Tamás Vargas Reformbewegung und der ungarische Guided Discovery-Ansatz

2020 ◽  
pp. 9-26
Author(s):  
Katalin Gosztonyi
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
History Of Mathematics ◽  
Historical Context ◽  
Education History ◽  
Mathematical Culture ◽  
Guided Discovery ◽  
Reform Project ◽  
History Of ◽  
New Math

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.

scholarly journals Perspectivas do Uso de Biografias na Formação de Professores de Matemática

2018 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Luiz Adriano Gonçalves Borges ◽  
Barbara Winiarski Diesel Novaes
Keyword(s):  
Mathematics Education ◽  
History Of Mathematics ◽  
Historical Context ◽  
Mathematical Education ◽  
Education History ◽  
General Philosophy ◽  
General Didactics ◽  
History Of ◽  
And Mathematics ◽  
Afro Brazilian

O presente trabalho tem por objetivo apresentar alguns elementos metodológicos de utilização de biografias como recurso articulador no ensino de matemática. Argumentamos em torno de um uso ponderativo de biografias ao invés do ornamental, isto é, de uma abordagem histórica que envolve um aprofundamento de conceitos e não somente de temáticas triviais. Apresentaremos uma metodologia que tenha profunda relação com o desenvolvimento histórico das ideias matemáticas e a história da educação matemática. Agindo nesse sentido, objetivamos propor a utilização de biografias de educadores matemático, matemáticos e cientistas como um recurso de aprofundamento em disciplinas dos cursos de licenciatura, mais especificamente no nosso caso, História da Matemática, Filosofia Geral, Tendências em Educação Matemática, Didática Geral e História e Cultura Afro-brasileira. Traçaremos uma breve trajetória da utilização de biografias como metodologia em história, ciências e matemática, procurando perceber como a historicidade do conhecimento científico é importante na elaboração deste tipo de trabalho. Procurando perceber paralelos, vemos que que o desenvolvimento da matemática não é independente do meio-cultural em que está inserido, sendo importante atentar para o contexto histórico da formação das ideias. Utilizamos esse conceitual metodológico no curso de Licenciatura em Matemática da UTFPR campus Toledo, nas disciplinas de História da Matemática, Filosofia Geral e História e Cultura Afro-brasileira (esta optativa), cuja metodologia de trabalho explicaremos neste presente texto. Por fim, ressaltamos o uso potencial da utilização de biografias de educadores matemáticos de renome para serem trabalhados em disciplinas em que prevalecem os saberes para ensinar.Palavras-chave: História da Educação Matemática. História da Ciência. Formação de professores. Biografias.AbstractThis present work aims to present some methodological elements of the use of biographies as an articulating resource in the teaching of Mathematics. We argue about a ponderous use of biographies instead of an ornamental, that is, of a historical approach that involves a deepening of concepts and not only of trivial themes. We will present a methodology that has a deep relation with the historical development of mathematical ideas and the history of mathematical education. Acting in this sense, we aim to propose the use of biographies of mathematical educators, mathematicians and scientists as a deepening resource in disciplines of undergraduate courses, specifically in our case, History of Mathematics, General Philosophy, Trends in Mathematics Education, General Didactics and Afro-Brazilian History and Culture. We will trace a brief trajectory of the use of biographies as methodology in History, Science and Mathematics, trying to understand how the historicity of scientific knowledge is important in the elaboration of this type of work. Looking for parallels, we understand that the development of mathematics is not independent of the cultural environment in which it is inserted, and it is important to look at the historical context of the formation of ideas. We use this methodological concept in the course of Mathematics Degree of the UTFPR campus Toledo, in the disciplines of History of Mathematics, General Philosophy and History and Afro-Brazilian Culture (this optional), whose working methodology will be explained in this text. Finally, we highlight the potential use of the use of biographies of renowned mathematical educators to be worked in disciplines in which the “knowledge to teach” prevails.Keywords: History of Mathematics Education. History of Science. Formation of Professors. Biographies.

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

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

2019 ◽  
pp. 137-148
Author(s):  
Katalin Gosztonyi
Keyword(s):  
Mathematics Education ◽  
Historical Perspective ◽  
Teaching Practice ◽  
History Of Mathematics ◽  
Guided Discovery ◽  
Mathematics History ◽  
History Of ◽  
Nature Of Mathematics ◽  
Written Sources

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.

scholarly journals Um Mapeamento de Estudos Históricos da Matemática nos Periódicos Nacionais de Qualis A1, A2 e B1 em Ensino no Período de 2013 a 2018

2021 ◽  
Vol 14 (1) ◽  
pp. 110-118
Author(s):  
Eliane Siviero da Silva Dalbon ◽  
Dulcyene Maria Ribeiro
Keyword(s):  
Mathematics Education ◽  
Philosophy Of Mathematics ◽  
History Of Mathematics ◽  
Mathematical Education ◽  
Education History ◽  
History Of Mathematics Education ◽  
Mathematics History ◽  
History Of ◽  
Em 12 ◽  
Education Field

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.

Tamás Varga und sein inspirierender Einfluss auf den Mathematikunterricht – ein Blick zurück

2020 ◽  
pp. 247-272
Author(s):  
Tünde Kántor
Keyword(s):  
Mathematics Education ◽  
Middle Schools ◽  
Secondary Schools ◽  
History Of Mathematics ◽  
Mathematical Journal ◽  
Mathematics Textbook ◽  
Guided Discovery ◽  
History Of ◽  
Object Area ◽  
School Books

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

On the history of mathematics trails

2020 ◽  
pp. 369-382
Author(s):  
Jörg Zender
Keyword(s):  
United Kingdom ◽  
Mathematics Education ◽  
Learning Environment ◽  
Outdoor Education ◽  
History Of Mathematics ◽  
Education History ◽  
Outdoor Learning ◽  
The United Kingdom ◽  
History Of ◽  
New Forms Of Learning

Mathematics trails have been in use for more than 40 years. A special outdoor learning environment that provides us interesting insides in the dissemination of such new forms of learning through its history. Both ways of dissemination can be found. We will first have a look at the steady development through a community of practitioners in the United Kingdom. The second way is the fast dissemination through a single multiplier, starting with Dudley Blane in Australia. In addition, the evolving variety of ways to do a mathematics trail is also part of this article. Keywords: mathematics trails, ICMI, mathematics education, history, outdoor education

scholarly journals História da Educação Matemática e a formação de professores primários: ensino de medidas

2018 ◽  
Vol 17 (1) ◽  
pp. 245
Author(s):  
Maria Célia Leme Da Silva
Keyword(s):  
Mathematics Education ◽  
21St Century ◽  
Mathematical Knowledge ◽  
History Of Mathematics ◽  
Historical Context ◽  
The Past ◽  
New Knowledge ◽  
History Of ◽  
National Literacy ◽  
Siglo Xix

O estudo busca responder às questões: De que maneira o conhecimento da história da educação matemática pode contribuir para as reflexões e desafios postos nos documentos atuais? Para tanto, analisa-se como a medida de superfícies em dois momentos históricos: final do século XIX, período caracterizado pela pedagogia moderna e início do século XXI no âmbito do Plano Nacional de Alfabetização. As fontes examinadas são: Caderno do PNAIC (2014), Parecer de Rui Barbosa (1883) e a Proposta de Gabriel Prestes (1895, 1896). Propõe-se pensar e conhecer os saberes matemáticos elementares do passado em seu contexto histórico, perceber que a institucionalização da expertise participa poderosamente da produção de novos saberes no campo pedagógico, porém seu processo de legitimação, de reconhecimento por seus pares é longo, complexo e conflituoso.Palavras-chave: PNAIC, Rui Barbosa, Gabriel Prestes. Expertise. AbstractThe study seeks to answer the questions: How can the knowledge of the history of mathematics education contribute to the reflections and challenges posed in the current documents? To this end, it is analyzed as the measurement of surfaces in two historical moments: the end of the nineteenth century, a period characterized by modern pedagogy and the beginning of the 21st century within the scope of the National Literacy Plan. The sources examined are: Notebook of the PNAIC (2014), Opinion of Rui Barbosa (1883) and the Proposal of Gabriel Prestes (1895, 1896). It is proposed to think and know the elementary mathematical knowledge of the past in its historical context, to realize that the institutionalization of expertise participates powerfully in the production of new knowledge in the pedagogical field, but its process of legitimation, recognition by its couple is long, complex and conflicting.Keywords: PNAIC, Rui Barbosa, Gabriel Prestes. Expertise.ResumenEl estudio busca responder a las preguntas: ¿De qué manera el conocimiento de la historia de la educación matemática puede contribuir a las reflexiones y desafíos planteados en los documentos actuales? Para ello, se analiza como la medida de superficies en dos momentos históricos: final del siglo XIX, período caracterizado por la pedagogía moderna e inicio del siglo XXI en el marco del Plan Nacional de Alfabetización. Las fuentes examinadas son: Cuaderno del PNAIC (2014), Dictamen de Rui Barbosa (1883) y la Propuesta de Gabriel Prestes (1895, 1896). Se propone pensar y conocer los saberes matemáticos elementales del pasado en su contexto histórico, percibir que la institucionalización de la expertise participa poderosamente de la producción de nuevos saberes en el campo pedagógico, pero su proceso de legitimación, de reconocimiento por sus pares es largo, complejo y complejo, conflicto.Palabras clave: PNAIC, Rui Barbosa, Gabriel Prestes. Expertise.Recebido  

A Matemática para o Professor dos Primeiros Anos Escolares – a Álgebra Entre a Cultura Enciclopédica e a Formação Profissional

2017 ◽  
Vol 10 (1) ◽  
pp. 8
Author(s):  
Wagner Rodrigues Valente
Keyword(s):  
Mathematics Education ◽  
Primary School ◽  
Cultural History ◽  
History Of Mathematics ◽  
Education History ◽  
School Teachers ◽  
Primary School Teachers ◽  
Training Models ◽  
History Of ◽  
The 19Th Century

Este texto analisa a entrada da Álgebra nos saberes matemáticos de formação de normalistas, a partir das últimas décadas do século XIX. Considera o debate entre dois modelos diferentes, para a formação dos professores dos primeiros anos escolares: o modelo ilustrado, para o ensino de cultura geral e o modelo de formação profissional restrita. A análise realizada toma os referentes da História Cultural. O estudo orienta-se pela questão: que razões justificam a entrada da Álgebra na formação do professor do ensino primário? Os resultados da investigação mostram a presença de rudimentos algébricos que amplificam o domínio da Aritmética tradicional. Em sentido mais amplo, tais conclusões indicam que para o estudo dos modelos de formação é necessário considerarem-se as finalidades de cada um dos saberes particulares, de cada conteúdo matemático.Palavras-chave: Formação de Professores. Educação Matemática. História da Educação Matemática.AbstractThis text analyzes the entrance of Algebra into the mathematical knowledge for the formation of normalists, starting in the last decades of the 19th century. It considers the debate between two different models, for the training of the teachers of primary school: the illustrated model, for the teaching of general culture, and the model of restricted professional formation. The analysis takes the referents of Cultural History. This study is guided by the question: What reasons justify the entry of Algebra into the training of primary school teachers? The results of this investigation show the presence of algebraic rudiments that amplify the domain of traditional Arithmetic. More broadly, these conclusions indicate that for the study of training models it is necessary to consider the purposes of each particular knowledge, of each mathematical content.Keywords: Teacher Training. Mathematics Education. History of Mathematics Education.

scholarly journals DIFFERENTIAL CALCULUS: THE USE OF NEWTON’S METHODUS FLUXIONUM ET SERIERUM INFINITARUM IN AN EDUCATION CONTEXT

2015 ◽  
Vol 65 (1) ◽  
pp. 39-65
Author(s):  
Paolo Bussotti
Keyword(s):  
Mathematics Education ◽  
General Theory ◽  
Differential Calculus ◽  
History Of Mathematics ◽  
First Year ◽  
Education History ◽  
Mathematical Concepts ◽  
History Of ◽  
One Year ◽  
The University

What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton’s Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise. Key words: mathematics education, history of mathematics, Newton, fluxions, tangents, maxima and minima, problem solving approach to mathematics education.

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