Identifica����es do feminino em materiais did��ticos contempor��neos

Dada a persistente restri����o da presen��a feminina em diferentes espa��os-tempos das sociedades contempor��neas, desenvolvemos esta pesquisa com o objetivo de discutir os significados atribu��dos ao feminino em materiais did��ticos da atualidade. Partindo da hip��tese de que a educa����o escolar, embora n��o determine, participa dos processos sociais que resultam em tal quadro de subalterniza����o da mulher, focalizamos as apostilas utilizadas pelos anos finais do ensino fundamental das escolas p��blicas da rede da Secretaria Municipal de Educa����o da Cidade do Rio de Janeiro, durante o ano de 2013. Foram selecionadas as apostilas das disciplinas Ci��ncia, História e Matemática. Desenvolvemos tamb��m estudo sobre a apropria����o da no����o de g��nero na produ����o acad��mica recente da pesquisa em Educa����o, de modo a mapear e discutir sobre esta outra importante inst��ncia de atribui����o de sentido ao ser mulher. Em di��logo com o fil��sofo Jacques Derrida e suas teoriza����es sobre os processos sociais de constru����o de sentidos, nossas an��lises se basearam no entendimento de que as palavras possuem significados inst��veis, provis��rios e prec��rios, institu��dos de modo relacional e diferencial. Com as teoriza����es de Joan Scott e Judith Butler, trazemos as proposi����es de Derrida para pensar os mecanismos de produ����o do feminino no social, atrav��s do conceito de g��nero e da no����o de identidade performativa. Entre os resultados constru��dos, est�� a invisibilidade que a história das mulheres apresenta no material de História, a naturaliza����o de fun����es apresentadas como femininas nas apostilas de Ci��ncia e a reprodu����o de concep����es tradicionais sobre o lugar de meninas e meninos no corpus de Matemática. Mas conclu��mos tamb��m que os materiais did��ticos pesquisados j�� possuem concep����es menos sexistas na forma de significar o feminino, observando-se deslocamentos que sugerem certa hibrida����o. Por��m, esses deslocamentos s��o inseridos nos textos de forma t��mida, fazendo com que os postulados com maior poder de itera����o sejam aqueles que ainda reproduzem velhas formas de ser mulher e de ser homem, podendo refor��ar os estere��tipos de g��nero, caso n��o haja acesso a informa����es que se contraponham ��s encontradas.

A transmiss��o de conceitos matem��ticos para Portugal: integrais e fun����es el��pticas

Esta tese considera a transmiss��o de conceitos matem��ticos para Portugal no s��culo XIX, particularmente no campo dos Integrais El��pticos e das Fun����es El��pticas, tal como foi realizado no trabalho de Ant��nio Zeferino C��ndido. Depois de uma introdu����o hist��rica geral ao assunto no cap��tulo 1, o cap��tulo 2 estuda a vida de Ant��nio Zeferino C��ndido da Piedade. Ele foi, talvez, o primeiro matem��tico portugu��s a publicar uma tese sobre este assunto. A parte principal, isto ��, o cap��tulo 3, �� dedicada �� an��lise do seu trabalho ���Integraes e Func����es Ellipticas���. Mostra detalhes da sua abordagem baseada, n��o s��, no livro dos autores Franceses Briot e Bouquet, mas tamb��m do autor alem��o Schloemilch, o que reflecte as mudan��as que ocorreram naquela ��poca na lideran��a matemática na Europa.

Tanto para ensinar, outro tanto para aprender!

Este relat��rio descreve a experi��ncia adquirida no decorrer de uma cadeira do mestrado em ensino da matemática no 3��.ciclo do ensino b��sico e no ensino secund��rio denominada pr��tica de ensino supervisionada (PES). A PES, dividida em tr��s per��odos coincidentes com os per��odos escolares, teve in��cio numa escola secund��ria. O segundo per��odo decorreu numa escola b��sica e o terceiro per��odo foi dedicado �� elabora����o do presente relat��rio e �� apresenta����o de dois semin��rios, cada um deles apresentando uma planifica����o de uma unidade da disciplina. A escola, o sistema educativo portugu��s, o ensino da matemática, a história da matemática, o uso de materiais manipul��veis e a tecnologia na sala de aula s��o temas te��ricos abordados neste trabalho. Neste trabalho est��o descritas as minhas viv��ncias, as dificuldades sentidas, o trabalho realizado, as reflex��es feitas ap��s cada per��odo e uma reflex��o final sobre todo o percurso desenvolvido.

Um estudo sobre as origens da L��gica Matem��itca

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

Uma an��lise hist��rico-epistemol��gica 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 Par�� (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

A obra de triangulis omnimodis libri quinque de Johann M��ller Regiomontanus (1436 1476): uma contribui����o para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann M��ller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos N��meros

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 Trocad��ro 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

Problemas e modelos que contribu��ram com o desenvolvimento do c��lculo diferencial e integral: dos gregos �� 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

Reconceitualiza����o das categorias de skemp de compreens��o relacional e compreens��o instrumental como crit��rios globais

The thesis presents a systematic description about the meaning, as Skemp, relational understanding and understanding instrumental, in the context of mathematics learning, being that we had as a guide his understanding of the schema. Especially, we analyze some academic productions, in the area of Mathematics Education, who used the categories of understanding relational and instrumental understanding how evaluative instrument and we see that in most cases the analysis is punctual. Being so, whereas the inherent understanding relational schema has a network of connected ideas and non-insulated, we investigated if the global analysis, where it is the understanding of the diversity of contributory concepts for formation of the concept to be learned, is more appropriate than the punctual, where does the understanding of concepts so isolated. For this, we apply a teaching module, having as main content the Quaternos Pythagoreans using History of Mathematics and the work of Bahier (1916). With the data we obtained the teaching module to use the global analysis and the punctual analysis, using research methodology the Case Study, and consequently we conduct our inferences about the levels of understanding of the subject which has made it possible for us to investigate the ownership of global analysis at the expense of punctual analysis. On the opportunity, we prove the thesis that we espouse in the course of the study and, in addition, we highlight as a contribution of our research evidence of need for a teaching of mathematics that entices the relational understanding and that evaluation should be global, being necessary to consider the notion of schema and therefore know the schematic diagram of the concept that will be evaluated

Um estudo sobre a aprecia����o do racioc��nio matem��tico na forma����o 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

Uma an��lise dos questionamentos dos alunos nas aulas de n��meros complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educa����o Tecnol��gica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

Contribui����es da investiga����o em sala de aula para uma aprendizagem das sec����es c��nicas com significado

In this work, the didactical possibilities of investigation use in classroom, through an experience with high school students from Federal Center of Technological Education of Para��ba, as well as the study of conic sections were analysed. In order to fulfill our goals the theoretical conceptions concerning the meaninful learning in conection with the investigation of mathematics history were taken into account. The classroom research occurred by means of activities which encouraged the learner to investigate his own concepts on the conic sections. The results of the proposed activities showed the effectiveness and the efficiency of such a methodology as regards the making up of the required knowledge. They also reveal that the investigation in the classroom guides the ones involved, in this process, to have a wider look at the origins, the methods used and the several representations presented by mathematics that certainly lead, specially the students, to a meaninful learning

A dif��cil aceita����o dos n��meros negativos: um estudo da teoria dos n��meros de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

O uso pedag��gico de uma seq����ncia did��tica para a aquisi����o de algumas id��ias relacionadas ao conceito de n��meros complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Estudo hist��rico e pedag��gico sobre ternos pitag��ricos �� luz de eug��ne bahier

At the present investigation had the purpose to achieve a descritive analysis pedagogy in the work of Recherche m��thodique et propri��t��s des triangles rectangles en nombres entiers. According to the analysis achieved, we made and applyed the teaching module called Pitagories: one of tools to comprehension Pitagory Theorema, there were studying by public students in mathematic course in the UFRN , the new mathematic teachers in future. The analysis the was made with writen test the was showed that all students got the view comprehension in the teaching approach module, to apointed the difference in the learning qualytative with other reseach that was made with quastionaire and enterview. With this module that was made with the new future teacheres there was more attention the better comprehension with the Pitagory Theorema, that was good focus in the pitagory about the potential historical pedagogyc in the work studied.