Conteúdos de matemática do ensino médio com abordagem de raciocínio recursivo e questões do ENEM e OBMEP

In this work, we have the purpose of reminding the math teacher of High School the recursive process so that he/she can use this tool to introduce contents, using recursion as an alternative to the teaching of mathematics. For this, we used questions taken from the Exame Nacional do Ensino M´edio (ENEM) [National Examination of High School] and from the Olimp´ıada Brasileira de Matem´atica das Escolas P´ublicas (OBMEP) [Brazilian Mathematics Olympiad of Public Schools], in addition to present some contents of mathematics that are defined by recursion. In this dissertation, we also showed some activities that involved the recursive reasoning and were applied in a 3rd grade class of high school in a public school in Natal / RN.

Escolarização de surdos no ensino médio em Natal/RN: vendo e ouvindo vozes

La Escuela Secundaria es la etapa final de la Educación Básica y su objetivo es profundizar los conocimientos adquiridos anteriormente, con vistas tanto a la continuidad de los estudios por parte de los alumnos como también a su formación profesional. Considerando el carácter excluyente y elitista de la Escuela Secundaria brasileña, solo recientemente las matrículas de los estudiantes sordos comienzan a ampliarse, y los profesores se deparan con el desafío de lidiar con ese tipo de discente en aulas regulares. Tanto la política de educación especial, desde una perspectiva inclusiva, como la Ley nº 10.436/2002 – reglamentada por el Decreto nº 5.626/2005 – posibilitaron un gran salto para la educación de los sordos en el país. La primera, por la defensa de una escuela atenta a las peculiaridades y demandas de sus discentes; la segunda, por reconocer la Lengua de Señas Brasileña como medio de comunicación y expresión legítimo de la comunidad de sordos y por indicar medidas que garanticen el derecho al acceso y al éxito escolar de la población sorda dentro de la escuela. Amparado en esas discusiones, este estudio tuvo como objetivo analizar el proceso de escolaridad de alumnos sordos de una Escuela Secundaria pública y estatal del municipio de Natal, Rio Grande do Norte. Se realizó un estudio de caso de tipo cualitativo. Los sujetos fueron tres discentes sordos que estaban terminando la Escuela Secundaria, una profesora de Portugués y dos intérpretes de Lengua de Señas Brasileña. Como procedimiento de investigación, se utilizaron entrevistas (grabadas en audio y video), observaciones y análisis de documentos. La participación de los sujetos sordos demandó cuidados éticos adicionales, tales como la traducción del Término de Consentimiento Libre y Aclarado y del guion de la entrevista a la Lengua de Señas Brasileña. Los resultados apuntan que el acceso y la permanencia en la escuela secundaria fueron garantizados, no obstante había poca participación en las clases y el aprendizaje de los contenidos escolares estaba comprometido. Había traductores/intérpretes de Lengua de Señas Brasileña, los cuales, sin embargo, solo iniciaron sus actividades tres meses después del comienzo del periodo lectivo. La profesora y los intérpretes no mantuvieron interacciones que facilitasen el aprendizaje o la participación de los estudiantes, quienes se encontraban siempre juntos y en un lugar determinado del aula, sin mayores interacciones con sus pares normo-oyentes. Los discentes sordos estaban terminando la Escuela Secundaria con edades superiores a 17-18 años, los cuales revelaron no tener perspectivas de continuidad en sus estudios o de inserción en el mercado laboral. Se concluye que la escolaridad de los alumnos sordos en la escuela investigada apunta a la necesidad de una reorganización curricular que atienda a las especificidades lingüísticas y sociales de esos estudiantes.

Aprendizagem significativa: uma proposta de ensino e aprendizagem da geometria euclidiana espacial no ensino médio

This dissertation is a research based on the Meaningful Learning Theory, with students from the second year of High School, in the city named Capinzal do Norte, state of Maranhão. The pedagogic approach of this research focuses on what to do and how to do so students can better grasp knowledge inherent to the Euclidean Special Geometry in a more meaningful and changing way, also that information may be kept longer in their brain, so it can last longer in the present and future. The methodological strategy adopted was the research-action, followed by the constant observance of a researcher on the matter with the purpose to ensure consistent results, which come from the use of a variety of data collector instruments, such as: Concept Maps, manipulatives, educational softwares and application of evaluative tests, besides the observations made throughout the process of investigation and the diagnosis itself. It is all due to the fact that we rely on the premise that knowledge is assimilated in particular and idiosyncratic ways, which means each and every student learns in different ways and in different periods of time. That is why it is so important to develop diversified methodologies to the same subject. This research adds to the other ones related to the theoretical frameworks of the Meaningful Learning Theory, of Concept Maps, of the use of technology on the educational process and of manipulatives, which purpose is to connect their common dots. This pedagogical intervention also focuses on the construction of the educational orientations with applicability directly on class, directed specially by the Mathematics teacher of the basic education, who might use them during your teaching practice. Such guidelines established here as an educational product aim to follow the Theory's assumptions that serves as basis to this research, thus becoming an educational element with a relevant significance. The results, with which we are faced, proved overwhelming to the proposed objectives in terms of learning, which were evident in the construction of Conceptual Maps, as well as in the use of Concrete Materials, in addition to serving as a motivational element to participating students of research. The results obtained are indeed reliable in terms of learning, considered the expected goals, and made us certain that the way we have approached the subject is consistent with a holistic education and that at the same time values the tiniest details, which are fundamental to all the learning-teaching process.

A compreensão de reação química como um sistema complexo a partir da discussão dos erros e dificuldades de aprendizagem de estudantes do ensino médio

The study of chemical reactions is among the most important contents to the understanding of Chemistry discipline in basic education. However, there are still few studies about chemical reactions as a complex system because, generally, this content is presented in textbooks, taught and even researched in a fragmented form. The thesis here presented aims to investigate, identify and characterize the mistakes and learning difficulties of the students about chemical reactions as a complex system, using for that purpose the analysis of the answers of 126 exams of candidates for the bachelor’s degree in Chemistry Teaching on the entrance exam for the Federal University of Rio Grande do Norte (UFRN). The mistakes and learning difficulties about the parameters ΔG°, Kp, Ea and of the calculation of the amount of substance in a chemical reaction have been identified, as well as the levels of development of the ability to interpret the chemical reaction as a system. The main theoretical source of this study is structured based on the mistakes and learning difficulties (NÚÑEZ, RAMALHO, 2012), of the chemical reactions as complex systems (NÚÑEZ, 1994; RESHETOVA, 1988; SANDERSON, 1968). As methodology, it was prioritized the analysis of the answers to the exams and the interview with the teachers. The results showed typical mistakes in the study of this subject, especially low levels and skill development. No student was able to integrate the different aspects in the systemic understanding of the chemical reaction. From the interviews with Chemistry teachers from High School, it was determined the reasons the teachers assign to those mistakes and learning difficulties. The interviews revealed that the teachers do not work in the perspective of integration of the contents which leads the students to present difficulties and make mistakes related to the content previously mentioned. The study presents a proposal for the organization of the contents of Chemistry discipline for High School as a possibility of a dialectic systemic integration of contents, understanding that this systematic vision, leads to important contributions to the development of the theoretical thinking of the students. We can mention as one of the conclusions of this study, the fact that the non-systemic organization of contents do not favor this kind of thinking in students.

Da arenga ao debate: o aprimoramento da competência argumentativa por estudantes do ensino médio

In order to understand the factors involved in the improvement process of argumentative competence by students of 2nd year of high school, we undertook a qualitative approach research and interventional nature, during which we adopted the conduct of participant observation in a school belonging to the state schools of Rio Grande do Norte, located on the outskirts of the city of Natal. The analyzed corpus consisted in the interim intervention and entails the answers to a semi-structured questionnaire, fourteen opinion articles and three regrados debates, produced by the students, in addition to video recordings of ten sessions and personal notes pertaining to another six, totaling sixteen sessions observed during the school year 2014. As the most important bibliographical references we study skills and reasoning from the perspective of discursive social interactionism. Analyzing the data we loan the principle of categorization, opting for critical-descriptive presentation and were revealed to us, via the classified evidences, that among the factors involved in the study process, it appears with more relevance to set up an effective intellectual community, which meets in constant interaction subjects, which alternate assuming the conditions of speakers and audience. The constitution of this community depends largely on the teaching mediation and is indispensable to the (re)design of the studied competence, in interactions with her the subjects afforded learn and develop their competence, reshaping the limits of their zone of proximal development.

Da arenga ao debate: o aprimoramento da competência argumentativa por estudantes do ensino médio

In order to understand the factors involved in the improvement process of argumentative competence by students of 2nd year of high school, we undertook a qualitative approach research and interventional nature, during which we adopted the conduct of participant observation in a school belonging to the state schools of Rio Grande do Norte, located on the outskirts of the city of Natal. The analyzed corpus consisted in the interim intervention and entails the answers to a semi-structured questionnaire, fourteen opinion articles and three regrados debates, produced by the students, in addition to video recordings of ten sessions and personal notes pertaining to another six, totaling sixteen sessions observed during the school year 2014. As the most important bibliographical references we study skills and reasoning from the perspective of discursive social interactionism. Analyzing the data we loan the principle of categorization, opting for critical-descriptive presentation and were revealed to us, via the classified evidences, that among the factors involved in the study process, it appears with more relevance to set up an effective intellectual community, which meets in constant interaction subjects, which alternate assuming the conditions of speakers and audience. The constitution of this community depends largely on the teaching mediation and is indispensable to the (re)design of the studied competence, in interactions with her the subjects afforded learn and develop their competence, reshaping the limits of their zone of proximal development.

Transição demográfica e a questão educacional: uma abordagem para o ensino médio do Rio Grande do Norte

Due to demographic transition process, the educational public sector politics formers encounter a highly specific demographic situation because, nowadays, despite the demographic transition, population is still growing because of the demographic inertia; however, due to steady decline in fertility, young population tends to decrease in next years. In this way, aiming to make high school widely accessible in the country, the issue of education quality is highlighted as well the importance of the physical structure of schools and their teaching equipments to confirm a favorable or not environment for developing educational processes. In this way, this work aims to relate the enrollment of students as school types with the demand of young people who will be able to attend high school on the Rio Grande do Norte state by the year of 2020, emphasizing teaching unities structural aspects, from a school profiling to the design of three prospective alternatives. So, from INEP's Scholar Census data and IBGE population's projections, this work is composed by four stages: i) literature review about research related subjects; ii) database design and build; iii) school profiling; and, iv) prospective alternatives creation. As results, three alternatives relate potential demand and enrollment using the built profiles and they are: i) “Alternative A” attends PEE's requirements related to demands but do not provide improvements in the school structural aspects; ii) “Alternative B” points into an increase of enrollment offering to the detriment of school's structural conditions which are offered to these students; iii) “Alternative C” propitiates a quantitative enrollment increasing combined with improvements on school's physical structure. These alternatives help to support decision making related to goals and realization of universal access with physical conditions which are necessary to a favorable environment to educational activity development.

O Ensino de ligações químicas por meio do conceito de energia: uma proposta didática para o ensino médio

This work presents discussions on the teaching of Chemical Bonds in high school and some implications of this approach in learning chemistry by students. In general, understanding how the chemicals combine to form substances and compounds, it is a key point for understanding the properties of substances and their structure. In this sense, the chemical bonds represent an extremely important issue, and their knowledge is essential for a better understanding of the changes occurring in our world. Despite these findings, it is observed that the way in which this concept is discussed in chemistry class has contributed, paradoxically, to the emergence of several alternative designs, making the understanding of the subject by students. It is believed that one of the explanations for these observations is the exclusive use of the "octet rule" as an explanatory model for the Chemical Bonds. The use of such a model over time eventually replace chemical principles that gave rise to it, transforming knowledge into a series of uninteresting rituals and even confusing for students. Based on these findings, it is deemed necessary a reformulation in the way to approach this content in the classroom, taking into account especially the fact that the explanations of the formation of substances should be based on the energy concept, which is fundamental to understanding how atoms combine. Thus, the main question of the survey and described here of the following question: Can the development of an explanatory model for the Chemical Bonds in high school based on the concept of energy and without the need to use the "octet rule"? Based on the concepts and methodologies of modeling activity, we sought the development of a teaching model was made through Teaching Units designed to give subsidies to high school teachers to address the chemical bonds through the concept of energy. Through this work it is intended to make the process of teaching and learning of Chemical Bonds content becomes more meaningful to students, developing models that contribute to the learning of this and hence other basic fundamentals of chemistry.

Contradições como força de mudança: o processo de formação continuada de professores do ensino médio enquanto potencializador da práxis transformadora à luz da teoria histórico-cultural

The intervention research proposed was based on the Cultural-Historical Theory based on the laws and logic of materialism historical-dialectical. Therefore, we tried to design a research process that involved all as responsible for the process. In the field of continuous teacher's training usually has been found dualistic relationship / paradoxical processes as a result of the adopted training models which are characterized by individualist human processes. The teacher training work sought to overcome this dualism, to promote the unveiling of the contradictions with regard to teaching models. As a hypothesis, we imagined that immersed in this process, teachers recognize such contradictions, and this recognition would make the contradictions become the driving force of change in teaching practice, realizing the teaching-learning-development triad as the basis of praxis. Aiming to develop a process of continuing education to bring results to the professional teachers development looking for answer the following research question: How and what the changes of teachers who participated in the Didactic-Formative Intervention process raised the quality of their teaching practices? In this context, the objective of the research was to develop a process of Didactic-Formative Intervention from the perspective of Cultural-Historical Theory with high school teachers in order to theorize about the changes in pedagogical practices of teachers and learn aspects that transform the essence teaching practice. The research involved two high school teachers of a public school in Uberlândia-MG. The training meetings took place at the school through a collective study group between the years 2013 and 2015. As procedures were used two interconnected aspects: classes observations, and a theoretical and methodological training, both for diagnosis and for the process evaluation, the second aspect has a formative dimension, and a didactic dimension (double meaning) to form didactically the teacher and to elaborate didactic procedures. The collected data were analyzed by observing the assumptions of the method, analysis by units and the processuality. As results teachers showed changes in their teaching practices regarding the organization of the pedagogical work and also centered their design educational actions based on learning and development of the students. The presence of continuous diagnosis during the classes, work with a systems of concepts and their conceptual links, problematization as a teaching method can be pointed as meaningful changes in their praxis. Regarding the training activities that emerged from the analysis of the compiled materials and analyzed throughout the process can be emphasized: forming a collective group of school teachers continuous training, diagnostics, development of practical activities, increase relationships among participants, the choice of scientific material used should have direct relation to the needs of the participants, promoting conditions that enable the emergence of contradictions between the pedagogical practice of teachers and teaching based on the perspective of the Cultural-Historical Theory. This research craved to develop and design a teachers' training processes that increase the quality of teachers life and ways of teaching in the Brazilian public school.

O Ensino de ligações químicas por meio do conceito de energia: uma proposta didática para o ensino médio

This work presents discussions on the teaching of Chemical Bonds in high school and some implications of this approach in learning chemistry by students. In general, understanding how the chemicals combine to form substances and compounds, it is a key point for understanding the properties of substances and their structure. In this sense, the chemical bonds represent an extremely important issue, and their knowledge is essential for a better understanding of the changes occurring in our world. Despite these findings, it is observed that the way in which this concept is discussed in chemistry class has contributed, paradoxically, to the emergence of several alternative designs, making the understanding of the subject by students. It is believed that one of the explanations for these observations is the exclusive use of the "octet rule" as an explanatory model for the Chemical Bonds. The use of such a model over time eventually replace chemical principles that gave rise to it, transforming knowledge into a series of uninteresting rituals and even confusing for students. Based on these findings, it is deemed necessary a reformulation in the way to approach this content in the classroom, taking into account especially the fact that the explanations of the formation of substances should be based on the energy concept, which is fundamental to understanding how atoms combine. Thus, the main question of the survey and described here of the following question: Can the development of an explanatory model for the Chemical Bonds in high school based on the concept of energy and without the need to use the "octet rule"? Based on the concepts and methodologies of modeling activity, we sought the development of a teaching model was made through Teaching Units designed to give subsidies to high school teachers to address the chemical bonds through the concept of energy. Through this work it is intended to make the process of teaching and learning of Chemical Bonds content becomes more meaningful to students, developing models that contribute to the learning of this and hence other basic fundamentals of chemistry.

O ensino de química na educação de jovens e adultos do ensino médio no município de Itumbiara-GO

For this study, a research was conducted in order to answer the question "What chemistry teaching has been developed in the Youth and Adult Education (EJA) ?". The research provides an overview of the object to the proposed changes, leading students to live with different realities and investigating the issue of contextualization based on the daily lives of these students related to the subject of chemistry. The methodology focuses ethnographic research of the case study, in which a case is studied in depth using the participant observation. In the survey data a mixed qualitative and quantitative approach was used. The work involved 6 schools that offer adult education high school; 6 directors of these schools; 6 coordinators who work in adult education; 6 Chemistry teachers and 123 students of the EJA, level high school, enrolled in the 1st, 2nd, 3rd and 4th periods. The first stage of the research consisted of questionnaires in schools where everyone involved responded closed and open questions applied to each specific group. In the second stage two schools were selected in order to conduct a deeper knowledge of adult education through practical activities of Chemistry and subsequent interview conducted in groups with students. Three teachers were also interviewed to enable a deepening of issues relating to EJA and Chemistry Teaching. The interviews were analyzed by the technique of Discursive Textual Analysis (ATD). The main issues addressed in the questionnaires and interviews were on the school structure, reasons that lead students to drop out or remained in adult education and those who make the stay, the view of those involved of the importance of chemistry discipline for students of EJA and how this should be offered. It is necessary that we need to promote changes in the chemistry class and its activities, respecting the experiences and experience already gained by the student during his life story. Another factor to be highlighted is the need for ongoing training of teachers working in adult education. Note that your continued education is given more by the experience and the ways in which they try to overcome adverse situations. The Chemistry subject taught is not agree with the principles of EJA and practiced curriculum is just an adaptation or content reduction from the regular curriculum. The improvement in chemistry teaching of EJA will take place through a dialogue between those involved in the process, clearer educational policies and willingness to implement change. Thus the teaching of chemistry contribute to the students of the EJA are actually scientifically literate and integrated into society.

Transposição didática da interação do laser com sistmas biológicos no ensino médio: uma proposta de guia didático para professores

In this dissertation was elaborated an interdisciplinary didactic sequence for the development of Physical concepts involved in the interaction of laser radiation with biological matter in order to make a relation between Physics and other fields of knowledge aiming to enlarge the contextualization of scientific knowledge. The objective was to develop an educational product which theme is “Laser’s Interaction with Biological Tissues”. In this work, basic physical concepts related to laser radiation were presented, its interaction with matter and applicability in the student's daily life, with emphasis on Public Health. The inclusion of the subject in schools was effected through didactic transposition as theoretical foundation and the three pedagogical moments as teaching support. The development of the project involved discussions of scientific knowledge applied in society’s daily life. In the product's design the didactic sequence was projected and the use of varied teaching resources has been proposed, such as videos, texts, experiments, simulators and de Software “Tracker”. The construction of paradidactic material was performed considering different stages of equal importance for a teacher's reflection process. The work prioritizes the alternative conceptions of student, transforming him in a direct agent of the construction of knowledge and this aspect is based on the profile of the Student's Material. Another important point is the evaluation's proposal, this was systematized to be done class after class through building texts, essay questions, presentation of papers, among others activities. The didactic sequence guides the introduction of relevant topics of the students and society’s daily life, the ideas are not closed and in many times the teacher make changes which deem relevant to the teaching for better development of their practice.

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

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.

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.