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

Atividades experimentais no ensino de biologia em escolas públicas do estado do Rio Grande do Norte, Brasil: caracterização geral e concepção de professores

Recent research has revealed that the majority of Biology teachers believe the practice of experimental activities as a didactical means would be the solution for the improvement of the Biology teaching-learning process. There are, however, studies which signal the lack of efficiency in such practice lessons as far as building scientific knowledge is concerned. It is also said that despite the enthusiasm on the teachers‟ part, such classes are rarely taught in high school. Several studies point pedagogical difficulties as well as nonexistence of a minimal infrastructure needed in laboratories as cause of low frequency in experimental activities. The poor teacher performance in terms of planning and development of classes; the large number of students per class; lack of financial stimulus for teachers are other reasons to be taken into account among others, in which can also be included difficulties of epistemological nature. That means an unfavorable eye of the teacher towards experimental activities. Our study aimed to clarify if such scenario is generalized in high schools throughout the state of Rio Grande do Norte Brazil. During our investigation a sample of twenty teaching institutions were used. They were divided in two groups: in the first group, five IFRN- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte schools. Two of those in Natal, and the other three from the country side. The second group is represented by fifteen state schools belonging to the Natal metropolitan area. The objectives of the research were to label schools concerning laboratory facilities; to identify difficulties pointed by teachers when performing experiment classes, and to become familiar with the conceptions of the teachers in regarding biology experiment classes. To perform such task, a questionnaire was used as instrument of data collecting. It contained multiple choice, essay questions and a semi-structured interview with the assistance of a voice recorder. The data analysis and the in loco observation allowed the conclusion that the federal schools do present better facilities for the practice of experimental activities when compared to state schools. Another aspect pointed is the fact that teachers of federal schools have more time available for planning the experiments; they are also better paid and are given access a career development, which leads to better salaries. All those advantages however, do not show a significantly higher frequency regarding the development of experiments when compared to state school teachers. Both teachers of federal and state schools pointed infra-structure problems such as the availability of reactants, equipments and consumption supplies as main obstacle to the practice of experiments in biology classes. Such fact leads us to conclude that maybe there are other problems not covered by the questionnaire such as poor ability to plan and execute experimental activities. As far as conceptions about experimental activities, it was verified in the majority of the interviewees a inductive-empiric point of view of science possibly inherited during their academic formation and such point of view reflected on the way they plan and execute experiments with students

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

Representações de professores de língua inglesa de Natal-RN: um estudo sistêmico-funcional

Teaching and learning representations have been more and more investigated in the Brazilian applied linguistics field, as it allows the understanding of the teachers representations and how they conceive the learning process. This practice facilitates the planning of actions to improve the educational system. This study aims at identifying, interpreting and discussing some representations related to the identity and professional view of English as a foreign language teachers in different school contexts of Natal-RN. The theoretical and methodological foundation for this research is Halliday s Systemic- Functional Linguistics (1994; HALLIDAY; MATHIESSEN, 2004; EGGINS, 1994, among others). Our goal was to reveal the teachers representations embedded in their language, mainly through the ideational metafunction, as language is the tool we use to express ourselves about the external world (events, qualities, things, etc) and the internal world (thoughts, beliefs, feelings, etc). The research corpus is made of 21 teacher narratives, generated from a questionnaire sent to the teachers, who were divided in two groups: Group 1 (public schools teachers) and Group 2 (private schools and English course teachers). Most of the participants seemed to be satisfied with their professional choice. Many of them see the job as a challenge and an opportunity to transmit knowledge. All of them affirmed that the English teacher is a professional, for different reasons; however, the low professional appreciation was a recurrent aspect among the studied narratives. When asked about where they work, the private school teachers seemed to be more satisfied with the teaching-learning process than the ones from the public schools. We believe that the data analyzed in this study is important to show how some English teachers from Natal-RN see their profession. The results might be used in continuing education courses as food-for-thought in group discussions, as it is extremely important to emphasize and stimulate this practice

Sujeitos e atores sociais nas representações discursivas de docentes da rede estadual de ensino em Sergipe: uma análise crítica em tempos de Ideb

According to the studies in Applied Linguistics, this thesis is based on an interdisciplinary perspective (Critical Discourse Analysis, Sociology towards Social Change, Cultural Studies and Systemic-Functional Linguistics). The overall objective of the research was to analyze the discourses of Elementary School teachers in the state of Sergipe, by means of the discursive representations of the social actors, the processes of subjectivity and their fragmented identities in the context of standardized evaluations before the requirements of globalized pedagogical practices, based on the result-based management. The critical analysis of such discourses was motivated by the rapid pace with which the demands of innovation become part of the classroom, aiming at reaching the target in what concerns the indexes of the rankings which characterize the globalized discourse of the national education management, like Ideb (Basic Education Development Index), which makes teachers change their discourses, become silent or keep resistant. The work was initially endorsed by the theoretical lines of the Critical Discourse Analysis (FAIRCLOUGH, 2001, 2006), and poses a proposal for such purpose: the ASCD Discourse Sociological and Communicative Approach (PEDROSA, 2012, 2013). This is an interpretative-qualitative study of the Critical Discourse Analysis (FAIRCLOUGH, 2001, 2003; RAMALHO ; RESENDE, 2011) and to carry it out, semi-structured interviews were used as instruments of data generation (BAUER; GASKELL, 2011; GILL, 2011). Its corpus is composed of thirteen accounts of teachers from the Elementary school who teach Portuguese and work in the fifteen schools which were chosen to be the universe of the research at the Regional Board of Education (02) in the state of Sergipe. Such narratives are related to their impressions, expectations and actions which favor the management of results to which they have to submit themselves. The analytical overview of sociological and discursive line comes from the pan-semiotic categories (Inclusion and Exclusion) which appear in the theory of Representation of Social Actors (VAN LEEUWEN, 1997, 2008). To present the processes of subjectivity of these teachers, this work is based on the socio-analytical proposal of the classification of the subjects, which stems from the individual s work in the Gestão Relacional de Si , which comes from the Applied Sociology (towards) Social Change (BAJOIT, 2006, 2009). The discursive analyses were guided word for word, in their majority, by having the Systemic Functional Grammar as their theoretical basis, specifically by the processes of the Transitivity System postulated by Halliday, (1985); Halliday and Mathiessen, (2004); Eggins (2004); Cunha and Souza (2011). The work makes the field of Cultural Studies emerge towards the dialogue and the presentation of the fragmented identities of the teachers in the context of late modernity (GIDDENS, 2002; HALL, 2011). The thesis promoted a reflection over the teacher s condition, who is immerse in this context of knowledge construction of the present Brazilian educational system, the standardized evaluations, the indexes of development, the targets and the rankings. The considerations and outcomes of such a research dealt with the teachers emerging social practices and the need of planned initial and continuing teacher education towards the new moment which is foreseeable

Memórias de uma Escola Isolada Rural: estudo de um Livro de Visitas (1928-1948)

Cet article étudie le livre de visites de l'ancienne école mixte de la Fazenda Ponte Alta/Bela Vista, liée au groupe scolaire de la ville de Bariri, dans l'état de São Paulo (SP). À partir des registres de vingt ans d'activités (1928-1948), nous retraçons les exigences des inspecteurs primaires et si ces exigences provenaient (ou non) de professeurs et de la communauté paysanne pour ébaucher un cadre socio-historique de l'enseignement des premières lettres dans la zone rurale de l'intérieur de l'état de São Paulo. Il en résulte que le discours qui défendait l'égalité de chances pour les populations urbaines et rurales négligeait généralement le besoin de promouvoir l'égalité de conditions pour que la communauté rurale puisse profiter des chances qui lui étaient promises.

Contribuições da CADES para a Educação (Matemática) Secundária no Brasil: uma Descrição da Produção Bibliográfica (1953-1971)

The so called Campaign for the Improvement and Diffusion of High School (in Portuguese, CADES) took place between 1953 and 1971, in Brazil. During this period, the Campaign published or helped publish dozens of books, in different teaching areas, and several of them were located by the authors of this article. These books guided high school teachers with respect to curriculum planning, legal aspects and methods of teaching. In this article, we contextualize historically this Campaign and also mention its objectives. We briefly describe some of the books found - especially those related to the teaching of mathematics - in order to open perspectives for future approaches and research that can be done based on this written material. Our main aim is to discuss its orientations and to provide ingredients that enable the construction of considerations related to this perspective of training mathematics teachers during a period when there were few colleges and universities to prepare teachers in Brazil.

Estresse entre professoras do ensino fundamental de escolas públicas estaduais

O artigo relata pesquisa que visou, entre outros objetivos, identificar a presença do estresse, a sintomatologia e as fases apresentadas pelos professores de 1ª a 4ª série do Ensino Fundamental atuantes em escolas públicas estaduais de uma cidade do Interior de São Paulo. Participaram do estudo 175 professores, perfazendo, aproximadamente, 70% dos profissionais de Ensino Básico I (PEB-I) em atuação no município. Para obtenção dos objetivos foram utilizados dois instrumentos de coleta de dados: o ISSL (Inventário de Sintomas de Estresse) e um questionário para caracterizar a população pesquisada. A pesquisa revelou que 56,6% dos professores estão experimentando estresse, cujos principais sintomas presentes são: sensação de desgaste físico constante, cansaço constante, tensão muscular, problemas com a memória, irritabilidade excessiva, cansaço excessivo, angústia/ansiedade diária, pensar constantemente em um só assunto e irritabilidade sem causa aparente.

Caracterização do ciclo sono/vigília de professores do ensino médio em natal/rn

In the school environment is fundamental the knowledge about the sleep-wake cycle (SWC), because we find children and adolescents with excessive sleepiness and learning difficulties. Furthermore, teachers with high demand and with different work schedule, which may contribute to changes in SWC. The aim of this study was to describe the SWC of high school teachers in Natal/RN. Habits and knowledge about sleep, chronotype, SWC, daytime sleepiness, sleep quality and job satisfaction were described in 98 high school teachers from public and private school. These parameters were compared according to the characteristics of work, family structure and gender. Data collection was performed with the use of questionnaires in two stages: 1) "health and sleep" (general characterization of sleep habits), Horne & Ostberg questionnaire (characterization of chronotype), Epworth Sleepiness Scale and the Index of Pittsburg Sleep Quality, 2) The sleep diary for 14 days. From the results, we observe that the teachers woke up and went to bed earlier in the week and showed a reduction of time in bed around 42min comparing to weekend. This reduction in time in bed during the week was accompanied by an increase in nap duration on weekend. In addition the teachers woke up earlier on Saturdays than on Sundays, probably due to housework and leisure. The teachers' knowledge about sleep was low in relation to individual differences and effect of alcoholic beverages on sleep, and high in the consequences of sleep deprivation. The differences found in comparisons on the characteristics of work, family structure and gender were punctual, except concerning the work schedule. The teacher who started work in the morning and finished in the night, woke up earlier, went to bed later and had less time in bed, when compared to teachers who work only in two shifts. In addition, teachers with late chronotypes who begin the work in the morning had a greater irregularity in the wake up time compared to teachers with earlier and intermediate chronotypes. Half of teachers have excessive sleepiness, which was positive correlated with work dissatisfaction. In general, teachers showed IPSQ averages equivalent to poor sleep quality and the women showed worst averages. From the results, it is suggested that the SWC of teachers varies according to work schedule, leading to irregularity and partial sleep deprivation in the week, although these responses vary according to chronotype. These changes are accompanied by excessive daytime sleepiness and poor sleep quality. However, it is necessary to expand the sample to clarify the influence of variables related to work, family structure and gender together

Inserção de alunos com deficiência no ensino regular: perfil da cidade de Marília

Objetivou-se com esse estudo identificar o perfil de professores de ensino regular da cidade de Marília que tinham alunos com deficiências matriculados em suas salas de aula, bem como o perfil da clientela atendida por estes professores. Participaram do estudo 68 professores da cidade de Marília - SP que tinham alunos com deficiência matriculados em suas salas. O instrumento de coleta de dados utilizado foi um questionário contendo 13 questões divididas em 2 partes: 1) identificação dos participantes e 2) identificação dos alunos com deficiência. Os dados colhidos nos questionários foram submetidos à análise da freqüência absoluta e relativa. Foram identificadas 10 categorias. de acordo com os resultados dessa pesquisa, concluiu-se que a inserção do aluno com deficiência no ensino regular ocorre com a modificação da formação que favorece ao profissional o conhecimento e a compreensão das distintas formas de aprendizagem do seu alunado, a fim de estruturar sua própria prática pedagógica para atender, com qualidade, a diversidade.

Projeto criança saudável, educação dez: resultados com e sem intervenção do nutricionista

OBJETIVO: Planejar e aplicar um programa de orientação em nutrição, realizado por nutricionista e destinado a professores de 1ª a 4ª série do ensino fundamental, visando analisar a contribuição desse profissional no resultado do projeto Criança Saudável, Educação Dez quanto ao conhecimento dos escolares. MÉTODOS: O trabalho foi realizado em duas escolas públicas, A e B, nas quais foi desenvolvido o projeto educativo, sendo que na primeira os professores foram apoiados por um programa de orientação realizado por profissional nutricionista. Antes e depois do desenvolvimento do projeto educativo foi aplicado um instrumento para avaliar o conhecimento dos escolares sobre alimentação e nutrição. RESULTADOS: Os escolares da Escola A apresentaram mudança significante (p<0,01) no conhecimento de alimentação e nutrição após o desenvolvimento do projeto educativo, o que não ocorreu entre os estudantes da Escola B (p>0,05). CONCLUSÃO: Os resultados obtidos sugerem que a realização de programa de orientação, prestada por nutricionistas aos professores para desenvolverem o projeto educativo, maximizou os resultados, gerando mudança significante no conhecimento dos escolares sobre alimentação e nutrição. Tais resultados apontam a importância da capacitação do nutricionista para atuar em educação nutricional, indicando que o campo pedagógico merece aprofundamento nos cursos de graduação, de modo a permitir ao aluno e futuro profissional uma compreensão alicerçada e sólida do processo educativo.

Construir com os professores do 2º ciclo práticas letivas inovadoras: um projeto de pesquisa sobre o ensino do tema curricular 'alimentação humana'

O propósito neste texto é divulgar um projeto de investigação que foi desenvolvido com professores do 2º ciclo, no qual se utilizou uma metodologia do tipo investigação-ação. Por intermédio deste projeto foi possível avaliar o impacto do uso de estratégias do Ensino por Pesquisa (EPP), com vista ao desenvolvimento de novas competências científico-didáticas (atitudes e saberes). Tais estratégias foram desenvolvidas com base em preceitos da Nova Didática e no âmbito de um programa de formação. Os dados levantados e analisados mostraram que esse tipo de metodologia contribui para a superação de dificuldades de aprendizagem inerentes a processos de formação profissional (inicial e continuada), como a de aprender por meio do trabalho cooperativo na Escola.

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Educação ambiental em praça pública: relato de experiência com oficinas pedagógicas

Oficinas para professores do ensino fundamental foram organizadas com a finalidade de elaborar uma Proposta de Educação Ambiental em uma praça pública no centro histórico da cidade de Botucatu, no estado de São Paulo. Tais oficinas basearam-se em informações sobre o município e informações botânicas da Praça Rubião Júnior, em Botucatu, no âmbito da Educação Ambiental. O resultado foi uma proposta de Educação Ambiental para a praça com a participação efetiva dos professores, em que foi possível resgatar a história da cidade e seus aspectos sócio-econômicos. Foi também demarcada uma trilha ecológica nessa praça utilizando-se as plantas presentes no local, as quais foram previamente identificadas. O trabalho com os professores durante a oficina mostrou-se de fundamental importância para a formação desses profissionais e também estimulou seu interesse a respeito da história local. Essa abordagem, articulada com a diversidade cultural local, enriqueceu a proposta de E. A. e trouxe benefícios para a prática educativa.

Reações ácido-base: conceito, representação e generalização a partir das energias envolvidas nas transformações

Undergraduate students on the first year of Chemistry Courses are unfamiliar with the representation of acid-base reactions using the ionic equation H+ + OH- → H2O. A chemistry class was proposed about acid-base reactions using theory and experimental evaluation of neutralization heat to discuss the energy involved when water is formed from H+ and OH- ions. The experiment is suggested using different strong acids and strong base pairs. The presentation of the theme within a chemistry class for high school teachers increased the number of individuals that saw the acid-base reaction from this perspective.