Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2004 / This research is in the field of ethnomathematics. The study was carried out in three phases with the Tchadji-game being its principal focus. Tchadji is a traditional game played at Ilha de MOyambique, a small Island situated on the northeast coast of Mozambique. Tchadji belongs to a class of board games known as Mancala, which are thousands of years old and are played throughout the African continent as well as in other parts of the world. Mancala games have only recently received due attention as a topic for research. The first phase of the research was carried out in the school mathematics classroom. The outcomes of this phase indicated that games like Tchadji and the three stones (a variant of the Muravarava game) as a part of Mozambican culture are also rich in providing opportunities for activities in the mathematics classroom related to the development of key probabilistic concepts. Quasi-experimental research involving the researcher, 4 mathematics teachers and 162 students showed statistically significant positive effects on attitude towards the learning of, and performance in probability. These outcomes were corroborated by qualitative research. The second phase of this study consisted of ethnographic research amongst master Tchadji players, which explored the mathematical ideas embedded in the Tchadji-game and in the procedures for playing the game. The results of this phase of the research revealed that, the Tchadji-players had mathematical knowledge, skills and ways of thinking such as counting, logical thinking, calculation, visualisation, recognition of different numerical patterns and infinity. These results are described in terms of examples taken from different critical moments of the recorded matches of Tchadji. This way of iii Abstract (PhD thesis) presenting the results gives insight into the complexity of the methodology used. It also uncovers different aspects of playing Tchadji, like rules, strategies and tactics. A need for further investigations of this nature for uncovering mathematical ideas in traditional culture is also indicated by this research. As advocated in ethnomathematical research an intervention with (pre and in-service) student teachers formed the third phase of the research. The results of this phase indicated that the 24 teachers, who participated in the research, showed enthusiasm, satisfaction and excitement in experiencing the mathematical richness of Tchadji and in appreciating possibilities for the use of Tchadji in the mathematics classroom. They were able to analyse the game independently and to identify embedded mathematical ideas in the game, like logical thinking, counting and empirical and mental calculation. The research makes contributions to the field of ethnomathematics itself, to ethnographic research methodology and to the pedagogy of mathematics.

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Made available in DSpace on 2014-06-11T19:24:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-03-29Bitstream added on 2014-06-13T20:13:12Z : No. of bitstreams: 1 shinkawa_gz_me_bauru.pdf: 913427 bytes, checksum: 01f2fdcfa9991d42690cba86bdd94b29 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho teve como propósito identificar, num primeiro momento, os saberes matemáticos presentes em um empreendimento em Economia Solidária e as dificuldades encontradas pelas integrantes deste no trato com o conhecimento matemático. Num segundo momento, buscou-se traçar ações pedagógicas visando sanar algumas dessas dificuldades, na direção de favorecer a autogestão (em matemática) do grupo. O enfoque teórico fundamenta-se nos princípios da Etnomatemática e Economia Solidária, trazendo também discussões sobre Tecnologia Social e autogestão. Os sujeitos da pesquisa são três senhoras que constituem o empreendimento aqui denominado Grupo de fabricação de sabão caseiro, o qual é composto por moradoras de um bairro proveniente de desfavelamento, donas de casa e que apresentam dificuldades em deixar o trabalho doméstico para se dedicar a outra profissão, mas precisam garantir renda para manutenção de suas famílias. A metodologia empregada tem caráter qualitativo e caracteriza-se como pesquisa-ação e; a coleta de dados ocorreu por meio de observação participante e entrevistas semiestruturadas. Após a análise dos dados obtidos possou-se à atuação pedagógica em Matemática buscando a autogestão dos sujeitos de pesquisa. As análises indicaram que os saberes matemáticos, pautados principalmente no trabalho colaborativo e cooperação entre as sócias, e que já diversas dificuldades enfrentadas; apontando para a necessidade de uma melhor compreensão de alguns conhecimentos matemáticos cotidianos, os quais foram parcialmente possibilitados através deste estudo / The present study aimed to initially identify the mathematical knowledge present in an enterprise in Solidary Economy and the dificulties encountered by members of treat dealing with mathematical knowledge. At a second moment, we sought to draw pedagogical actions aimed at remedying some of these difficulties, in the direction of promoting self-management (in mathematics) by the group. The theoretical approach is based on the principles of Ethnomathematics and Solidarity Economy, brinding discussions about technology and social management. The subjects of the research are three ladies constituing the enterprise which are here called the venture group making homemade soap, which is composed of residents of a neighborhood from a dissolved Shantytown, housewives and who have difficulties to abandon the housework to devote themselves to another profession, but they need to guarantee income to maintain their families. The applied methodology is qualitative and is characterized as action research; and the data were collected through participant observation and semistructured interviews. After analyzing the data were passed to its role in mathematics teaching self-management seeking research subjects. The analyzes indicated the mathematical knowledges, which are primarily based on collaborative work and cooperation among members, and there are some difficulties faced, pointing to the necessity for a better understanding of some mathematical skills used in everyday life, which became partly possible through this study

Orientador: Pedro Paulo Scandiuzzi / Banca: Marcos Vieira Teixeira / Banca: Arlindo José de Souza Júnior / Banca: João Frederico da Costa Azevedo / Resumo: A presente dissertação aborda o tema referente ao uso de medidas não-oficiais no cotidiano das pessoas ligadas à área rural, moradoras do Distrito de Talhado (SP). Para o desenvolvimento da parte teórica, foi construída uma cronologia que apresenta um panorama dos principais acontecimentos na Europa e na América à época da concepção do sistema métrico decimal para que, com isso a explicação sobre a reforma do sistema métrico decimal na França, em Portugal e no Brasil seja mais bem compreendida. Para o desenvolvimento da parte empírica, fez-se uso da pesquisa qualitativa de caráter etnográfico, onde as técnicas utilizadas compreenderam a observação participante e entrevistas não-estruturadas, tendo como instrumento de coleta de dados o diário de campo. A análise teve como referencial teórico principal publicações na área do Programa de Pesquisa em Etnomatemática. / Abstract: The present dissertation is concerned with the theme which refers to the use of non-official measurements in everyday life of people who work and live in the rural area of Talhado (SP). In order to develop the theoretical part, a chronology which presents an overview of the main facts occurred in Europe and America at the time when the decimal metric system was formed. By doing so, the explanation about the reforms on the decimal metric system becomes clearer and easier to understand. For the development of the empirical part made use of an ethnographic qualitative research and the techniques embodied in such methodology were the participatory observation, non-structured interviews and a diary for registering the main parts of the obtained information. The theoretical references for analysing the data were papers on the field of the Ethnomathematics Research Program. / Mestre

Working paper summarizing research into cataloging theory, history of science, mathematics, and information science. / The report summarizes a research program that has been investigating how catalogers, other Cultural Heritage information workers, World Wide Web/Semantic Web technologists, and the general public understand, explain, and manage resource description tasks by creating, counting, measuring, classifying, and otherwise arranging descriptions of Cultural Heritage resources within the Bibliographic Universe and beyond it.

Este trabalho de investigação tem como objetivo compreender e analisar o desenvolvimento do Curso de Formação dos Professores Indígenas do Estado de São Paulo - MagIND, uma parceria entre a Secretaria de Estado da Educação e a Faculdade de Educação da Universidade de São Paulo, FE-USP, realizado em 2002 e 2003. Os indígenas que concluiram o curso estão aptos a serem professores de Educação Infantil e das quatro séries iniciais do Ensino Fundamental I. Para a pesquisa, foram considerados os pontos de vista dos professores indígenas e dos professores/formadores não-indígenas, partindo do pressuposto de que a escola é um espaço de diálogo e conflito entre os conhecimentos indígenas e aqueles da escola não-indígena. O recurso de entrevista foi o procedimento básico da pesquisa cujas categorias de análise que emergiram das respostas às entrevistas são: (a) duração do curso, ritmos docentes e discentes; (b) oralidade, leitura e escrita; (c) o preconceito vivido e o poder alcançado pelos professores indígenas, (d) a matemática escolar e os professores indígenas. No âmbito dos fundamentos, procurei contribuições na Antropologia Social e na Etnomatemática para entender os limites e as possibilidades da educação escolar indígena e, de modo especial, para compreender as contradições e os progressos que ocorrem no processo ensino-aprendizagem quando são tomadas como objetivos e valores a interculturalidade e a Etnomatemática. / This work of inquiry intends to understand and to analyze the development of the São Paulo State indigenous teachers\' formation program - MagIND, a program developed through a partnership between the São Paulo State Secretary of Education and the College of Education at the University of São Paulo, FE-USP, Brazil, carried in 2002 and 2003. The indigenous people that have concluded the course have been qualified to be k - 4/ kindergarten and elementary education teachers. This research has been devised according to the point of view of the indigenous teachers and non-indigenous teachers and teacher educators, starting from the assumption that the school is a space of dialogue and conflict between the indigenous people knowledge and the non-indigenous school one. The resource of interviewing was the basic research procedure whose categories of analysis that emerged from the answers to the interviews are: (a) duration of the course, teacher and student rhythms; (b) speaking, reading and writing; (c) the living prejudice and the power achieved by the indigenous teachers (d) the school mathematics and the indigenous teachers. In regards to the background theory I have looked for contributions in the Social Anthropology and Ethnomathematics to understand the limits and the possibilities of indigenous school education and, more specifically to understand the contradictions and the progress in the teaching-learning process when interculturality and Ethnomathematics are considered as objective and values.

Este trabalho apresenta reflexões acerca dos movimentos que configuraram as primeiras ideias do campo científico da Etnomatemática. Teve como objetivo compreender tais movimentos, principalmente no que se refere à dimensão educacional da Etnomatemática, a partir das trajetórias de quatro pesquisadores neste contexto. A busca por reflexões nessa dimensão justifica-se por ser consenso, entre os educadores envolvidos nessa perspectiva, que é natural considerar a Etnomatemática como um caminho/método de pesquisa, embora para a educação escolar seja uma tarefa/proposta mais complexa. A investigação privilegiou a História Oral como metodologia para a coleta de dados por meio de entrevistas semiestruturadas. Realizaram-se entrevistas com quatro educadores matemáticos: dois brasileiros e dois estrangeiros, considerados, para o contexto do trabalho, como pesquisadores dos primeiros movimentos em Etnomatemática, com contribuições nacionais e internacionais para o contexto da Educação Matemática. A investigação evidenciou, a partir de três eixos (matemática como produção cultural, valorização do conhecimento do outro e Etnomatemática como proposta pedagógica),que os primeiros movimentos em Etnomatemática tiveram como referência principal as ideias propostas por Ubiratan D`Ambrosio; que o discurso dos depoentes revelou o respeito com o outro na diversidade de culturas; e que se torna necessário refletir sobre a possibilidade de ampliar as abordagens práticas da Etnomatemática, a fim de fortalecê-la como postura ou atitude pedagógica. / This work represents reflections on the movements that configure the first ideas in the scientific field of Ethnomathematics. Its aim is the understanding of such movements, mainly the ones referring to the educational dimension of Ethnomathematics, based on the studies of four researchers in this field. The search for reflections in this dimension is justified by the fact that there is a consensus among educators involved in this perspective, that it is natural to consider Ethnomathematics as a way/method of research, although for school education this is a more complex task/proposal. The investigation prioritized the Oral History as the methodology to collect data through semi structured interviews. Interviews with four Mathematics educators were made - two Brazilians and two non-Brazilians, who were considered, in terms of this work, researchers of the first movements in Etnomathematics with national and international contributions to the Mathematics Education context. The investigation, from three axes, Mathematics as a cultural production, the valorization of someone else´s knowledge and Ethnomathematics as a pedagogical proposal, emphasized that the first movements in Etnomathematics had as main reference the ideas proposed by Ubiratan D´Ambrosio, showing that the discourse of the ones interviewed revealed the respect to the other in cultural diversity, which makes it necessary to reflect on the possibility of broadening the practical approaches of the Ethnomathematics, in order to strengthen it as a behavior or pedagogical attitude.

Orientador: Pedro Paulo Scandiuzzi / Banca: Maria Teresa Eglér Mantoan / Banca: Rosana Giaretta Sguerra Miskulin / Resumo: O trabalho intitulado "A Etnomatemática no contexto do ensino inclusivo: possibilidades e desafios" é uma pesquisa, de caráter etnográfico, que tem como objetivo observar, descrever e analisar como os professores de uma escola inclusiva lidam com os alunos, na disciplina Matemática, de modo a corroborar com o processo de inclusão. A pesquisa foi realizada em uma escola do projeto CIEJA - Centro Integrado de Educação de Jovens e Adultos - da Secretaria de Educação da cidade de São Paulo, que oferece o ensino fundamental na modalidade supletivo para 1308 alunos. Foram observados quatro professores, sendo três formados em matemática e um formado em pedagogia. O trabalho aponta que o processo de inclusão, baseado na perspectiva etnomatemática, está ligado à postura ética em que se preza o respeito, a solidariedade e a cooperação, ambiente onde as diferenças são valorizadas e, portanto, propício à inclusão. Salienta também que, para o processo de inclusão, não há um modelo pronto; o que existe é a transição da integração para a inclusão e, por isso, podem ser detectadas práticas não inclusivas mesmo em um ambiente com proposta inclusiva. / Abstract: The work entitled "Ethnomathematics in the teaching context for inclusion: possibility and challenge" is an investigation of ethnographic type that has the purpose to observe, describe and analyse how the teachers of an inclusive school deal with the students in the mathematics subject so as to corroborate with the process of inclusion. The research was accomplished in a school of the project CIEJA - Integrated Center of Youngs and Adults Education - of Education Secretaryship of São Paulo's city, that offer adult education fundamental teaching for 1308 students. Four teachers were observed, of which three are graduated in mathematics and one is graduated in pedagogy. The work indicates that the process of inclusion, grounded in the ethnomathematics perspective, is linked with the ethical posture that values the respect, solidarity and co-operation, environment where the differences are valorized and, thus, propitious for the inclusion. It emphasizes too that the process of inclusion isn't a ready model, on the contrary what exists is the transition from the integration to the inclusion and, therefore, it can be detect non-inclusive practices even so in this environment with inclusive proposal. / Mestre

Denna studie har undersökt på vilket sätt elevers slöjdarbete kan stödja elevers lärande i matematik. Studien utgår ifrån det s.k. sociokulturella perspektivet där kunskap och lärande utvecklas i samspelet mellan människor och där situationella betingelser och språket spelar en central roll för kunskapsutvecklingen. Studien bygger på en kvalitativ undersökning med inspiration från den metod som på engelska benämns grounded theory. Det empiriska materialet utgörs av observationer av elevers slöjdarbeten i textilslöjdens årskurs 3-9. Observationerna har pågått under 2 års tid och utmynnat i dagboksanteckningar av elevers slöjdarbeten. Den nya svenska läroplanen, Lgr 11, och dess kursplan i matematik utgör det ramverk mot vilket elevers slöjdarbeten, och dess möjlighet att stödja elevers lärande i matematik, analyseras. Kursplanens förmågor kompletteras i analysen av Kilpatricks fem matematiska kompetenser. Resultatet visar hur matematik från kursplanens samtliga sex områden visar sig i elevers slöjdarbeten. Eleverna använder sig av matematik vid beräkningar, problemlösning och i vissa fall som inspiration till ett slöjdarbete. Det visar också på hur elevers slöjdarbeten kan bidra till att utveckla de förmågor som kursplanen i matematik beskriver och som även Kilpatrick redogör för genom sina fem matematiska kompetenser. Den teoretiska modell som arbetet utmynnat i bidrar till förståelsen av hur elevers slöjdarbete kan användas genom att visa hur matematik naturligt inspirerar elever i utformningen av slöjdarbeten och hur matematiken används som ett redskap vid exempelvis beräkningar och mätning (”in vivo”). Modellen visar också på hur slöjdarbetet skapar en kontext som hjälper till att synliggöra matematik, hjälper elever att skapa mentala bilder och stödjer elevernas utveckling av matematiska förmågor (”in vitro”). Modellen skall ses som ett försök till att skapa förståelse kring hur slöjdarbeten (och andra liknande verksamheter) kan bidra till att stödja elevers lärande i matematik. Förhoppningen är att modellen kan utgöra ett stöd vid utformningen av en mer ämnesövergripande undervisning där matematiken kan ges ett relevant och begripligt innehåll och samtidigt utgöra ett viktigt verktyg och en källa till inspiration. / This study has examined how students' craft projects can support their learning in mathematics. The study proceeds from the sociocultural perspective. This is where knowledge and learning develop with interaction between people and where situational conditions and the language play a central role for the development of knowledge. The study is based on a qualitative method inspired by the Grounded Theory approach. The empirical material consists of observations of students' craft projects in needle work from grade 3-9. These observations were made during two years and concluded in diary notes containing students' craft projects. The new Swedish curriculum, Lgr11, and its syllabus in mathematics form the framework, to which the analysis on how students' craft projects can support learning in mathematics is matched. The abilities from the syllabus are supplemented in the analysis by Kilpatrick's five strands of mathematical proficiency. The result shows how mathematics from the six areas of the syllabus is displayed in the students' craft projects. The students use mathematics in calculations, problem solving and in certain cases as inspiration for a craft project. It also shows how students' craft projects can contribute to the development of the abilities from the syllabus in mathematics and from Kilpatrick's five strands of mathematical proficiency. The study concluded in a theoretical model that contributes to the understanding of how students' craft projects can be used. This is by showing how mathematics naturally inspires students in their designing of craft projects and how mathematics is used as a tool for calculation and measuring ("in vivo"). The model also shows how craft projects create a context that will help making mathematics visible and help students creating mental images and support the students' development of mathematical abilities ("in vitro"). The model should be seen as an attempt to create understanding on how craft projects (and similar activities) can contribute to supporting students' learning in mathematics. Hopefully the model can support a more interdisciplinary teaching where mathematics can be given a relevant and comprehensible content which can also be an important tool and a source of inspiration.

Orientador: Renata Cristina Geromel Meneghetti / Banca: Alexandrina Monteiro / Banca: Ivete Maria Baraldi / Resumo: O presente trabalho teve como propósito identificar, num primeiro momento, os saberes matemáticos presentes em um empreendimento em Economia Solidária e as dificuldades encontradas pelas integrantes deste no trato com o conhecimento matemático. Num segundo momento, buscou-se traçar ações pedagógicas visando sanar algumas dessas dificuldades, na direção de favorecer a autogestão (em matemática) do grupo. O enfoque teórico fundamenta-se nos princípios da Etnomatemática e Economia Solidária, trazendo também discussões sobre Tecnologia Social e autogestão. Os sujeitos da pesquisa são três senhoras que constituem o empreendimento aqui denominado Grupo de fabricação de sabão caseiro, o qual é composto por moradoras de um bairro proveniente de desfavelamento, donas de casa e que apresentam dificuldades em deixar o trabalho doméstico para se dedicar a outra profissão, mas precisam garantir renda para manutenção de suas famílias. A metodologia empregada tem caráter qualitativo e caracteriza-se como pesquisa-ação e; a coleta de dados ocorreu por meio de observação participante e entrevistas semiestruturadas. Após a análise dos dados obtidos possou-se à atuação pedagógica em Matemática buscando a autogestão dos sujeitos de pesquisa. As análises indicaram que os saberes matemáticos, pautados principalmente no trabalho colaborativo e cooperação entre as sócias, e que já diversas dificuldades enfrentadas; apontando para a necessidade de uma melhor compreensão de alguns conhecimentos matemáticos cotidianos, os quais foram parcialmente possibilitados através deste estudo / Abstract: The present study aimed to initially identify the mathematical knowledge present in an enterprise in Solidary Economy and the dificulties encountered by members of treat dealing with mathematical knowledge. At a second moment, we sought to draw pedagogical actions aimed at remedying some of these difficulties, in the direction of promoting self-management (in mathematics) by the group. The theoretical approach is based on the principles of Ethnomathematics and Solidarity Economy, brinding discussions about technology and social management. The subjects of the research are three ladies constituing the enterprise which are here called the venture group making homemade soap, which is composed of residents of a neighborhood from a dissolved Shantytown, housewives and who have difficulties to abandon the housework to devote themselves to another profession, but they need to guarantee income to maintain their families. The applied methodology is qualitative and is characterized as action research; and the data were collected through participant observation and semistructured interviews. After analyzing the data were passed to its role in mathematics teaching self-management seeking research subjects. The analyzes indicated the mathematical knowledges, which are primarily based on collaborative work and cooperation among members, and there are some difficulties faced, pointing to the necessity for a better understanding of some mathematical skills used in everyday life, which became partly possible through this study / Mestre