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

Participatory design in the project of virtual learning environment of histology

This present article describes a research on the development, under the approach of participatory design, a virtual teaching-learning of Histology in which students and teachers participated actively in all stages of development of the educational environment. We postulates that the development of virtual learning environment of Histology, through the Participatory Design approach, contributes to greater acceptance and use by students and that the adoption of virtual environment for teaching and learning by teachers is a determining factor of use by students

Como vão se formando os professores em física e química: embates entre o ser, o ter e o fazer na formação de licenciandos da UFRN sob a perspectiva da teoria das representações sociais

The purpose of this work is to approach and understand the Social Representations (SR) (MOSCOVICI, 2003) about Physics and Chemistry from people who are major in these courses, as well as their Social Representations about teaching . We took as principle that approaching these representations it would be possible to relate their symbolic contents, in order to show how people who are following the first segments of bachelor degree courses in Physics and Chemistry become teachers, taking into account a psychosocial view. Two source of data was used during this research: Free-association Technique FA (ABRIC, 1994); and Multiple Classification Procedure (MCP) (ROAZZI, 1995). The analytical treatment of the collected data from FA was done according to the proposition of Grize, Vergés and Silem (1987 apud ABRIC, 1994, p. 66). MCP data were analyzed through MSA (Multidimensional Scalogram Analysis) and SSA (Singular Spectrum Analysis) methods associated with the Facet Theory (BILSKY, 2003). The discourses of MCP discussing groups at the moment of explanations were studied by Content Analysis as it was proposed by Bardin (1977) and Franco (2005). Indicative of an approach to the relations with knowledge (CHARLOT, 2000), the connections which aroused from the analyses showed that the group of future majors in Physics thought that this scientific field was based on a rationalist conception, influencing the idealization sense of the phenomena to be explained by Physics. Thus, Physics as school content started to require the student of the fundamental and high school to think abstractly as a cognitive skill of learning. The identifying elements observed in the relations between SR about Physics and Teaching aroused from the antagonism between future majors and their teacher, as well as from the speculation between their fundamental and high school students and themselves, mainly when they had to face the act of teaching due to the obstacles imposed by the own educational system, and by the weakness of the initial preparation. The group of future majors in Chemistry, through its discourses, showed these relations when they conceived empiricist Chemistry and said that teaching was the way of transmission of this knowledge, and didactics of Chemistry teaching was the direction to learning through pedagogic methods in order to lead the students to discoveries. The psychosocial contents which were built and showed from the symbolic relations in the studied SR achieved the relation of identity. This relation revealed identifying elements for these people, resulting from the traffic between their condition as students of Chemistry, and as teachers regarding their work, what placed the current relational contents in the teaching space, named as Knowledge changing and Adaptability . In order to study emerging questions in the discussing environment about formation and teaching professionalization, we focused the psychosocial view on this traffic and managed to observe epistemological practical and pedagogic obstacles that limited a configuration of the teaching work as a professional activity, especially from the particular conditions which led the relations of senses to Physics , Chemistry and Teaching ; and Chemistry and Physics as it was seen in this research. Generally speaking, we noted that these obstacles can denounce such obstacles concerning to the pedagogic doings which mainly impair the learning process of fundamental and high school students

Os ateliês (auto)formativos na constituição do sujeito docente da educação matemática

The object of study of this thesis is the use of (self)training workshops as a fundamental process for the constitution of the teaching subject in mathematics education. The central purposes of the study were to describe and analyze a learning process of mathematics teachers supported by the training-research methodology, which procedures have been affected with the practice of (self)training workshops as a way of collaborating to the constitution of the teaching subject in Mathematics Education. The survey was conducted with a group of teachers in the city of Nova Cruz, Rio Grande do Norte through a process of continued education realized in the training workshops having as main goal the realization of the group s (self)training sessions in order to lead participants to the extent of their autonomy in their personal and professional transformations. The results obtained in the formative processes have shown the need to develop activities of mathematics teaching as a contribution to overcome the conceptual difficulties of the teachers, apart from their (self)reflections about themselves and the educational processes in which they belong. The results raised some propositions about (self)training workshops that may be incurred in practices to be included in the curriculum frameworks or materialize as a strategy of pedagogical work in training courses for teachers of mathematics. Also, they can constitute an administrative and educational activity to be instituted in the public schools of Basic Education

A aproximação entre educação escolar e trabalho: a experiência da Casa do Menor Trabalhador

It aims to consider the possible relationship between formal school education and work, from the experience of the State School House of the Minor Worker CMT of Natal-RN in this first decade of the 21st century. In this institution, children and adolescents are enrolled in the Fundamental Teaching sponsored by the State Public System studying the regular curriculum contents defined for this level of teaching, and in the opposite shift they take part in career workshops which are kept by members of a religious congregation. CMT has had as its object, since its foundation, to take children and adolescents from the streets and to provide them with a full time education associating basic education and training/qualification for the job market. In our research, we tried to learn a little bit of the expectations, concerns and knowledge of the young participants of two workshops: carpentry and bakery, so that we could gain sufficient understanding of the learning process of these youths, while still keeping an approximation with the reality of the aforementioned subjects. It was possible for us to conduct a description of the contexts and of characteristics of the subjects which make up CMT, capturing concrete aspects and aspects of the thoughts of students, teachers, instructors and coordinators. The main point of our research was: how does the approximation between formal school education and work take place in the House of the Minor Worker? To search for possible answers we have made use of basic techniques for the data construction - questionnaire, observation, conversation groups, assessment drills which allowed an approximation and a good dialogue with the participants. We also discussed the job world in the context of the capitalist exploration, from the contributions of Mèszáros (2005), Frigotto (1989); (1993); (1999); (2002); Ferretti (1994); (2004); Kuenzer (1989); (1997), in order to understand the skills demanded of the worker and the necessity of an education which allows the professional qualification of youths eager to enter the job market, through the first job. In this perspective, the study that we have systematized here aims to show the relevance of an education which manages to take a firm and conscientious stand in connection with the hegemonic capitalist project and to provide for a humane, ethical, responsible, critical and civic background

Um estudo sobre a aprendizagem de números irracionais no ensino médio

The present study describes theoretical practical relationships between development and application of activities in Mathematics education. It s proposed a methodological approach to Mathematics in the first grade of Ensino Médio, supported by an experiment involving Irrational Numbers education by using constructive activities, applied obeying an educational sequence. Constructivism is used as an important theoretical reference in teaching learning process of Mathematics. The methodological intervention was done with two classes of students of the first grade of Ensino Médio, in two public schools, a state one and a federal one, located on the city of Natal, Rio Grande do Norte. The development, application and testing of the activities used on this experiment led us to think more profoundly about the value of constructivism ideas and understand that the use of activities that obey an educational sequence favors the learning. It s also discussed the research results, commented on a way to contribute to the advances of the proposal and it s more constant use. The participation and testing of the students were analyzed and judged using Skemp s Instrumental Understanding and Relational Understanding concepts. The results of the research were considered good, so we believe this methodological intervention can be used more frequently in the classes of Ensino Médio and also be applied to teachers in courses of initial education and continuous formation

A função mediadora do planejamento na aula de leitura de textos literários

This dissertation sutdies the mediative function in the planning of literary text reading classes of Portuguese. Its main central focus proposes that planning favors the pedagogical reading work of literary texts in the teaching of Portuguese, for they are regarded as one of the mediative elements the teaching-learning process. It also allows for its subjects to rethink the practice, theorizing it. As a theoretical basis the studies on participative planning are used, especially the studies concerning dialogic planning. The language/literature teaching perspective adopted in this work is guided by the socio-interactive conception of language, in a way that reading is seen as a comprehensive and interactive activity. Given the research process, the analysis of the reading process involved the Reader s Response, once that this theory considers the role of the reader and her/his interaction with the text. The study is grounded upon the following research question: which role(s) does the pedagogical planning play as a mediator of the reading teaching-learning process? The main objective of this dissertation is to investigate the pedagogical planning activity as a mediative instrument in the practice of reading in the Portuguese classes. The study is constituted of three stages, the third being emphasized (2002/2005) in which the direction of the participative action-research was used, as a way of acknowledging the pedagogical role in the teaching plan, as an instrument capable of rendering reorganization in the teaching-learning process of reading classes. We have as participants teachers of Portuguese in the elementary school (Ensino Fundamental, 3º ciclo), besides other segments of public schools, in the city of Pau dos Ferros RN, in which the previous studies were developed. The results point to the relevance in the role of the teacher, as a more experienced reader, in developing of pedagogical strategies that may come to favor the teaching of reading, having in the pedagogical sphere an instrument of theoretical reflection and sistematization of activities to be implemented in the classroom. The conclusions highlight the class plan as the mediative instrument to be incorporated and internalized into the teaching practice, amplifying and modifying the teacher s intervention forms, favoring, thus, her/his pedagogical mediation

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.

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

Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

Citologia: uma proposta formativa na EaD - UFRN a partir de concepções alternativas

Learning difficulties can have a direct influence on the teaching-learning process of students by reducing their school performance. One factor that may contribute to this negative influence on learning refers to the presence of alternative conceptions, which may have different origins in the educational process. It is of paramount importance, for teachers, for example, to identify the concepts and the difficulties of their students in order for that knowledge can be able to contribute significantly to improve the teaching and learning process. From the following considerations, the present study (still in progress) aims to investigate aspects related to the concepts and difficulties of graduating students in relation to the contents of Biology. The participants of the research were undergraduate students in Biological Sciences from UFRN, studying by Distance Learning (Educação a Distância). To develop the survey, questionnaires were developed to identify the contents in Biology that these students have more difficulties as well as an interview to raise misconceptions regarding the content of cytology. Another tool developed was a textbook evaluation form, which was applied in conjunction with a questionnaire in workshops (short courses) in order to identify possible errors and mistakes that could jeopardize the process of teaching and learning, such as the importance that these learners assign to textbooks in the educational process. From the data collected, a booklet on the content of cytology was developed as a product. It is expected that it can be applied in classrooms in order to improve the teaching and learning in references to Biology, to minimize, for example, alternative conceptions than can occur related to the theme

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.

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

Referências culturais e heterogeneidade discursiva :Uma proposta para o ensino-aprendizagem de língua inglesa

The purpose of this research is to approach the English literary text from the point of view of the culture and the heterogeneity of discourse in its role as a source of elements that facilitate the teaching/learning process of English as a foreign language. Several instances of discourse heterogeneity are analyzed through cultural references in the original texts of the following English novels: Jane Eyre, by Charlotte Brontë (1816-1855), published in 1847; The Mill on the Floss, by George Eliot (1819-1890), published in 1860 and Great Expectations, by Charles Dickens (1812-1870), published between 1860 and 1861. Theoretical support was sought in Kramsch, Bakhtin, Maingueneau, Authier-Revuz, Widdowson and Larsen-Freeman. Activities in English are proposed in the end whereby it can be seen that the questions at issue can be used extensively in the classroom.

Análise das dificuldades de aprendizagem numa disciplina de química orgânica do curso de química na modalidade à distância da UFRN

In today`s society the use of so-called information technology and communication (ICT), is promoting a revolution in the forms of teaching and learning through the methods of distance learning courses, especially in higher education. Studies show that students in this way have great difficulties in the learning process, especially when dealing with experimental subjects that require high power of abstraction as chemistry. The goal of this work is to promote improvement in the teaching and learning in the discipline Chemistry of Life offered for the Bachelor`s Degree in Chemistry in distance UFRN. For this we analyzed evidence of the semester 2011.2, in order to identify what are the main difficulties of the students on the assessments. That`s why video lessons related to matters that create the majority of difficulties for students were developed, the final product this work. Being obtained the improvements by video classes in the learning process of the students, from a questionnaire answered by the students in the virtual learning environment, and from their success rate at the end of the course