Uma Proposta de utilização de um software educacional para o ensino de poliedros

This paper presents an educational proposal to use an educational software for the teaching of mathematics, following in the conduct of activities, the main aspects of sociocultural theory of Vygotsky. For this, it chose the Poly educational software, with which were developed teaching and learning activities for the polyhedra content provided in the São Paulo State Mathematics curriculum for the 7th year of elementary school. The objectives of this pedagogical proposal are to stimulate situations of social interaction among students and between students and the teacher, using an educational software as a mediator instrument and present a different way of using digital technology in math classes, aiming production of mathematical knowledge

Mídias na educação matemática: projeto CONDIGITAL

This work aims to understand the multimedia Learning Objects (LO's) developed within the CONDIGITAL project, subsidized by the federal government. The CONDIGITAL aimed to encourage the production and the use of media in teaching in high school classrooms. This work presents a reflection on the contribution of media to the construction of significant learning of student users. The research was conducted through a literature study. Therefore, it was considered the work of some researchers related to the study of the potential of these technologies in education, such as Valente (1995), Tauroco (2007) and Mussoi (2010). These readings made possible to discern some common evaluation criteria that may be used as parameters to analyze the quality of these media as educational tools. The theme of exploration is guided by a research on the motivation of the mentioned project and on its amplitude and its results, which is directed later to the LO's developed by UNICAMP team, particularly in the Mathematics productions developed by the M³ project, some of the which are presented and evaluated in this monograph

A visualização no ensino de geometria com o Geogebra 3D

This research presents an investigation about the relevance of visualization in teaching geometry. Our interest turns to analyzing the use of technology in teaching geometry, seeking to highlight their contribution to learning. The students of today - second decade of the 21st century - require that, each time more, the school move towards the integration of technologies for teaching since tablets, smartphone, netbook, notebook are items present on daily life of most students. Thereby, we investigate, taking the phenomenological orientation, the potential of educational software, especially the Geogebra 3D, directed at teaching math and favoring the work with the geometry viewing. At work we bring some theoretical considerations about the importance of viewing for the geometric learning and the use of technologies. We build an intervention proposal for the classroom of the 7th year of elementary school with tasks aimed at visual exploration and allow the teacher to work the concept of volume of geometric solids

O Ensino de Geometria por meio de atividades investigativas: uma experiência com alunos do primeiro ano do Ensino Médio

This qualitative nature of work was developed with the participation of a group of students enrolled in the first year of high school from a public school of the state of São Paulo, in the city of Taubaté. Their goal was to determine how students deal with geometry tasks in investigative classes. To guide this research was drawn up the following question: As students of the first year of high school express their knowledge of building triangles and quads in classes of investigative activities?. The choice of investigative nature of this activity occurred by enhancing student participation and thus generate a greater chance of it not be guided only by what the teacher wants, but by his own curiosity and using their own tools for this. In the data analysis process stands out the interest generated in students for this type of activity and posture maintained throughout the work, mobilizing their expertise to answer the questions posed

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

Pós-graduação em Matemática em Rede Nacional - IBILCE

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.

Educação matemática: pesquisas e possibilidades

This book presents a current overview of themes that entangle research in Mathematics Education, which were produced in conjunction with professors who act in the Mathematics Education field at PPGECM (Science and Mathematics Post-graduation Program), that counts with professors from many universities, especially UFPR (Paraná's Federal University), UTFPR (Paraná's Technological Federal University) and UDESC (Santa Catarina's Federal University).The set of texts brings some areas of interest, studies that are in development and research that have been completed. It is expected that the chapters present the program, aspects of its production, interests and theoretical/methodological relations, contributing to the strengthening of Mathematics Education as a research field and familiarization and deepening of the topics discussed.

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.

O contributo da intervenção psicomotora para a aprendizagem da matemática : estudo do seu impacto na aprendizagem das pré-aptidões matemáticas em crianças de cinco anos de idade

A presente dissertação tem como objetivo analisar a importância da intervenção psicomotora no desenvolvimento das pré-competências matemáticas. Para tal foram discutidos conceitos e noções sobre a utilização da psicomotricidade como contributo para a aprendizagem das pré-aptidões matemáticas no pré-escolar. Num primeiro momento, será feito um breve enquadramento teórico sobre a temática em estudo – o contributo da intervenção psicomotora na aprendizagem da matemática no pré-escolar. Num segundo momento, apresenta-se a metodologia desenvolvida para o caso de estudo (programa) e expõem-se os resultados obtidos nos diversos momentos de avaliação. Por fim, apresenta-se a conclusão onde se sugere que a intervenção psicomotora promoveu uma evolução positiva na aquisição e na consolidação das pré-aptidões da matemática.

Ensaio da Ferramenta DIA Diagnóstico e Informação do aluno

Apresentamos os resultados de nossa pesquisa para concepção, execuçãoo e avaliação de uma ferramenta adaptativa informatizada, denominada DIA, que permita tanto avaliar como fornecer feedback a estudantes sob uma perspectiva de avaliação formativa. Na primeira etapa, usamos os PCN: Ciências da Natureza, Matemática e suas Tecnologias (BRASIL, 1998) e as Matrizes Curriculares de Referência do Instituto Nacional de Estudos e Pesquisas Educacionais - INEP, para o Sistema de Avaliação para a Educação Básica- SAEB (BRASIL, 2005), para construir uma escala, em que os objetivos estão em ordem crescente, de acordo com o desenvolvimento vertical da construção do conhecimento em Matemática. Entrelaçamos os objetivos propostos para criar um Banco de Itens (BI), que foi usado em nossas simulações. Analisamos os resultados obtidos em nosso ensaio para avaliar o diálogo entre o BI e a escala sob a perspectiva de oferecer um diagnóstico de lacunas na construção do conhecimento matemático. Em nosso ensaio, simulamos o funcionamento da ferramenta DIA através de um teste adaptativo informatizado baseado na Teoria de Resposta ao Item (TRI). Também estamos interessados em determinar um perfil de um Banco de Itens, que seja capaz de forma significativa de dialogar com nossa escala através de TRI. A escala e o banco de itens a ela associado devem viabilizar um feedback construtivo que ajude os alunos a desenvolverem competências metacognitivas.