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.

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.

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.

Concepções de interdisciplinaridade: o Programa Ensino Médio Inovador

The Interdisciplinary practice opens in the context of Basic Education guiding new looks in the production of knowledge. It is necessary to reflect the interdisciplinarity as scientific and epistemological stance and its conditions of possibility of expanding the horizon before the theoretical and methodological challenges posed by modernity. Thus, this work aimed to analyze interdisciplinary concepts present in the proposal of the High School Program Innovator. Therefore, the theoretical route initially had the search for understanding of high school in Brazil, interdisciplinarity as the possibility of tensioning the production of scientific knowledge, mainly anchored in the studies of Acácia Kuenzer, Dermeval Saviani, Boaventura de Sousa Santos, Claude Raynaut, Henrique Leff and Edgar Morin. The study was methodological subsidy document research and principles of content analysis. The analysis took place from the seven documents that make up the construction path of High School Program Innovator and a semi-structured interview. So, we sought to understand the concepts of the documents establishing analytical categories from more evoked content. In this process identified three categories with regard to the construction of the Program proposal: pedagogical innovations, curriculum organization and teaching quality and three categories with regard to interdisciplinary concepts present in the program: dialogue between curriculum components, joint knowledge and role of high school students. From the studies it was observed that the program came up with the prospect of directing a new identity for the final stage of basic education, listing Documents Guiding Plans and actions for a new curricular organization of secondary education. It was noted that the Program, though explicit in its guiding documents of the interdisciplinary perspective, in no time he calls himself as interdisciplinary. Interdisciplinary actions should run or from school understanding, as well as the preparation of the Redesign Project Curriculum encompassing dialogue between disciplines. Realized by the analysis of the guiding documents is a back program even for a technical rationality practiced by the particular understanding of the school and the practice being expressed from the same concepts that high school is developed, with each teacher teaching the contents of their disciplines and performing cross designs. Break the existing paradigm is still one of the challenges to the teaching-learning process. Break the existing paradigm is still one of the challenges to the teaching-learning process.

Internacionalização da educação superior: estratégias e ações da Universidade Tecnológica Federal do Paraná

The present dissertation is inserted in the internationalization of the university-level education research field and aimed to analyze the strategies and internationalization actions of the Universidade Tecnológica Federal do Paraná (UTFPR), locus of research. The study sought to establish the current context in which the internationalization is inserted and contextualize the research problematic presenting definitions, concepts, reasons and strategies linked to an international dimension. It also presents a historical context of the internationalization of Brazil and current public policies related to this topic. This research used content analysis to analyze institutional documents (Institutional Development Plans (2004-2017) and Management Reports (2000-2014)); semi-structured interviews (Director of International Relations, Coordinator of programs and actions related to the mobility of students, Head of the Department of Education and Dean of Research and Graduate Studies); information pertaining to the theme from the university’s website and events held in the Campus of the institution. Data were analyzed using the procedures prescribed for this type of analysis with the establishment of three categories: concepts, strategies and actions. Based on the foregoing, in terms of synthesis, could be understood that increasing the participation of UTFPR on the international scene has always been linked to the institution’s policies and goals, yet without an political institutional plan without objectives, strategies and goals established systematically. In the case of the conception of the internationalization of UTFPR it was realized that the theme currently gained more focus and greater coverage in the institution. In this context, Ciência Sem Fronteiras program contributed to, giving greater visibility to UTFPR on the world stage. From then on, specific strategies and actions are being developed in seeking internationalization under institutional perspective, of the servers, the expansion of mobility, and greater visibility of the institution in the international arena, regional integration and promotion of internationalization at the university. Overall, the management of internationalization in the institution does not have a formal project, but has specific strategies and actions seeking their expansion. Thus, the process of internationalization in UTFPR presents itself in an early stage, with strategies and actions seeking to expand the international dimension in the institution who takes singular importance to its expansion and consolidation.

Implementação de programas de educação ambiental nas escolas municipais de Curitiba, Paraná, Brasil

O presente trabalho pretende analisar a implementação dos programas de Educação Ambiental nas escolas de ensino fundamental, da Rede Municipal de Ensino Público, do Município de Curitiba, no estado do Paraná, Brasil. Esta análise tem por objeto de estudo as ações desenvolvidas pelas escolas, no que se refere às condições de saúde e bem-estar, a partir do que estabelecem os Parâmetros Curriculares Nacionais. Buscou-se compreender como os conteúdos definidos por ‘temas transversais' propiciam a constituição de um espaço de transformação em nível municipal. Este trabalho se constrói com base em discussões sobre o conhecimento produzido na área de Educação Ambiental e pelo levantamento de informações por meio de entrevistas e questionários junto aos profissionais ligados aos órgãos municipais responsáveis e às escolas. A análise realizada demonstrou que os projetos implementados vêm surtindo efeito positivo sobre as transformações dos pensamentos relativos às questões ambientais, sofrendo descontinuidades devido às mudanças nas gestões políticas. ABSTRACT; This study aims to analyze the implementation of the Environment Education Programs in the schools of the Municipal Public Education Network, in the City of Curitiba, in the state of Paraná, Brazil. The object study on this analysis is the actions developed by the schools, referring the conditions of health and well-being, from what is established by the National Curricular Parameters. We try to understand how the contents defined for 'transversal subjects' can propitiate the constitution of a space of transformation in municipal level. This work is built on discussion about the knowledge produced in the area of Environment Education besides the survey of informations through interviews and questionnaires with professionals connected to the responsible offices and the schools. This analysis demonstrated that the implemented projects is causing positive effects on the transformations of the relative thoughts to the environment questions, come suffering discontinuities due to the changes in the managements politics. RESUMEN; Este proyecto tiene por objetivo examinar la implementación de los programas de educación ambiental en las escuelas de educación básica de la Red Municipal de Educación Pública, en la ciudad de Curitiba, Paraná, Brasil. El objeto de estudio de la análisis son las medidas adoptadas por las escuelas, con respecto a la salud y el bienestar, de acuerdo con lo establecido por los Parámetros Curriculares Nacionales. Tratamos de comprender como el contenido, tal como se define por "temas transversales" puede ofertar un espacio de transformación en el nivel municipal. Este trabajo se basa en los debates de los conocimientos producidos en el ámbito de la educación ambiental y por las informaciones planteadas a través de entrevistas y cuestionarios con los profesionales de los departamentos responsables y en las escuelas. El análisis mostró que los proyectos ejecutados han tenido efecto positiva en la transformación de ideas sobre cuestiones ambientales, sufriendo discontinuidades debidas a cambios en las gestiones políticas.

Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

Experiência do núcleo de atendimentos a pessoas com necessidades educacionais especiais da Universidade Tecnológica Federal do Paraná Campus Pato Branco

Trabalho publicado também na XIII Jornadas Transandinas de Aprendizagem

Proposta de avaliação de práticas sustentáveis nas operações de serviço em instituições de ensino superior da Rede Federal de Educação Profissional, Científica e Tecnológica

Higher Education Institutions (HEIs) have an extremely important social role, they are responsible for the place where they work and to form citizens who contribute to a fair and cooperative society. Universities can engage with sustainable development in planning, management, education, research, operations, community services, procurement of materials, transportation and infrastructure; this research seeks to analyze the sustainability practices in service operations in the Higher Education Institutions of the Federal Network of Professional, Scientific and Technological Education in Brazil through the development and application of a model called the Sustainability Assessment for Higher Technological Education (SAHTE). To achieve the proposed goal, a systematic survey of the scientific literature on sustainability assessment models in higher education institutions was conducted, making it possible to identify the characteristics and features of existing models. The model was applied through multiple case studies. The proposal compares the sustainability performance of service operations among individual institutions using a common methodology. It presents five areas to be evaluated in the HEI: Governance and Policies, People, Food, Water and Energy, and Waste and Environment, with a total of 134 questions. The need for greater support from the senior management of institutions to formulate and implement policies on sustainable development was identified when the lack of policies on sustainability in service operations was found; initiatives tend to be isolated. The participation of students and teachers in studies on the daily operations of the campus can be expanded and more widespread. The model seeks to evaluate sustainable practices in the service operations of the Brazilian Federal Network of Professional, Scientific and Technological Education; studies related to the evaluation of teaching sustainability are absent and the applicability of the model in private institutions and other countries is needed. The results obtained with the application of the SAHTE model are useful for the preparation and development of policies on sustainable development, especially in the service operations of the surveyed HEI. The results can sensitize staff and students, who can reflect on their roles in the HEI, as well as the community and suppliers.

Mapeamento projetivo, associação de palavras e escala hedônica como instrumentos de avaliação da percepção de produtos de pescado por crianças da rede pública de ensino

Brazil is a country that is characterized by its low consumption of fish. With consumption records of 10.6 kg/ inhabitant/ year, it is lower than the recommended by the UN, that is 12 kg/ inhabitant/ year. The regular consumption of fish provides health gain for people and their introduction into the school feeding is an important strategy for the insertion of this food consumption habits in a population. In this context, the objective of this study was to understand the perception of fish with children from the public school system through the technical Projective Mapping (MP) and Association of Words (AP); and evaluate the acceptability of fish derivative in school meals. In the first instance with the intention to better understand the perception of children from different ages about the fish-based products, Projective Mapping techniques were applied through the use of food figures and word association. A total of 149 children from three public schools from Pato Branco, Paraná State, Brazil, took part in this study. Three groups of children aged 5-6, 7-8 and 9-10 years old were interviewed individually by six monitors experienced in applied sensory methods. Ten figures with healthy foods drawings (sushi, salad, fruit, fish, chicken), and less healthy foods (pizza, pudding, cake, hamburger, fries) were distributed to the children, who were asked to paste the figures in A3 sheet, so that the products they considered similar stayed near each other, and the ones considered very different stayed apart. After this, the children described the images and the image groups (Ultra Flash Profile). The results revealed that the MP technique was easily operated and understood by all the children and the use of images made its implementation easier. The results analysis also revealed different perceptions came from children from different ages and hedonic perceptions regarding the fish-based products had a greater weight in the percentage from older children. AP technique proved to be an important tool to understand the perception of fish by children, and strengthened the results previously obtained by the MP. In a second step it was evaluated the acceptance of fish burger (tilapia) in school meals. For this task, the school cooks were trained to prepare the hamburgers. For the evaluation of acceptance, the hedonic scale was used with 5 facial ratings (1 = disliked very much to 5 = liked a lot). Students from both genders, between 5 to 10 years old (n = 142) proved the burgers at lunchtime, representing the protein portion of the meal. The tilapia derivative products shown to be foods with important nutritional value and low calorie value. For the application of the multinomial logistic regression analysis there was no significant effect from the age and gender variation in the acceptance by children. However, statistical significance was determined in the interaction between these two variables. With 87 % acceptance rate there was potential for consumption of fish burgers in school meals.

TERRITÓRIO E FRONTEIRA: NOVAS PERSPECTIVAS PARA O ENSINO DE GEOGRAFIA POLÍTICA

A articulação entre as disciplinas escolares e as acadêmicas é complexa. A Geografia Escolar exige especial reflexão acerca do método de tratamento dos conteúdos escolares. O objetivo do presente trabalho é discutir métodos de ensino da Geografia e avaliar as reais possibilidades de utilização, enquanto aporte metodológico para fins escolares, da fronteira internacional como instituição territorial. Fundamentando-se nas abordagens sobre território e fronteira a partir da Geografia Política, da Geografia Social e da Geografia Cultural, fez-se o estudo de livro didático analisando-se seus conteúdos a respeito do tema. Como resultado, apresenta-se proposição metodológica de ensino da fronteira considerando-se as escalas geográficas de análise. Esta multiescalaridade pode contemplar, a um só tempo, o exercício do controle arbitrário sobre um território que se inscreve numa jurisdição, a questão da inviolabilidade das fronteiras, bem como as práticas sociais que se desenvolvem de acordo com o grau de abertura da fronteira. Desse modo, o estudo da fronteira serve tanto como referência para a seleção de temas e conteúdos, como possibilita que se evitem as armadilhas decorrentes do uso do método de ensino dos círculos concêntricos.

APLICAÇÃO DIDÁTICA PARA O ENSINO DA GEOGRAFIA ATRAVÉS DA CONSTRUÇÃO E UTILIZAÇÃO DE MAQUETES

Este trabalho visa o ensino da Geografia, que se constitui em uma preocupação recorrente para os professores que buscam contribuir para uma educação de qualidade, comprometida com a formação de novos cidadãos, visto a importância de se estudar a natureza (relevo, solo, vegetação, hidrografia) abordando de forma integrada, a discussão ambiental, atividades produtivas, econômicas e sociais. A busca por práticas inovadoras que permita ao professor, estimular a participação ativa do aluno no processo de aprendizagem e a descoberta do conhecimento dentro das orientações metodológicas de um ensino diferenciado foi o motivo para utilizar maquetes interativas como recurso didático. Assim pretende-se contribuir na compressão e interpretação de conteúdos geográficos auxiliando o aluno no seu desenvolvimento perceptivo, estimulando a capacidade de observar, pensar, interpretar a realidade física e humana da Terra. Elaborou-se também um caderno de apoio explicativo e instruções para a confecção da maquete interativa, servindo de apoio em aulas práticas. O trabalho com maquetes serve como um recurso didático interessante que proporciona ao aluno, dependendo do seu desenvolvimento cognitivo, dominar conceitos espaciais e as representações em diversas escalas. Proporcionando desta forma melhor entendimento dos fenômenos geográficos através do estudo integrado entre as diferentes formas de relevo e a relação com os elementos do sistema ambiental, sua evolução e a transformação da paisagem de forma prática e construtiva.