Educação matemática crítica: a sua importância na formação de uma sociedade do futuro

Este trabalho foi elaborado no âmbito do Mestrado de Ensino de Matemática do 3º Ciclo do Ensino Básico e Secundário da Universidade da Madeira, no ano lectivo de 2010/2011. Tem como grandes objectivos apresentar, de forma sucinta, o trabalho desenvolvido pelo grupo de estágio ao longo do estágio pedagógico e analisar a importância da educação^matemática crítica na formação de cidadãos críticos e conscientes. Assim, no estudo realizado procuraremos compreender o modo como os alunos reagem e aplicam os seus conhecimentos matemáticos quando se encontram em contextos sociais. Neste trabalho alertamos para os perigos de uma sociedade cegamente obediente e abordaremos ainda de que forma a educação matemática crítica poderá desenvolver o sentido crítico dos alunos e exploraremos a importância da investigação na educação matemática. Para isso, incentivaremos os alunos a explorarem e analisarem vários anúncios publicitários e cartazes políticos e tirarem as suas conclusões acerca dessas informações, tomando desta forma uma decisão consciente em relação a essa informação.

Educação matemática crítica: professor, isto serve para quê?

O princípio básico da educação é fomentar o desenvolvimento pleno dos indivíduos no sentido de se tornarem cidadãos livres, responsáveis e autónomos, capazes de julgarem com espírito crítico e criativo o seu meio social. O presente estudo visou compreender como se pode integrar uma dimensão social e política no ensino da matemática. Pretendeu-se reconhecer que aberturas e impedimentos existiam no sistema educativo português a uma educação matemática crítica (EMC), que mudanças ocorriam na forma de os alunos fazerem matemática e, ainda, se estes valorizavam ou estavam preparados para este tipo de atividades. O estudo foi do tipo qualitativo e tomou como método a observação participante. Recorreu-se a um conjunto de notícias acerca do preço dos combustíveis, de forma a possibilitar análises críticas desta temática, por parte dos alunos, ligadas a um conjunto de competências transversais e de conteúdos específicos do programa da disciplina de matemática. Foi observado que, para realizarem a análise crítica das situações, os alunos tomaram por referência duas dimensões, a da matemática e/ou a do seu “senso comum”. Mostraram interesse e motivação no estudo do modelo dos preços dos combustíveis e valorizaram o papel da matemática na compreensão/análise desse modelo. Os resultados sugeriram que, para além do conhecimento matemático e do “senso comum” dos alunos, a capacidade crítica assume-se como um fator relevante na profundidade da análise produzida. Os alunos reconheceram o papel potenciador da EMC na compreensão e aprendizagem de conceitos matemáticos, o que, por sua vez, torna as aprendizagens mais significativas.

Educação matemática crítica: o seu contributo na formação de cidadãos críticos e responsáveis

Universidade da Madeira

Aprender a ser crítico com a matemática: educação matemática crítica na sala de aula

A educação é uma práxis social presente em diferentes lugares e instantes da vida em sociedade. A Educação Matemática pretende contribuir para o total desenvolvimento de conhecimentos e de competências nos indivíduos de forma a torná-los cidadãos críticos, responsáveis e autónomos, capazes de participarem livre e ativamente na sociedade. Este estudo teve por objetivo compreender como é que a Educação Matemática Crítica contribui para formar alunos participativos, críticos e responsáveis, capazes de analisar, perceber e desmistificar algumas situações do nosso quotidiano, por exemplo promoções e publicidades, presentes na nossa sociedade. Sendo este problema definido de forma global, surge a necessidade de o fracionar em duas questões: 1) como pode a Educação Matemática Crítica contribuir para o “empowerment1” dos alunos com a matemática?; 2) como pode a Educação Matemática Crítica contribuir para que os alunos desenvolvam competências matemáticas e sociais que lhes permita analisar, perceber e desmistificar situações do dia a dia? 1 A noção de “empowerment” está discutida no capítulo II deste trabalho. Para analisar/discutir estas questões, escolheu-se uma metodologia de investigação de natureza qualitativa, em que a principal agente de recolha de dados foi a investigadora e que a mesma foi feita no ambiente natural de sala de aula. Adotou-se, ainda como método, a observação participante. É importante referir que os documentos de análise são constituídos pelos trabalhos escritos dos alunos, onde importou mais o processo que propriamente o resultado final. A tarefa apresentada aos alunos teve por base um panfleto publicitário sobre promoções de uma rede de hipermercados, de maneira a promover uma análise crítica, por parte dos alunos, desta situação aliada a várias competências transversais e de conteúdos como a proporcionalidade direta: percentagens e regra de três simples, próprios do programa da disciplina de matemática. Da observação feita, verificou-se que os alunos, ao analisarem criticamente a situação proposta, enveredaram por duas perspetivas: numa primeira fase sobre o que dizia o seu entendimento (senso comum) e, após debate em grande grupo, tendo em conta a matemática. Os resultados do estudo mostraram que é possível desenvolver uma prática pedagógica que valorize os aspetos da Educação Matemática Crítica, isto é, permite iv aprofundar os saberes matemáticos e ampliar o espírito crítico nos alunos permitindo-lhes participar livre e ativamente na sociedade de que fazem parte.

Espaços transversais em educação matemática :uma contribuição para a formação de professores na perspectiva etnomatemática

This PH.D. thesis is an attempt to show the beginning, evolution and unfolding of the making of a pedagogical work proposal based on culturally-built knowings in the heart of a traditional community, having as one of its starting points the knowings and doings experienced by dish-making women from Maruanum living in the city of Macapá, State of Amapá, Brazil. This proposal is strongly associated with the need we have to think about the nature of (ethnological)-mathematical knowledge generated by particular communities and about the way such knowledge can be discussed, worked out, and validated in learning environments, regardless of the level of instruction and the constraints imposed by government programs and educational institutions. Among its theoretical foundations are studies on instrumental activities that are typical of the Maruanum ceramics and investigative studies from the point of view of ethnomathematics. Methodological development took place with the application of activities, where traditional and instrumental knowledge observed in the production of ceramics had been adapted for and brought into the school environment , participative observation, as well as data collecting and organization techniques, such as interviews, statements, and audio an visual recordings. Analysis of the data collected focused on the relationship between the data-generating potential and the purpose of this study. Our aim is to make and estimate of the potential contributions from local situations and/or problems it would possibly bring to the formative learning of people involved in the educational processes of these communities, with a view to a spatial and temporal transformation of reality

Itinerários e marcas na formação do sujeito formador: reflexões acerca de um caminho na educação matemática

This Study inserts in Mathematical Education & Education that search to investigate the (self) formation of formers that gets graduation e pass to graduate others that get graduation and are formers in Mathematical Education. This Is a qualitative search in a perspective from search-formation.The work is formed of four topics. First topic talks about : The self-formation of formers. Second topic: at way of suppositions theorical-methodological from search. Third topic tells over: The life of a former life. Fouth topic A Station called Ubiratan D´Ambrosio created in his reverence and for build all the Knowledge´s Corpus developed by his studies and searches. It´s in sense of come and go from knowledge created at action by mankind to get finality of Transcendency and Survive. Look for to investigate aspects of academical, professional and personal life where are translated in language, thinking and practices oriented for one know-how holistical and transdiciplined in a reflexion, search and the critical it constitute to be a Professor, Teacher, Searcher and Etnomathematic that confered him the merit in 2005 the Prize Félix Klein, that declared Valente (2007), maximum distinction that can receive someone from Mathematical Education. The results point that the narratives of life´s stories are prominences to one re-direction of teach practical in formation´s courses of Mathematical teachers, opening spaces for what the teachers and particularly of Mathematical thinking and take position about your process of formation to be Formers. The Study also given possibilities to propose fourteen stoppages in Station that are beginnings with direction that emerge from studies and searches about the trajectory of life of Professor Ubiratan D´Ambrosio in perspective of re-signify the formative process in education and Mathematical Education

Educação matemática, ciência e tradição: tudo no mesmo barco

Les connaissances de la tradition et position de la Science dehors pour un non-hiérarchique dialoguez qui frappe pour les distinguer mais ils sont undésavouer inséparable étant donné les compléments ils composent. Cet essai assume la possibilité de ce roi de dialogue dans un place spéciale: la classe. Sur ce qui vient au connaissance de la tradition, le centre remarquable est pour la construction de bateaux du travail manuel, una pratique culturellement déployé dans la ville d'Abaetetuba, dans le État de Pará, Brésil. En revanche, la Science est concentrée par le le contenu d'école a adopté dans l'Ensino Fundamental (École primaire). La construction du dialogue est faite en utilisant des activités de l'enseignement qui accentuez des aspects géométriques (solide, géométrique, angles et symétries) aussi bien que par information qui implique le tableau, poésie, histoire, géographie et physique - les deux inspiré dans le chiffre de bateau résumé dans un CD-ROM interactif. Les activités ont eu lieu dans D'Escola Ensino Pedro Teixeira Fondamental (Abaetetuba-Pa), avec étudiants du 6e niveau (plus spécifiquement avec un groupe de 13 étudiants) d'août à octobre2004. Ethnomathématiques et transdisciplinarité sont le support théorique sous-jacent du projet. Dans résumé, c'est possible pour dire que l'interaction entre Science et Tradition, à travers activités au-delà lesquelles vont le le contenu a restreint à mathématiques d'école, contribuées à,: identifiez le contenu a appris pas sur dans série antérieure; renouveler le rôle joué par école dans ses fonctions didactique pédagogiques; réduire le isolement entre information passée historique et les étudiants présent culturel; indiquer des obstacles à l'érudition des mathématiques intéresser aux aspects cognitifs et behavioristes; et provoquer un participation affective qui rôle principal à la qualité d'apprendre l'école contenu aussi bien que les connaissances de la tradition

Os ateliês (auto)formativos na constituição do sujeito docente da educação matemática

The object of study of this thesis is the use of (self)training workshops as a fundamental process for the constitution of the teaching subject in mathematics education. The central purposes of the study were to describe and analyze a learning process of mathematics teachers supported by the training-research methodology, which procedures have been affected with the practice of (self)training workshops as a way of collaborating to the constitution of the teaching subject in Mathematics Education. The survey was conducted with a group of teachers in the city of Nova Cruz, Rio Grande do Norte through a process of continued education realized in the training workshops having as main goal the realization of the group s (self)training sessions in order to lead participants to the extent of their autonomy in their personal and professional transformations. The results obtained in the formative processes have shown the need to develop activities of mathematics teaching as a contribution to overcome the conceptual difficulties of the teachers, apart from their (self)reflections about themselves and the educational processes in which they belong. The results raised some propositions about (self)training workshops that may be incurred in practices to be included in the curriculum frameworks or materialize as a strategy of pedagogical work in training courses for teachers of mathematics. Also, they can constitute an administrative and educational activity to be instituted in the public schools of Basic Education

Os jogos com regras na perspectiva do desenho universal: contribuições à educação matemática inclusiva

To think about a school that is for everyone has been a challenge for many people connected to education worldwide demanding from researchers of each level of knowledge an association to such effort. The study presented on this paper unites itself to the voices, movements and researches of these scholars, seeking to contribute on building possibilities on which mathematics can be thought and worked on schools in order for every student to learn, whether they have some sort of deficiency, disorders, syndromes or not. This essay has the goal to investigate the possibilities of inclusive pedagogical practices mediated by math games with rules, developed and used throughout the Universal Design perspective; a qualitative research took place with a collaborative methodology that involved managers, teachers and students from a public school situated on the city of Natal/Brazil. On the investigation math games with rules were developed and made according to the Universal Design concept, starting from initial studies which articulated theoretical groundings to the reality of school and the teacher s conceptions. After that, classes using these tools were planned collectively which oriented inclusive pedagogical practices of classes from the 1st to the 4th year of elementary school. Throughout the process many instruments such as: tape recording, video footages, notes from the researcher; the teachers and the students were used for constant work evaluation and also to record the research data. In the end, the data indicated effective contributions of the mediated pedagogical practices by games with rules under the perspective of Universal Design for Inclusive Mathematics Education

Um Ensaio Sobre História Oral e Educação Matemática: pontuando princípios e procedimentos

Recently, we can perceive an intensification of assignments developed into Mathematical Education with the use of oral history as a research methodology. In this article, facing the living experiences during the preparation of our Phd tasks and later, when we had the role of advisors of scientific papers and of Postgraduate students in their researches also using the same methodology, we discussed the implication of ethics, mathematical education and oral history. Furthermore, we enunciated possibilities of the posture of the researcher before interviews, texts and iconography - photos and several images-provided by collaborators of our projects on Oral history and Mathematical Education.

Contribuições da CADES para a Educação (Matemática) Secundária no Brasil: uma Descrição da Produção Bibliográfica (1953-1971)

The so called Campaign for the Improvement and Diffusion of High School (in Portuguese, CADES) took place between 1953 and 1971, in Brazil. During this period, the Campaign published or helped publish dozens of books, in different teaching areas, and several of them were located by the authors of this article. These books guided high school teachers with respect to curriculum planning, legal aspects and methods of teaching. In this article, we contextualize historically this Campaign and also mention its objectives. We briefly describe some of the books found - especially those related to the teaching of mathematics - in order to open perspectives for future approaches and research that can be done based on this written material. Our main aim is to discuss its orientations and to provide ingredients that enable the construction of considerations related to this perspective of training mathematics teachers during a period when there were few colleges and universities to prepare teachers in Brazil.

Avaliação de Interações entre Professor e Alunos na Educação Matemática: ensino e aprendizagem de recursos pedagógicos

The aim of this paper is to discuss the teachers' need, as autonomous professionals, to evaluate their own pratice. Considering that Descriptive Functional Analysis (DFA) may be a pedagogical method for analysis, implementation, and change of teachers' mathematics teaching practices, the objective of the present research was to teach repertoires compatible with DFA to two mathematics teachers in elementary schools of São Paulo state. When teachers are responsible for evaluation and self evaluation, they recognize themselves as fundamental agents of transformation in education.

Os jogos com regras na educação matemática inclusiva

This present study aimed to examine the use of games with rules in working with math education in regular classes included in Elementary School, in the municipal education schools of Natal/RN, observing the learning process and development of all students, especially those with disabilities. The theoretical references used are based on Vygotsky's works and other authors from the historical-cultural perspective, as well as researchers in the field of Inclusive Education and Mathematics Education. The investigation was based on the qualitative research guidelines, with the application of semi-structured interviews with educational coordinators and teachers from the schools involved as well as classroom observations, looking for, in the speeches of those involved and in their teaching practices, elements to reflect on the Mathematics Inclusive Education, the use of games with rules -starting from its goals, the participation of disabled students, the pedagogical mediations, up to its accessibility - and from the learning of disabled students. The analysis results showed that the concepts underlying the development of inclusive teaching practices still refer to the clinical-medical paradigm, understanding the student with disabilities from their deficiencies; which teachers use, in their majority, the mathematical games with rules in their classes, but which the teaching mediation, during these activities, still needs to be qualified so that they can, effectively, contribute to the learning and development of all students; students with disabilities do not always participate in games with others colleagues; games with rules are rarely accessible; and that the Universal Design principles are not adopted in the selected classrooms for this study. Thus, it is clear that much remains to be done so that Mathematics Education can contribute to the learning and development of all students, and among those actions the teacher continuing education is recommended

Pesquisas em Modelagem Matemática e diferentes tendências em Educação e em Educação Matemática

Esse artigo é um ensaio teórico que tem como objetivo apresentar, a partir de uma revisão da literatura sobre Modelagem Matemática, como algumas tendências em Educação e em Educação Matemática são tratadas em pesquisas acadêmicas, assim como salientar alguns dos principais suportes teóricos utilizados nesses estudos, a saber, Educação Matemática Crítica, Interesse, Interdisciplinaridade e Contextualização. Um panorama das pesquisas realizadas em Modelagem no território nacional, relacionadas a outras tendências educacionais, é traçado, do mesmo modo que alguns dos principais referenciais teóricos abordados pela maioria dos autores das mesmas são apresentados. São apontadas perspectivas futuras de pesquisas, e é destacada a necessidade da continuidade do debate teórico acerca dessas temáticas.