Review: Mathematics, Culture, and Power

1998 ◽  
Vol 29 (3) ◽  
pp. 357-363
Author(s):  
Richard S. Kitchen ◽  
Joanne Rossi Becker

Arthur B. Powell and Marilyn Frankenstein's new book, Ethnomathematics: Challenging Eurocentrism in Mathematics Education, illuminates for our consideration a body of very practical mathematical knowledge largely discounted in the traditional mathematical community when compared with the abstract, theoretical mathematical knowledge typically valued highly by mathematicians. Ethnomathematics has caused us to call into question which mathematical knowledge really counts and thus has come to signify more than just “the study of mathematical ideas of nonliterate peoples” (a definition first offered by Marcia and Robert Ascher in the early 1980s in their paper, “Ethnomathematics,” reprinted as chapter 2 of this volume, p. 26). Editors Powell and Frankenstein use, instead, the broader definition of ethnomathematics provided in the book's opening chapter, “Ethnomathematics and Its Place in the History and Pedagogy of Mathematics,” by Ubiratan D'Ambrosio, a Brazilian mathematics educator whom many consider the intellectual progenitor of ethnomathematics. D'Ambrosio defines ethnomathematics as the mathematics that all cultural groups engage in, including “national tribal societies, labor groups, children of a certain age bracket, professional classes, and so on” (p. 16). Each group, including mathematicians, has its own mathematics. From D'Ambrosio's perspective, ethnomathematics exists at the confluence of the history of mathematics and cultural anthropology, overcoming the Egyptian/Greek differentiation between practical and academic mathematics.

2016 ◽  
Vol 29 (3) ◽  
pp. 273-304 ◽  
Author(s):  
François Lê

ArgumentThis paper challenges the use of the notion of “culture” to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to “geometrical equations,” objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to “geometrical equations,” and especially the technical aspects of these activities, is made on the basis of a sociological definition of “culture.” More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a “cultural system.”


2014 ◽  
Vol 10 (4) ◽  
Author(s):  
Peng Xu

AbstractPeirce expressed his pragmatic maxim in the 1870s. If, as Peirce maintained, this original definition is a maxim of logic, it is mainly a maxim of the logic of science, as the title “Illustrations of the Logic of Science” indicates. Pure mathematical conceptions, and the logic of mathematics, if not totally excluded, have at least not been emphasized. During his years at Johns Hopkins University, pure mathematics became his subject of most concern, while logic was also conceived as semiotics during this time. So around the turn of the century, when the popular movement of pragmatism began with James’ “Berkeley Address”, Peirce found that the main difficulty with his original definition of the pragmatic maxim was how to make pure mathematical conceptions clear. He mentioned this problem repeatedly but only gave a tentative solution admitting that, at least according to his original definition, some meanings of pure mathematical conceptions cannot be clarified. This, I believe, is the most important reason for Peirce’s renaming and redefining the pragmatic maxim in semiotic terms. If other pragmatists, and scholars of pragmatism, had noticed this, then most criticisms of pragmatism could have been avoided and the history of pragmatism may have taken a different direction.


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.


2008 ◽  
Vol 14 (1) ◽  
pp. 4-10
Author(s):  
Jane M. Watson ◽  
Noleine E. Fitzallen ◽  
Karen G. Wilson ◽  
Julie F. Creed

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic relationships to summaries of data sets. Traditionally, textbooks delineate the rules to be followed in creating conventional graphical forms, and software offers alternatives for attractive presentations. Is there anything new to introduce in the way of graphical representations for middle school students?


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.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 349
Author(s):  
María José Madrid ◽  
Alexander Maz-Machado ◽  
Fernando Almaraz-Menéndez ◽  
Carmen León-Mantero

Different studies consider the possibility of including history of mathematics in the classroom. However, its inclusion in the teaching and learning of mathematics depends on the conceptions of it that teachers have, among other factors. This study displays a comparative analysis between the opinions of primary education teachers-to-be and the opinions of mathematics teachers-to-be at secondary school and A-levels after the realization of an activity related to two historical or unusual multiplication methods. These trainee teachers were asked to identify the differences between these methods and the multiplication algorithm usually used in Spain. We collected these data and conducted an exploratory, descriptive and qualitative study. In order to analyse the information obtained, we used the technique content analysis. The answers given by these trainee teachers show their lack of knowledge about other multiplication methods and the various differences which they observed. These differences are mainly related to the structure of each method, the procedure and application of these methods and the mathematical processes carried out for each method. The comparison between the opinions of the teachers-to-be at different levels shows similarities but also some differences, probably due to the different mathematical knowledge they have.


PARADIGMA ◽  
2020 ◽  
pp. 212-239
Author(s):  
Ligia Arantes Sad ◽  
Claudia Alessandra C. de Araujo Lorenzoni

El texto discute el potencial y las contribuciones de la Historia de las Matemáticas en las prácticas de enseñanza de la Educación Matemática, ilustrada por dos episodios específicos de la práctica pedagógica de los autores. Toma como notas teóricas estudios como los de Ferreira, D'Ambrosio, Barbin, Jankivist y Vianna sobre los argumentos, implicaciones y sugerencias dirigidas al uso didáctico de la historia de las matemáticas. Los fundamentos de los autores se basan en un diálogo con la etnomatemática, entendiendo así las matemáticas escolares o las matemáticas, vistas en una forma occidental dominante, como una entre otras posibilidades de hacer y pensar matemáticamente. A lo largo del texto, la historia se destaca como un subsidio para la creación, tanto individual como colectiva, de explicaciones, relaciones de significados, objetos y significados que no se constituyeron hasta entonces. La creatividad, desde la perspectiva de Karwowski, Jankovska y Szwajkowski, y la investigación, en la línea de Ponte, se presentan como elementos relevantes en el proceso de enseñanza para estimular en cada estudiante una relación de construcción y apropiación del conocimiento matemático escolar de manera participativa. , interrogador y productor de nuevos conocimientos. Como resultado, señalamos: ser capaces de unir teorías e ideas científicas al analizar el potencial y las contribuciones de la Historia de las Matemáticas en las prácticas de enseñanza de la enseñanza de las matemáticas en la escuela, involucrando investigación y creatividad en metodologías y contextos híbridos de diferentes culturas.Palabras clave: Historia de las matemáticas. Educación matemática escolar. Juegos indígenas tradicionales. Investigación y creatividad.  HISTORY OF MATHEMATICS IN MATHEMATICAL EDUCATION, A ROUTE OF RESEARCH, CREATIVITY AND CULTURAL DIVERSITY AbstractThe text discusses the potential and contributions of the History of Mathematics in teaching practices in Mathematical Education, illustrated by two specific episodes of the authors' pedagogical practice. It takes as theoretical notes studies like those of Ferreira, D'Ambrosio, Barbin, Jankivist and Vianna about the arguments, implications and suggestions directed to the didactic use of the history of mathematics. The authors' foundations are based on a dialogue with Ethnomathematics, thus understanding school mathematics or mathematics - seen in a dominant Western way - as one among other possibilities of doing and thinking mathematically. Throughout the text, history stands out as a subsidy for the creation, both individual and collective, of explanations, relations of meanings, objects and meanings that were not constituted until then. Creativity, from the perspective of Karwowski, Jankovska and Szwajkowski, and research, in the Ponte line, are presented as relevant elements in the teaching process in order to stimulate in each student a relationship of construction and appropriation of school mathematical knowledge in a participatory way, questioner and producer of new knowledge. As a result we point out - being able to unite theories and scientific ideas when analyzing potentialities and contributions of the History of Mathematics in teaching practices of school Mathematics teaching, involving research and creativity in hybrid methodologies and contexts of different cultures.Keywords: History of Mathematics. School mathematical education. Traditional indigenous games. Research and creativity. HISTÓRIA DA MATEMÁTICA NA EDUCAÇÃO MATEMÁTICA, UMA VIA DE INVESTIGAÇÃO, CRIATIVIDADE E DIVERSIDADE CULTURAL ResumoO texto discute potencialidades e contribuições da História da Matemática em práticas docentes da Educação Matemática, ilustradas por dois episódios específicos da prática pedagógica das autoras. Toma como apontamentos teóricos estudos como os de Ferreira, D’Ambrosio, Barbin, Jankivist e Vianna acerca dos argumentos, implicações e sugestões direcionadas ao uso didático da história da matemática. Os fundamentos das autoras são alicerçados em diálogo com a Etnomatemática, entendendo, assim, a matemática ou a matemática escolar - vista de modo ocidental dominante – como uma entre outras possibilidades do fazer e pensar matematicamente. Ao longo do texto, destaca-se a história como subsídio para criação, tanto individual quanto coletiva, de explicações, relações de significados, objetos e sentidos que não estavam até então constituídos. A criatividade, na perspectiva de Karwowski, Jankovska e Szwajkowski, e a investigação, na linha de Ponte, são apresentadas como elementos relevantes no processo de ensino a fim de estimular em cada estudante uma relação de construção e apropriação do conhecimento matemático escolar de forma participativa, questionadora e produtora de novos conhecimentos. Como resultado apontamos - poder unir teorias e ideias científicas ao analisar  potencialidades e contribuições da História da Matemática em práticas docentes do ensino da Matemática escolar, envolvendo a investigação e a criatividade em metodologias híbridas e contextos de diferentes culturas.Palavras-chave: História da Matemática. Educação matemática escolar. Jogos tradicionais indígenas. Investigação e criatividade.


2021 ◽  
Vol 5 (8) ◽  
pp. 148-154
Author(s):  
Linfeng Han ◽  
Qian Tao

History and Pedagogy of Mathematics (HPM) is one of the important research fields in mathematics education, which has received widespread attention from the mathematics education community because of its educational value. Modern mathematics education technology plays an important auxiliary role in mathematics teaching. Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically. In view of this, this research takes “the recognition of circle” as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects: analyze the contents and uncover the history of mathematics, make the products and show the history of mathematics, design the teaching and integrate the history of Mathematics.


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