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

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.

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

Atribuição de significado ao conceito de proporcionalidade: contribuições da história da matemática

This study is the result of a work which approaches the Mathematics History how source of the meaning s attribution in the proportionality concept. We adopt the methodology of the source qualitative and we work with a group of teachers from instruction s public system of the fundamental and medium level from Pocinhos City Paraíba. For the data collection, we use the field notes, the questionnaire, a sequence of activities and the interview semistructured like instruments. The study had how objective to know the significates attributeds to proportionality concept through of the activity mediate from Mathematics History, besides to investigate if a approach of the nature enables modification according to this sense. The results obtaineds though the data analysis indicate that the activities bring contributions which refer to achieve objectives. On the other hand they also showed that we have a long trajectory to be trailed in the meaning of to turn the Mathematics History a subsidy effective in the teachers practice, in view of the formation absence in the knowledge area, besides the necessity of the approach adequated of the Mathematics History in the didatics books of Mathematic

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

História da matemática na formação do professor: dificuldades e sugestões

This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Luís de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation

História da matemática e teatro nas aulas sobre Teorema de Tales: um script proposto

This study will present the results of an investigation of how the history of mathematics and theater can contribute to the construction of mathematical knowledge of students in the 9th year of elementary school, through the experience, preparation and execution of a play, beyond presentation of the script. This brings a historical approach, defining space and time of events, putting the reader and viewer to do the route in the biography of Thales of Miletus (624-546 a.C), creating situations that led to the study and discussion of the content related to the episode possible to measure the height of the pyramid Khufu and the Theorem of Thales. That said, the pedagogical proposal implemented in this work was based on theoretical and methodological assumptions of the History of Mathematics and Theatre, drawing upon authors such as Mendes (2006), Miguel (1993), Gutierre (2010), Desgrandes (2011), Cabral (2012). Regarding the methodological procedures used qualitative research because it responds to particular issues, analyzing and interpreting the data generated in the research field. As methodological tools we have used participant observation, the questionnaire given to the students, field diary and dissertativos texts produced by students. The processing and analysis of data collected through the questionnaires were organized, classified and quantified in tables and graphs for easy viewing, interpretation, understanding and analysis of data. Data analysis corroborated our hypothesis and contributed to improving the use and display of the play as a motivating activity in mathematics classrooms. Thus, we consider that the script developed, ie the educational product proposed will bring significant contributions to the teaching of Mathematics in Primary Education

Cenário da produção acadêmica em história da matemática no ensino de matemática: uma análise reflexiva das teses e dissertações (1990-2010)

This research aims to make a reflective analysis about the academic production originated in the stricto sensu post graduation programs in the country, produced in the period of 1990 to 2010, in the field of History of Mathematics, especifically on works about the History of Mathematics in Mathematics education and that present pedagogical proposals that make use of the History of Mathematics in order to teach Mathematics. Defending the thesis that the researches on mathematics education with goals turned to the use of didactic proposals related to the history of mathematic that take in consideration the coherency between epistemological aspects inherent to mathematics history and anthological elements materialized on the conceptions of mathematics and mathematics history and of apprenticeship (implicitly or explicitly exposed) may originate significant contribution to the field of history of mathematics on education. Among these, nine were Master’s Degree dissertations and five PHD’s theses. The reflective analysis was accomplished from two matrixes; one from theoretical nature and the other, ontologic nature, elaborated from the pretexts of Sanches Gamboa, about the epistemological analysis from academic production in the field of Mathematics Education and the following theoretical perspectives in the field of History of Mathematics Education, that are: linear evolutionary theory, structural construtivist operative, evolutionary discontinuous, historical and socialcultural investigation and the use of activities estimulating the usage of verbal and nonverbal expressions. These perspectives were based on the works of Miguel and Miorim, Mendes and Radford. As results, we have detected some established dissonances between the categories related to theoretical and ontologic levels and the pedagogical proposal presented in these researches. On the other hand, we have discovered works that are able to establish consonances between the theoretical and ontological elements and the presented pedagogical proposal. These works carry significative contributions to the field of History of Mathematics applied to Mathematics pedagogical practice, inclusively presenting significative theoretical elements to the production of knowledge recognized as scientific in the Mathematics field

História da matemática na formação de professores: sistemas de numeração antigos

This essay aims to present and describe a proposal of insertion of Mathematics History into teachers undergraduation. Such addition proposal is expected to take place as curricular component to be taught on initial undergraduation for mathematics teachers. The selection of contents for the proposal has been based on the national Curriculum Guidelines (DCN, 2001, acronym in portugueses) for bachelor’s degree in Mathematics; the National Curricular Guidelines for Elementary School (PCNEF, 1998, acronym in Portuguese); and the National Curricular Guidelines for High School (PCNEM, 1999, acronym in Portuguese). The curricular component now presented is supposed to take a 60 hour workload, and includes the following topics: History of Ancient Numbering Systems, History of Trigonometriy and History of fuctions. For the sake of exemplification, the topic History of Ancient Numbering Systems is discussed and analysed in detail as practice for the new curricular component.

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Recorte dos produtos educacionais em história no ensino da matemática e em didática da matemática a partir das dissertações e teses defendidas no brasil entre 1990-2010

This work has the main purpose of conducting a survey of educational products present in dissertations and doctoral theses focused on the use of history in mathematics teaching and Didactics of mathematics with a French foundation produced in graduate programs in the strict sense of the Brazil between 1990 and 2010, the areas of Education, Mathematics Education, school of Natural Sciences and Mathematics and related areas, according to the research proposal of Mendes (2010). Our interest was to select the products that present concrete proposals for educational activities that can be used in the classroom of Basic Education and Training of Teachers of Mathematics. The research was implemented through a bibliographic study documents the Bank of dissertations and theses from CAPES, libraries and archives of some Postgraduate programs in the country who focus their studies on the subject object of this research, besides the Brazilian Digital Library Theses and Dissertations (BDBTD). From this survey we selected works that present educational products materialized in blocks of activities based on the use of teaching history of mathematics to the classroom as well as the sequence of activities based on the Teaching of Mathematics. In possession of material, produce a CD-ROM containing the selected activities, in order to help support the work of teachers regarding the use of these activities, as a supplementary material to textbooks in their math classes

Correspondências científicas como uma relação didática entre história e ensino de matemática: o exemplo das cartas de Euler a uma princesa da Alemanha

Lettres àune Princesse d'Allemagne sur divers sujets de physique et de philosophie (Letters to a Princess of Germany on various topics of physics and philosophy) is the work taken as an object of study of this thesis. It is a literary success written in the eighteenth century by the Swiss mathematician and physicist Leonhard Paul Euler (1707-1783) in order to meet a request from the Prussian king, Frederick II, the Great (1712-1786) to accept to guide the intellectual education of his niece, the young princess Anhalt-Dessau (1745-1808). The method of teaching and learning through letters elected to the education of the German monarch resulted in a collection of 234 matches in which Euler theory is about music, Philosophy, Mechanics, Optics, Astronomy, Theology and Ethics among others. The research seeks to point out mathematical content contained in this reference work based on the exploitation and adaptation of original historical works as an articulator of development activities for teaching mathematics in basic education and in accordance with the National Curriculum Parameters of Mathematics (NCP) work. The general objective point out the limits and didactic potential of Lettres à une Princesse d'Allemagne sur divers sujets de physique et de philosophie as a source of support for teachers of basic education in developing activities for teaching mathematics. The discussions raised point to concrete possibilities of entanglement between the extracted mathematical content of the bulge of the work with current teaching methodologies from resizing the use of letters according to Freire's pedagogical perspective of the correspondence, and especially the use of new communication channels in the century XXI, both aimed at dialogue and approximation between those who write and those who read.

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

Guilherme de La Penha: uma história do seu itinerário intelectual em três dimensões

This study focuses on the central Brazilian historiography of science, focusing specifically on the life and work of a contemporaneous mathematician-physicist, and becomes part of the set of research results that investigate, organize and describe personal, intellectual and professional itineraries of Brazilian scientists and educators. The theme chosen for the study ran from seminars on Mathematics in Pará and is up to organize and describe the life history, education, professional experience and scientific production of William Mauricio Souza Marcos de La Penha (Guilherme de La Penha), considering their academic, professional and intellectual life history, so that their academic and intellectual production be spread over the Brazilian scientific and academic community. We adopted the historical research as theoretical and methodological base for the development of this study, rising arguments about the profile of Guilherme de La Penha to characterize him as a multiskill intellectual and to reveal that his thoughts about science, technology, training scientists and educators were in accordance with their writings and their professional practice in order to build a first story about the life and work of William de La Penha. In this sense, we took the theoretical aspects related to historical research, biographies, intellectual itineraries, files and inventories as sources and historical construction vehicles in order to point out the essential elements to form a profile of the transdisciplinary intellectual historians, ie a profile scientist who carries out the research, management and administration, as well as a committed educator to the on-going training and forming process. The results pointed in different directions, among which we highlight the creation of Seção Guilherme de La Penha at Universidade da Amazonia, producing several articles about the life and work of William de La Penha presented at national and international conferences and the proposal for documentary displays which could contribute to understanding the implementation of a scientific area in Pará State, an area that would not only be restricted to the production of knowledge, but more than that, it would include the spreading, which provides various means, primarily through education. Thus it was possible to ensure that La Penha has an intellectual profile that can be considered a multi-and transdisciplinary intellectual who defends the possibility of forming a scientist one and multiple, non-linear attitudes and dialogues with all other areas in order to be understood under a model scientist for the twenty-first century based on the model clearly inspired by the scientist authors with which he identified throughout their training and professional activities, like the three that stood out in their relationship science: Archimedes, Leonhard Euler and Cliford Ambrose Truesdell

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools