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In this text, we will present the basics of a project connecting mathematics and culture. This project pretends also to bring information and communication technologies to help dissemination on non-formal settings associated with tourism., Dans ce texte, nous présenterons les bases d’un projet associant mathématiques et culture. Ce projet prétend également intégrer les technologies de l’information et de la communication pour faciliter la diffusion dans des environnements non formels associés au tourisme., Portuguese national funds through the FCT (Foundation for Science and Technology) within the framework of the CIEC (Research Center for Child Studies of the University of Minho) project under the reference UID/CED/00317/2019

SOARES JÚNIOR, Jair Lino. A construção do conceito de simetria: contribuições da matemática e cultura e das atividades didáticas - UFC. 2018. 105f. - Dissertação (Mestrado) - Universidade Federal do Ceará, Programa de Pós-graduação em Educação Brasileira, Fortaleza (CE), 2018. Mathematics is a science full of meanings, also in everyday life. Cultural practices can and should be used in the teaching of this discipline. However, the mathematical interrelationship and culture is not a reality in public schools, because in most cases the main pedagogical resource is the textbook and the presentation of content is given in a hierarchical way, teaching first the easiest contents which will be a prerequisite for learning more complex content. The purpose of this study was to analyze the learning process of a class of students from the 9th grade of elementary school in the final years, especially on the mathematical concepts involving symmetry and isometry from Didactic Activities (AD) that relate bobbin lace and the cultural mathematics elaborated by Santos (2012). The study is qualitative, of the inductive type, with exploratory purposes, aiming at the approximation of the mathematical learning with the culture. We outlined the work based on the participant observation, the subjects were 30 students of the 9th grade of elementary school final years of a school in the municipal public school of Caucaia - Ceará. As a source of data collection we adopted the record from photographs and the field diary, for annotations of the responses produced by the students in the Didactic Activities (AD), as well as comments of facts occurred during the investigative process during the Didactic Session (SD), based in the methodological assumptions of the Fedathi Sequence (SF). Our results allowed to identify conceptual gaps of the students with respect to the geometric transformations, mainly in relation to the concept of reflection. We also observed the students' primary difficulties regarding the concept of laterality. From the analysis we verified that the AD proposed by Santos (2012) corroborate the learning of the concepts of geometric transformation, specifically, rotation, translation and reflection, mainly for evidencing the visualization and representation skills, fundamental for learning these concepts. A matemática é uma ciência repleta de significados, também no cotidiano. As práticas culturais podem e devem ser utilizadas no ensino dessa disciplina. Entretanto, a inter-relação matemática e cultura ainda não é uma realidade nas escolas públicas, pois, na maioria dos casos, o principal recurso pedagógico é o livro didático e a apresentação dos conteúdos se dá de forma hierarquizada, ensinando primeiro os conteúdos mais fáceis que servirão de pré-requisito para a aprendizagem de conteúdos mais complexos. Objetivamos com esse estudo analisar o processo de aprendizagem de uma turma de alunos do 9.º ano do ensino fundamental dos anos finais, especialmente sobre os conceitos matemáticos que envolvem simetria e isometria a partir de Atividades Didáticas (AD) que relacionam as rendas de bilros e a matemática cultural elaboradas por Santos (2012). O estudo é de natureza qualitativa, do tipo indutivo, com fins exploratórios, visando a aproximação da aprendizagem matemática com a cultura. Delineamos o trabalho baseados na observação participante. Os sujeitos foram 30 alunos do 9.º ano do Ensino Fundamental anos finais de uma escola da rede pública municipal de ensino de Caucaia-Ceará. Como fonte de coleta de dados, adotamos o registro a partir de fotografias e o diário de campo, para anotações das respostas produzidas pelos alunos nas AD, bem como comentários de fatos ocorridos durante o processo investigativo durante a Sessão Didática (SD), fundamentada nos pressupostos metodológicos da Sequência Fedathi (SF). Nossos resultados permitiram identificar lacunas conceituais dos estudantes com relação às transformações geométricas, principalmente com relação ao conceito de reflexão. Observamos, ainda, dificuldades primárias dos estudantes acerca do conceito de lateralidade. A partir das análises, verificamos que as AD propostas por Santos (2012) corroboram a aprendizagem dos conceitos de transformação geométrica, especificamente rotação, translação e reflexão, principalmente por evidenciar as habilidades de visualização e representação, fundamentais para aprendizagem desses conceitos.

International audience; 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.; Dans la première partie de cet article, nous examinons les apports de la philosophie de Wittgenstein à la discussion sur l’existence (simultanée) de pratiques mathématiques différentes, culturellement déterminées. Nous avançons que les derniers travaux de Wittgenstein offrent un cadre fructueux pouvant servir de fondation philosophique aux ethnomathématiques. De fait, Wittgenstein a été cité dans nombre de travaux - dont nous donnons un aperçu dans cet article - menés dans le champ de l’ethnomathématique. La question philosophique centrale discutée ici concerne l’abandon par Wittgenstein du concept essentialiste de « langage », niant ainsi l’existence d’un langage universel. Les langues - ou « jeux de langage » selon l’expression de Wittgenstein - sont plongé(e)s dans une certaine « forme de vie », dans des formations sociales et culturelles, et dans un ensemble d’activités collectives. Cette idée incite à analyser la rationalité (mathématique) comme une invention - ou une construction - qui a lieu dans des contextes locaux/sociaux spécifiques. Dans une deuxième partie, nous illustrons les idées de Wittgenstein en analysant les aspects mathématiques de deux activités généralement évoquées sous l’appellation « jeux de ficelle » et « dessins de sable », et pratiquées dans diverses sociétés. Une analyse ethnomathématique comparative permet de mettre en évidence des caractéristiques communes et des traits distinctifs dans l’expression d’une rationalité mathématique telle qu’elle s’exprime dans ces deux pratiques, d’une société à l’autre. Enfin, nous suggérons qu’une approche philosophico-anthropologique des pratiques mathématiques est susceptible d’offrir un éclairage nouveau sur les interrelations entre « mathématiques » et « cultures ». Des recherches philosophiques permettent d’avancer sur la question de l’existence des (ethno-)mathématiques culturellement déterminées, alors que dans le même temps l’approche anthropologique - et ethnographique - offre de nouveaux matériaux pour étudier des pratiques à caractère mathématique dans leurs liens avec le contexte culturel. Nous proposons cette double approche dans la perspective de mieux caractériser les pratiques mathématiques dans des termes à la fois sociologiques et épistémologiques.