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

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

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.

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

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

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

Dificuldades na construção de gráficos de funções

This study describes about graduation s students difficulties of to draw functions graph. Specifically, we intend to observe their abilities evolution, as well as their difficulties during Calculus I subject in engineering course. For that, we show them publications about the elaboration of graphs and its difficulties in obstacle terms and some researches witch contain this subject and that it was done during postgraduate studies in mathematical education. It shows by research methodology aspects related to French didatic s mathematic and some theories of cognitive psychology considering the high value between theoretical-methodological relation that was evidenced in both theoretical conceptions about ways to understand and teach mathematic. This methodology is based on didactic engineering purpose, that consist in preliminaries analysis, conception and didactic sequence analysis prior, trials by application followed analysis up and conclusion. We had also used pedagogicals actions and analysis of results achieved, to classify types of errors made by the 2005 s students during second semester, from conceptions related to the episthemologic and didactics obstacles

O gênero crônica na sala de aula do ensino médio

In this work we present the results of a research that aims to study the chronicle gender produced in a class of native language. The texts were written by students of a high-school class, under the orientation of the teacher who conducted a didactic sequence in order to explore this gender. In our analysis we observed aspect such as the structure of the general structure of the texts, types of speech and linguistic sequences, some mechanisms of textualization and the characteristics of the gender. In order to attain that, we adopted the theoretical presuppositions of Textual Linguistics and of the Socio-discursive Interactionism, grounding the study of texts and gender in Bronckart (2003; 2006) and Koch (2002; 2004). As a background of the Chronicle Gender we used the studies of Coutinho (1987); Moisés (2003); Sá (2005); Bender; Laurito (1993); Melo (1994); Cândido et al. (1992) among others. The corpus, made up of 15 texts, showed that the narrative is the most used linguistic sequence in the producing of the texts, the discursive world prevailing in the narrative and some instances of the world of exposing. As for the gender characteristics, the daily life was used in order to amuse the reader and make him to reflect upon the daily life. Humor, irony, social criticism and colloquial language were also observed in the texts produced by the students. Although some texts presented the characteristics of the gender, explored in the classroom, some were typically school narratives. That make us believe that a work with textual production under the approach of a text gender is viable, but it is not consolidated yet in many schools as the main object of the central teaching of the Portuguese language. This make us defend a better systematization of the teaching contents having as the main point the reading practice and text production in order to contribute for the growing of the students´ discursive potentialities and, therefore, their effective participation in the language social practices

Pedagogia do esporte: livro didático aplicado aos jogos esportivos coletivos

The study deals with the pedagogical possibilities of text books as a resource for Physical Education (PE) classes based on sports, specifically team sports. It started from a bibliographical review on the cited terms and after that we advanced our studies in order to propose a didactic text book on Team Sports for PE classes considering two benchmarks: one technical-tactic and the other social-educational. In order to do so, we used methods from linguistics, and the development of a Didactic Sequence allowed the selection and distribution of the contents to be presented in the book in an orderly and judicious way. The focus in Team Sports is justified by its social-cultural insertion and by the need to transform recent studies into new pedagogical procedures for practicing them. The didactic text book, as well as the adequate preparation of the professionals who will use it, is pointed out as facilitator in the process of teaching, experiencing and learning team sports.

Ensino de biologia e o desenvolvimento de habilidades cognitivas por meio de atividades práticas e contextualizadas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

(Res)significando a Educação Estatística no Ensino Fundamental: análise de uma sequência didática apoiada nas Tecnologias de Informação e Comunicação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relação espaço-plano: uma intervenção pedagógica para o desenvolvimento do pensamento geométrico

Pós-graduação em Educação - FCT

Experimentos mentais no ensino de ciências: implementação de uma sequência didática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Formação continuada de professores: a experiência de uma temática sociocienfítica na perspectiva do Agir Comunicativo

Pós-graduação em Educação para a Ciência - FC

As práticas de ensino-aprendizagem de leitura no ensino fundamental II: do texto ao hipertexto

O presente trabalho versa sobre as práticas de ensino-aprendizagem da leitura em língua materna, tendo o computador como uma das principais ferramentas didáticas. Trata-se de uma pesquisa-ação fundamentada em pressupostos sociointeracionistas de língua, linguagem e leitura. Portanto, faz-se referência à perspectiva dialógica, aos gêneros discursivos - concepções teóricas e como objeto de ensino - à sequência didática, ao blog como suporte virtual e gênero relato de experiência em blog, assim como ao ensino da compreensão escrita em língua materna e ai computador como ferramenta didática. Esse aparato teórico é utilizado para analisar parte de uma sequência didática que priorizou o trabalho com a competência de leitura e escrita (sendo a primeira o foco de nossos estudos) desenvolvida com uma turma do ensino fundamental II do Município de Benevides/PA. E tenta verificar em que medida essas práticas, ao se utilizar da ferramenta didático-tecnológica computador, contribuem para o aprimoramento da compreensão escrita dos aprendentes.