scholarly journals Estratégias e Metodologias para o Ensino-Aprendizagem da Operação Aritmética da Multiplicação utilizando Tópicos da História da Matemática

2019 ◽  
Vol 20 ◽  
pp. 381-394
Author(s):  
Helena de Fátima Sousa Melo ◽  
Maria do Carmo Carvalho Sousa da Cunha Martins
Keyword(s):  
History Of Mathematics ◽  
Ancient Egypt ◽  
Arithmetic Operations ◽  
Mathematical Skills ◽  
Multiplication Operation ◽  
Multiplication Process ◽  
History Of ◽  
Medieval India ◽  
Teaching Learning ◽  
Everyday Problems

Resumo As dificuldades no ensino-aprendizagem das operações aritméticas podem interferir na aquisição de algumas competências matemáticas básicas e, de certo modo, influenciar futuros processos de cálculo. Uma abordagem diferente, como a utilização de tópicos de História da Matemática, pode revelar-se uma boa estratégia para motivar os alunos e encaminhá-los para um conhecimento eficaz das referidas operações. Muitos foram os povos que aplicaram técnicas, processos, métodos e algoritmos na resolução de problemas do quotidiano ao longo da história. A Matemática de então tinha um cunho mais prático do que teórico, que decorria diretamente das necessidades diárias. Abordando estes meios ancestrais podemos cativar e estimular os alunos para as operações aritméticas, nomeadamente, a operação de multiplicação.Neste trabalho descrevemos o modo como alguns povos procediam à operação de multiplicação, bem como os métodos usados para tal, nomeadamente: a duplicação no Antigo Egito; a gelosia e o zigzag na India medieval; os bastões de Napier; a multiplicação com as mãos no Renascimento; e o processo de multiplicação do povo Yoruba.A utilização de diversos ábacos e o uso de outros materiais de efeito similar, como os bastões de Napier, podem ser um excelente complemento às estratégias para a aprendizagem da operação de multiplicação. Palavras-chave: operação de multiplicação; história da matemática Abstract The difficulties in teaching-learning of arithmetic operations can interfere with the acquisition of some basic mathematical skills and, in a way, influence future computation processes. A different approach, such as the use of topics in the History of Mathematics, may prove to be a good strategy to motivate students and direct them to an effective knowledge of such operations. Many people have applied techniques, processes, methods, and algorithms to solve everyday problems throughout history. The Mathematics of that time had a more practical rather than a theoretical character, which came directly from the daily necessities. Approaching these ancestral techniques, we can call attention for and stimulate students for arithmetic operations, namely, the multiplication operation. In this presentation we present the way in which some people performed the multiplication operation, as well as the methods used for such: duplication in Ancient Egypt; “gelosia” and zigzag in medieval India; Napier's bones; multiplication with hands in the Renaissance; and the multiplication process of the Yoruba people. The use of several abacuses and of other materials of similar effect, such as the Napier rods, can be an excellent complement to the strategies for learning the multiplication operation. Keywords: multiplication operation; History of Mathematics

scholarly journals The Use of History of Mathematics in the Mathematics Classroom: An Action Study

2020 ◽  
Vol 8 (2) ◽  
pp. 92 ◽  
Author(s):  
Suphi Önder Bütüner ◽  
Adnan Baki
Keyword(s):  
Mathematics Classroom ◽  
History Of Mathematics ◽  
Structured Interviews ◽  
Grade Levels ◽  
Beliefs About Mathematics ◽  
Multiple Data ◽  
Instructional Environments ◽  
8Th Grade ◽  
History Of ◽  
Everyday Problems

In this action study, instructional environments were enriched with activities related to the history of mathematics in order to deepen students’ beliefs about mathematics and reveal for them fun, interesting, and useful activities. The study enrolled twenty-four 8th-grade students. Data were collected by using multiple data collection tools. The data regarding the students’ beliefs about mathematics were collected via written opinion forms and semi-structured interviews. Prior to the study, the students perceived mathematics as a branch of science that is closed to development and did not know why or how it flourished. After the study, they stated that mathematics is open to development and is used to solve everyday problems. The study revealed a decrease in students’ absolutist beliefs about mathematics, and students found math fun and interesting as a result of engaging in activities that promote active problem-solving. In the future, other action studies involving the history of mathematics may be used to teach different topics at different grade levels.

Mathematics in the study of African culture

1973 ◽  
Vol 20 (7) ◽  
pp. 532-535
Author(s):  
Claudia Zaslavsky
Keyword(s):  
History Of Mathematics ◽  
Ancient Egypt ◽  
African Culture ◽  
History Of

What do we know about the development and applications of mathematics in Africa, outside of ancient Egypt? My attempts to discover the answer to this question Jed me to a field of research that has barely been touched by mathematical historians. In fact, the treatment of Africa in the books on the history of mathematics leaves one with the impression that Africans could barely count before the advent of Europeans.

scholarly journals LA HISTORIA Y DIDÁCTICA DE LAS MATEMÁTICAS: UM ENCUENTRO POSIBLE

PARADIGMA ◽  
2020 ◽  
pp. 133-159
Author(s):  
Edilene Simões Costa dos Santos ◽  
Cristiano Alberto Muniz ◽  
Maria Terezinha Jesus Gaspar
Keyword(s):  
Public Schools ◽  
Mathematics Education ◽  
History Of Mathematics ◽  
Federal District ◽  
Fifth Grade ◽  
History Of ◽  
Distrito Federal ◽  
Teaching Of Mathematics ◽  
Teaching Learning ◽  
Didactics Of Mathematics

Este estudio aborda el valor didáctico de la historia de las matemáticas en la educación matemática, buscando resaltar una posible relación entre la historia y la didáctica de las matemáticas. La investigación analizó la enseñanza-aprendizaje utilizando la historia de las matemáticas en la concepción de producir y sistematizar circunstancias del concepto de área como cantidad autónoma y procedimientos para su medición. La realización de la propuesta de trabajo se realizó a través de la organización, aplicación y análisis de la secuencia didáctica realizada en dos clases de quinto grado, en dos escuelas públicas del Distrito Federal-Brasil. Las conclusiones de esta investigación se centran en el análisis de los procedimientos, dificultades, representaciones, movilización de teoremas y conceptos en acción presentados por los estudiantes que participan en el estudio. A través de los análisis, encontramos el crecimiento gradual del estudiante en la construcción y el significado del concepto del área y su medición, y en la comprensión del conocimiento no está listo y se construye en un proceso que involucra tiempo, conocimiento, contextos y personas. Además, a través del análisis basado en la teoría de los campos conceptuales, fue posible afirmar que los estudiantes demostraron identificar el área como magnitud, en las decisiones de resolución no confundieron superficie con su área ni área con numeroPalabras clave: Área, Historia de las matemáticas, Teoría de los Campos Conceptuales THE HISTORY AND TEACHING OF MATHEMATICS: A POSSIBLE MEETING AbstractThis study approaches the didactic value of the history of mathematics in mathematics education, seeking to highlight a possible relationship between history and didactics of mathematics. The research analyzed teaching-learning using history of mathematics in the conception of circumstances that produce and systematize area concept as autonomous quantity and procedures for its measurement. The realization of the work proposal occurred through organization, application and analysis of a didactic sequence conducted in two fifth grade classes in two public schools in Federal District - Brazil. The conclusions of this investigation focus on the analysis of procedures, difficulties, representations, and mobilization of theorems and concepts in action presented by the students participating in the study. Through the analyzes we found the student’s gradual growth in construction and signification of area concept and its measure and in understanding that knowledge is not ready, but it’s built in a process that involves time, knowledge, contexts and people. It was also possible, through analysis based on the theory of conceptual fields, to state that students demonstrated to identify area as magnitude, and in decisions for resolution they did not confuse surface with its area nor area with number.Keywords: Area, History of Mathematics, Theory of conceptual fields A HISTÓRIA E A DIDÁTICA DA MATEMÁTICA: UM ENCONTRO POSSÍVEL ResumoO presente estudo aborda o valor didático da História da Matemática na educação matemática, analisando o ensino-aprendizagem ao se utilizar a história da matemática na concepção de circunstâncias produtoras e sistematizadoras do conceito de área como grandeza autônoma e procedimentos para sua medida. A efetivação da proposta do trabalho ocorreu por meio da organização, aplicação e análise de sequência didática realizada em duas turmas de quinto ano do Ensino Fundamental, em duas escolas da rede de ensino público do Distrito Federal-Brasil. As conclusões desta investigação centram-se na análise acerca dos procedimentos, dificuldades, representações, mobilização de teoremas e conceitos em ação apresentados pelos alunos participantes do estudo. Por meio dessa análise, constatamos o crescimento gradativo dos alunos na construção e significação do conceito de área e sua medida, além da compreensão de que os conhecimentos não estão prontos, sendo construídos em processo que envolve tempo, conhecimentos, contextos e pessoas.  Assim, tendo por base a teoria dos campos conceituais, foi possível afirmar que os alunos demonstraram identificar área como grandeza nas decisões para resolução, não confundindo superfície com sua área e nem área com número.Palavras-chave: Área, História da matemática, Teoria dos Campos Conceituais, 

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.

Sign in / Sign up

Export Citation Format

Share Document