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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Atuação do enfermeiro na estratégia de atenção integrada às doenças prevalentes na infância

This study aimed to describe nurses' actions in the strategy of Integrated Management of Childhood Illness in the city of Natal, Rio Grande do Norte. This is a qualitative study with descriptive approach. The universe consisted of nurses from the Family Health Strategy, totaling 16 participants. For the research project was submitted for approval by the Ethics Committee of the Universidade Federal do Rio Grande do Norte, obtaining Opinion No. 187/2012. Data were obtained in two ways: a questionnaire survey to profile the training of nurses and an interview guided by a structured interview. Interviews were treated in the light of analysis of thematic category Bardin. The results showed the central thematic study "Integrated Management of Childhood Illness in the context of nursing activities" category and three analyzes: "Understanding the Integrated Management of Childhood Illness", "Difficulties invibializam use IMCI "and" Working conditions for nurses in the Integrated Management of Childhood Illness. " It is observed that nurses consider the Integrated Management of Childhood Illness useful, effective and important to keep sick children within the logic curative. However disregard the character of health promotion and disease prevention thereof. It was found that the participants still hold the attendance of crinaças within the biomedical model and that these same professionals are subjected to increasingly precarious working conditions and unhealthy due to lack of human and material resources. It was found that the interviewees do not follow the protocols of strategy because of barriers related to prescription medications by nurses, the medical, the lack of incentives, training and supervision by the municipal health and the Regional Nursing Council

Balanced Scorecard como ferramenta de avaliação da consistência estratégica: um estudo em instituição de ensino superior privada

This Master of Science Thesis investigates in an exploratory modeling the idea of strategy consistency applying as an assessment tool a model of performance indicators of a higher education institution based on the balanced scorecard (BSC). It is carried on a review of conceptual BSC perspective hierarchy models and of studies on higher education institution in Brazil and worldwide. From a BSC model with three indicators at each perspective is carried on a case study with directors and coordinators of a private higher education institution with a descriptive and multivariate analysis using cluster analysis. The main findings point to a different perception of respondents on the importance level of the perspectives with a higher importance level given to Learning and Growth and Process that to Customer and Financial. Particularly, the financial perspective got a importance level significantly lower that the others, what suggests an inconsistency on the strategy deployment on the institution considered in terms of the perception of the managerial levels of the importance level of the perspectives

Gestão estratégica no terceiro setor: uma análise comparativa da construção de mapas estratégicos de organizações sem fins lucrativos

The strategy has an important role in organizations by identifying factors that need to be emphasized to organizational success and strategic map currently contemplates as a preview of organizational strategy, prepared from your planning. Third sector organizations need to take a competitive posture, establishing a sustainable position and maximizing the use of resources towards their social or humanitarian goals. This research aims to investigate the process of building strategic maps of two non-profit organizations by identifying and characterizing the steps common to these organizations. The research is characterized as qualitative descriptive and applied knowledge. Developed from bibliographical reviews and participant observation gathered in a case study, the data was collected in two third sector organizations and the results show that how to conduct the process may influence directly on your result lists. Among the steps identified, emphasis can be given to the formation of a team, the definition of strategy, the definition of strategic objectives, the gathering of those goals into perspective and the identification of the cause-effect relationship that relate. Marked as optional, but effective, conducting an event outside the premises of the company to complete the process, or any portion thereof. However, stands out as essential the active participation of senior management in the process, as a way to give credit to the initiative. These steps, its characteristics and its factors are described from comparisons between the processes adopted by the organizations surveyed

Gestão de organizações sem fins lucrativos: uma avaliação de desempenho através do balanced scorecard

The methodology Balanced Scorecard (BSC) focuses on the major critical issues of modern organizations, whether with or without profit. The measurement of the effective performance of the latter is by evaluating the successful implementation of organizational strategy. The aim of this paper is to present the development of a system of performance measurement strategy for a nonprofit organization, whose object of study is the Associação de Apoio as Comunidades do Campo - AACC, in the context of the BSC methodology of Kaplan and Norton. The methodology of this case study is an exploratory, descriptive and qualitative, and diagnose the coherence of the Strategy Map in an organization, based strategic planning from 2010 to 2012. Initially conducted a literature review covering the main aspects of strategy maps and performance evaluation involving the translation of the BSC and strategy evaluation. The main results of the proposed approach refers to evaluation of overall scores for each dimension of the BSC methodology, financial, customer, internal processes, learning and growth. These results are able to help the organization evaluate and revise their strategy and, in general, to adopt management methods more accurately. Data collection is centered on interviews with semi-structured questionnaire. The findings highlight on balancing and alignment of strategic objectives, low causality map, strategic communication insufficient and fragmented. For interviewees organizational culture is the biggest impediment to structuring a management model based on indicators and strategic process should be initiated by non-financial indicators gradually. The performance indicators of the AACC/RN portray more meritocracy operational procedures of social projects in the context of the Strategic Map determined in a shortterm over the long term. However, there is evidence of improved performance management and strategic taken as a basis of planning as both the strategic map structured. Therefore, the nonprofits need to adopt a form of management that enables planning, setting objectives and targets that provide the continuity of its activities, and generating instruments that can measure the financial performance and non-financial, in order to develop strategic actions for growth and sustainability