scholarly journals That Was Then…This is Now: Utilizing the History of Mathematics and Dynamic Geometry Software

2021 ◽  
Vol 9 (2) ◽  
pp. 198-212
Author(s):  
Michelle Meadows ◽  
Joanne Caniglia
Keyword(s):  
Mathematics Teacher ◽  
History Of Mathematics ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Dynamic Nature ◽  
Pedagogical Approach ◽  
History Of ◽  
Toulmin’S Model

Pre-service mathematics teacher (PST) education often addresses within Geometry Classes how to utilize Dynamic Geometric Software (DGS). Other classes may also incorporate teaching pre-service teachers about the history of mathematics. Although research has documented the use of Dynamic Geometric Software (DGS) in teaching the history of mathematics (HoM) (Zengin, 2018), the focus of this research specifically targets the development of proof for pre-service teachers by utilizing DGS to revisit historical proofs with a modern lens. The findings concur with Fujita et.al. (2010), Zengin (2018), and Conners (2007) work on proof. The novelty of this article was the combination of incorporating the history of mathematics (HoM), dynamic geometry software (DGS), and Toulmin’s model of argumentation. A pedagogical approach appeared to emerge: DGS’s dynamic nature allowed PSTs to see several examples of a method to provide them with an illustration that may be used in proofs.   

Out of Our Past

2006 ◽  
Vol 100 (5) ◽  
pp. 4-5
Keyword(s):  
Mathematics Teacher ◽  
History Of Mathematics ◽  
Retrospective View ◽  
History Of

A retrospective view on a history of Mathematics Teacher since its inception in 1908 till now. The author highlights most remarkable and pivotal events in its history displaying how the Tree of Mathematics grew up through the years.

On the classification of convex quadrilaterals

2016 ◽  
Vol 100 (547) ◽  
pp. 68-85 ◽  
Author(s):  
Martin Josefsson
Keyword(s):  
Golden Age ◽  
Euclidean Geometry ◽  
History Of Mathematics ◽  
Dynamic Geometry ◽  
Computer Programs ◽  
Primary Reason ◽  
Triangle Geometry ◽  
History Of

We live in a golden age regarding the opportunities to explore Euclidean geometry. The access to dynamic geometry computer programs for everyone has made it very easy to study complex configurations in a way that has never been possible before. This is especially apparent in the study of triangle geometry, where the flow of new problems, properties, and papers is probably the highest it has ever been in the history of mathematics. Even though it has increased a bit in recent years, the interest in quadrilateral geometry is significantly lower. Why are triangles so much more popular than quadrilaterals? In fact, we think it would be more logical if the situation were reversed, since there are so many classes of quadrilaterals to explore. This is the primary reason we think that quadrilaterals are a lot more interesting to study than triangles.

scholarly journals Uma discussão sobre legitimidades matemáticas utilizando o contexto dos números irracionaisA discussion about mathematical legitimacies using the irrational numbers context

2018 ◽  
Vol 20 (1) ◽  
Author(s):  
Rejane Siqueira Julio ◽  
Guilherme Francisco Ferreira ◽  
Romulo Campos Lins
Keyword(s):  
Teacher Education ◽  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Mathematics Teacher Education ◽  
History Of Mathematics ◽  
Mathematical Activity ◽  
Irrational Numbers ◽  
History Of ◽  
And Mathematics

Este artigo tem o objetivo de discutir legitimidades matemáticas para responder a certos questionamentos sobre a “matemática do professor de matemática” ser considerada um modo de pensar a matemática na formação de professores. Para isso, abordamos as noções de matemática do professor de matemática, matemática do matemático e atividade matemática, na ótica do Modelo dos Campos Semânticos, por meio de comentários hipotéticos sobre a realização de uma proposta de atividade, de cunho histórico, envolvendo os números irracionais. Para concluir, argumentamos sobre a caracterização de atividade matemática ser uma possibilidade de compreender o compartilhamento de legitimidades entre a matemática praticada pelos professores de matemática e a matemática praticada por matemáticos.This paper aims to discuss mathematical legitimacies as an answer to some questions about “mathematics of the mathematics teacher” as a way to think the mathematics in the mathematics teacher education. In this discussion, we approach the notions of mathematics of the mathematics teacher, mathematics of the mathematician and mathematical activity according to the Model of Semantics Fields, through hypothetical comments about the realization of a task, based on history of mathematics, involving irrational numbers. In conclusion, we argue about the possibility to consider the characterization of mathematical activity as a way of understanding the sharing of legitimacies between mathematics practiced by mathematics teachers and mathematics practiced by mathematicians.

scholarly journals INVESTIGACIÓN SOBRE LA HISTORIA DEL SABER PROFESIONAL DE LOS DOCENTES QUE ENSEÑAN MATEMÁTICAS: INTERROGATORIOS METODOLÓGICOS

PARADIGMA ◽  
2020 ◽  
pp. 900-911
Author(s):  
Wagner Rodrigues Valente
Keyword(s):  
Mathematics Teacher ◽  
Mathematics Teaching ◽  
History Of Mathematics ◽  
Professional Knowledge ◽  
Second Step ◽  
Teaching History ◽  
History Of ◽  
Mathematics For Teaching ◽  
And Mathematics

En este artículo presentamos algunos resultados de investigación que se han obtenido con el desarrollo de un amplio proyecto de investigación sobre el saber profesional del maestro que enseña matemáticas. En particular, nos centraremos en las discusiones metodológicas que están presentes en la vida diaria de las investigaciones que integran el proyecto. Así, las sistematizaciones que se están llevando a cabo desde los diferentes caminos seguidos por los investigadores que forman parte del proyecto, en la investigación del saber profesional del maestro que enseña matemáticas, se recogen en este texto. En forma de etapas de un proceso metodológico, los pasajes de la recopilación de información se analizan inicialmente, teniendo en cuenta las experiencias de enseñanza; en un segundo paso, es el conocimiento organizado a través de estas experiencias y, finalmente, la etapa de transformar el conocimiento en saber se hace explícita. En la caracterización del saber, se utilizan dos categorías: matemáticas a enseñar y matemáticas para enseñar. A partir de estas dos matemáticas, se establecen relaciones entre ellas para construir teóricamente el objeto identificado como el saber profesional del maestro que enseña matemáticas.Palabras clave: saber profesional, matemáticas, enseñanza, historia de las matemáticas, formación de maestros.A Pesquisa sobre História do Saber Profissional do Professor que Ensina Matemática: Interrogações MetodológicasResumoNeste artigo apresentamos alguns resultados de pesquisa que vêm sendo obtidos com o desenvolvimento de projeto amplo de investigação sobre o saber profissional do professor que ensina matemática. Em específico, iremos nos concentrar sobre as discussões metodológicas que estão presentes no cotidiano das pesquisas que integram o projeto. Assim, as sistematizações que estão sendo realizadas a partir dos diferentes caminhos trilhados pelos pesquisadores integrantes do projeto, na investigação do saber profissional do professor que ensina matemática, estão reunidas neste texto. Em forma de etapas de um processo metodológico, analisam-se, inicialmente, as passagens da coleta de informações, tendo em conta as experiências docentes; num segundo momento, o tratam-se dos conhecimentos organizados por meio dessas experiências e, por fim, explicita-se a etapa de transformação dos conhecimentos em saberes. Na caracterização dos saberes, são mobilizadas duas categorias: a matemática a ensinar e a matemática para ensinar. A partir dessas duas matemáticas, estabelecem-se relações entre elas de modo a poder-se construir teoricamente o objeto identificado como saber profissional do professor que ensina matemática.Palavras-chave: saber profissional, matemática, ensino, história da matemática, formação de professores.Research on the History of Professional Knowledge of the Mathematics Teacher: Methodological InterrogationsAbstractIn this article we present some research results that have been obtained with the development of a broad research project on the professional knowledge of the teacher who teaches mathematics. In particular, we will focus on the methodological discussions that are present in the daily life of the researches that integrate the project. Thus, the systematizations that are being carried out from the different paths followed by the researchers who are part of the project, in the investigation of the professional knowledge of the teacher who teaches mathematics, are gathered in this text. In the form of stages of a methodological process, the transformation of information is initially analyzed, taking into account the teaching experiences; in a second step, the are the knowledge organized through these experiences and, finally, the stage of transformation of knowledge from experiences into socially available knowledge is made explicit. In the characterization of knowledge, two categories are used: mathematics to teach and mathematics for teaching. From these two mathematics, relationships are established between them in order to theoretically construct the object identified as the professional knowledge of the teacher who teaches mathematics.Keywords: professional knowledge, mathematics, teaching, history of mathematics, teacher training

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.

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