Pub Date : 2016-10-25DOI: 10.22267/RELATEM.1693.12
Ángela Patricia Valencia Salas
Resumen Este documento presenta algunas reflexiones sobre los discursos raciales de tipo historico establecidos en Colombia desde el establecimiento de la Nueva Granada (1750 - 1816) en relacion a la ilustracion, la ciencia y la raza; y su influencia en las practicas de ensenanza de las matematicas escolares asociadas a estos discursos. Para ello se presenta en un primer momento algunos discursos utilizados por los ilustrados en ese periodo historico, luego la incidencia de estos en la ciencia y finalmente algunas relaciones e influencias de estos en las practicas de ensenanza de las matematicas a nivel curricular. Se retoman algunos estudios estadounidenses, latinoamericanos y del contexto colombiano en relacion a la raza, ensenanza de las matematicas, ademas de aquellos relacionados con perspectivas socioculturales de las matematicas. Abstract This document presents some reflections on the racial discourses of historical type, established in Colombia since the establishment of New Granada (19750-1816) regarding the illustration, science and race; and its influence on school teaching practices of mathematics associated to these speeches. To do so, some of the illustrated speeches in this historical are firstly presented illustrated, then the incidence of these in science and finally some relationships and influences of these practices in teaching mathematics at curricular level. Some North American, Latin American and of Colombian context in its relation to race, mathematics teaching, in addition to those related to sociocultural perspectives of mathematics.
最后，我们提出了一种新的方法，通过这种方法，我们可以确定一个国家的经济和社会状况，以及它的经济和社会状况。以及它对与这些演讲相关的学校数学教学实践的影响。本文首先介绍了这一历史时期插画家使用的一些话语，然后介绍了这些话语对科学的影响，最后介绍了这些话语对课程水平数学教学实践的一些关系和影响。本文回顾了美国、拉丁美洲和哥伦比亚背景下与种族、数学教学有关的一些研究，以及与数学的社会文化视角有关的研究。本文件对新格拉纳达建国(1975 -1816年)以来在哥伦比亚建立的关于插图、科学和种族的历史类型的种族论述提出了一些思考;= =地理= =根据美国人口普查，这个县的面积为。To do so some of the画报菁华in this历史are firstly年画报,然后介绍的这些科学和最后的一些关系和influences这些做法》教学数学at level课程。一些北美、拉丁美洲和of派context in its关于to race,数学教学,in addition to那些关于社会文化的视角of数学。
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A. Sartori, Juliano Espezim Soares Faria, C. G. Duarte, Valdirene Teixeira Flor
O artigo tem como objetivo analisar a racionalidade empregada na producao da farinha de mandioca por agricultores em um engenho localizado no bairro de Ibiraquera, na cidade de Imbituba em Santa Catarina - Brasil. Neste estudo iremos enfatizar a plantacao e a colheita da mandioca, e os procedimentos ate que seja transformada em farinha, baseados em uma metodologia qualitativa de inspiracao etnografica. Realizamos uma descricao a partir de observacoes diretas e entrevistas semiestruturadas, alem de diarios de campo, registros fotograficos e filmicos. Analisamos o material a partir do referencial teorico da Etnomatematica. Nosso principal interesse com esta vertente se distancia radicalmente das tentativas de enquadrar os saberes do cotidiano com base nos saberes hegemonicos da matematica. Este trabalho pretende discutir a insurreicao de saberes legitimos inseridos em jogos de linguagem especificos da producao de farinha de mandioca. Neste sentido, utilizamos as teorizacoes de Michel Foucault sobre os saberes sujeitados e as contribuicoes da segunda fase de Ludwig Wittgenstein a respeito da problematizacao da linguagem. Por fim, sugerimos que a investigacao pode possibilitar uma reflexao de praticas no âmbito escolar, no que se refere ao curriculo e os modos de lidar com o conhecimento matematico escolar e o conhecimento produzido por outras formas de vida.
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In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.
{"title":"Reassembling mathematical practices: a philosophical-anthropological approach","authors":"Karen François, E. Vandendriessche","doi":"10.22267/RELATEM.1692.7","DOIUrl":"https://doi.org/10.22267/RELATEM.1692.7","url":null,"abstract":"In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resumo Este estudo discute aspetos relativos a aprendizagens informais, evidenciadas em um grupo de mulheres artesas, residentes na cidade Santarem/PA, Regiao do Aritapera, e de que forma estas aprendizagens e saberes informais se interconectam com a perspetiva do Programa Etnomatematica. Suas praticas sociais, refletidas no artesanato regional, mostram particularidades, envolvendo a transmissao e producao de saberes, organizacao de comunidades de praticas e trocas simbolicas evidenciadas, durante o trabalho de elaboracao das cuias ornamentais. Os procedimentos metodologicos utilizados nesta investigacao foram organizados de acordo com uma abordagem etnografica, a partir da observacao e inferencia dos processos de construcao e incisoes de registros nas superficies que compoem as cuias regionais. Os resultados da investigacao indicam que a iconografia refletida nas cuias, aponta motivacoes especialmente relacionadas com representacoes sociais evidenciadas na dinâmica da comunidade e das relacoes comerciais envolvidas. As interacoes sociais possiveis e existentes no meio permeiam, assim, um fluxo de trocas permanentes de conhecimentos multifacetados diversos. A producao e ornamentacao das cuias estao muito relacionadas com uma especie de saber instrumental e tecnico, mais geral, o qual envolve a comunidade, como um todo. Ao mesmo tempo, agrega elementos particulares as praticas das artesas, de forma estreitamente conectada com a natureza revelando um saber dinâmico integrado e equilibrado com o meio ambiente, sem desconsiderar o fato de que qualquer alteracao ambiental coloca em risco a pratica cultural, ou seja, traz mudancas nos modos de producao.Abstract This study discusses aspects of informal learning, evidenced in a group of women artisans living in the city Santarem / PA, Aritapera region, and how these learning styles and informal knowledge interconnect with the perspective of the Ethnomatematics Program. Their social practices, reflected in their regional craft, show particularities involving the transmission and production of knowledge, organization of communities of practice and evidenced symbolic exchanges during the preparation work of ornamental gourds. Methodological procedures used in this research were organized, according to an ethnographic approach, from observation and inference of construction processes and incisions recorded on surfaces that create the regional gourds. Research results indicate that the iconography reflected in bowls, indicate motivations especially related with social representations evidenced in the community dynamics and commercial relations involved. Possible social interactions existing in this context thus permeate a permanent flow of diversified multifaceted knowledge exchange. The production and ornamentation of gourds are closely related to a kind of technical and instrumental knowledge, which involves the community as a whole. At the same time, it adds particular elements to the practices of the arti
{"title":"Artesãs de Aritapera/PA: técnicas e processos em uma perspetiva Etnomatemática","authors":"J. R. S. Mafra, M. Fantinato","doi":"10.22267/RELATEM.1692.9","DOIUrl":"https://doi.org/10.22267/RELATEM.1692.9","url":null,"abstract":"Resumo Este estudo discute aspetos relativos a aprendizagens informais, evidenciadas em um grupo de mulheres artesas, residentes na cidade Santarem/PA, Regiao do Aritapera, e de que forma estas aprendizagens e saberes informais se interconectam com a perspetiva do Programa Etnomatematica. Suas praticas sociais, refletidas no artesanato regional, mostram particularidades, envolvendo a transmissao e producao de saberes, organizacao de comunidades de praticas e trocas simbolicas evidenciadas, durante o trabalho de elaboracao das cuias ornamentais. Os procedimentos metodologicos utilizados nesta investigacao foram organizados de acordo com uma abordagem etnografica, a partir da observacao e inferencia dos processos de construcao e incisoes de registros nas superficies que compoem as cuias regionais. Os resultados da investigacao indicam que a iconografia refletida nas cuias, aponta motivacoes especialmente relacionadas com representacoes sociais evidenciadas na dinâmica da comunidade e das relacoes comerciais envolvidas. As interacoes sociais possiveis e existentes no meio permeiam, assim, um fluxo de trocas permanentes de conhecimentos multifacetados diversos. A producao e ornamentacao das cuias estao muito relacionadas com uma especie de saber instrumental e tecnico, mais geral, o qual envolve a comunidade, como um todo. Ao mesmo tempo, agrega elementos particulares as praticas das artesas, de forma estreitamente conectada com a natureza revelando um saber dinâmico integrado e equilibrado com o meio ambiente, sem desconsiderar o fato de que qualquer alteracao ambiental coloca em risco a pratica cultural, ou seja, traz mudancas nos modos de producao.Abstract This study discusses aspects of informal learning, evidenced in a group of women artisans living in the city Santarem / PA, Aritapera region, and how these learning styles and informal knowledge interconnect with the perspective of the Ethnomatematics Program. Their social practices, reflected in their regional craft, show particularities involving the transmission and production of knowledge, organization of communities of practice and evidenced symbolic exchanges during the preparation work of ornamental gourds. Methodological procedures used in this research were organized, according to an ethnographic approach, from observation and inference of construction processes and incisions recorded on surfaces that create the regional gourds. Research results indicate that the iconography reflected in bowls, indicate motivations especially related with social representations evidenced in the community dynamics and commercial relations involved. Possible social interactions existing in this context thus permeate a permanent flow of diversified multifaceted knowledge exchange. The production and ornamentation of gourds are closely related to a kind of technical and instrumental knowledge, which involves the community as a whole. At the same time, it adds particular elements to the practices of the arti","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-19DOI: 10.22267/RELATEM.1692.10
Domingo Yojcom Rocché, E. C. Guerra, M. E. Gavarrete, M. Tun, Sergio Pou Alberú, W. López, Leonel Morales Aldana, Armando Aroca
Este articulo presenta una aproximacion al estado del arte del Programa Etnomatematica en Centroamerica y Norteamerica. La metodologia parte de una revision bibliografica de las diferentes investigaciones realizadas en esta region desde la decada de los 80’s. Esta empresa no fue facil, pues cada coordinador tuvo la responsabilidad de elaborar una sintesis del trabajo realizado en el campo etnomatematico de su pais, bajo criterios establecidos que delimitaron el numero de aportes. Los resultados muestran aportes significativos al desarrollo del Programa Etnomatematica, asi como a otras areas de conocimiento como la historia, la antropologia, la sociologia y la educacion matematica. Evidencian la consolidacion de grupos de investigacion en diversas lineas, con una vasta participacion en congresos y publicaciones que representan la edificacion de una comunidad de practica de etnomatematicos en toda la region, desde Panama hasta los Estados Unidos.
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Pub Date : 2016-06-19DOI: 10.22267/RELATEM.1692.11
Armando Aroca
Resumen El objetivo principal de estas entrevistas es dar a conocer diversas concepciones de quince investigadores sobre el desarrollo del Programa Etnomatematica en el mundo y especificamente en Latinoamerica. Para ello, se elaboraron un conjunto de preguntas que fueron abordadas bajo la metodologia focus group. Estas preguntas hacen relacion a los avances del Programa Etnomatematica, sus desafios y el papel que juega dicho programa dentro de la globalizacion economica y el proyecto neoliberal. Consideramos que el conjunto de preguntas abordadas dara una vision mas amplia sobre la etnomatematica, sobre la educacion en general, sobre el potencial pedagogico que tiene en torno a la educacion matematica y las concepciones mismas que cada uno de nosotros tiene sobre la matematica. Abstract The principal objective of these interviews was to present a diversity of perceptions taken from fifteen researchers in ethnomathematics from Latin America and from the rest of the world. A methodology was developed consisting of a set of questions that were addressed by a focus group. These questions regarded the progress of Ethnomathematics, included challenges to the program itself as well as the role of the program in relation to economic globalization and neoliberalism. We believe that the set of questions addressed give a broader view of ethnomathematics in relation to general education, its pedagogical potential in mathematics education, and the ideas that each of us have about mathematics.
本文提出了一种新的方法，通过这种方法，我们可以确定一种新的方法，在这种方法中，一个人可以在他或她的职业生涯中，在他或她的职业生涯中，在他或她的职业生涯中，在他或她的职业生涯中，在他或她的职业生涯中，在他或她的职业生涯中。为此目的，拟订了一套问题，并在焦点小组方法下加以处理。这些问题与Etnomatematica项目的进展、挑战以及该项目在经济全球化和新自由主义项目中所扮演的角色有关。我们认为，所涉及的一系列问题将提供一个更广泛的观点，关于民族数学，关于一般教育，关于数学教育的教学潜力，以及我们每个人对数学的相同概念。Abstract这些交谈的主要目标was to目前采取的多样性of perceptions从fifteen研究in ethnomathematics from Latin America and from The rest of The world。已经制定了一种方法，其中包括由一个焦点小组处理的一套问题。这些问题涉及民族数学的发展，包括对该方案本身的挑战，以及该方案在经济全球化和新自由主义方面的作用。我们相信that the set的问题给broader view of ethnomathematics总关于数学的教育中的教育,其pedagogical潜力,and the想法处理每of us have about数学。
{"title":"El Programa Etnomatemática: Avances, Desafíos y su Papel en la Globalización Económica y el Proyecto Neoliberal","authors":"Armando Aroca","doi":"10.22267/RELATEM.1692.11","DOIUrl":"https://doi.org/10.22267/RELATEM.1692.11","url":null,"abstract":"Resumen El objetivo principal de estas entrevistas es dar a conocer diversas concepciones de quince investigadores sobre el desarrollo del Programa Etnomatematica en el mundo y especificamente en Latinoamerica. Para ello, se elaboraron un conjunto de preguntas que fueron abordadas bajo la metodologia focus group. Estas preguntas hacen relacion a los avances del Programa Etnomatematica, sus desafios y el papel que juega dicho programa dentro de la globalizacion economica y el proyecto neoliberal. Consideramos que el conjunto de preguntas abordadas dara una vision mas amplia sobre la etnomatematica, sobre la educacion en general, sobre el potencial pedagogico que tiene en torno a la educacion matematica y las concepciones mismas que cada uno de nosotros tiene sobre la matematica. Abstract The principal objective of these interviews was to present a diversity of perceptions taken from fifteen researchers in ethnomathematics from Latin America and from the rest of the world. A methodology was developed consisting of a set of questions that were addressed by a focus group. These questions regarded the progress of Ethnomathematics, included challenges to the program itself as well as the role of the program in relation to economic globalization and neoliberalism. We believe that the set of questions addressed give a broader view of ethnomathematics in relation to general education, its pedagogical potential in mathematics education, and the ideas that each of us have about mathematics.","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resumen En este documento damos cuenta de la creacion y analisis de un ambiente de modelacion matematica desde la perspectiva socio-critica (Araujo, 2009), desarrollado con un grupo de estudiantes de grado undecimo en un colegio publico de Bogota, Colombia, donde no se trabaja habitualmente este enfoque. El objetivo central del ambiente fue evidenciar posibilidades y desafios que pudieran encontrarse al incorporar: i) problemas socialmente relevantes, ii) participacion activa de los estudiantes en la construccion del modelo, iii) participacion activa de los estudiantes en la sociedad y, iv) actuacion del profesor como mediador. Para dar cuenta de lo anterior, se adopto una metodologia critica (Vithal, 2000; Skovsmose & Borba, 2004 y Valero, 2012), ademas de un analisis de los discursos producidos por los participantes del ambiente creado. Se encontro, como posibilidad, que los estudiantes trabajan en grupos, evidencian posicionamientos criticos y actitudes democraticas en clases. Como desafios se establecio que la participacion activa de los estudiantes en la sociedad debe reflexionarse y trabajarse mas profundamente. Abstract In this paper we account for the creation and analysis of an environment of mathematical modeling from the socio-critical perspective (Araujo, 2009). It was developed with a group of eleventh graders at a public school in Bogota, Colombia, where this approach does not usually work. The main aim of the environment was to make evident opportunities and challenges that could be found incorporating: i) non mathematical problems in the math class, ii) Students' active participation in the model construction, iii) Students' active participation in the society and, iv) teacher's performance as mediator. To account for this, a critical methodological approach was adopted (Vithal, 2000; Skovsmose & Borba, 2004 and Valero, 2012), as well as an analysis of the discourses produced by participants in the environment created. It was found, as a possibility, that students work in groups, demonstrate critical positions and democratic attitudes in class. As challenges, it was established that students’ active participation in the society needs to be thought over and more deeply worked.
{"title":"Prácticas de modelación matemática desde una perspectiva socio crítica con estudiantes de grado undécimo","authors":"F. Camelo, W. Perilla, G. Mancera","doi":"10.22267/RELATEM.1692.3","DOIUrl":"https://doi.org/10.22267/RELATEM.1692.3","url":null,"abstract":"Resumen En este documento damos cuenta de la creacion y analisis de un ambiente de modelacion matematica desde la perspectiva socio-critica (Araujo, 2009), desarrollado con un grupo de estudiantes de grado undecimo en un colegio publico de Bogota, Colombia, donde no se trabaja habitualmente este enfoque. El objetivo central del ambiente fue evidenciar posibilidades y desafios que pudieran encontrarse al incorporar: i) problemas socialmente relevantes, ii) participacion activa de los estudiantes en la construccion del modelo, iii) participacion activa de los estudiantes en la sociedad y, iv) actuacion del profesor como mediador. Para dar cuenta de lo anterior, se adopto una metodologia critica (Vithal, 2000; Skovsmose & Borba, 2004 y Valero, 2012), ademas de un analisis de los discursos producidos por los participantes del ambiente creado. Se encontro, como posibilidad, que los estudiantes trabajan en grupos, evidencian posicionamientos criticos y actitudes democraticas en clases. Como desafios se establecio que la participacion activa de los estudiantes en la sociedad debe reflexionarse y trabajarse mas profundamente. Abstract In this paper we account for the creation and analysis of an environment of mathematical modeling from the socio-critical perspective (Araujo, 2009). It was developed with a group of eleventh graders at a public school in Bogota, Colombia, where this approach does not usually work. The main aim of the environment was to make evident opportunities and challenges that could be found incorporating: i) non mathematical problems in the math class, ii) Students' active participation in the model construction, iii) Students' active participation in the society and, iv) teacher's performance as mediator. To account for this, a critical methodological approach was adopted (Vithal, 2000; Skovsmose & Borba, 2004 and Valero, 2012), as well as an analysis of the discourses produced by participants in the environment created. It was found, as a possibility, that students work in groups, demonstrate critical positions and democratic attitudes in class. As challenges, it was established that students’ active participation in the society needs to be thought over and more deeply worked.","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ever Enrique De la hoz Molinares, J. P. Fernández, Omar Enrique Trujillo Varilla
Resumen En este trabajo se investiga la representacion simbolica del sistema de numeracion de la cultura arhuaca de la sierra nevada de Santa Marta y el significado que tiene los numeros para esta comunidad; ademas se establecen similitudes y diferencias con el sistema decimal que hoy se les impone a los “hermanos mayores”. Es fundamental conocer como utilizan el sistema de numeracion autoctono en sus practicas tradicionales. Para los Arhuacos, los numeros influyeron en la creacion del universo y la conservacion y estos representan el origen de los seres. Existen numeros sagrados, como son: uno, dos, cuatro y nueve. El cuatro es un numero fundamental en sus practicas tradicionales, este representa los cuatro elementos de la naturaleza. El nueve representa el equilibrio con el universo. Los numeros expresan orden, cohesion, las concepciones de espacio, el entorno, una vision integral de su universo y su ley de origen, carecen de representacion simbolica, existen algunas figuras asociadas con los numeros, el sistema carece del cero, porque desde su cosmovision para los miembros de la cultura arhuaca no existe el vacio o la nada. Los conocimientos se transmiten de forma oral de generacion en generacion, a traves sus diferentes actividades socioculturales. El uso del sistema de numeracion en las practicas tradicionales, ha logrado su trascendencia hasta nuestros tiempos, pero poco conocido, por los escasos trabajos realizados sobre sus conocimientos matematicos. El sistema es posicional de base decimal, cardinal, sistematizado en su lengua ancestral Ikᵾ. Abstract This work presents the investigation about the symbolic representation of the numbering system of the arhuaco culture of the Sierra Nevada of Santa Marta and the significance of numbers for this community; it also establishes similarities and differences with the decimal system that is imposed today on "big brothers". It is essential to know how they use their indigenous numbering system in their traditional practices. For Arhuacos, numbers influenced the creation of the universe and its conservation, and they represent the origin of beings. There are sacred numbers such as one, two, four and nine. The number four is fundamental in their traditional practices, it represents the four elements of nature. Nine represents the balance with the universe. The numbers express order, cohesion, conceptions of space, the environment, a holistic view of their universe, and their law of origin. They don’t have symbolic representation; they have some figures associated with numbers; this system lacks zero, because from their worldview, the concepts of nothing and empty don’t exist. Knowledge is transmitted orally from generation to generation, through their diverse cultural activities. The use of the numbering system in traditional practices has achieved its importance to our time, but is little known, due to poor work done on their mathematical knowledge. The system is positional with a decimal bas
摘要在该项工作调查系统第八条作为simbolica numeracion文化arhuaca sierra nevada de Santa Marta和这个社会有数字的意义;此外，它还建立了与今天强加于“大哥”的十进制系统的相似和不同之处。了解他们在传统实践中如何使用自动编号系统是至关重要的。对阿瓦克人来说，数字影响了宇宙的创造和保护，它们代表了生命的起源。有神圣的数字，如:一、二、四和九。在他们的传统实践中，四是一个基本的数字，它代表了自然的四种元素。九代表与宇宙的平衡。这些数字的表达顺序、融合、概念空间,一个环境,这个宇宙的全面远景和法第八条作为simbolica,有一些数字的相关人物,缺乏系统重置,因为自cosmovision文化成员arhuaca迹或什么都不存在。知识是通过不同的社会文化活动代代相传的。在传统实践中使用数字系统，已经达到了它的重要性，直到我们的时代，但鲜为人知，因为在数学知识上所做的少数工作。系统是十进制,关键位置、收养的祖先语言Ikᵾ。本文介绍了对圣玛尔塔内华达山脉阿瓦科文化数字系统的符号表示和数字对这个社区的意义的调查;= =地理= =根据美国人口普查，这个县的面积为。了解他们如何在传统做法中使用本国的编号制度是至关重要的。= =地理= =根据美国人口普查，这个县的面积为。这是一个神圣的数字，比如一、二、四和九。= =地理= =根据美国人口普查，这个县的面积为。= =地理= =根据美国人口普查局的数据，该县的总面积为，其中土地和(1.)水。The numbers express秩序、融合、conceptions of space The environment,人口基金view of their宇宙,及其law of origin)。它们没有符号表示;它们有一些与数字有关的数字;= =地理= =根据美国人口普查，这个县的面积为。知识通过各种文化活动代代相传。在传统实践中使用数字系统对我们的时代具有重要意义，但由于在数学知识方面所做的工作很差，人们对数字系统知之甚少。The system is positional with a十进制基数基础上,is, and systematized in Ikᵾ。
{"title":"Números y universo arhuaco","authors":"Ever Enrique De la hoz Molinares, J. P. Fernández, Omar Enrique Trujillo Varilla","doi":"10.22267/relatem.1692.1","DOIUrl":"https://doi.org/10.22267/relatem.1692.1","url":null,"abstract":"Resumen En este trabajo se investiga la representacion simbolica del sistema de numeracion de la cultura arhuaca de la sierra nevada de Santa Marta y el significado que tiene los numeros para esta comunidad; ademas se establecen similitudes y diferencias con el sistema decimal que hoy se les impone a los “hermanos mayores”. Es fundamental conocer como utilizan el sistema de numeracion autoctono en sus practicas tradicionales. Para los Arhuacos, los numeros influyeron en la creacion del universo y la conservacion y estos representan el origen de los seres. Existen numeros sagrados, como son: uno, dos, cuatro y nueve. El cuatro es un numero fundamental en sus practicas tradicionales, este representa los cuatro elementos de la naturaleza. El nueve representa el equilibrio con el universo. Los numeros expresan orden, cohesion, las concepciones de espacio, el entorno, una vision integral de su universo y su ley de origen, carecen de representacion simbolica, existen algunas figuras asociadas con los numeros, el sistema carece del cero, porque desde su cosmovision para los miembros de la cultura arhuaca no existe el vacio o la nada. Los conocimientos se transmiten de forma oral de generacion en generacion, a traves sus diferentes actividades socioculturales. El uso del sistema de numeracion en las practicas tradicionales, ha logrado su trascendencia hasta nuestros tiempos, pero poco conocido, por los escasos trabajos realizados sobre sus conocimientos matematicos. El sistema es posicional de base decimal, cardinal, sistematizado en su lengua ancestral Ikᵾ. Abstract This work presents the investigation about the symbolic representation of the numbering system of the arhuaco culture of the Sierra Nevada of Santa Marta and the significance of numbers for this community; it also establishes similarities and differences with the decimal system that is imposed today on \"big brothers\". It is essential to know how they use their indigenous numbering system in their traditional practices. For Arhuacos, numbers influenced the creation of the universe and its conservation, and they represent the origin of beings. There are sacred numbers such as one, two, four and nine. The number four is fundamental in their traditional practices, it represents the four elements of nature. Nine represents the balance with the universe. The numbers express order, cohesion, conceptions of space, the environment, a holistic view of their universe, and their law of origin. They don’t have symbolic representation; they have some figures associated with numbers; this system lacks zero, because from their worldview, the concepts of nothing and empty don’t exist. Knowledge is transmitted orally from generation to generation, through their diverse cultural activities. The use of the numbering system in traditional practices has achieved its importance to our time, but is little known, due to poor work done on their mathematical knowledge. The system is positional with a decimal bas","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-18DOI: 10.22267/RELATEM.1692.21
Gloria Quidel Catrilaf, Karla Viviana Sepúlveda Obreque
El estudio esta referido al sistema de numeracion y las formas de conteo del pueblo mapuche. La necesidad de cuantificar hizo que este pueblo creara su propia forma de conteo (Rakin), dando origen a un sistema de numeracion decimal perfecto que se ha traspasado oralmente de generacion en generacion, por lo que no tiene simbolos para representar los numeros. El Rakin como practica social del pueblo mapuche encuentra valor en su uso, es un conocimiento situado producto de la construccion social de un pueblo en un contexto especifico. Este sistema de numeracion tiene una logica decimal en donde basta saber contar hasta diez para poder continuar contando. Para esto utiliza principios agregativos y repetitivos o multiplicativos. Es de interes de este estudio sistematizar y visibilizar un conocimiento de origen social como alternativa epistemica que permita validar otros conocimientos mas alla del conocimiento cientifico y cooperar a la generacion de una relatividad epistemica que reconozca distintos tipos de conocimiento de los seres humanos organizados en sociedades. El metodo de analisis utilizado es cualitativa etnografica y los instrumentos que se utilizaron fueron entrevistas.
{"title":"El Rakin, conteo mapuche, un conocimiento con valor de uso","authors":"Gloria Quidel Catrilaf, Karla Viviana Sepúlveda Obreque","doi":"10.22267/RELATEM.1692.21","DOIUrl":"https://doi.org/10.22267/RELATEM.1692.21","url":null,"abstract":"El estudio esta referido al sistema de numeracion y las formas de conteo del pueblo mapuche. La necesidad de cuantificar hizo que este pueblo creara su propia forma de conteo (Rakin), dando origen a un sistema de numeracion decimal perfecto que se ha traspasado oralmente de generacion en generacion, por lo que no tiene simbolos para representar los numeros. El Rakin como practica social del pueblo mapuche encuentra valor en su uso, es un conocimiento situado producto de la construccion social de un pueblo en un contexto especifico. Este sistema de numeracion tiene una logica decimal en donde basta saber contar hasta diez para poder continuar contando. Para esto utiliza principios agregativos y repetitivos o multiplicativos. Es de interes de este estudio sistematizar y visibilizar un conocimiento de origen social como alternativa epistemica que permita validar otros conocimientos mas alla del conocimiento cientifico y cooperar a la generacion de una relatividad epistemica que reconozca distintos tipos de conocimiento de los seres humanos organizados en sociedades. El metodo de analisis utilizado es cualitativa etnografica y los instrumentos que se utilizaron fueron entrevistas.","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resumo O sistema de medida foi fundamental para o desenvolvimento dos povos, tanto que as mais diversas culturas orientais e ocidentais desenvolveram paralelamente ferramentas proprias, o que levou o homem a estabelecer os padroes e regras de medida universal. No Brasil, os livros de matematica do 6° ano do ensino fundamental trazem para os alunos o contato formal com o sistema metrico e seus multiplos e submultiplos, porem o aluno nao e induzido a raciocinar outras formas de medicao presente no seu cotidiano. Este trabalho mostra atraves de relatos do povo indigena Kanamari de Maraa-AM, como seus antepassados mediam o comprimento das distancias, dos terrenos e ate da altura das casas. Esses relatos foram introduzidos dentro da sala de aula e apresentado aos alunos com o objetivo de ensinar as unidades de medida com enfoque etnomatematico para uma turma do 6° ano do ensino fundamental da Escola Municipal Indigena Kanamari. Alem do resgate de uma pequena parte dessa cultura, essa atividade favoreceu uma reflexao da parte dos docentes quanto suas praticas pedagogicas, uma vez que, lideres comunitarios, professores indigenas e nao indigenas puderam constatar que o ensino institucionalizado aliado ao conhecimento tradicional, favoreceu a aprendizagem dos alunos quanto ao conteudo abordado, propiciando a perpetuacao da cultura kanamari. Abstract Systems of measurement were fundamental to the development of peoples, so that the most diverse oriental and western cultures developed their own tools parallel to one another, bringing man to the creation of norms and rules of universal measurement. In Brazil, the 6th-grade math books of elementary school students bring them into formal contact with the metric system and their multiples and sub-multiples, but the students are not induced to think about other forms of measuring present in their daily lives. This paper shows, through narratives of the Kanamari indigenous people of Maraa-AM, how their ancestors measured length, distances, lands and even the height of the houses. These narratives were introduced into the classroom and presented to the 6th-grade students of the Indigneous Municipal School of Kanamari in order to teach the units of measurement with an ethnomathematical approach. Beyond rescuing a small part of their culture, this activity favored a reflection on the part of teachers about their pedagogical practices, since, community leaders, indigenous teachers and non-indigenous have noted that an institutionalized education allied to indigenous knowledge favors student learning of content, allowing for the perpetuation of Kanamari culture.
{"title":"Etnomatemática: O ensino de medida de comprimento no 6º ano do ensino fundamental na Escola Indígena Kanamari Maraã-AM, Brasil","authors":"B. Júnior, Edilanê Mendes dos Santos","doi":"10.22267/relatem.1692.2","DOIUrl":"https://doi.org/10.22267/relatem.1692.2","url":null,"abstract":"Resumo O sistema de medida foi fundamental para o desenvolvimento dos povos, tanto que as mais diversas culturas orientais e ocidentais desenvolveram paralelamente ferramentas proprias, o que levou o homem a estabelecer os padroes e regras de medida universal. No Brasil, os livros de matematica do 6° ano do ensino fundamental trazem para os alunos o contato formal com o sistema metrico e seus multiplos e submultiplos, porem o aluno nao e induzido a raciocinar outras formas de medicao presente no seu cotidiano. Este trabalho mostra atraves de relatos do povo indigena Kanamari de Maraa-AM, como seus antepassados mediam o comprimento das distancias, dos terrenos e ate da altura das casas. Esses relatos foram introduzidos dentro da sala de aula e apresentado aos alunos com o objetivo de ensinar as unidades de medida com enfoque etnomatematico para uma turma do 6° ano do ensino fundamental da Escola Municipal Indigena Kanamari. Alem do resgate de uma pequena parte dessa cultura, essa atividade favoreceu uma reflexao da parte dos docentes quanto suas praticas pedagogicas, uma vez que, lideres comunitarios, professores indigenas e nao indigenas puderam constatar que o ensino institucionalizado aliado ao conhecimento tradicional, favoreceu a aprendizagem dos alunos quanto ao conteudo abordado, propiciando a perpetuacao da cultura kanamari. Abstract Systems of measurement were fundamental to the development of peoples, so that the most diverse oriental and western cultures developed their own tools parallel to one another, bringing man to the creation of norms and rules of universal measurement. In Brazil, the 6th-grade math books of elementary school students bring them into formal contact with the metric system and their multiples and sub-multiples, but the students are not induced to think about other forms of measuring present in their daily lives. This paper shows, through narratives of the Kanamari indigenous people of Maraa-AM, how their ancestors measured length, distances, lands and even the height of the houses. These narratives were introduced into the classroom and presented to the 6th-grade students of the Indigneous Municipal School of Kanamari in order to teach the units of measurement with an ethnomathematical approach. Beyond rescuing a small part of their culture, this activity favored a reflection on the part of teachers about their pedagogical practices, since, community leaders, indigenous teachers and non-indigenous have noted that an institutionalized education allied to indigenous knowledge favors student learning of content, allowing for the perpetuation of Kanamari culture.","PeriodicalId":30076,"journal":{"name":"Revista Latinoamericana de Etnomatematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68288472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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