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.

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.

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.

Uma prática colaborativa na construção do portifólio educacional

Acompanha: Unidade didática: elementos de astronomia e energia

O uso de filme como recurso pedagógico no estudo das epidemias: possibilidades na aprendizagem significativa

Acompanha: Epidemias na escola? Só em filmes: possibilidades de contaminação na aprendizagem significativa

Princípios e fundamentos da pedagogia da alternância: alguns desdobramentos atuais

The Pedagogy of Alternation (PA) is a differentiated teaching methodology, originally created to meet the needs that involve the population of the field. Through its educational procedures, distinct from the traditional education, demand, with autonomy, to form children and young people through the articulation of time and space, and involve the family and community in the educational process and in local development. Having been established as an alternative that generated positive results, the PA has expanded the world and today, with the formation of various movements, is present on five continents. In Brazil, there are two active movements using the PA, the Italian, which afforded the EFAs and the French, responsible for implantation the CFRs. Is in this context, the present research is inserted, which the following objective: to analyse the origins, principles and theoretical-methodological foundations of Pedagogy of Alternation and its implantation in Brazil, as well as some of its current unfolding. With this, it takes into consideration, besides the Brazilian movements, those who influenced its origin, the raised in France and the raised in Italy. The study is characterized as a theoretical, qualitative, bibliographic and documental. The data collection was carried out by searching in the CEPAD/UTFPR database and in the web pages of the institutions involved. After the identification and selection of documents and bibliographies, was realized the qualitative analysis of the data. The results indicate that the Pedagogy of Alternation practiced by the Italian EFAs and the Brazilian CFRs has undergone significant changes over time, keeping only firm the principle alternation of time and space, while the French MFRs and Brazilian EFAs, passed by adaptations, but still solid to principles of PA. The survey also showed that the CFRs in Parana are in a situation of instability about their future, since the links with the government are weakened. Thus, the present study sought to reflect on the meaning and the scope of the PA and its foundations that guarantee the autonomy and strength of this methodology in their places of origin. Therefore, the research presents contributions regarding the elucidation about expansion process of the movements in the three covered countries as well as those faced tensions by each and their transformations in order to highlight the importance of PA for education, comprehensive training of young and to development of the middle.

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.