History of mathematics, mathematical histories, storytelling in Hungarian mathematics education

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.

2015 ◽  
Vol 28 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Michael N. Fried ◽  
Hans Niels Jahnke

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.


Author(s):  
Eliane Siviero da Silva Dalbon ◽  
Dulcyene Maria Ribeiro

ResumoO trabalho tem por objetivo apresentar um mapeamento dos artigos envolvendo estudos históricos da Matemática publicados nos periódicos nacionais de qualis A1, A2 e B1 em ensino, no período de 2013 a 2018. Os dados foram coletados a partir da leitura dos títulos, resumos e palavras-chave dos artigos, que foram classificados entre os campos temáticos: História da Matemática, História da Educação Matemática e História na Educação Matemática. De um total de 13 revistas com 212 edições e 2516 publicações, foram categorizados 255 artigos, sendo 91 no campo História da Matemática, 123 no campo História da Educação Matemática e 41 no campo História na Educação Matemática. Dentre os periódicos analisados, a Revista Brasileira de História da Matemática (RBHM), que tem como foco a publicação de trabalhos acadêmicos originais sobre História da Matemática em geral e sobre suas relações com outros campos, como a Educação Matemática e a Filosofia da Matemática, foi o periódico com maior número de artigos identificados na análise, 72 ao todo. Com relação a quantidade de trabalhos classificados em História da Matemática, apesar de serem computados 91 artigos, desses, 59 se encontram na Revista Brasileira de História da Matemática (RBHM), restando 32 artigos identificados em 12 periódicos. Todos os outros periódicos tiveram um volume maior de artigos classificados no campo História da Educação Matemática, 113 ao todo, incluindo duas edições temáticas em dois periódicos. O campo História na Educação Matemática, foi o que teve menos trabalhos classificados, 41 ao todo. Os dados refletem uma mudança no panorama das produções de estudos históricos da Matemática, que inicialmente eram voltados principalmente para a História da Matemática e que, no decorrer do tempo passou-se a ter o crescimento de um movimento em torno da História da Educação Matemática. Palavras-chave: Publicações em Periódicos. História da Matemática. História da Educação Matemática. História na Educação Matemática. AbstractThe work aims to present a mapping of articles involving historical studies of Mathematics published in national journals of qualis A1, A2 and B1 in teaching, from 2013 to 2018. Data were collected from the reading of titles, abstracts and words -key of the articles, which were classified among the thematic fields: History of Mathematics, History of Mathematics Education and History in Mathematics Education. From a total of 13 magazines with 212 editions and 2516 publications, 255 articles were categorized, 91 in the History of Mathematics field, 123 in the History of Mathematics Education field and 41 in the History in Mathematics Education field. Among the journals analyzed, the Revista Brasileira de História da Matemática (RBHM), which focuses on the publication of original academic works on the History of Mathematics in general and on their relations with other fields, such as Mathematics Education and the Philosophy of Mathematics, was the journal with the largest number of articles identified in the analysis, 72 in all. Regarding the number of papers classified in the History of Mathematics, although 91 articles are computed, of these, 59 are in the Revista Brasileira de História da Matemática (RBHM), leaving 32 articles identified in 12 journals. All other journals had a higher volume of articles classified in the History of Mathematical Education field, 113 in all, including two thematic editions in two journals. The History in Mathematics Education field had the least classified jobs, 41 in all. The data reflect a change in the panorama of the production of historical studies of Mathematics, which initially were mainly focused on the History of Mathematics and which, over time, began to have the growth of a movement around the History of Mathematics Education. Keywords: Publications in Journals. History of Mathematics. History of Mathematics Education. History in Mathematics Education.


Author(s):  
Katalin Gosztonyi

This paper presents Tamás Varga’s work focusing especially on the Hungarian Complex Mathematics Education reform project led by him between 1963 and 1978 and the underlying conception on mathematics education named “guided discovery approach”. In the first part, I describe Varga’s career. In the second part, I situate his reform project in its international and national historical context, including the international New Math movement and the Guided Discovery teaching tradition, something which is embedded in Hungarian mathematical culture. In the third part, I propose a didactic analysis of Varga’s conception on mathematics education, underlining especially certain of its characteristics which can be related to Inquiry Based Mathematics Education. Finally I briefly discuss Varga’s legacy today. Classification: A30, D30, D40, D50. Keywords: Tamás Varga, Guided Discovery approach, Inquiry Based Mathematics Education, history of mathematics education, curricular reform.


Author(s):  
Tünde Kántor

This article takes up some details of Tamás Varga's legacy from the perspective of a former student. The focus is on his ideas, opinions, reviews and articles on mathematics education in secondary schools. Two school books had a special impact at that time in Hungary, the mathematics textbook (1949/50) by Rózsa Péter and Tibor Gallai for the 1st class of middle schools (14-15 years) and its continuation „Mathematics for the 1st class of middle schools“ (1956) by Tamás Varga and László Faragó. Some of the problems Tamás Varga posed in the Mathematical Journal (e.g. Farkas Bolyai's theorem about the decomposing equality of plane figures and problems with the object area of the definitions of plane figures) are also important. The following explanations refer to his articles on mathematics education and his dissertation on complex mathematics education (1975). Classification: A30, C10, D30, U20. Keywords: History of mathematics education, Hungarian math books for secondary schools, beginning of math lessons by guided discovery


2017 ◽  
Vol 12 (12) ◽  
pp. 7023-7029
Author(s):  
Liang Fang ◽  
Rui Chen

This article researches the understanding and evaluation of tf mathematics history and its applying to the higher mathematics teaching, discusses the significance and role of history of mathematics in higher mathematics teaching, researches the method and means which the history of mathematics is introduced into higher mathematics teaching.


Author(s):  
Eunice Joana Ribeiro Tavares ◽  
Ana Paula Florêncio Aires

Resumo Num tempo em que se multiplicam diversas ferramentas tecnológicas para o ensino, em alguns momentos os professores esquecem-se de que os recursos mais simples, devidamente integrados, podem constituir-se como poderosas ferramentas pedagógicas. Nesta comunicação apresentamos uma intervenção didática, realizada numa turma do 5.o ano do 2.o Ciclo do Ensino Básico, que teve por base a integração da História da Matemática, em contexto de Prática de Ensino Supervisionada. Foi construída e implementada uma tarefa matemática, de acordo com os conteúdos programáticos que estavam a ser lecionados e tendo como suporte um material que designamos por “Baú Matemático”. Este estava organizado em cinco seções: A história ajuda, Curiosidades Matemáticas, Jogos Matemáticos, Explora e Biblioteca de Matemáticos, sendo que neste trabalho apenas exploramos a última seção. A concretização desta tarefa constituiu-se como uma experiência muito enriquecedora, pela confirmação da possibilidade e das potencialidades que a integração da História da Matemática acarreta para o ensino da matemática.Palavras-chave: Matemática, História da Matemática, Tarefas, Ensino. Abstract At a time when many technological tools for teaching are multiplying, at some moments, teachers forget that the simplest resources, properly integrated, can be powerful pedagogical tools. In this communication we present a didactic intervention carried out in a class of the 5th year of the 2nd Cycle of Basic Education, based on the integration of the History of Mathematics, in the context of Supervised Teaching Practice. A mathematical task was constructed and implemented, according to the programmatic contents that were being taught and supported by a material called "Mathematical Chest". This was organized into five sections: The Help Story, Mathematical Curiosities, Mathematical Games, Explore and Library of Mathematicians, and in this work we only explore the last section. Carrying out this task constituted a very enriching experience, by the confirmation of the possibility and the potential that the integration of the History of Mathematics entails for the teaching of mathematics. Keywords: Mathematics, History of Mathematics, Tasks, Teaching.


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.


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