Investigação da capacidade intelectiva de pacientes pediátricos diagnosticados com tumores de fossa posterior

Central Nervous System are the most common pediatric solid tumors. 60% of these tumors arise in posterior fossa, mainly in cerebellum. The first therapeutic approach is surgical resection. Malignant tumors require additional strategies - chemotherapy and radiotherapy. The increasing survival evidences that childhood brain tumors result in academic and social difficulties that compromise the quality of life of the patients. This study investigated the intellectual functioning of children between 7 to 15 years diagnosed with posterior fossa tumors and treated at CEHOPE - Recife / PE. 21 children were eligible - including 13 children with pilocytic astrocytoma (G1) who underwent only surgery resection, and eight children with medulloblastoma (G2) - submitted to surgical resection, chemotherapy and craniospinal radiotherapy. Participants were evaluated by the Wechsler Intelligence Scale for Children - WISC-III. Children of G1 scored better than children of G2. Inferential tools (Mann-Whitney Ü Test) identified significant diferences (p ≤ 0.05) between the Performance IQ (PIQ) and Processing Speed Index (PSI) as a function of treatment modality; Full Scale IQ (FSIQ), PIQ and PSI as a function of parental educational level; PIQ, FSIQ, IVP and Freedom from Distractibility (FDI) as a function of time between diagnosis and evaluation. These results showed the late and progressive impact of radiotherapy on white matter and information processing speed. Furthermore, children whose parents have higher educational level showed better intellectual performance, indicating the influence of xxii socio-cultural variables on cognitive development. The impact of cancer and its treatment on cognitive development and learning should not be underestimated. These results support the need to increase the understanding of such effects in order to propose therapeutic strategies which ensure that, in addition to the cure, the full development of children with this pathology

As compreensões do construtivismo de Ernst Von Glasersfeld e John Fossa: intermediando um diálogo em busca de novas significações

The present thesis, orientated by a letter sent by Ernst von Glasersfeld to John Fossa, is the product of a theoretical investigation of radical constructivism. In this letter, von Glasersfeld made three observations about Fossa’s understanding of radical constructivism. However, we limited our study to the second of these considerations since it de als with some of the core issues of constructivism. Consequently, we investigated what issues are raised by von Glasersfeld’s observation and whether these issues are relevant to a better understanding of constructivism and its implications for the mathema tics classroom . In order to realize the investigation, it was necessary to characterize von Glasersfeld’s epistemological approach to constructivism, to identify which questions about radical constructivism are raised by von Glasersfeld’s observation, to i nvestigate whether these issues are relevant to a better understanding of constructivism and to analyze the implications of these issues for the mathematics classroom. Upon making a hermeneutic study of radical constructivism, we found that what is central to it is its radicalism, in the sense that it breaks with tradition by its absence of an ontology. Thus, we defend the thesis that the absence of an ontology, although it has advantages for radical constructivism, incurs serious problems not only for the theory itself, but also for its implications for the mathematics classroom. The advantages that we were able to identify include a change from the usual philosophical paths to a very different rational view of the world, an overcoming of a naive way of thi nking, an understanding of the subject as active in the construction of his/her experiential reality, an interpretation of cognition as an instrument of adaptation, a new concept of knowledge and a vision of knowledge as fallible (or provisional). The prob lems are associated with the impossibility of radical constructivism to explain adequately why the reality that we build up is regular, stable, non - arbitrary and publicly shared. With regard to the educational implications of radical constructivism, the ab sence of an ontology brings to the mathematics classroom not only certain relevant aspects (or favorable points) that make teaching a process of researching student learning, empowering the student to learn and changing the classroom design, but also certa in weaknesses or limitations. These weaknesses or limitations of constructivism in the classroom are due to its conception of knowledge as being essentially subjective. This requires it to work with one - on - one situations and, likewise, makes the success of teaching dependent on the teacher’s individual skills. Perhaps the most important weakness or limitation, in this sense, is that it makes teaching orientated by constructivist principles unable to reach the goal of the formation of a community. We conclud e that issues raised by von Glasersfeld’s observation are absolutely relevant to the context of a better understanding of radical constructivism and its implications for education, especially for Mathematics Education.

Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

Geometrizando no segundo ciclo :relato de uma intervenção pedagógica voltada à construção de conceitos geométricos no ensino fundamental

This work has proposed to relate the experience product of a pedagogical intervention, performed in a public institution of teaching situated in this capital. It had as objective to validade the applying of a teaching module of geometry, more specifically about the conceptions of perimeter and área in the second cycle of fundamental teaching. This dissertation has presented the problematic which involves the teaching of geometry in different contexts. It has adopted the broach of the radical constructivism while methodological theoretical referencial through which it has tried to explain the phenomena that involves the teaching and the apprenticeship. It appropriates Jean s Piaget contributions related to the development stages, while referencial that will dialogue in the search by sense and comprehension of the geometric apprenticeship process and it runs over Richard s Skemp (1980) theory in order to explicit the student s apprenticeship according to the levels of instrumental comprehesion and relacional comprehension . The research has presented datum related to initial diagnosis evaluantion, the pedagogical intervention and analysis of the activities and students perfomance displaying still the results of the final evaluation. According to the results got, we could check the students group growth front to the acquisition of the concepts of perimeter and área in comparison with the previous knowledges presented in the initial diagnosis evoluation of the students participants of the research. We have concluded evaluating the objectives of the research, connecting the strategies and reasoning employed by the students in order to resolve the questions and then to reach the objectives proposed by the teaching module. We have presented still the main obstacles to the apprenticeship of such concepts

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

Um estudo sobre a relação entre matemática e religião na obra de Blaise Pascal

The aim of the present study is to investigate the way through which the relations between Mathematics and Religion emerge in the work of Blaise Pascal. This research is justified by the need to deepen these relations, so far little explored if compared to intersection points between Mathematics and other fields of knowledge. The choice for Pascal is given by the fact that he was one of the mathematicians who elaborated best one reflection in the religious field thus provoking contradictory reactions. As a methodology, it is a bibliographical and documental research with analytical-comparative reading of referential texts, among them the Oeuvres complètes de Pascal (1954), Le fonds pascalien à Clermont-Ferrand (2001), Mathematics in a postmodern age: a cristian perspective by Howell & Bradley (2001), Mathematics and the divine: a historical study by Koetsier & Bergmans (2005), the Anais dos Seminários Nacionais de História da Matemática and the Revista Brasileira de História da Matemática. The research involving Pascal's life as a mathematician and his religious experience was made. A wider background in which the subject matter emerges was also researched. Seven categories connected to the relation between mathematics and religion were identified from the reading of texts written by mathematicians and historians of mathematics. As a conclusion, the presence of four of these seven categories was verified in Pascal's work

Pedagogia de projetos e etnomatemática: caminhos e diálogos na zona rural de Mossoró - RN

Teaching Mathematics in a contextualized and significant manner, in the world of the child and the adolescent, requires a solid theoretical and methodological basis on the part of the researcher. The present work found this foundation in two ways: teaching with projects and ethnomathematics. It is understood that these ways have points in common, such as: the real, interdisciplinarity, teaching methods, flexibility in sequencing the curriculum and interactive learning. This makes possible a theoretical cross-fertilization, which is important for the teaching/learning of Mathematics. Those points are merged in the present proposal, making possible new strategies, distinct from those of the Traditional Teaching Methodology and giving raise to an Alternative Teaching Methodology, which is to be lived in the Mathematics classrooms. This work gives a new direction to teaching, going beyond the traditional forms of education by allowing the teaching of Mathematics to become integrated with other school subjects, resulting in significant learning. In order to implement the proposal, it is necessary to form partnerships with teachers, pupils and the whole community, so that the way can be traced by continual dialogue

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Espaços transversais em educação matemática :uma contribuição para a formação de professores na perspectiva etnomatemática

This PH.D. thesis is an attempt to show the beginning, evolution and unfolding of the making of a pedagogical work proposal based on culturally-built knowings in the heart of a traditional community, having as one of its starting points the knowings and doings experienced by dish-making women from Maruanum living in the city of Macapá, State of Amapá, Brazil. This proposal is strongly associated with the need we have to think about the nature of (ethnological)-mathematical knowledge generated by particular communities and about the way such knowledge can be discussed, worked out, and validated in learning environments, regardless of the level of instruction and the constraints imposed by government programs and educational institutions. Among its theoretical foundations are studies on instrumental activities that are typical of the Maruanum ceramics and investigative studies from the point of view of ethnomathematics. Methodological development took place with the application of activities, where traditional and instrumental knowledge observed in the production of ceramics had been adapted for and brought into the school environment , participative observation, as well as data collecting and organization techniques, such as interviews, statements, and audio an visual recordings. Analysis of the data collected focused on the relationship between the data-generating potential and the purpose of this study. Our aim is to make and estimate of the potential contributions from local situations and/or problems it would possibly bring to the formative learning of people involved in the educational processes of these communities, with a view to a spatial and temporal transformation of reality

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

Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

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

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Problemas e modelos que contribuíram com o desenvolvimento do cálculo diferencial e integral: dos gregos à Newton

This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article