Algumas técnicas de construção de alguns poliedros e suas aplicações no ensino

Pós-graduação em Matemática em Rede Nacional - IBILCE

O processo histórico de disciplinarização da Metodologia do Ensino de Matemática

Desde as primeiras décadas do século XX, foi constatada nos currículos dos cursos de formação de professores a existência de uma disciplina cuja constituição, funcionamento e objetivos têm como pressuposto ensinar a ensinar a matemática. Historicamente, a disciplina Metodologia do Ensino de Matemática tem aparecido nos cursos de Licenciatura em Matemática com distintas denominações. Ao longo dessas mudanças, os pressupostos e as características dessa disciplina foram se modificando. Tomando como metodologia de pesquisa a análise documental e a história oral, e como referencial teórico os estudos de André Chervel (1990), este trabalho teve como objetivo compreender o processo histórico de disciplinarização da Metodologia do Ensino de Matemática em cursos de licenciatura em Matemática de instituições públicas de ensino superior do estado de São Paulo (USP, UNICAMP e UNESP-Rio Claro), buscando conhecer a gênese e o desenvolvimento histórico da disciplina, identificando conteúdos e métodos propostos bem como as mudanças pelas quais passou a disciplina.

Inércia e Natureza da Ciência no Ensino de Física: uma sequência didática centrada no desenvolvimento histórico do conceito de inércia

During the last decades the area of science education has discussed issues related to the inclusion of the History and Philosophy of Science (HFS) in the practice of science teaching. Among the arguments put forward in favour of this approach, it is pointed out the possible enhancement of scientific content learning and the understanding of the nature of Science (NoS). In spite of such considerations, we still have a very small number of research papers reporting results of practical interventions that utilize the historical approach, moreover, there is a lack of teaching materials in this perspective. Our work has sought to contribute to this area with regard to two aspects: on the one hand, with the production of didactic material, by drawing up texts on the history of inertia for graduate students. On the other hand, we investigate whether the arguments mentioned above in relation to the didactic use of HFS sustain themselves, in a particular context. We developed and applied a didactic sequence, using the texts that we built, to teach the concept of inertia and discuss selected contents of NoS. The didactic sequence was applied in two graduate classes, one from a course of Geophysics (BSc.) and another from the Physics (teaching formation), both from the Federal University of Rio Grande do Norte (UFRN). An initial survey exposed that students, even having approached the concept of inertia in basic education, presented conceptions of common sense regarding the relationship between force and motion. The questionnaire also allowed us to identify the existence of elements of concepts considered inadequate as regards to NoS. At the end of our research, our data indicated a greater number of positive hits on the issues concerning the concept of inertia. Regarding the aspects of NoS, we were able to identify, in a few cases, a move towards a more appropriate understanding, however, certain distortions persisted, highlighting the limitations of the approach used

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

Uma proposta de ensino de frações no 6º ano do ensino fundamental a partir da teoria histórico-cultural

This text presents developed in the Graduate Program in Science and Mathematics Education at the Federal University of Uberlândia, in which it was intended to answer the question: What are the pedagogical implications for the fractions concept learning for students of the 6th grade of elementary school that the teaching guide activities can provide? The objectives of this research were: a) analyze the possible pedagogical implications for the learning of the fraction's concept for students of the 6th grade of elementary school through guiding teaching activities; b) using the conceptual connections of the fraction to enable students to develop an abstract thought and c) investigate whether guiding teaching activities reflect on 'how to think' and 'how to do' of the student. Five teaching activities have been developed (MOURA, 2002) from the perspective of teaching guiding activity (TGA) and had as object of study the teaching of fractions for students in 6th year of elementary school. They have been prepared and proposed activities in which it was intended to investigate the use of history of mathematics as an aid in learning the conceptual fraction links (CARAÇA, 1951) by students. Such activities, for analysis, were organized into episodes and scenes (MOURA, 2004) and discussed how students deal with the measurement of whole quantity (all) and subunits (part); how they represent in verbal or written language. It is hoped that the research is set up as an important contribution to mathematics teaching area and may contribute to the initial and continuing training of mathematics teacher sand the formation of theoretical thinking of elementary school students.

Formação inicial do professor de matemática com uso de tecnologias da informação e comunicação no contexto da escola pública

This paper intends to analyze which contribution for teachers formative training the participation on extension projects can bring to the bachelors in Mathematics teaching. The research was conducted during the developing of a Project from the Program of Extension - Programa de Extensão UFU/Comunidade (PEIC) in a municipal school located in a country zone from Uberlândia-MG. The research was constituted by a series of activities with students from the ninth year of the Fundamental Education, Middle School. The main focus is the work developed by two bachelors of Mathemactics teaching from the Federal University from Uberlândia who were part of the PEIC team. This present research intends to answer the following question: How the extension project “Information technology and communication on Mathematics problem resolution in country zone schools” has contribited to reinforce and to (re)criate the fomative experiences of students from the Mathematics teaching course who have developed such project? The presente study is from a qualitative nature and has made use of the partaker searching methodology. The presente paper was organized in three chapters. On chapter I evidence is given to theoretical discussion made, having as main references the works of Larrosa, Ponte e Shön. Chapter II brings the description of the three activities that were developed and aplied during the PEIC Project, which are: Problems in the Park, Inaccessible Hight and Lili Game. On chapter III, the data analysis is presented. The data was obtained through instruments of registration such as: camera recording, photografic material, meetings reports, field notes, surveys and semi-structured interviews. The initial hypothesis aim is on the fact that the participation on extention projects during the graduation course can bring rich contribution for the teachers to be, since it’s going to provide the knowledge and chalenge close to the one from the future profession. With the analysis of the obtained results from the colected data, it was possible to conclude that the PEIC has provided the bachelors in Mathematics teching the opportunity of recreate and potenciate their formative experiences. Such opportunity happened in situations that involved, for example, planning makings, development of colective work, softwares usage, different school spaces and the direct interaction with school bureaucracy. Beyond that, it was possible to work with the cocepts of reflection in action in a way to contribute to the professional development of the future Mathematics teachers. Thereby, in our final considerations, is possible to conclude that extension projects performed during the graduation course can bring great contributions to the professional formation of the bachelors in Mathematics teaching, among them we highlight the potentiation of the previous formative experiences and the development of colective work and behavior related to a reflexive teacher.

A interdisciplinaridade entre a Expressão Criativa e a Matemática no 2º ciclo da Escola de Dança Ana Luísa Mendonça

Relatório Final de Estágio apresentado à Escola Superior de Dança, com vista à obtenção do grau de Mestre em Ensino de Dança.

O ensino da estatística nos anos finais do ensino fundamental

Result of a professional master course of research work in Teaching Science and Technology of the Federal Technological University of Paraná (UTFPR), this work aims to provide the mathematics teacher of the final years of elementary school a teaching sequence (SE) which includes basic content of Statistics provided in the curriculum. In this book a text about the importance of the teaching of statistics is presented, as well as issues related to literacy skills, reasoning and statistical thinking. The development of the SE was designed considering the presuppositions of contextualization, being structured in six steps. We chose to develop a work with the basic contents of Statistics through real data collected with the participation of students, within a context for them significant. This option was due to be possible to develop with the students situations such as: raising hypotheses , communication situations experienced by different graphs and tables , results of discussion and understanding of the significance of the results obtained by means of statistical calculations. Thus, it is believed to be possible to contribute to the development of statistical skills by the students.

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.

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.

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.

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.

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.