The role of diagram materiality in mathematics

2018 ◽  
Vol 9 (2) ◽  
pp. 183-201 ◽  
Author(s):  
Anna Kiel Steensen ◽  
Mikkel Willum Johansen

Abstract Based on semiotic analyses of examples from the history of mathematics, we claim that the influence of the material aspects of diagram tokens is anything but trivial. We offer an interpretation of examples of diagrammatic reasoning processes in mathematics according to which the mathematical ideas, arguments, and concepts in question are shaped by the physical features of the chosen diagram tokens.

Pythagoras ◽  
2008 ◽  
Vol 0 (68) ◽  
Author(s):  
Michael De Villiers

This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.


Author(s):  
Katalin Gosztonyi

History of mathematics is rarely used in Hungarian mathematics education, and even more rarely goes beyond anecdotic mentions of history. In this paper I will argue that despite of this phenomenon, a historical perspective on mathematics, in a more general way, plays a crucial role in a specific Hungarian tradition of mathematics education, called felfedeztető matematikaoktatás (“teaching mathematics by guided discovery”). I will revisit the epistemological background of this approach, analyse the role of history in this view on the nature of mathematics and its teaching, and illustrate the analysis by some examples from written sources and nowadays teaching practice. Classification: A30, D20, D40. Keywords: History of mathematics, history in mathematics education, guided discovery in mathematics education.


PARADIGMA ◽  
2020 ◽  
pp. 317-332
Author(s):  
Mônica De Cássia Siqueira Martines

Este artículo describe los resultados de un experimento que involucró la enseñanza y la investigación en la disciplina de Historia de las Matemáticas, impartido por el autor en la Universidad Federal de Triângulo Mineiro (UFTM) desde el comienzo de la oferta del Grado en Matemáticas en esa institución de educación superior. En este sentido, presentamos el formato de las clases y evaluaciones que se realizan para el tema del estudio que originó este artículo. La investigación desarrollada fue del tipo cualitativo, en particular un estudio de caso, ya que la experiencia descrita y explicada se centra en la preocupación por los aspectos de la realidad del aula de una sola situación específica. Los resultados muestran la necesidad de reflexión constante, diálogo y posibles cambios en la didáctica en el aula, ya que los estudiantes, cada día, son diferentes en un mundo globalizado e informatizado. También revelan la necesidad de invitar a los estudiantes a asumir el papel de protagonistas, de modo que las formas de evaluación para cada clase puedan modificarse.Palabras clave: Historia de las matemáticas; Evaluación; Formación inicial de profesores de matemáticas. THE DISCIPLINE HISTORY OF MATHEMATICS AT THE FEDERAL UNIVERSITY OF THE MINING TRIANGLE: A BRIEF REPORT AbstractThis article describes the results of an experiment that involved teaching and research in the History of Mathematics discipline, taught by the author at the Federal University of Triângulo Mineiro (UFTM) since the beginning of the offer of the Degree in Mathematics at that institution of higher education. In this sense, we present the format of the classes and assessments that are carried out for the subject of the study that originated this article. The research developed was of the qualitative type, particularly a case study, since the experience described and explained is centered on the concern with aspects of the classroom reality of a single specific situation. The results show the need for constant reflection, dialogue and possible change in the didactics in the classroom, since the students, each day, are different in a globalized and computerized world. They also reveal the need to invite students to assume the role of protagonists, so that the forms of assessment for each class can be modified.Keywords: History of Mathematics; Evaluation; Initial training of mathematics teachers.A DISCIPLINA HISTÓRIA DA MATEMÁTICA NA UNIVERSIDADE FEDERAL DO TRIÂNGULO MINEIRO:UM BREVE RELATO ResumoEste artigo descreve os resultados de uma experiência que envolveu ensino e pesquisa na disciplina História da Matemática, ministrada pela autora na Universidade Federal do Triângulo Mineiro (UFTM) desde o início da oferta do curso de Licenciatura em Matemática na referida instituição de ensino superior. Neste sentido apresentamos o formato das aulas e avaliações que são realizadas para a disciplina foco do estudo que originou este artigo. A pesquisa desenvolvida foi do tipo qualitativa, particularmente um estudo de caso, uma vez que a experiência descrita e explicada está centrada na preocupação com os aspectos da realidade da sala de aula de uma única situação especifica. Os resultados mostram a necessidade de constante reflexão, diálogo e possível alteração na didática em sala de aula, visto que os(as) alunos(as), a cada dia, se mostram diferentes perante um mundo globalizado e informatizado. Revelam, também, a necessidade de convidar os(as) alunos(as) a assumirem o papel de protagonistas, fazendo com que as formas de avaliação de cada turma possam ser modificadas.Palavras-chave: História da Matemática; Avaliação; Formação inicial de professores de matemática.


10.28945/2591 ◽  
2003 ◽  
Author(s):  
Saeed Seyed Agha Banihashemi

In this article we are going to discuss how new and old mathematics are related on works of Islamic mathematician and how history of mathematics can help education of mathematics to improve and motivate it.


2000 ◽  
Vol 8 (4) ◽  
pp. 487-497
Author(s):  
Hansjörg Geiges

This article highlights the position of mathematics within general culture at various stages of the development of Western civilization. Special emphasis is given to the role of mathematics in Greek philosophy, the influence of mathematics on Gothic architecture and the place of mathematics in 17th and 18th century society. Literary quotations illustrate the shifts in the view of mathematics in society.


2021 ◽  
Vol 4 (1) ◽  
pp. 23-32
Author(s):  
Krishna Kanta Parajuli

South Asian region has made a glorious history of mathematics. This area is considered as fer- tile land for the birth of pioneer mathematicians who developed various mathematical ideas and creations. Among them, three innovative personalities are Bhaskaracarya, Gopal Pande and Bharati Krishna Tirthaji and their specific methods to find cube root are mainly focused on this study. The article is trying to explore the comparative study among the procedures they adopt. Gopal Pande disagrees with the Bhaskaracarya's verse. He used the unitary method against that method mentioned in Bhaskaracarya's famous book Lilavati to prove his procedures. However, the Vedic method by Tirthaji was not influenced by the other two except for minor cases. In the case of practicality and simplicity, the Vedic method is more practical and simpler to understand for all mathematical learners and teachers in comparison to the other two methods.


2021 ◽  
pp. 097318492110645
Author(s):  
Dhruv Raina

The nineteenth century has been characterised as a period in which mathematics proper acquired a disciplinary and institutional autonomy. This article explores the intertwining of three intersecting worlds of the history of mathematics inasmuch as it engages with historicising the pursuit of novel mathematics, the history of disciplines and, more specifically, that of the British Indological writings on Indian mathematics, and finally, the history of mathematics education in nineteenth century India. But, more importantly, the article is concerned with a class of science and mathematics teaching problems that are taken up by researchers—in other words, science and mathematics teaching problems that lead to scientific and mathematical research. The article argues that over a period of 50 years, a network of scholars crystallised around a discussion on mathematics proper, the history of mathematics and education. This discussion spanned not just nineteenth-century England but India as well, involving scholars from both worlds. This network included Scottish mathematicians, East India Company officials and administrators who went on to constitute the first generation of British Indologists, a group of mathematicians in England referred to as the Analytics, and traditional Indian scholars and mathematics teachers. The focus will be on the concerns and genealogies of investigation that forged this network and sustained it for over half a century.


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