cury (1994; 2008); Pinto (2000); Torre (2007). To carry out the study, we applied a semi-structured questionnaire containing 14 questions, out of which 10 were open questions. The questions were methodologically based on the Thematic Analysis – One of the techniques for Content Analysis schemed by Bardin (1977) – and it was also used the computer program Modalisa 6.0 (A software designed by faculties the University of Paris VIII). The results indicate that most of the teachers training instructors in their pedagogical practice view the mistakes made by their students only as a guide for grading and, in this procedure, the student is frequently labeled as guilty. Conclusive analyses, therefore, signal to the necessity of orienting the teachers training instructors in the sense of building a new theoretical contemplation of the students’ mistakes and their pedagogical potentialities and so making those professionals perceive the importance of such mistakes, since they reveal gaps in the process of learning and provide valuable avenues for the teaching procedures.