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

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course

O pedagogo como agente de transformação social para além dos muros escolares

This thesis concerns the problem about the pedagogue actuation in the social education into no scholars places. It search to understand the context and the social pedagogue role to his praxis and formation that enlarger the possibilities of the social educative practices into no scholars places. In this direction, we developed an investigation about the actuation of the pedagogues-educators in Natal city, in the 2007-2010 periods, into Municipal Secretary of the Labor and Social Assistance (SEMTAS). Considering that pedagogues are regularly attached in social educators profession as municipals public employees, we re the objective to evaluate their role into the social executed in the no scholars places, with the focus in the environmental dimensions of theirs work s places, pedagogical organization, institutional management and the professional formation. It privileged in this research the Specialized Reference Center of Social Assistance II (CREAS II), the Passages Houses I, II and III, the Social-Educative Measures in Open Environment Execution Program of Natal city (PENSEMA) and the Pitimbú Educational Center (CEDUC-Pitimbú). To realize this study it developed a research with qualitative nature by critic ethnography approach privileging those information collected with the social pedagogue-educators of the mentioned places. Through the methodological procedures adopted; beyond the bibliographical review we remarked the documental research, the semi-structured interview, the questionnaires-routes and the field observations. The analytical results revealed that the politics to the social education in Brazil historically came been dimensioned by the fight of social movements demanding the fundamental rights to the excluded people; that the SEMTAS politics of social education present a relative basic social protection to the excluded children and young people specially into law view; that the politics of social education in Natal city it s close of the logic of sanitarian attention about the disadvantaged groups; that the conceptual, methodological and formatives fragilities needs to the social pedagogues-educators praxis into non scholars places made difficult the operation capacity of a educative proposition anchored in a institutional action guided by the idea of emancipator education; that the SEMTAS take face several difficulties to developed a web assistance as preview in the reception proposition elaborated by the social pedagogues-educators. However in despite the tensions we remarked the value of this potentiality to the non scholar social education in her attempt to constitute herself in a legitimate space to the pedagogue professional actuation. In despite the obstacles to work and formation quotidian, across those non scholar spaces in the municipalities institutes to the social politics, it demonstrated personal sensibility and professional creativity in learning mediations and educative action to the children and younger derived from exclusion process and the social iniquities

Educação inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

Educação inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

SINAES: as diferentes faces da avaliação na UFRN

This thesis entitled SINAES: the different faces of the evaluation at UFRN, aims to analyze the configuration that the national policy for assessment in higher education has taken on UFRN. We assume that in recent years there are an oscillation between the concepts of evaluation, according with the logic of public administration it has preferred an approach that presents itself as a promoter of quality, sometimes with regulatory aspects, sometimes with educational ones. The text discusses the use of the new assessment tools for higher education placing them under the new demands on state reform context in which this is to promote and measure quality based on the values of excellence and competitiveness. This movement arises from the redefinition of the role of the State that has been taking features of Evaluator State. From a historical review of government initiatives in the field of evaluation, we analyze the characteristics of assessment policies outlined over the past decades. We are based on the theoretical method that aims to examine the multiple determinants that shape a particular reality from the larger movement of totality. To identify, in this case, connections and ruptures that have emerged over the history of assessment policies aimed at higher education by checking their determinants in order to better explain the reality. To investigate the object of this study we used as instruments: the research literature and research documents, the semi-structured interviews and non-participant observation. The study revealed that there are different practices of evaluation and that before to establishment the SINAES program, the UFRN already had a culture of an institutional assessment, more participatory and democratic, opposing to the rigidity of the self-assessment in SINAES program that it was instituted by the Commission for assessment (CPA). We also noticed that the implementation of the SINAES at URFN has been performed very slowly and the breadth and complexity of the evaluation process has contributed to hinder its implementation in all dimensions provided by MEC. Although it was observed that in its operationalization the SINAES has assumed a more normative assessment and directed to establish rankings between courses and higher education schools than to establish a more qualitative assessment in this system. As regards the evaluation of the undergraduate course studied on this research and subjected to the three dimensions of evaluation proposed by SINAES (self-assessment, Evaluation of Courses and ENADE) it was not possible to verify an effective integration between the methods of assessing conducted. The results are considered separately, in only a partial view of the course evaluated the proposal what pits the SINAES as a system that involves the totality

A implementação do programa Gestão nota 10 no sistema municipal de educação em Mossoró/RN (2005 a 2009)

This research work is focused to show the changes in educational administration from the agreements between the Mossoró / RN and the Ayrton Senna Institute IAS, for education provision. Nowadays, the partnership policy is a constitutive element of the reform of the Brazilian State, which dropped its action on social policies and to strengthen its regulatory role, encouraging private participation in planning, preparation and implementation of public policies, new printing setting the political-social. In this context, the 10 Note Management Programme, developed by the IAS, is part of the neoliberal logic of modernization of public school systems, focusing on results and developing strategies for control and regulation of schools work and its efficiency, effectiveness and greater productivity. The 10 Note focuses on two dimensions: the management of learning and teaching in networking, in a managerial perspective to overcome the culture of failure (expressed as age-grade, dropout and repetition rates in) and implantation of culture of success (as measured in the improvement of the indices). To understanding the process, we have delimited as the object of study, the process of implementing them mentioned program in the city, which its objective is to analyze implications for the school community from the perspective of democratic management, adopting the dimensions of autonomy and participation in institutional processes as a criterion of analysis. From a methodological point of view, the survey was conducted from a literature review and documentary about educational policy developed in the country since the 1990´s, seeking to understand, in a dialectical perspective, the political dimensions of teaching, training and performance of the subjects involved in the school work. Besides the empirical observation, it was also used semi-structured interviews with a methodological tool for gathering information and opinions about the partnership and the implementation of the 10 Note Management Program in the county. The interviewee participants were ex-former education managers, coordinators, school managers, secretaries and teachers. Regarding the dimensions inside the analysis (autonomy and participation), the research led to the conclusion: that GEED, under the guidance of IAS promoted regulation of school autonomy, set up the selection process for exercising the office of school administration and system awards to schools, pupils and teachers, subject to results, there is mismatch between the managerial logic and the democratic management principles, that the ideological discourse of modernization of municipal management coexists with traditional practices, centralizing patronage, which ignores the democratic participation in the school decisions processes, the goals of the partnership were partially achieved, since that the city has improved over the approval and dropouts, although the approval of the Education Municipal Plan of the rules institutional (administrative, financial and educational) and the creation of the Councils observed that the school community participation is still limited, not being characterized as a coordinated intervention, capable of promoting the transformation and improvement its quality in the county. In the same way, the orientation of networking is a limit to the autonomy of schools, given the external definition of goals and strategies to be adopted, along with pressure exerted through the accountability of each school community for their achievements

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

Mestres e aprendiz: perambulando por ilhas de resistência

Monoculture of mind This idea, presented by Vandana Shiva, reflects the phase that we have experienced in the world: a notion of civilization that, since many decades, characterized by a technocratic big trend, has been shown as dominant and hegemonic. Based on a thinking and acting, felling and whishing standardization, this wave ends implying in what can be called of humanity‟s crisis at civilizational process. Destruction of simpler and more harmonious lifestyles with nature, human relations increasingly distant, values embrittlement, as respect, goodness and love, are some consequences of that behavioral homogenization. In the other hand, appears an archipelago of cultural and cognitive resistance against this devastating wave. Edgar Morin and Ceiça Almeida refer to this archipelago as a South Thought , what is not just a geographic question. Report, therefore, to some places, peoples, island that keep ancient costumes and knowledge, orally transmitted, for instance, from elders to younger, or vice versa, in an almost constant flow. Particular ways of experiencing the world around themselves, the men, animals, plants, rocks, or even not alive beings, masters or enchanted, spiritual guides. Next to a logic of sensitive, as Claude Levi-Strauss proposes, this reading, which is a more attentive, observer and wiser posture of surroundings, is based on touching, smelling, eating, seeing, and, I would add, felling. In light of this, I try to expatiate about certain experiences that I had the pleasure of living in some of these islands of resistance. Talks, perceptions, observations, sensations Stories, prose, poetries, music, photos, graphics Whatever could serve to portray even a bit of the reflections and forms to understand (ourselves) and produce knowledge, such as from a formation/Education to life, was well used at this ethnographic work. Space to the subjectivity and emotions I had, have, and will have a lot Everything for the dear reader may fell traveling around the world of tradition, resistance

Análise de critérios de decisão em estratégia de arranjos produtivos locais: um estudo aplicando o processo de hierarquia analítica (AHP) no setor de cerâmica

This master thesis has the objective of investigating the strategic decision criteria of participants of Local Production Arrangements (LPA) in Brazil. The LPA s are an initiative of support agents to enterprises with the purpose of organizing joint actions for the development of groups (clusters) of enterprises. The choice of the actions is a decision of the participating enterprises and this paper aims at applying a Multi-criteria Analysis Method to analyze the criteria of entrepreneurs that are participating of a LPA. The used method is the Process of Analytical Hierarchy (PAH) and an application is presented along with questionnaires to participants of a ceramic LPA in the northeast of Brazil. The main results show that, in first place, from the implicit strategy of each enterprise there is only one objective for the LPA group and so, at the beginning, an action decided by all of them tends to favor some more than others. In second place, it was observed that there are general inconsistencies between the strategic objectives and the importance as to criteria, even though there have been cases of coherency. As the main conclusion it is pointed that the use of Methods of MCDA is useful to improve the decision making process and to bring more transparency to the logic of the found results

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developing the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. It s important to point out that, in spite of the loads being normally connected to the transformer s secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Uma Fundamentação Intervalar Aplicada à Morfologia Matemática

This work present a interval approach to deal with images with that contain uncertainties, as well, as treating these uncertainties through morphologic operations. Had been presented two intervals models. For the first, is introduced an algebraic space with three values, that was constructed based in the tri-valorada logic of Lukasiewiecz. With this algebraic structure, the theory of the interval binary images, that extends the classic binary model with the inclusion of the uncertainty information, was introduced. The same one can be applied to represent certain binary images with uncertainty in pixels, that it was originated, for example, during the process of the acquisition of the image. The lattice structure of these images, allow the definition of the morphologic operators, where the uncertainties are treated locally. The second model, extend the classic model to the images in gray levels, where the functions that represent these images are mapping in a finite set of interval values. The algebraic structure belong the complete lattices class, what also it allow the definition of the elementary operators of the mathematical morphology, dilation and erosion for this images. Thus, it is established a interval theory applied to the mathematical morphology to deal with problems of uncertainties in images

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developping the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. Its important to point out that, in spite of the loads being normally connected to the transformers secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Um hipermídia sobre fases da lua para o ensino de astronomia a distância

The interdisciplinary nature of Astronomy makes it a field of great potential to explore various scientific concepts. However, studies show a great lack of understanding of fundamental subjects, including models that explain phenomena that mark everyday life, like the phases of the moon. Particularly in the context of distance education, learning of such models can be favored by the use of technologies of information and communication. Among other possibilities, we highlight the importance of digital materials that motivate and expand the forms of representation available about phenomena and models. It is also important, however, that these materials promote the explicitation of student's conceptions, as well as interaction with the most central aspects of the astronomical model for the phenomenon. In this dissertation we present a hypermedia module aimed at learning about the phases of the moon, drawn from an investigation on the difficulties with the subject during an Astronomy course for teaching training at undergraduate level at UFRN. The tests of three semesters of course were analyzed, taking into account also the alternative conceptions reported in the literature in astronomy education. The product makes use of small texts, questions, images and interactive animations. Emphasizes questions about the illumination of the Moon and other bodies, and their relationship to the sun, the perception from different angles of objects illuminated by a single source, the cause of the alternation between day and night, the identification of Moon's orbit around the Earth and the occurrence of the phases as a result of the position of observing it, and the perception of time involved in the phenomenon. The module incorporated considerations obtained from interviews with students in two poles where its given presential support for students of the course, and subjects from different pedagogical contexts. The final form of the material was used in a real situation of learning, as supplementary material for the final test of the discipline. The material was analyzed by 7 students and 4 tutors, among 56 users, in the period in question. Most students considered that the so called "Lunar Module" made a difference in their learning, the animations were considered the most prominent aspect, the images were indicated as stimulating and enlightening, and the text informative and enjoyable. The analysis of learning of these students, observing their responses to issues raised at the last evaluation, suggested gains in key aspects relating to the understanding of the phases, but also indicates more persistent difficulties. The work leads us to conclude that it is important to seek contributions for the training of science teachers making use of new technologies, with attention to the treatment of computer as a complementary resource. The interviews that preceded the use of the module, and the way student has sought the module if with questions and/or previous conflicts - established great difference in the effective contribution of the material, indicating that it should be used with the mediation of teacher or tutor, or via strategies that cause interactions between students. It is desirable that these interactions are associated with the recovery of memories of the subjects about previous observations and models, as well as the stimulus to new observations of phenomena