Ensino dos números racionais comparando medidas de unidade

This research aimed to investigate the possibility to develop the process of teaching and learning of the division of rational numbers with guided tasks in interpretation of measure. Adopted as methodology the Didactic Engineering and a didactic sequence in order to develop the work with students of High School. Participated of training sessions twelve students of one state school of Porto Barreiro city - Paran´a. The results of application of the didactic engineering suggest the importance of utilization of guided tasks in interpretation of measure, since strengthened the understanding, on the part of students, the concept of division of fractional rational numbers and contributed for them develop the comprehension of others questions associated to the concept of rational numbers, such as order, equivalence and density.

Controle social e políticas públicas: contribuições para aprimorar o controle social do programa nacional de alimentação escolar

The National School Feeding Programme (PNAE) is a public policy in Brazil for over 60 years and represents one of the most important programs of feeding and nutrition in the world. The role of family farming as a source of employment in rural areas, food provider and for ensuring much of the Brazil’s food security is constantly present at the government's and social movement’s agendas. Law 11.947 of 2009 marked its integration in the food supply for the National School Feeding Programme. Article 14 of aforementioned law highlights that a minimum of 30% (thirty percent) of the funds transferred by the National Development Fund Education (FNDE) to the Programme must be used for the purchase of food directly from family farmers or their organizations. The national school feeding policy under the responsibility of the FNDE and is subjected to agencies of internal control, such as the General Controllership of the Union (CGU), of external control, such as the Audit Courts of the Union and the of the states, and to the social control of the school feeding councils. Those funds are transferred to the implementing agencies, which are the education offices of the states, municipalities and of the Federal District. These entities must annually present their accountings to the School Feeding Councils, which analyze them and then issue a conclusive report to the FNDE, approving with or without reservations, or rejecting them. In this sense, this research aims to propose parameters that should contribute to the improvement of the social control over purchases from family farming for the National School Feeding Programme. The study was conducted by non parametric sampling alongside the managers of the implementing entities, school feeding councils and Family Farming Organizations all across Brazil, from the databases provided by FNDE and by the National Union of Cooperatives of Family Agriculture and Solidarity Economy (Unicafes). The study points out that the legal framework of PNAE seeks to ensure the participation of family farming in the food supply for the Programme, despite allowing the executing agencies to justify the non-compliance of the minimum required in a number of ways. The survey also signalizes that the school feeding councils follow the implementation of the Programme very shyly, and points out that there is room to expand and enhance the participation of these councils and organizations of family farming in the execution of PNAE. Its effectiveness requires a constant and effective process of training of the agents involved in the Programme.

Objetos de ensino, suas potencialidades e dificuldades para aprendizagem de física no ensino médio

Acompanha: Procedimento para o uso do Tracker como objeto de ensino, suas potencialidades e dificuldades para aprendizagem de física no ensino médio

Material paradidático em educação ambiental para o 6º ano do ensino fundamental

Acompanha: Material paradidático em educação ambiental para o 6º ano do ensino fundamental

A educação de jovens e adultos e o ensino de ciências naturais: contribuições da utilização dos conceitos unificadores

Acompanha: A educação de jovens e adultos e o ensino de ciências naturais: contribuições da utilização dos conceitos unificadores

Aplicação da metodologia numérica “fast bounds crack” para uma estimativa eficiente da evolução do tamanho de trinca

A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

Estatística com projetos: uma alternativa de ensino e aprendizagem

This work presents the use of projects as an alternative for teaching statistics, for that it was elaborated a Project that involves the educational socioeconomic reality from the families of the students and built a link between the reality and the scholastic knowledge. This project was applied in Sesi School - Pato Branco between the months of August to September 2014 with 25 students from the 1o and 2o grades from High School. To work the statistics concepts a questionnaire was applied for the parents of the students of the Project´s, they answer it and through these answers the students made frequency tables and graphs, besides measure calculations on measures of central tendency and dispersion measure. All of the construction were realized manually and in the Excel spreadsheet and some of them were chosen to be in this work to with the purpose of showing the hits and the mistakes done. The students worked in groups of 5 students, except in the last class when it was done a test referring to the contents taught in the classroom and a questionnaire for them to evaluate the project´s application. The results show that the teaching of Statistics trough projects motivate the students interest, stimulating the statistical reasoning, in addition made the students know a Math that was different from the one they have already known, with a lot of calculation but with no final objective.

GeoPlexo: um material manipulável para o ensino dos números complexos

This study aims to develop a manipulative material to assist the teaching and learning of Complex Numbers. Primarily, It tries to define the status of the current teaching of Complex Numbers, having as guide the bias of the research produced in dissertations and published on the website of Capes and the Virtual Library of Profmat from 2004 to 2014. It presents historical aspects of the theme, a mathematical foundation and a discussion of the use of manipulative materials as teaching resources for the teaching of mathematics. It introduces the manipulative material called GeoPlexo and a sequence of activities of potentiation and settling of complex numbers, explaining its use. It concludes with the importance of manipulative materials as a teaching resource for the teaching of Complex Numbers, especially regarding the geometric visualization of this mathematical object.

Educação financeira no ensino médio: uma abordagem por meio da análise de produtos financeiros com ênfase em consórcios

This paper presents a differential approach of financial mathematics developed in high school, focusing on financial education. We seek through the insertion of texts, analysis of some financial products and by the interpretation of problems to contribute to the financial training of students. Aiming to make financial mathematics more attractive and accessible to the day-today, there are available for studies some practical tools like the citizen calculator which are available for computers and mobile phones. As well as spreadsheets and software Geogebra, that allow you to compare and analyze the financial costs of consortia, financing and financial applications,in addition to being allied in the preparation and control of personal and family budget. By applying the teaching sequence proposed in a nocturnal class of high school, we realized some difficulties that have limited the financial learning of math concepts.Yet identified progress regarding the financial education of students. These observations were made through qualitative and quantitative analysis from notes in the field diary and also answers given by students in specific form.

Proposta de ensino de geometria euclidiana plana para o sexto ano do ensino fundamental sob a ótica do raciocínio lógico-dedutivo

This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

Construções geométricas como recurso pedagógico no ensino médio

This work aims to provide high school students an development in his mathematical and geometrical knowledge, through the use of Geometric Constructions as a teaching resource in Mathematics classes. First a literature search to understand how it emerged and evolved the field of geometry was carried out and the Geometric Constructions. The ways in which the teaching of geometry happened in our country, also were studied some theories related to learning and in particular the Van Hiele theory which deals with the geometric learning also through the literature search were diagnosed. Two forms of the Geometric Constructions approach are analyzed in class: through the design of hand tools - ruler and compass - and through the computational tool - geometric software - being that we chose to approach using the ruler and compass instruments. It is proposed a workshop with nine Geometric Construction activities which was applied with a group of 3rd year of high school, the Escola de Educac¸ ˜ao B´asica Professor Anacleto Damiani in the city of Abelardo Luz, Santa Catarina. Each workshop activity includes the following topics: Activity Goals, Activity Sheet, Steps of Construction Activity Background and activity of the solution. After application of the workshop, the data were analyzed through content analysis according to three categories: Drawing Instruments, angles and their implications and Parallel and its Implications. Was observed that most of the students managed to achieve the research objectives, and had an development in their mathematical and geometrical knowledge, which can be perceived through the analysis of questionnaires administered to students, audio recordings, observations made during the workshop and especially through the improvement of the students in the development of the proposed activities.

Programa Etnomatemática: ponderações da prática pedagógica

The aim of this present work is investigating the interest and motivation for learning, awakened in pupils when the educator practice is guided by the ethnomathematics perspective. The main question is: Can an ethnomathematic approach awaken enthusiasm in pupils, causing it to become more critic and active in building their knowledge? The methodology that guides the investigation is qualitative, based on technical arising of the ethnographic case study. Theoretical contributions that support the investigation are from the scientific methodology and from ethnomathematics. The research material is composed by: researcher’s field diary, audio recording of participant observation, interviews reports of community residents and students parents, highlighting the material produced by students. This study was developed on an 8º year of high school of rural community. During the work were prioritized the ethnomathematics concepts of the Ethnomathematic Program, which establish a link exchange, where the lecturers inserts themselves on the reality of pupils in a way that promote an appreciation of their identity and a commitment to their learning. The educator investigates and values the ideas of pupils throughout dialogues. There are challenges for the application of education with ethno mathematic perspective, pointed out by authors, listed and supplemented in the research. In this context, it is believed that the socio-cultural knowledge must be respect, and as they are understood their specialties, capabilities and characteristics, this can guide teaching practice, making significant process for pupils, providing appropriation of scientific knowledge. Analysis of research practice indicated that students, research subjects, when they decided contextual issues, with their way of life, felt appreciated. The conclusion is that, with continuous action of contextualized of school mathematics, from the recognition of the environment and of cultural identity, the educator has the opportunity of review their own participant condition, and therefore promote an enthusiasm for learning. Because a motivated pupil becomes active, since that the all project is guided in a significant theme.

Metodologia de ensino do conceito de função exponencial à luz da teoria das situações didáticas

This essay presents a proposal on methodology over the mathematical object Exponential Function which enables the development of interpretative and creative skills with potential meaning to the students starting from a didactic sequence structured on the light of The Theory of Didactic Situations from Guy Brousseau and, from the Records of Semiotic Representation of Duval, providing interactions among the students, the teacher and the environment of cooperative learning where the students feel free to express their own ideas as well as to suggest their own approaches. The methodology presented has been developed according to the students first knowledge, valuing their different ways of registering, which have such an important role during the teaching and learning processes. The proposal has been applied to the students from the first year of high school of Colégio Estadual José de Anchieta Ensino Fundamental e Médio, located in a town called Dois Vizinhos –Paraná. In order to the development of the research the methodological tool Didactic Engineering Artigue which consists in a methodology developed only to the research with didactic situations. The main goal has been reached at first, which was to work on the conceptual part of the Exponential Function, the relation of dependence and its main characteristic so that the variable part is in the exponent. Moreover with no imposition but starting from suitable didactic situations, the students were able to realize that they could solve the problems which involve the exponential function and furthermore create new problems (according to their universe) modeled by this kind of function. Its believed that the methodology based on the theory of didactic situations, analysis of students registers, observation on mistakes and obstacles as well as reflections over the aspects of the didactic contract are of fundamental importance to the teaching practice and determinant during the teaching-learning process.

O processo de implementação da educação do campo nas escolas do Núcleo Regional de Educação de Pato Branco: limites, desafios e possibilidades

This work is part of the Graduate Program in Regional Development of the Federal Technological University of Paraná, Pato Branco campus, the research line Education and Development. The line of research concerns the Regionality and Development. In this study, investigate sought the implementation of the Field Education Curriculum Guidelines in the State of Paraná, whose locus, SEED / PR, the NRE / Pato Branco and Field Schools belonging to the NRE. The theme is to respond to the research problem, to identify the limits and challenges of the implementation process of Rural Education in rural schools in the Regional Center of Pato Branco Education. Exploratory research covers a time frame comprising the years 2002-2014 in order to identify and analyze the documents and perceptions of the subjects that guide the implementation of the field of education in the state of Paraná. The results show that the education field has not yet overcame the challenge of implementing public policies, in particular the field of Education Curriculum Guidelines. In general, the texts point to the concerned school education with the urban environment, in an attempt to solve the problems related to truancy, low school enrollment,flunk, among others. The reality of the field displays more serious such problems, however, is visible the development of proposals in an attempt to achieve definitive solutions to the issues of the field. However, a positive factor is the increase in continuing education courses, some offered by the Department of Education Field Regional Center of Education, others initiatives by the own teacher, which demonstrate the concern in improving their teaching practices, concomitant with need to change the identity of the field school. In this sense, we seek to deepen the discussion in order to demystify the idea that the subject field to be synonymous with poor education, poor quality. Documents such as the Field Operational Guidelines established by the CNE - National Education Council in 2002, the Curriculum Guidelines field developed by SEED - Secretary of State and Education in the State of Paraná in 2004 and established as a public policy in 2010 provide data that allow make a study of public policy and educational field context in order to understand the challenges for the development of an education as culture, ways of life, history, finally, the specificities of the subject field.

Representações sociais sobre educação ambiental e objetivações em práticas pedagógicas no ensino fundamental

This work presents results, reflections, conclusions and considerations about the research entitled "Social representations of environmental education and objectivations in teaching practices in elementary school ". She intended to make known research whose objectives were to know the current environmental education framework (EA) developed by the teachers of the early years of elementary school of that city; identify their social representations about EA and the ways in which these representations are objectified in their teaching practices. Thus, the methodology is characterized by the qualitative approach; whose data collection instruments were the Free Evocation Questionnaire (QEV), the semi-structured interviews and documentary research. The QEV consists of free recall questions and essay questions, whose data is quantitative and qualitative. Data from this instrument were analyzed according to the procedures of the Structural Approach to Theory of Social Representations. In turn, the analysis of data obtained through the interview and reading the documents followed the guidelines of the Content Analysis method. The theoretical and methodological basis of this research was the Theory of Social Representations and critical approach to environmental education. Thus, the results obtained in the investigation allowed us to identify the social representations of EA of participants; confirm that such representations are being targeted in their pedagogical practices that are characterized as conservative. Also confirm that the teaching documents of the surveyed network are in line with the official documents on EA; the AE actions developed in the network are referenced in the teaching documents of the network and in the official documents of EA and the EA practices of survey participants teachers relate directly with their social representations on Environmental Education.