scholarly journals Investigating History of Mathematics for Teaching Mathematics: The Case of Logarithm

2021 ◽  
Author(s):  
Duygu ÖREN VURAL
Keyword(s):  
History Of Mathematics ◽  
Teaching Mathematics ◽  
History Of ◽  
Mathematics For Teaching

scholarly journals Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

Pythagoras ◽  
2008 ◽  
Vol 0 (68) ◽  
Author(s):  
Michael De Villiers
Keyword(s):  
History Of Mathematics ◽  
Genetic Approach ◽  
Mathematical Content ◽  
Euler Line ◽  
History Of ◽  
Mathematics For Teaching ◽  
The Creation ◽  
Reasoning By Analogy

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.

Scientific novelties implemented into teaching mathematics in secondary schools on the Polish territories in the 19th century. The case of descriptive geometry

2020 ◽  
pp. 205-218
Author(s):  
Karolina Karpińska
Keyword(s):  
Mathematics Education ◽  
19Th Century ◽  
18Th Century ◽  
History Of Mathematics ◽  
Descriptive Geometry ◽  
Teaching Mathematics ◽  
Education History ◽  
Secondary School Education ◽  
History Of ◽  
The 19Th Century

This article is dedicated to discussing the implementation of the descriptive geometry, i.e. the scientific novelty from the end of the 18th century, in secondary school education on the Polish territories in the 19th century. At that time, Polish lands were under the occupation of three empires: Prussia, Austria, and Russia. Over the time, the policy of the partition empires toward the Poles was changing in intensity. As a consequence, in the 19th century, there were schools on the Polish territories with Polish, Prussian, Austrian and Russian curricula and relevant lecture languages. The article analyses the implementation of descriptive geometry into teaching mathematics in schools located in all three partitions. Keywords: descriptive geometry, history of mathematics education, history of mathematics

Teaching Mathematics through Historic Environment. A Time-Travel Grounded Pedagogy

2019 ◽  
pp. 380-385
Author(s):  
Marguerite K. Miheso-O´Connor
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
History Of Mathematics ◽  
Time History ◽  
Time Travel ◽  
Teaching Mathematics ◽  
Historical Events ◽  
Long Period ◽  
Present Context ◽  
History Of

Mathematics has been used by generations to make important decisions for a long period of time. History is littered with problem solving events which are results of mathematization of tasks based on available tools in any given generation. While History of mathematics focuses on what each culture contributed to present day conventional mathematics as taught in schools as a subject, Mathematics in a Historic environment focuses on identifying mathematical thinking that exists in all historical events. Historical events when enacted through the Time Travel approach learners get the opportunity to relive past events in the present context. Teaching mathematics in historic environment uses the time travel events that are practised by bridging ages international, to provide a reflective meaningful conceptualization of mathematics is a living subject. The strategy illuminates the centrality of mathematical thinking in all historical events. This paper shares findings from a study carried out on the effectiveness of this approach for teaching mathematics and provides an opportunity to discuss the approach as a viable pedagogic strategy that can be replicated across the curriculum.

Projects: Historical Modules Project

2000 ◽  
Vol 93 (8) ◽  
pp. 728
Keyword(s):  
High School ◽  
High School Teachers ◽  
National Science Foundation ◽  
Mathematics Curriculum ◽  
History Of Mathematics ◽  
Secondary Mathematics ◽  
Teaching Mathematics ◽  
School Teachers ◽  
National Science ◽  
History Of

The Historical Modules Project, a part of the Institute in the History of Mathematics and Its Use in Teaching (IHMT), is sponsored by the Mathematical Association of America (MAA) and supported by the National Science Foundation. In the project, eighteen high school teachers and six college teachers with experience in the history of mathematics have been working in six teams to develop modules for various topics in the secondary mathematics curriculum. These modules are intended to show teachers how to use the history of mathematics in teaching mathematics.

scholarly journals APROXIMAÇÃO DA HISTÓRIA DA MATEMÁTICA PRESENTE NOS LIVROS DIDÁTICOS COM A ESCRITA HISTORIOGRÁFICA TRADICIONAL E ATUALIZADA

2018 ◽  
Vol 3 (2) ◽  
pp. 406-417
Author(s):  
Francisco Wagner Soares Oliveira ◽  
Eugeniano Brito Martins ◽  
Siziê Maria de Albuquerque ◽  
Ana Carolina Costa Pereira
Keyword(s):  
High School ◽  
Learning Process ◽  
Teaching And Learning ◽  
Basic Education ◽  
History Of Mathematics ◽  
Scientific Investigation ◽  
Teaching Mathematics ◽  
History Writing ◽  
Mathematics Textbook ◽  
History Of

Resumo: A história da matemática como campo de investigação cientifica tem possibilitado, por meio da observação e análise em tratados históricos que carregam em seu conteúdo e contexto uma gama de informações, a produção de narrativas historiográficas das quais são elencados desdobramentos para o ensino. Tal fato tem ocorrido a partir do pressuposto de que a incorporação de elementos da história em sala pode fornecer subsídios ao processo de ensino e aprendizagem. Visto isso, mediante a proximidade com a educação básica, em especial com o ensino médio, desenvolveu-se esse estudo na tentativa de identificar a aproximação das escritas baseadas na história da matemática presentes em livros didáticos do ensino médio com as vertentes historiográficas tradicional e atualizada. Nessa perspectiva, a pesquisa ora realizada foi de cunho qualitativa documental com uma contribuição bibliográfica. Verificou-se nesse estudo que os textos, em que informações da história são elucidadas, possuem características que condizem com a vertente historiográfica tradicional. Em nenhuma das alusões feitas à história foi possível observar um domínio de características que a indicasse como próxima a uma escrita da história nos moldes da vertente atualizada.Palavras-chave: Ensino de matemática. Livro didático. Escrita da história da matemática. Abstract: Tradução do resumo para o Inglês. The history of mathematics as a field of scientific investigation has made possible through observation and analysis in treaties and / or works that carry in their content and context a range of information to the production of some historiographical narratives, of which they are sometimes listed and / or some of its implications for teaching. This fact has occurred from the assumption that the incorporation of elements of the story into room may possibly provide subsidies to the teaching and learning process. Given this, and through proximity to basic education, especially with secondary education, this study was developed in an attempt to identify the approximation of the writings based on the history of mathematics present in high school textbooks with the traditional and updated historiographic aspect. From this perspective, the research carried out was qualitative documentary with a bibliographical contribution. It was mentioned in this study that the texts, in which information of the story are elucidated, have characteristics that correspond to the traditional historiographic aspect, in none of the allusions made history was it possible to observe a domain of characteristics that indicated it as close to a writing of history in the molds of the updated slope.Keywords: Teaching mathematics. Textbook. Math history writing.

Otto Toeplitz's 1927 Paper on the Genetic Method in the Teaching of Mathematics

2015 ◽  
Vol 28 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Michael N. Fried ◽  
Hans Niels Jahnke
Keyword(s):  
Mathematics Education ◽  
History Of Mathematics ◽  
Teaching Mathematics ◽  
Infinitesimal Calculus ◽  
Genetic Method ◽  
Mathematics History ◽  
University Courses ◽  
History Of ◽  
Teaching Of Mathematics

Argument“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” (1927) is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and assumptions about mathematics, history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research.

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

scholarly journals History of mathematics and teaching mathematics

2014 ◽  
Vol 27 (3) ◽  
pp. 15-30
Author(s):  
Mirko Dejic ◽  
Aleksandra Mihajlovic
Keyword(s):  
History Of Mathematics ◽  
Teaching Mathematics ◽  
History Of
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