Aplicações das atividades estruturadas de Skemp para a construção do conhecimento matemático

The present study constitutes a discussion about the application of Structured Activities to the construction of the mathematical knowledge, proposed by Richard Skemp. The discussion is based on the research that the author carried out in a public school of the state education chain buy using procedures of the research-action. It investigates the possibility of adoption of the proposal of Skemp in a new reality. It utilizes explanations from several theorists to understand the necessity and, at the same time, to enhance the efficiency of the referred activities in first grades of elementary school when students have their first mathematics teachings. It emphasizes the important rule of the teacher, as mediator to the mental constructions of the child. It presents considerations about the results achieved by the research, noticing the possibility of adoption of the studied proposal even though it is necessary an adjustment of the procedures to appropriate didactic-pedagogic requirements to the educational reality in which this project was done

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher

Opiniões de professores do ensino médio: refletindo sobre os projetos escolares e a interdisciplinaridade

Official documents indicate to a curriculum organization that promotes the dialogue in different areas of knowledge. Among the proposals strategies are the "School Projects". This research appears from the staff need evidenced in the development of practice of the researcher in recent years as Pedagogical Advisor in high school. The comments made in the daily work on the kinds of projects and how they were developed in the school, generated concerns. They aroused the interest in further the discussion, aiming to reflect with teachers about the implementation of a pedagogic action on the use of educational projects in the classroom, as a didactic strategy which promotes the learning of students. In this sense, it seeks to develop studies and discussions by the application of questionnaires and the holding of a workshop with teachers in the area of Science of Nature and Mathematics in private high school institutions from Natal, searching opinions of them as the preparation and development of school projects. As general purpose, it aims to contribute with elements to the reflection of the teachers on the use of this strategy of education. For both, we propose: the knowledge of ideas/opinions of teachers on planning, development and evaluation of projects, both disciplinary and interdisciplinary, identifying the main difficulties of these teachers about the work with projects at school; reviewing projects developed at school after the press conference in a meeting with teachers, incorporating the identified aspects as weak points. In the course of the methodology research, questionnaires were used with open and closed questions for the lifting of preliminary ideas for teachers in order to subsidize the planning of a developed meeting later in the school itself on the subject in question. 10 teachers took part of the first step and 17 in the second one (pressconference). In the third stage, an individual interview was carried out and analysis of projects already developed. It is observed that, as the main difficulty for the development of projects in school, pointed to the time factor in the planning team, followed by excessive working hours for teachers that, generally, also work in other schools. Some teachers say they do not develop projects for not having knowledge of how to develop school projects, neither disciplinary, nor interdisciplinary

Física para geografia: desafios de uma proposta pedagógica interdisciplinar

This study has as its aim the elaboration, presentation and application of a proposal which makes possible an inter-disciplinary relationship between knowledge of physics and geography in the graduation course for forming geography teachers in the Dom Aureliano Matos Faculty of Philosophy in the city of Limoeiro do Norte in the State of Ceára. Initially, we observe in pertinent literature and opinions of specialists what capacities and abilities are suggested for a future teacher of geography. Following that, we select subject matter which broaches upon physic concepts and may be contextualized within topics present in the daily fare of a geography teacher, such as natural phenomena related principally to natural environment and climate, envolving astronomic features, using didactic materials and resources in easily understood language and without the excessive presence of mathematical formulas. An evaluation of the experience allows us to affirm that inter-disciplinary treatment, as an important alternative for curriculam organization, when applied in the classroom shows that there is better learning, a reduction in class evasion and a significant fall in failures when compared with traditional proposals for the teaching of physics in relation to geography. On the other hand, it is notable that to maintain and augment such measures it is a challenge to be met, with the purpose that students of other courses may perceive that physic concepts have much to do with their reality, and that understanding them is relevant for their professional and personal formation

As Ciências Espaciais, o saber e o fazer docente no ensino fundamental

This study aims to include topics related to Space Science in elementary education from an experiment that aims to rescue the science teachers in public schools of São Tomé, RN, a taste for experimentation and exploration of advanced technologies. During this research with teachers found that they knew enough about the subject, but this knowledge was restricted to the events disclosed by the media. Regarding scientific knowledge, that same surface, they had many conceptual difficulties which hindered the approach of these topics in their classes. To overcome this difficulty, a workshop was held where teachers had the opportunity to discuss the historical aspect of Space Science, some physical concepts related to it, and the conduct of experiments with PET bottle rockets that recover from the curiosity typical of how the science. The results were outlined in the form of Planning Didactic built by teachers and using themes related to space science, from there, discussing content already provided in the composition of the schools curriculum. Therefore, this work allowed the teachers a minimum training required for them to not only reproduce, but readjusted and build, from this, their own paths in the classroom at the fundamental level

Despertando responsabilidade social no ensino médio por meio de temáticas associadas à física nuclear

Many discussions about the role of the school are on the agenda, in an increasingly complex society. Sociologists, educators, anthropologists, researchers of different areas seek that role. The objective of this dissertation is to contribute what we can consider the central role for the physics teaching, citizenship training. We have elaborated a didactic proposal to increase the interest of high school students on issues of social relevance and, throughout it, to promote the formation of attitudes of social responsibility, enhancing the formation of a more politically and socially active citizen. For the preparation of the proposal, studies were made on education for citizenship and on attitudes change, using as its main theoretical foundation the researches on the Science, Technology and Society curricular emphasis. The teaching of Nuclear Physics was integrated to our proposal, due to its pedagogical potential for the discussion of social, political and economic subjects related to scientific concepts and associated technologies. The educational proposal we have produced was applied on a high school class of a private school at Natal-RN. It was composed from the controversial issue involving the installation of nuclear power plants in Brazilian northeast. The methodology of role playing, in which students assumed social roles and produced specific subsidies for a public hearing and a later referendum, both simulated. In the analysis of the implementation of the proposal, we highlighted the difficulties but also the possibilities and the relevance of exercising skills such as reasoning, finding information, and arguing about of social problems. The results of the research showed the possibility of meaningful learning on Nuclear Physics contents, through this social, political, economic, scientific and technological contextualization using a controversial and real issue together with mechanisms that trigger for greater popular participation, as public hearing. It has also been identified changes in attitude by some students about issues related to Nuclear Physics. We hope, through this dissertation, to contribute to the formation of future citizens as well as to the initiative of teachers-researchers with pedagogical aims similar to those in the present work

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

Formação continuada de professores que ensinam matemática: o papel do ábaco na ressignificação da prática pedagógica

The present dissertation performs a study about abacus part on the continuous education of Elementary School s Mathematic teachers on what concerns the basic operations of addition and subtraction with (re)unification by using the manipulative and/or informatical abacus. Therefore, the research intends to answer the following question: How does a teacher reframe the pedagogical practice while teaching the Decimal Numeral System and the conventional operations of addition and subtraction with (re)unification through manipulative and informatical abacus? In order to do so, we rely ourselves on the Guy Brousseau s Theory of Didactic Situations (TDS) from 1996 that affirms the necessity to trace a way in accordance with the teaching situations that lead the student s learning; and on the work of Pierre Lévy (1993), in which the poles of communication oral, written and virtual create three ways of communication through which the learning process happens. The methodology of this paper was based on the Strategic Research-Action of Franco (2005). The didactic sequence was elaborated in accordance with TDS and used the manipulative and informatical abacus as didactic resource. With the application of the didactic sequence, it was verified that the continued formation of Elementary School s teachers concerning the operations of addition and subtraction on the initial years/levels is pertinent once it has been observed some difficulties of the teachers concerning this mathematical subject. Besides, the analysis of the didactic sequence has allowed one to realize that teachers had some difficulties concerning the numeric representation with order zero, the resolution of operations of addition and subtraction using the manipulative and informatical abacus and the realization of (re)unification on the subtraction with meaning. These observations has been discussed with the teachers and, after that, it has been done some didactic-methodological routings of the operations of addition and subtraction with re(unification) that contributes with the teaching and learning process.

Uma sequencia didática para o ensino da resolução da equação do 2. grau : adequação para o uso com professores

The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher

Linguagem matemática: uma proposta de ensino e avaliação da compreensão leitora dos objetos da matemática

This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Matemática Védica no ensino das quatro operações

This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school

Atividades estruturais de equações polinomiais numa abordagem histórica por meio de e-book

The present study investigates how the inter-relationship of the content of polynomial equations works with structured activities and with the history of mathematics through a sequence of activities presented in an e-book, so that the result of this research will proceed will result in a didactic and pedagogic proposal for the teaching of polynomial equations in a historical approach via the reported e-book. Therefore, we have considered in theoretical and methodological assumptions of the History of Mathematics, in structured activities and new technologies with an emphasis on e-book tool. We used as a methodological approach the qualitative research, as our research object adjusts to the objectives of this research mode. As methodological instruments, we used the e-book as a synthesis tool of the sequence of activities to be evaluated, while the questionnaires, semi-structured interviews and participant observation were designed to register and analyze the evaluation made by the research, participants in the structured activities. The processing and analysis of data collected though the questionnaires were organized, classified and quantified in summary tables to facilitate visualization, interpretation, understanding, and analysis of these data. As for participant observation was used to contribute to the qualitative analysis of the quantified data. The interviews were synthetically transcribed and qualitatively analyzed. The analysis ratified our research objectives and contributed to improve, approve and indicate the use of e-book for the teaching of polynomial equations. Thus, we consider that this educational product will bring significant contributions to the teaching of mathematical content, in Basic Education