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