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 de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

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

Adaptação sociocultural de gestores espanhóis expatriados no Brasil

This study aims at understanding how sociocultural adjustment occurs in the case of managers, and their spouses, expatriated to Brazil by private and public Spanish organizations. To do so, it adopts as main theoretical frame the expatriate adaptation model proponed by Parker & McEvoy (1993), based on Black, Mendenhall & Oddou s model (1991), which establishes three dimensions of adaptation: adjustment to work; adjustment to general environment and adjustment to interaction with host country nationals. This work, of exploratory and descriptive nature, used field research to gather primary data subsequently analyzed with a qualitative approach. Data collection came from individual in-depth interviews with three Spanish managers expatriated in Brazil and two of their spouses. Resulting data were analyzed through one of content analysis procedures, thematic analysis. This research shows that adjustment is obstructed by cultural distance or cultural novelty rather than by work role characteristics, being more successful in expatriates that carry previous solid sociocultural knowledge about host country. It also verifies that the degree of expatriate adjustment is enhanced by the comprehension of cultural differences that originate values and behaviors different from those of the expatriate. It points out that individual factors such as perception and relation skills, flexibility, empathy and self-efficacy are positively linked to the three dimensions of adjustment: work, general adjustment and interaction adjustment. It finds expatriate adjustment to be lowered by spouse unsuccessful adjustment and shows that location in an environment perceived as short in key infrastructures is negatively linked to adjustment in expatriates coming from strongly urban environments. It concludes that expatriate adjustment occurs through progressive understanding of host country environment and through comprehension of the sociocultural context that explains differences between host country behaviors and values and those from the country of origin, a process which is favored by expatriate individual characteristics not directly linked to his/her technical qualification, such as perception and relation skills, flexibility and empathy, together with solid sociocultural knowledge about the host country. This research propones, therefore, that organizations involved in expatriation processes should include in their selection criteria the degree to which candidates possess personal characteristics and sociocultural knowledge that may facilitate adaptation

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

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

Uma abordagem no ensino de frações baseadas em atividades para o 6º ano do ensino fundamantal

The objective of this work if constitutes in creation a proposal for activities, in the discipline of mathematics, for the 6th year of Elementary School, that stimulates the students the develop the learning of the content of fractions, from the awareness of the insufficiency of the natural numbers for solve several problems. Thus, we prepared a set with twelve activities, starting by the comparison between measures, presenting afterward some of the meanings of fractions and ending with the operations between fractions. For so much, use has been made of materials available for use in the classroom, of forma ludic, for resolution of challenges proposed. Through these activities, it becomes possible students to recognize the necessity of using fractions for solve a amount larger of problems

Probabilidade no ensino médio

This thesis aims to show teachers and students in teaching and learning in a study of Probability High School, a subject that sharpens the perception and understanding of the phenomea of the random nature that surrounds us. The same aims do with people who are involved in this process understand basic ideas of probability and, when necessary, apply them in the real world. We seek to draw a matched between intuition and rigor and hope therebyto contribute to the work of the teacher in the classroom and the learning process of students, consolidating, deepening and expaning what they have learned in previous contents

Um estudo dos sistemas de amortizações SAC e francês no ensino médio apoiado na construção de planilhas Eletrônicas

The aim of this work is to provide a text to support interested in the main systems of amortization of the current market: Constant Amortization System (SAC) and French System, also known as Table Price. We will use spreadsheets to facilitate calculations involving handling exponential and decimal. Based on [12], we show that the parcels of the SAC become smaller than the French system after a certain period. Further then that, we did a comparison to show that the total amount paid by SAC is less than the French System

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

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

Pesquisa em Modelagem Matemática no Brasil: a caminho de uma metacompreensão

Este estudo visou analisar as pesquisas em Modelagem Matemática na área da Educação Matemática no Brasil, investigando os trabalhos que adotam esse enfoque, publicados nos anais do 3º. Seminário Internacional de Pesquisa em Educação Matemática, em 2007. A postura assumida é a fenomenológica, e as interpretações são pautadas no movimento hermenêutico, que aponta para uma metacompreensão do tema. Os núcleos de ideias emergem dos invariantes articulados no processo de efetuar convergências, como, por exemplo, a pesquisa que se centra prioritariamente nos modos pelos quais o professor trabalha tópicos de conteúdos matemáticos com o recurso da modelagem. Esse invariante elucidativo pode indicar fragilidades quando os pesquisadores permanecem apenas no como fazer; pode também indicar possibilidades de compreender concepções e sua conversão em práticas desenvolvidas em sala de aula.

Modelagem Matemática e Tecnologias de Informação e Comunicação: a realidade do mundo cibernético como um vetor de virtualização

Neste artigo construímos um entrelaçamento teórico-filosófico que tem como objetivo discutir a relação entre Modelagem Matemática e realidade do mundo cibernético. em particular, essa abrangência da realidade é evidenciada como um possível vetor de virtualização, isto é, como um aspecto que pode influenciar o modo como a problemática que envolve uma determinada situação ou entidade é compreendida. Para tanto, fazemos uma associação entre Modelagem Matemática e as transformações que envolvem os modos de ser denotados por real, possível, atual e virtual, tendo como base ilustrativa as quatro causas aristotélicas. Complementando essa associação, assumimos uma concepção de problema que permite uma consolidação entre as relações estabelecidas e, também, uma concepção de realidade que entende o mundo cibernético como uma de suas dimensões. Por fim, apresentamos um exemplo de Modelagem Matemática ocorrido em sala de aula, que visa caracterizar a realidade do mundo cibernético como um vetor de virtualização.

Aprendizagem de conceitos geométricos pelo futuro professor das séries iniciais do Ensino Fundamental e as novas tecnologias

Com o movimento da Matemática Moderna, a partir de 1950, o ensino da matemática passou a enfatizar o simbolismo e a exigir dos alunos grandes abstrações, distanciando a matemática da vida real. O que se percebe é que o aluno formado por este currículo aprendeu muito pouco de geometria e não consegue perceber a relação deste conteúdo com sua realidade. Por outro lado, o professor que não conhece geometria não consegue perceber a beleza e a importância que a mesma possui para a formação do cidadão. A geometria estimula a criança a observar, perceber semelhanças, diferenças e a identificar regularidades. O objetivo deste trabalho é identificar o nível de conhecimento dos alunos do Centro Específico de Formação e Aperfeiçoamento ao Magistério (CEFAM), futuros professores da 1ª a 4ª séries do Ensino Fundamental do Estado de São Paulo, quanto aos conceitos de ponto, reta, plano, ângulos, polígonos e circunferências e também verificar as contribuições do computador para a construção de conceitos geométricos. Para atingir esses objetivos, foi desenvolvida uma pesquisa com 30 alunos do CEFAM de Presidente Prudente-SP, na qual, com base no diagnóstico das dificuldades de aprendizagem, organizaram e desenvolveram-se os momentos de formação, que utilizaram o computador como ferramenta de aprendizagem e projetos de trabalho tendo como aporte teórico a abordagem construcionista. O futuro professor que não dominar a geometria e não perceber sua relação com a natureza não conseguirá contribuir para o desenvolvimento do pensamento geométrico da criança. Esse pensamento é que permite a criança observar, compreender, descrever e representar, de forma organizada, o mundo em que vive.

Evolução da noção de conservação de quantidade e desempenho em matemática

Foram confrontadas nesta pesquisa a afirmação piagetiana de que o ensino da matemática deve basear-se no desenvolvimento das estruturas mentais da criança e a realidade do ensino dessa matéria na 1.ª série do primeiro grau. Estudou-se a relação existente entre a noção de conservação e o grau de desempenho em matemática. Constituíram a amostra 47 sujeitos da 1.ª série do 1.° grau (17 do sexo masc. e 30 do fem.), nível sócio-econômico médio-inferior para baixo-superior, idade de 6 anos e meio a 11 anos, sem escolarização anterior. A avaliação do desempenho relativo ao domínio da noção de conservação foi feita através do teste de conservação de quantidades descontínuas, e a do desempenho em matemática, através da observação sistemática e de uma prova. O coeficiente de correlação de postos de Good man e Kruskal (1945 e 1963] mostrou relação significante a um nível de 1% para conservação e porcentagem de acertos na prova (g = 0,7) e a um nível de 5% para a conservação e conceitos atribuídos pelo professor (G = 0,44). A análise dos dados categorizados pela técnica de Grizzle, Starmer e Koch (1969) a um nível de 5% indicou apenas efeito do fator sexo sobre a noção de conservação. Os resultados obtidos estão de acordo com a teoria piagetiana que indica ser a noção de conservação uma condição necessária para a aprendizagem da matemática, embora não suficiente.