Função Afifim: Teoria e aplicações

In this work we present a proposal to contribute to the teaching and learning of affine function in the first year of high school having as prerequisite mathematical knowledge of basic education. The proposal focuses on some properties, special cases and applications of affine functions in order to show the importance of the demonstrations while awaken student interest by showing how this function is important to solve everyday problems

Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

A história escolar e a teoria da atividade: relações e possibilidades formativas no ensinar e aprender

This study investigates the manner in which the Activity Theory by Alexei Nikolaevich Leontiev contributed to the performance of a teacher who teaches History at the 8th year of elementary school, Escola Estadual Coronel Fernandes, in Luís Gomes - RN city. Her goal is to analyze the contributions of this theory in her teaching practice. It was opted by collaborative approach as formative strategy and was used as procedures for training of knowing the courses of study and thoughtful reflection sessions. It was used as techniques in the development of these cycles, the semistructured interview and the reflection sessions, the autoscopy and observation in real life. Regarding the theoretical foundation, held in these cycles, the teacher demonstrated to have appropriated some contributions from Activity Theory, besides relating them to her practice and understanding her importance to the improvement of teaching and learning of History. Concerning to the reflection sessions, the analysis showed that the participant has used of constructions of this theory and improved their practice, developing lessons of History so as to encourage student participation in oral and promote his integral development. The educational process, carried out on the practice of teacher, has shown an increase in her conscious learning that contributed to the improvement in their professional development. Before these findings, as needs for new thinking, this research recommends, especially the organization of teaching activities, based on this theory, which allows the teacher to improve the teaching and learning process contributing to student's full education

Avaliar na alfabetização: uma reflexão sobre as dificuldades docentes

Our work leads up to the context of evaluation during alphabetization process as a moment of an educational action cycle that requires planning, teaching and learning of reading and writing. It aimed to research the difficulties lived by teachers of a public elementary school during the specific task of evaluating children in the alphabetization process. This qualitative research took place as a case study at Emília Ramos Municipal School, in Natal, capital city of Rio Grande do Norte State, Brazil. Semi-structured interview and questionnaire were used as fact-gathering proceedings. Two pedagogical advisers and seven teachers formed the group of research subjects. All of them worked with elementary school first cycle classes, in that school, in the year of 2003. The analysis shows that teachers difficulties concern to theoretic questions of conceptual and methodological orders, although these questions indicate an important knowledge of teachers about alphabetization and evaluation. Our reflection about these problems articulates two points: alphabetization and evaluation. Concerning alphabetization, we took reference on Psychogenetic studies of Ferreiro and Teberosky (1985) which emphasizes fundamental points for a coherent evaluation practice: a) objective knowledge is not a beginning data; it is a construction process, which the learner does not conquest step by step on a linear way; b) objective knowledge acquisition happens through a global re-construction, and some of them may seem mistakes if we consider conventional writing but these mistakes are constructive and necessary. We also took reference on Interactionist-constructivist theory. Here, Vygotsky (1984) proposes that writing must be specially understood as language, symbolical activity, cultural practice. So, acquisition of writing process, as language learning, must be understood as a development of abilities relative to symbolical and communicative activity of sense production. On this way, Hoffmann (1994) advises that is necessary to overtake current evaluation practices, limited by their terminality character, only pointing right or wrong questions. According to a new paradigm, valuation appears as one of the mediations by which teachers must indicate re-ordination of pupil s knowledge, and re-organize their own practices too. The comprehensions of these questions plays decisive part in order to overtake our difficulties in evaluating. Besides, it points a way to build a coherent valuate practice, with an emancipating character and able to create new teaching-and-learning situations, leading to a better alphabetization Pedagogy

O Evangelho segundo a Pastoral da Criança :por uma pedagogia da sobrevivência

This work aims to analyze social and educational actions at Pastoral da Criança, using education as a survival tool. This was done at Parque dos Coqueiros, a neighborhood in Natal, Rio Grande do Norte. The methodology for data collection was composed of comprehensive interview (Jean Kaufmann), participant observation (Robert Bogdan) and documental analysis (Le Goff); all os which bring reflections related to concepts such as strategies, tatics and know how (Michel de Certeau), configuration (Nobert Elias), and control technology (Michel de Foucault), care ethics (Leonardo Boff) and etno-theories (Natália Ramos). Pastoral da Criança is a social action organism that belongs to the National Conference of Bishops of Brazil, originated at Florestópolis, Londrina (Paraná), in the year of 1983. These actions have been an expression of a new logic of actions of the Catholic Church. It values the participation of laymen in the activities of the Pastoral. Thus, the parish is seen as a nucleus that irradiates the Church s Social Doctrine. At Rio Grande do Norte this institution has guided poverty stricken families on issues related to children s health as well as working with laymen for volunteer work. This is considered devotion, that is firmed by an individual and group mystique. The social and educational actions are done in three axes: 1) Monthly home visits, where there is mother-child support; 2) Life Celebration Day, where they weigh children and promote nutritional surveillance; 3) Meeting for Evaluation and Reflection, that aims to articulate community leaders to think about problems attached to the social actions they realize. This action tripod , as it is called by the Pastoral Agents are the types of actions that fundament survival education for poor children ranging from 0 to 6 years old. The families learn to deal with prevention, the essential, the alternative and probabilities of survival tactics due to exclusion matters or even social extermination. The Pastoral da Criança aims to recover childhood emotions in poverty stricken areas. It also has influence in the diminishing of malnutrition and mother and child mortality. This education for survival is the base on the art of teaching and learning of poverty stricken children. It is a social educational action, non assistencialist, but considered a shy action in order to promote mobilization of the communities that are accompanied for the emancipation and change of social conditions

O projeto politico pedagógico de enfermagem e o sistema único de saúde: a visão de discentes

This research aims to analyze, in the view of students, the pedagogic project of undergraduate nursing course, of UFRN, and its articulation with the SUS, in an attempt to understand the issues that permeate the teaching and learning of nursing. This is a qualitative study that used the focus group technique as a tool to collect empirical data. There were three meetings, where we had the collaboration of 23 graduating students from the eighth period of the semester 2009.1. For the analysis of information, we use a theoretical framework based on curriculum guidelines and basic principles of the SUS, making the analogy of the results with the metaphor of Greek mythology, Ariadne's thread, in dialogue with authors who discuss education as a transformative practice. Thus, the texture of the yarn was built of five thematic fields: joint the pedagogic project with the SUS; the teaching/service and theory/practice relation; interdisciplinarity or transdisciplinarity; didactic/methodological and relational approaches; and co-participation of students in the pedagogic project. According to the discussions, we find many difficulties in the teaching and learning process of undergraduate nursing in UFRN to strengthen the SUS, including: dislocation of educational institutions with services, professionals, managers and community; dichotomy between theory and practice; reality of services as a learning field and working process in health; posture adopted by professionals, teachers and other subjects included in the process of health education; decontextualization and fragmentation of teaching with the practice in health and nursing; excessive use of very illustrative methodologies, but little problem-solving; difficult and precarious situation in the relations between teachers and between teachers/students, regarding the acceptance of differences; absence of participation of students in the evaluation process and conduct of the educational project in progress. In this sense, we understand the need an auto-reflexive act of teaching and conducting collective pedagogical course with a view to achieving the SUS. Thus, it is necessary to support practices motivated by the polyphonic dialogue and the exercise of symbiosis and autopoiesis of subjects/actors jointly responsible for the ongoing process of learning for life.

Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

História da matemática na formação do professor: dificuldades e sugestões

This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Luís de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation

Uma proposta de ensino e aprendizagem de Língua Inglesa integrada ao uso das TICS para o desenvolvimento da autonomia dos aprendizes

This study focuses on the teaching and learning of English based on a new theoretical perspective concerning the Zone of Proximal Development (ZPD), which points to the apprehension of metacognitive processes as the way to reach learning autonomy. The theoretical set underline this study is those of a new pedagogy based on the symbiosis of Bruner‟s (2002) and Freire‟s (2009) concepts and in the metacognitive theory. In a social context dominated by the Communication and Information Technologies (CIT), the integration between teacher and learners with the support of the internet has been used as the way to operationalize this new emergent proposal of the theoretical perspectives. The analyses have been conducted through Systemic and Integral Action Research. The results at the end of this study corroborate our hypothesis that the enlargement of spontaneous knowledge of the learners can facilitate the understanding of scientific concepts, stimulating their metacognition and thus promoting their autonomy.

Estratégias de relativização no português brasileiro e implicações para o ensino: o caso das cortadoras

This work consists of a cognitive-functional approach of relativization strategies of Brazilian Portuguese (BP), this is, standard relatives (with preposition or without it) and non-standard relatives (copiadora and the deletion pattern), and it emphasizes the last one. We investigate the use of the relative construction strategies in spoken and written texts produced by speakers from different school levels in a specific situation: a face-to-face interviewing. Our database is the corpora Discurso & Gramática: a língua falada e escrita na cidade do Natal e a língua falada e escrita na cidade do Rio de Janeiro. We contrast the use of the standard relative to the deletion pattern in prepositional context, by considering cognitive, social and interactional motivations for the use of the deletion pattern instead of the standard one. Our research leads us to verify that the deletion pattern is fixing as the preferred relativization strategy in prepositional contexts, and, in this way, it brings out a grammaticalization process in working. For this reason, we propose to take this relative construction as a common way to structure a relative clause, in the same way we take the standard pattern. Finally, we discuss the treatment of questions related to the processes of teaching and learning of Portuguese language and some suggestions are given in terms of class activities. We expect that the development of this research may give both support for the Portuguese teachers and suggestions to improve the teaching and learning process of Portuguese language, contributing in special to the treatment of the syntax of complex clauses.

Representações discursivas de Ficar e Namorar em textos de vestibulandos e pré-vestibulandos

This doctoral thesis investigate the way vestibulandos and pré-vestibulandos construct their discursive representations of Ficar and Namorar in their textual production. At the same time, aims to discuss its implications for the ATD and for the teaching and learning of textual production in the context of Portuguese Language classes. Its theoretical framework is inspired mainly by three sources: textual linguistics, the textual analysis of discourses (ADAM, 2008), as well as by frames semantics (FILLMORE, 2006; FELTES, 2007). The methodology is based on a combination of qualitative and quantitative approaches (VIANNA et al., 2008). The data is composed of 168 empirical texts written by the vestibulandos of PSV/2005 da UFRN, Natal, RN, and by secondary school students who attended Escola Estadual Juscelino Kubitschek (EEJK), Assú, in the 2008 school year. The results indicate different categories of discursive representations of Ficar and Namorar , such as designation of referents, prediction, aspectualization, spatial-temporal circunstances , and metaphor, which reveal the influence of factors such as: the encyclopedic knowledge, the culture, as well as the cognitive components related to textual production. These results point out to the necessity of a teaching practice which enables the interaction among students, the discussion of current themes, as well as the student involvement with different textual genres, mainly the work with textual production in the classroom, so that it enables the students do acquire the textual production strategies. Thus, the overall goal is the (re)construction of their discursive representations, so that they can cope with new contexts of communicative interaction.

As práticas exitosas de leitura no ensino fundamental: vozes sociais de professores e de estudantes

The school is the social place which should provide the formation of critical readers. In this context, the role of the teacher is crucial when it comes to teaching reading. Thus, this doctoral research aims to explicit the reading practices evidenced from social voices of teachers and Fundamental School students from state public schools at RN that have successful results, according to IDEB 2009. Moreover, we seek to explicit, through the positions of teachers, the conceptions of reading underlying their reading activities, as well as elucidate the social voices related to teaching of reading that are present in the National Curriculum Guide for 9 years Fundamental School and in the Political-Pedagogical Projects of the educational institutions investigated. In order to accomplish this goal, we carried out observations in the classroom, applied questionnaires with teachers and students in the 9th grade of Fundamental School, in classes of Portuguese Language, and also performed dialogical meetings with the management and pedagogics schools teams. The theoretical foundation that guides the research comes from bakhtinian thinking (2009, 2010), which addresses the dialogical perspective of language and active responsive comprehension. Furthermore, this work is anchored in theoretical reflections of Antunes (2005, 2009) and Geraldi (2003, 2006, 2010) about the reading and writing in the country, which contribute to the resizing of the teaching and learning process of Portuguese Language. This study belongs to the field of Applied Linguistics, which investigates language as social practice in the context of learning mother language or in contexts where relevant questions about the use of language are evidenced. The parameters of qualitative research in a social-historic perspective are adopted seeking to understand the school context by the subjects involved in research. The research corpus is composed of: (i) information constructed through the use of questionnaires with teachers and students; (ii) information constructed from the observed lesson and dialogue with management and pedagogical teams; (iii) a set of selected information, i.e., empiricism built through documentary analysis of the National Curriculum Guide for 9 years Fundamental School (CONSELHO NACIONAL DE EDUCAÇÃO, 2010) and the Political- Pedagogical Projects of the investigated schools. The analysis of the sayings of teachers and students suggest reading practices from various texts, in particular, from the literary sphere, in activities involving discussions, reading and reading comprehension exercises, interviews, songs, seminars organizations, concerts, dramatizations, literary weeks, among other practices. Furthermore, these analyses reveal that teach Portuguese Language requires commitment, responsibility and satisfaction, as well as more grounded theoretical principles, which make teaching practice more efficient. The research also reveals that the success of the teaching-learning process occurs by virtue of the involvement of school s segments in the educational process, creating therefore a network of responsibilities. In this sense, this research may contribute to the production of knowledge that can guide and enrich the teaching and learning of reading, envisioning a pedagogical practice constructed from the relationship with the other, i.e., from the dialogism which provides formation of young people that exercise their citizenship