Formação docente e conhecimento profissional: desafios para o ensino da matemática na EJA

As for the Education for Youth and Adult (EYA), the challenge of training these teachers is to provide tools to understand and act on the teaching of mathematics. It is realized just how special education in this modality and as such teaching is lacking in an adequate and solid training in the area of knowledge. One of the major problems affecting this type of education is the high dropout and failure rates, and lack of motivation among students. Thus the need to provide differentiated profile with a professional to teach youth and adults students, so that they are able to mobilize didactic-pedagogic knowledge, methodologies and theoretical frameworks that serve as a basis for school-developed teaching practice. This thesis aims to investigate how the math teacher, who acts in adult education from elementary school, has developed its didactic and pedagogical action, and that professional knowledge has been mobilized to teach? It has highlighted the importance of initial and continuing training and professionalization of teachers dedicated to this specific type of education, when teachers should be the protagonists of their professional development. The methodological approach was begun with a literature review, then the research was anchored mainly on the ideas by Gauthier, Nuñez and Ramalho (2004); Imbernon (2011), Garcia (2006); Perrenoud (2000); Tardif (2007 ); Haddad, Di Pierro (2000), D'Ambrosio (2002), Mendes (2006, 2009), Freire (1996, 2011), and other theorists and official documents of field of adult education here and abroad. That work leads us to the understanding of the present moment from a foray into historical and conceptual aspects, as well as educational policies of EYA, as well as training, professionalism, knowledge and skills necessary for professional practice. Then, the subjects and the locus of research and the instrument for data collection were set up and led by the object of study. To consolidate the study was selected a sample of 27 mathematics teachers, working in municipal EYA Network Teaching of Natal. This research is in an investigative nature, within the quantitative and qualitative approaches focused on the responses of study subjects from the content analysis by Bardin (1977). Results from the analyzes have revealed that the initial training of mathematics teachers of adult education needs to be reconfigured in order to formalize the knowledge base of professionals (the mathematical content, didactics and professional knowledge). Thus the study suggests that this base knowledge is embedded in the pedagogical practice of these teachers, so that there is a completion of the teaching and learning process for young people and adults. The study also has pointed out that there is a need for teachers to participate in a continuing education plan that prioritizes learning situations of mathematical content considering the previous knowledge of the students. The final analyses thus indicate that knowledge of mathematics and the didactic and pedagogical strategies to be mobilized by teachers must be able to motivate the students in such a way that they feel need to incorporate in their knowledge, mathematical knowledge capable of making them more likely to have access to social, economic and labor market

A prática de atividade física de crianças e adolescentes com e sem epilepsia

The epilepsy is one of the neurological disorders more common in the pediatric period, and which interferes significantly in the psycho and social life of children and teenagers. The objective of this study was analyzing the practice of sedentary practices, physicals, traditional infant fun and games of children and teenagers with and without epilepsy. The study was prospective, transversal descriptive, done with 60 children and teenagers with epilepsy (Epileptic Group - EG) patients from Pediatric Neurology Clinic of the Centre Integrated Health Lineu Araújo and 60 children and teenagers without epilepsy (Control Group - CG) students from municipal public school, both of the two groups paired with the same age (age group 7 to 14 years) of both the genders (female = 25/41,6% and male = 35/58,3%) of the Teresina city Piauí. It was done two pattern questionnaires, one applied to children and teenagers of the EG and CG to identify the sedentary activities, physical and traditional infant games and other to the parents/responsible of the EG about the clinical and demographic information. The results permitted the elaboration of two manuscripts: a) the first one titled The Practice of Sedentary and Physical Activities of Children and Teenagers with Epilepsy which showed significant difference in the sedentary activities of playing with car toy (p=0,021) to the EG and reading to the CG (p=0,001); in the physical activities the school physical education (p=0,001) and riding a bike (p=0,014) to the CG; b) the second one The Practice of Infant Games and Fun the children and teenagers with and without Epilepsy in this one the playing with marble presented significant difference (p=0,016) to the CG, despite the girls of the two groups don t do this activity. Observing the distribution of frequencies, it was verified that in the play catch-up and hide-and-seek and burn the EG plays more than the CG both in female and male gender. The girls of the EG play less skip, 60 while the boys of the two groups don t play. Elastic jump the girls of the two groups play in a same frequency and the boys don t participate of this fun. The seizures were found to occur during: soccer (23,3%); hide-and-seek (6,6%) and running (3,3%). In the sedentary activities, seizures were reported to occur: resting and watching TV (18,3%), sleeping (36,0%); sitting (13,3%) and lying down (11,7%). Our results showed that the epileptic group and the controls group engage in the same activities, although the epileptic group participates less than the controls. Although the EG had presented a bigger percentage of generalized attacks, they don t occur during the practice of formal physical activities. The research was developed by a multidisciplinary team, and this contributed a lot to the realization of this study

Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Investigação etnomatemática em contextos indígenas: caminhos para a reorientação da prática pedagógica

From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community

Pedagogia etnomatemática : ações e reflexões em matemática do Ensino Fundamental com um grupo sócio cultural específico

mongst the trends in Mathematics Education, which have as their object a more significant and criticallearning, is the Ethnomathematics. This field of knowledge, still very recent amongst us, besides analyzing an externalist history of the sciences in a search for a relationship between the development of the scientific disciplines and the socio-cultural context, goes beyond this externalism, for it also approaches the intimate relationships betwe_n cognition and culture. In fact, the Ethnomathematics proposes an alternative epistemological approach associated with a wider historiography. It struggles to understand the reality and come to the pedagogical action by means of a cognitive approach with strong cultural basis. But the difficulty of inserting the Ethnomathematics into the educational context is met by resistance from some mathematics educators who seem indifferent to the influence of the culture on the understanding of the mathematics ideas. It was with such concerns in mind that I started this paper that had as object to develop a curricular reorientation pedagogical proposal in mathematics education, at the levei of the 5th grade of the Ensino Fundamental (Elementary School), built from the mathematical knowledge of a vegetable farmers community, 30 km away from the center of Natal/RN, but in accordance with the teaching dimensions of mathematics of the 1 st and 2nd cycles proposed by the Parâmetros Curriculares Nacionais - PCN: Numbers and Operations, Space and Form, Units and Measures, and Information Treatment. To achieve that, I developed pedagogical activities from the mathematical concepts of the vegetable farmers of that community, explained in my dissertation research in the period 2000 through 2002. The pedagogical process was developed from August through Oecember 2007 with 24 students of the 5th Grade of the Ensino Fundamental (Elementary School) of the school of that community. The qualitative analysis of the data was conducted taking into account three categories of students: one made up of students that helped their parents in the work with vegetables. Another one by students whose parents and relatives worked with vegetables, though they did not participate directly of this working process and one third category of students that never worked with vegetables, not to mention their parents, but lived adjacent to that community. From the analyses and results of the data gathered by these three distinct categories of students, I concluded that those students that assisted their parents with the daily work with vegetables solved the problem-situations with understanding, and, sometimes, with enriching contributions to the proposed problems. The other categories of students, in spite of the various field researches to the gardens of that community, before and during the pedagogical activities, did not show the same results as those students/vegetable farmers, but showed interest and motivation in ali activities of the pedagogical process in that period

Ensino de matemática, história da matemática e artefatos: Possibilidade de interligar saberes em cursos de formação de professores da Educação Infantil e anos iniciais do Ensino Fundamental.

This work is located at the shield of research that defends the use of Mathematics History, based on the utilization of historical artifacts at teaching activities, at Mathematics classrooms, and at graduation courses for teachers of Elementary School and of the first grades of High School. The general objective is to examine the possibility of the use of historical artifacts, at teaching activities, at graduation courses for teachers of Elementary School and of the first grades of High School. Artifact, at this work, is comprehended as objects, documents, monuments, images and other kinds of materials that make sense to the Human actions at the past and that represent what have been said and done at the Human history. At the construction of the theoretical-methodological way of the research we have based ourselves upon the ideas of the authors that are engaged at the teachers formation; at researchers adherents to the use of Mathematics History (MH) as a methodological resource, and at studies accomplished that elucidate the role of the artifacts at the history and as a mediatory element of learning. We defend the thesis that the utilization of historical artifacts at teaching activities enables the increasing of the knowledge, the development of competencies and essential abilities to the teacher acting, as well as interact at different areas of the knowledge, that provides a conception of formation where the teacher improves his learning, learning-doing and learning-being. We have adopted a qualitative research approach with a theoretical and pratic study disposition about the elements that contribute to the teachers works at the classroom, emphasizing the role of the Mathematics history at the teacher s formation and as a pedagogical resource at the mathematics classroom; the knowledge, the competencies and abilities of the historical artifacts as an integrative link between the different areas of the knowledge. As result, we emphasize that the proposition of using the MH, through learning activities, at the course of teacher graduation is relevant, because it allows the investigation of ideas that originate the knowledge generated at every social context, considering the contribution of the social and cultural, political and economical aspects at this construction, making easy the dialog among the areas and inside of each one The historical artifact represents a research source that can be deciphered, comprehended, questioned, extracting from it information about knowledge of the past, trace and vestiges of the culture when it was created, consisting of a testimony of a period. These aspects grant to it consideration to be explored as a mediatory element of the learning. The artifacts incorporated at teaching activities of the graduation courses for teachers promote changes on the view about the Mathematics teaching, in view of to privilege the active participation of the student at the construction of his knowledge, at the reflection about the action that has been accomplished, promoting stimulus so the teachers can create their own artifacts, and offer, either, traces linking the Mathematics with others knowledge areas.

A cultura da produção de farinha: um estudo da matemática nos saberes dessa tradição

This research argues about the mathematical knowledge built in the tradition of the cassava flour production, seeking to analyse these mathematical knowledge in the perspective of the categories of time and measure, built and practiced in the flour production, located in Serra do Navio and Calçoene, in Amapá - Brazil. The following work discuss the identification and the description of the mathematics during the production activities of the flour, where is presented elements related to generation and transmission of the traditional knowledge, which is the basis for maintenance of the tradition of the flour, characterizing the research as an Ethnomathematic study. The methodological procedures highlight ethnographical techniques and elements that characterize the participating observation. The results obtained showed us that the flour workers articulate some length, area and volume measure due to own and traditionally acquired systems, which is apprehended and countersigned by other kind of culturally established system; thus they relativism the measures systems and the official calendars. And it lifts as one of the main proposal that the academic mathematics and the tradition establish knowledge make conjunction of the both knowledge, that is important for a possible reflection and application in the construction of a pedagogical practice in mathematical education, trying to establish points of socio-economic and cultural mark

Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Política de formação de professores: uma leitura a partir da análise do programa especial de formação de professores para a educação básica PROEB/UFMA

Study of Teacher Education Policy: a reading from the analysis of Programa Especial de Formação de Professores para a Educação Básica Proeb - aims to analyze the initial teacher training developed by the Universidade Federal do Maranhão - UFMA. Proeb is a policy of in-service training of teachers, formulated and implemented in the context of current educational policies for basic education. This work assumes that the guidelines developed in the last decades of the twentieth century are linked to international organizations that spread in Latin America continent a homogeneous model of training which has as main features to be held in service through the mode the distance and the school as a leading locus. In Brazil, these guidelines are supported on the Law of Directives and Bases of National Education No. 9.394/96 and Report 09/2001, which deals with the Syllabus Guidelines for the formation of Basic Education Teachers. To carry out the study was taken as reference, the syllabus developed for the deployment of Proeb from 1998 to 2002, specifically the proposal operationalized in the Degree Course of Mathematics in the city of Vitória do Mearim in Maranhão. To conduct the study, it was used literature as a way to deepen understanding, clarify and aim the conceptual aspect of the object researched. The documental research was consisted in the analysis of legal documents concerning the reform of education policies, teacher training and pedagogical project Proeb/UFMA and, finally, the semi-structured interviews were used to allow a better understanding of the subjects involved with research. The data analysis has shown that the curriculum designed to operationalize the course of undergraduate mathematics Proeb/UFMA, despite having guidelines that point to the separation of theory/practice dichotomy and establish as a principle work as an educational principle, has an disciplinary curriculum organization that reinforces the instrumental view of the syllabus, not enabling in practice, the execution of their initial proposal. Concerning to the view of graduates on the course, they highlight the weaknesses of the course, but also evidence that it has allowed an improvement of initial training, through the disciplines of the common core syllabus of courses and special training. It is possible seeing in graduates words, that the course have had repercussions in their teaching and improving their integration into the labor market and in the community of Vitória do Mearim. Overall, these developments have indicated evidence of teacher professionalization, although they are incipient. The work has shown that for the professionalization of teachers is introduced, the syllabus of undergraduate teacher education must overcome the traditional view of syllabus and implement contextualized curricula in a multidisciplinary approach involving, in equal proportions, the general education and training specific course. Accordingly, it is believed in need to review the role of the University in the formative process, as well as recovering as part of educational policies, the omnilateral size of teacher education

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Simetria na dança: vestígios matemáticos na prática da dança esportiva em cadeira de rodas

To investigate in practice of the Wheelchair Dancesport (WDS), the mathematics of the characteristic isometric movements of the dance of ChaChaCha was the generating subject of this study. The subjects and the locus of the research were the athletes dancers of the Associação Baiana de Dança em Cadeira de Rodas (ABDCR). Referred him study aimed at to describe reflections concerning the athletes' practicing dancers of the technical acting Wheelchair Dancesport, using the inherent mathematical knowledge to the isometric movements executed in the ChaChaCha. For that, I stimulated in the athlete dancer the need to be investigating of his/her own practice, motivating him/it to be searching of information that they collaborate with his/her technical refinement, proposing like this roads to make possible his/her growth, while dancer and, also, promoting of their own movements. To reach my objectives I dialogued with some specialists to understand, to the light of their theories as, Espaçonumerática, Sociology of the mathematics, Etnomathematical, Dance and Symmetry, as those spaces they interact with the atmosphere of the Wheelchair Dancesport and that contributions could supply to the study. However, two authors of the Dancesport for walking , Ried e Laird, they brought contributions that aided in the creation of a prototype for the study of isometric movements in practice of the modality promoting the interface between the theory and the practice. The study showed to be possible to navigate still with the Mathematical Education in an universe little known as the one of the Wheelchair Dancesport. And it is in this adapts that propose a more attentive glance to the illustrations executed by the athlete dancer wheelchair and walking , in the dance of the ChaChaCha, verifying and proposing an analysis with focus investigate, looking for mathematical tracks concerning the symmetry that you/they characterize some of their illustrations

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo

Uma fundamentação matemática para processamento digital de sinais intervalares

This work deals with a mathematical fundament for digital signal processing under point view of interval mathematics. Intend treat the open problem of precision and repesention of data in digital systems, with a intertval version of signals representation. Signals processing is a rich and complex area, therefore, this work makes a cutting with focus in systems linear invariant in the time. A vast literature in the area exists, but, some concepts in interval mathematics need to be redefined or to be elaborated for the construction of a solid theory of interval signal processing. We will construct a basic fundaments for signal processing in the interval version, such as basic properties linearity, stability, causality, a version to intervalar of linear systems e its properties. They will be presented interval versions of the convolution and the Z-transform. Will be made analysis of convergences of systems using interval Z-transform , a essentially interval distance, interval complex numbers , application in a interval filter.