scholarly journals O estudo de definições matemáticas no contexto de investigação histórica: um experimento didático envolvendo Engenharia Didática e Sequências Polinomiais de Fibonacci

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Rannyelly Rodrigues de Oliveira ◽  
Francisco Régis Vieira Alves ◽  
Rodrigo Sychocki da Silva
Keyword(s):  
History Of Mathematics ◽  
Fibonacci Sequence ◽  
Research Approach ◽  
Polynomial Sequence ◽  
Internal Validation ◽  
Generalized Fibonacci Sequence ◽  
Research Activities ◽  
Didactic Engineering ◽  
History Of ◽  
Fibonacci Polynomial

Resumo: O presente artigo apresenta uma abordagem de investigação no contexto da História da Matemática, envolvendo situações que visam oportunizar o entendimento da extensão, evolução e generalização de propriedades da Sequência de Fibonacci. Dessa forma, abordam-se duas situações. A primeira, envolvendo a descrição da fórmula de Binnet no campo dos inteiros. Logo em seguida, apresenta-se uma descrição e análise dos termos explícitos presentes na Sequência Polinomial de Fibonacci. O escopo da presente proposta de atividade busca a divulgação científica de noções envolvendo a generalização, ainda atual, fato que acentua o caráter ubíquo da Sequência de Fibonacci. À vista disso, a proposta de experimento didático está fundamentada na organização das características da Engenharia Didática. Almeja-se, além da validação interna das hipóteses levantadas durante a investigação, contribuir com a formação inicial de estudantes dos cursos de Licenciatura em Matemática que virem a estudar o tema.Palavras-chave: Atividades de investigação. Engenharia Didática. História da Matemática. Sequência Generalizada de Fibonacci.  THE STUDY OF MATHEMATICAL DEFINITIONS IN THE CONTEXT OF HISTORICAL RESEARCH: A DIDACTIC EXPERIMENT INVOLVING DIDACTIC ENGINEERING AND FIBONACCI POLYNOMIAL SEQUENCESAbstract: This article presents a research approach within the context of History of Mathematics, involving situations that aim to provide an understanding of the extension, evolution and generalization of properties of the Fibonacci Sequence. In this way, two situations are addressed. The first, involving the description of Binet's formula in the integer field. Then, a description and analysis of the explicit terms present in the Fibonacci Polynomial Sequence is presented. The scope of this activity proposal seeks the scientific dissemination of notions involving generalization, still current, a fact that accentuates the ubiquitous character of the Fibonacci Sequence. Thus the proposal of didactic experiment is based on the organized in the characteristics of Didactic Engineering, beyond the internal validation of the hypotheses raised during the investigation this paper aims at contributing to initial education of undergrad   Mathematicsof students that may come to study the subject.Keywords: Research activities. Didactic Engineering. History of Mathematics. Generalized Fibonacci Sequence.

A Didactic Engineering in the Research Process of the Generalization of the Padovan Sequence: An Experience in a Pre-Service Teacher Training Course

2020 ◽  
Vol 22 (6) ◽  
Author(s):  
Renata Passos Machado Vieira ◽  
Francisco Regis Vieira Alves ◽  
Paula Maria Machado Cruz Catarino
Keyword(s):  
Teacher Training ◽  
History Of Mathematics ◽  
Research Process ◽  
Teaching Methodology ◽  
Engineering Research ◽  
Training Course ◽  
Theory Of Didactic Situations ◽  
Short Period ◽  
Didactic Engineering ◽  
History Of

Background: Obstacles are found during the epistemological construction of mathematical concepts research, aiming to contribute to the Didactics of Mathematics through a study of Padovan sequence.  Objectives: describe elements of a systematic study, based on Didactic Engineering in conjunction with the Theory of Didactic Situations. I addition, referring to the generalization model of Padovan sequence and promoting a historical-evolutionary understanding and its mathematical properties. Design: it presents the most representative data of an investigation supported by the foundations of Didactic Engineering research design, in association with the Theory of Didactic Situations teaching methodology. Setting and Participants: the research was developed in 2019 and applied in a Pre-Service Mathematics Teacher Training Course in the History of Mathematics discipline, with the eight students enrolled. Data collection and analysis: data validation occurred internally due to the short period of the research. Results: it describes an investigation around the object of study, the Padovan sequence, focusing on the generalization process of this sequence and its properties. Thus, three problem situations are elaborated and analyzed based on the assumed research and teaching methodologies, seeking to examine their properties and the student's intuitive thinking, before the insertion of a historical-epistemological conception of this investigation. Conclusions: the research makes it possible to extract repercussions, suggest and promote research scripts aiming at the formation of teachers (initial) in the context of the teaching of History of Mathematics.

An investigation of the Bivariate Complex Fibonacci Polynomials supported in Didactic Engineering: an application of Theory of Didactics Situations (TSD)

2019 ◽  
Vol 21 (3) ◽  
pp. 170-195 ◽  
Author(s):  
Rannyelly Rodrigues de Oliveira ◽  
Francisco Régis Vieira Alves
Keyword(s):  
History Of Mathematics ◽  
Inferential Reasoning ◽  
Fibonacci Polynomials ◽  
Intuitive Thinking ◽  
Theory Of Didactic Situations ◽  
Epistemological Conception ◽  
Didactic Engineering ◽  
History Of

A research cut will be presented in the Academic Master of the Programa de Pós-Graduação em Ensino de Ciências e Matemática (PGECM) of the Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE). This research used Didactic Engineering with a focus on the Theory of Didactic Situations, evidencing epistemological, cognitive and didactic elements articulated among themselves. This made it possible to mobilize the student's intuitive thinking towards inferential reasoning during the study of the Bivariate Complex Fibonacci Polynomials. Moreover, it had the purpose of inserting an epistemological conception in the teaching of History of Mathematics, considering that the research was applied in the course of Degree in Mathematics in the discipline of History of Mathematics.

ROBOTICS PROJECTS IN SCHOOL INFORMATICS COURSE

2019 ◽  
pp. 52-56
Author(s):  
V. V. Tarapata
Keyword(s):  
Information Transmission ◽  
Educational Robotics ◽  
Project Approach ◽  
Teaching Tools ◽  
Modern School ◽  
Research Activities ◽  
Information Processes ◽  
History Of ◽  
Normative Basis ◽  
Typical Model

The article describes the prerequisites for the use of educational robotics in the school course of informatics, the history of the development of its directions and the normative basis for its use in modern school education. A typical model of an educational robotic project for the organization of research and project activities of students has been proposed. The technological chart of the lesson as an example of the implementation of a robotic project in the framework of the research activities on informatics is considered. Approaches to the organization of educational activities, teaching tools and ways of evaluation in informatics class on the theme “Information processes. Information transmission” when using the project approach are described.

Apocrypha from the History of the Jewish Military Union and its Authors

2008 ◽  
pp. 147-176
Author(s):  
Dariusz Libionka
Keyword(s):  
Comparative Analysis ◽  
Critical Analysis ◽  
Communist Regime ◽  
Research Approach ◽  
Warsaw Ghetto ◽  
History Of

This article is an attempt at a critical analysis of the history of the Jewish Fighting Union (JFU) and a presentation of their authors based on documents kept in the archives of the Institute of National Remembrance in Warsaw. The author believes that an uncritical approach and such a treatment of these materials, which were generated under the communist regime and used for political purposes resulted in a perverted and lasting picture of the history of this fighting organisation of Zionists-revisionists both in Poland and Israel. The author has focused on a deconsturction of the most important and best known “testimonies regarding the Warsaw Ghetto Uprising”, the development and JFU participation in this struggle, given by Henryk Iwaƒski, WΠadysΠaw Zajdler, Tadeusz Bednarczyk and Janusz Ketling–Szemley.A comparative analysis of these materials, supplemented by important details of their war-time and postwar biographies, leaves no doubt as to the fact that they should not be analysed in terms of their historical credibility and leads one to conclude that a profound revision of research approach to JFU history is necessary.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

Newton and the Origin of Civilization

2012 ◽  
Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold
Keyword(s):  
Good Reason ◽  
History Of Mathematics ◽  
Primary Sources ◽  
Ancient History ◽  
Isaac Newton ◽  
History Of ◽  
Ancient Civilizations ◽  
And Mathematics ◽  
One Year ◽  
Radical Ideas

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.

International Relations at the Beginning of the XX Century in the Works of Vladimir Mikhailovich Khvostov

2019 ◽  
Vol 9 (4) ◽  
pp. 218-221
Author(s):  
Albina Imamutdinova ◽  
Nikita Kuvshinov ◽  
Elena Andreeva ◽  
Elena Venidiktova
Keyword(s):  
Social Sciences ◽  
Foreign Policy ◽  
International Relations ◽  
Significant Role ◽  
Research Activities ◽  
History Of

Abstract The article discusses the research activities of Vladimir Mikhailovich Khvostov, his creative legacy on issues and problems of international relations of the early ХХ century; the life of V.M. Khvostov, characterization and evolution of his approaches and views on the history of international relations, foreign policy. A prominent organizer and theorist in the field of pedagogical Sciences, academician Vladimir Mikhailovich Khvostov played a significant role in the formation of the Academy of pedagogical Sciences of the USSR – the all-Union center of pedagogical thought. As its first President, he paid great attention to the development and improvement of the system of humanitarian education in the school, taking into account all the tasks and requirements imposed by the practice of Communist construction in our country. In his reports and speeches at various scientific sessions and conferences, he repeatedly emphasized the exceptional importance of social Sciences in the training of not only educated girls and boys, but also in the formation of politically literate youth.

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