Navegando por Assunto "History of mathematics"

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Aproximações e distanciamentos entre as obras réflexions sur la métaphysique du calcul infinitésimal e théorie des fonctions analytiques a partir da análise de conteúdo
(Universidade Federal do Pará, 2022-03-31) LIRA, Alailson Silva de; QUARESMA, João Cláudio Brandemberg; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
In the 18th century period, several mathematicians contributed to the development of Infinitesimal Calculus (IC). Among the exponents of this context, Joseph-Louis Lagrange (1736 – 1813) and Lazare Nicolas Marguerite Carnot (1753 – 1823) stood out. Thus, as a research question, the present work raised the following problem: what points of closeness and distance do the works Réflexions sur la Métaphysique du Calcul Infinitésimal (RMCI), of 1813, by Lazare Carnot, and Théorie des Fonctions Analytiques (TFA), of 1813, by Lagrange, present, concerning the concepts of the Infinitesimal Calculus? To answer it, we used the methodological contributions of content analysis as well as the steps established in Bardin (2016), adapted for this research. Therefore, this thesis aimed to compare, based on content analysis, the approximations and detachments between the works RMCI and TFA. With this, we realized, as approximations, that both perform descriptions about their concepts and definitions and involve the same problems with the infinitesimals about the infinitely large and infinitely small quantities. As detachments, we observe that the central elements in Lagrange's work are functions and series and only the algebraic method is under discussion, while in Carnot's work infinitely small quantities and the theory of error compensation are present, and it conceives the use of infinitesimals without disregarding the other methods.
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Contribuições de um ambiente virtual para a divulgação das pesquisas em história da matemática no Brasil
(Universidade Federal do Pará, 1991-02-27) CASTILLO BRACHO, Luis Andres; MENDES, Iran Abreu; http://lattes.cnpq.br/4490674057492872; https://orcid.org/0000-0001-7910-1602
In this work, we present a reflexive description of a research focused on the materialization of an interactive virtual environment called Brazilian Reference Center for Research in Mathematical History - CREPHIMat, linked to two broader research projects funded by the National Council for Scientific and Technological Development (CNPq), in the field of relations between history and teaching of Mathematics. The research carried out had the objective of virtually materializing the environment and evaluating the impact of this creation by the academic community, with the purpose of identifying its contributions in the dissemination of research productions in the History of Mathematics, developed in Brazil between 1990 and 2018, without neglecting the expansion of the collection of productions that may come out from future studies in this field. The collection and classification of productions in this field of studies was carried out by a team of graduate students at the master's and doctoral level, together with the Coordinator of CREPHIMat, based on previous research already carried out by Mendes (2010, 2015, 2018a), related to academic-scientific productions originated in Brazilian research in the field of the History of Mathematics in the period 1990-2018. Approximately 2.100 archives were organized, including theses, dissertations, articles from scientific journals, conference proceedings, mini-course books, educational products, teaching materials, and other productions aimed at undergraduate and graduate students, professors, and researchers interested in the History of Maths. In addition to these actions, an evaluation of the initial impact of the CREPHIMat virtual environment with the academic community has also been carried out since its launch in August 2019. The result pointed to favorable considerations for the implementation of a variety of activities in this environment, such as contributions to the work of the professor and researcher in this field, as well as to undergraduate and graduate students in Mathematical Education. At the end of the study, we point out the instructions for the exploration of the environment by the entire academic community related to the research topic, as well as the potential for training activities for teachers in the form of conferences, workshops, training courses, among others.
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Um estudo acerca da inserção de aspectos históricos dos conceitos de dependência e independência linear em cursos de álgebra linear
(Universidade Federal do Pará, 2022-02-22) DIAS, Renan Marcelo da Costa; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
The present study aimed to investigate how the historical development of the concepts of Linear Dependence and Independence can be approached in Linear Algebra courses to enable a better understanding of these concepts by Mathematics undergraduates. To this end, we developed a Bibliographic Research with a qualitative approach for data analysis consisting of two moments. In the first moment, based on Dorier (1995b; 2000) and Moore (1995), we discuss the historical constitution of Linear Algebra, in which we identify four different preceding notions of the current concepts of Linear Dependence and Independence, whether they are inclusive dependence (Euler), unified dependence for equations and n-tuples (Frobenius), generalization of dependence to n-dimensional space (Grassmann) and axiomatization of dependence and linear independence (Peano). In the second moment, we present didactic suggestions, based on Mendes (2006; 2015; 2016) and Brandemberg (2018; 2021), on how to approach these different notions in Linear Algebra courses. Such suggestions aim to give students the opportunity to have contact with different aspects that allow them to broaden their understanding of linearity as a relationship between vectors, as well as to visualize the current definitions of Linear Dependence and Independence as a language that does not discard the notions given by Euler, Frobenius, Grassmann or Peano, but keep them in a unifying and generalizing character.
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Um estudo do liber quadratorum (1225) de Leonardo Fibonacci (1180 – 1250) e suas potencialidades para o ensino de matemática
(Universidade Federal do Pará, 2018-03-15) GUIMARÃES FILHO, José dos Santos; QUARESMA, João Cláudio Brandemberg; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
In this research report we show the Italian mathematician Leonardo de Pisa, better known as Fibonacci, who we refer to as Leonardo Fibonacci, who contributed significantly to the mathematical community of his time, attracting attention from important people of this period such as King Frederick II, and to his invitation Leonardo Fibonacci participates of a mathematical tournament, which, as a follow up the construction of his fourth work (that we have known) the Liber Quadratorum. In this way the following question occurs to us: what are the didactic / pedagogical potentialities that can be evidenced from these propositions and their demonstrations that can be used in the classroom to effect the teaching / learning of mathematical contents? In order to answer this question, we aim in this research report to analyze the problems contained in Leonardo Fibonacci 's Liber Quadratorum, in which we aim at a better understanding of the concepts, providing a material in Portuguese and searching for possible didactic / pedagogical potentials. To do so, we searched for materials that subsidized the study and a basic text for the construction of the material in Portuguese referring to twelve propositions contained in the Liber Quadratorum, which deal with the sequence of consecutive odd numbers and square numbers. The book of squares of LE Sigler of 1987, as our main reference and BR McClenon in his work titled Leonardo of Pisa his Liber Quadratorum of 1919 as our secondary reference. We took a tour of the period experienced by this important character, who was a teacher and wrote about mathematics, so we highlight its influence for the development and dissemination of algorithmic methods of Arab mathematics in Europe in the early thirteenth century, from a proposed model diagram by Chaquiam (2015, 2016), thus, a basis was built so that we could point out the didactic / pedagogical potentialities of this book by Leonardo Fibonacci, especially considering the reinforcing arguments of Miguel (1997) and Miguel and Miorim (2004). After the analysis, it was possible to respond to our questioning and we could point out potentialities such as: construction of several ways to find the Pythagorean triples, potentiation activities, mainly squares, activities with square root, among others described in this report. In this way, to maintain the Liber Quadratorum for explicitly pedagogical purposes, by vectorizing the teaching, can greatly assist the mathematical educator who wants to trace paths that meet the needs of the student.
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História para o ensino de geometria analítica nas produções de história da matemática do Brasil
(Universidade Federal do Pará, 2020-02-10) MARQUES, Rubens Matheus dos Santos; MENDES, Iran Abreu; http://lattes.cnpq.br/4490674057492872; https://orcid.org/0000-0001-7910-1602
This research refers to the history of analytic geometry in the productions of History of Mathematics in Brazil, so this research is research type research. For the methodological development we base on the epistemological assumptions of Gamboa (2012), so that it subsidizes the analysis of each identified production according to the research objective that concerns the proposed activities for the teaching of analytical geometry in the research productions centered on its historical and methodological aspects, for its use in mathematics classes exposed in the Brazilian productions of History of Mathematics, within the scope of postgraduate dissertation and thesis level, event annals, education journals and short course books offered by SBHMat in SNHM. To guide the research, we consider the following question: What approaches and contributions emerge for the teaching of analytic geometry in the production of History of Mathematics in Brazil? As results we identified thirty-seven works referring to the history of analytical geometry classified in the research trends in History of Mathematics, namely; History and Epistemology of Mathematics (HEpM), History of Mathematical Education (HEdM) and History for Teaching Mathematics (HEnM) Thus, sixteen productions were identified in relation to the master's level scientific production, twelve related to the works published in the annals of events, three in the journals of the area and finally six short course books were identified. From this finding we elaborate referrals for teachers of basic education from the information contained in the productions classified in HEnM in order to reveal how the approaches presented in the research can be worked in line with the textbook.
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Histórias do sistema de numeração decimal produzidas na pós-graduação brasileira (1990-2018): potencialidades para o ensino de aritmética nos anos iniciais
(Universidade Federal do Pará, 2021-02-07) PIRES, Lucas Silva; MENDES, Iran Abreu; http://lattes.cnpq.br/4490674057492872; https://orcid.org/0000-0001-7910-1602
This dissertation is a result of an investigation linked to two research projects funded by the National Council for Scientific and Technological Development (CNPq). It comprises a bibliographical documentary study in the modality of a research on thesis and dissertations about the History of Mathematics produced in Brazilian stricto sensu Postgraduate programs. The corpus has analyzed short course books of the Brazilian Society of Mathematical History (SBHMat), proceedings of national academic events discussing the History of Mathematics (SNHM), Mathematical Education (ENEM), among others. Worth mentioning too articles published in journals qualified by the evaluation system of the Higher Education Personnel Improvement Coordination (CAPES). Our objective was to characterize the histories that make it possible to teach the Decimal Numbering System in Primary school, based on researches that deal with history for the teaching of Mathematics in that country. In this sense, we established the following research question: how was the history for the teaching of the Decimal Numbering System in Primary school treated in Brazil, in a pedagogical sense, in the History of Mathematics productions ranging from 1990 to 2018? To answer this question, we ground our reflections on four concepts established by Mendes (2006; 2008; 2013; 2015; 2017): 1) history as an agent of cognition in Mathematical Education; 2) history as a cognitive reorganizer in mathematical learning; 3) history of mathematics as a didactic and conceptual mediator and 4) history for the teaching of mathematics as a didactic reinvention for the classroom. To accomplish this study, we initially conducted a survey of these productions, dividing them into three trends in the History of Mathematics: 1) Mathematics History and Epistemology; 2) History for the Teaching of Mathematics and 3) History of Mathematical Education. Then, we took into consideration the productions listed in the second trend, selected and grouped those which explored histories in order to teach the Decimal Numbering System in Primary school, so as to characterize these productions based on an analytical tool elaborated from the four concepts previously mentioned. Subsequently, we proposed some pedagogical suggestions and didactic activities to support the teacher's work in the classroom. Finally, we combine the activities that deal with this content, potentially elaborated in the researches, with the content addressed in 4th and 5th grades textbooks. Based on the results, we understand that these activities can be implemented by the teacher in the classroom. Likewise, we point out that there are researches that suggest activities, but some of them need adaptations so they can be effectively used in a didactic way by the teacher. Therefore, we consider that the researches potentially related to histories for the teaching of the Decimal Numbering System in Primary school, when they do exist, can be inserted in classrooms in association with textbook contents, and thus enrich the teacher's didactic approach in the teaching of arithmetic within the importance of the students learning.
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Matemática nas grandes navegações: instrumentos de aferição de medidas angulares
(Universidade Federal do Pará, 2023-05-23) Pinheiro, Ranielle Afonso; Barros, Osvaldo dos Santos; http://lattes.cnpq.br/8886478452699437; https://orcid.org/0000-0002-7185-4009
The present work focuses on the study of the use of mathematical knowledge in the Age of Exploration, specifically the angular measurements used for celestial navigation. The aim is to address the concept of angular units and their measurement systems, as well as their historical context, through the use of measurement instruments such as protractors and theodolites. The goal is to provide a contextualized understanding of angles, their measurements, and applications, by incorporating the history of mathematics into teaching. As an educational product, a supplementary textbook has been developed that explores the concept of angular units and their measurements within the context of maritime exploration, linking them to other teaching and learning elements such as coordinates on a grid.
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Potencialidades didáticas de textos e problemas históricos egípcios e babilônicos para o ensino de matemática na educação básica
(Universidade Federal do Pará, 2022-05-28) PEREIRA, Patricia Sheila Figueiredo; BRANDEMBERG, João Cláudio; http://lattes.cnpq.br/3873561463033176; https://orcid.org/0000-0001-8848-3550
This research aimed to investigate which texts and historical problems present in the mathematics of Egypt and Babylon have didactic potentialities to be explored in the teaching of mathematics. For this, a bibliographical research was carried out in the literature of Boyer (1974) and Eves (2011), which provided the historical context of mathematics, as revealed several forms of solving ancient mathematical problems and that these are possible to be solved through the current notation. When studying the History of Mathematics, several potentialities that enable the development of mathematical skills were identified in the texts and historical problems that enable the development of mathematical skills, which were evidenced according to the arguments of Miguel (1997) and the studies of Mendes and Chaquiam (2016), Brandemberg (2020) and Brandemberg (2021), which corroborate the relevance of history in mathematics teaching. From this study, it was possible to select the texts of the Plimpton Table 322, the historical problems of the Rhind Papyrus and those of The BM Table 13901 as sources of/with potentialities, which are: to enable the conceptual development of the polynomial equation of the 1st degree; enable the development of the concept of the quadratic equation; to provide the student with new discourses on pythagoras' theorem and, with this, enable the development of skills foreseen in the National Common Curriculum Base (BNCC). In addition, it was suggested, through didactic activities, a way for the teacher to use the texts and historical problems in the teaching of school mathematics. Thus, it can be inferred that the selected texts and historical problems have potentialities that contribute to the construction of mathematical knowledge, as well as it was evidenced that they can be used in the process of teaching and learning mathematics in Basic Education.
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Potencialidades pedagógicas do livro réflexions sur la métaphysique du calcul infinitésimal de Lazare Carnot para o ensino de cálculo diferencial
(Universidade Federal do Pará, 2019-02-08) SOUSA, Fabrício Santos de; ROCHA, Maria Lúcia Pessoa Chaves; http://lattes.cnpq.br/4291670232604529
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Propostas no ensino de aritmética para pessoas com surdocegueira
(Universidade Federal do Pará, 2019-06-26) SANTOS, Felipe Moraes dos; SALES, Elielson Ribeiro de; http://lattes.cnpq.br/5467537517169068; https://orcid.org/0000-0001-6242-582X
This study deals with the use of the History of Mathematics in conjunction with concrete materials as an educational proposal to teach principles of arithmetic for deafblind students. We aim to develop arithmetic teaching activities that are attractive to the learning of people with deafblindness. Due to the condition of the deafblind person, there was a need to develop more consistent strategies in order to attract the student to the content, thus exploring as much as possible, their remaining perceptions. The methodology adopted is qualitative in nature. The construction of suggested and applied activities were guided by the educational strategies of deafblinds, the perspectives of Mathematical History, solid materials and learning factors, exposing the history of Mathematics and concrete objects as a previous organizer. In addition, in order to strengthen the study we develop materials and adapt existing ones to further encourage student learning. The study was carried out in a Specialized Educational Unit in the state of Pará. The unraveling of the proposal promoted the intrinsic motivation allowing the student's involvement in the activity, being aided by tactile resources. The approach linking history of mathematics, concrete materials and counting, proved to be efficient by providing the best organization of the conceptual counting structure, the successful learning outlined by the student revealed that the intent of the proposal was achieved.