”Kunskaperna gömmer sig lite i roliga gubbar” : Pedagogers syn på iPadsanvändning som en del av matematikundervisningen i förskoleklass och årskurs 1-3

Syftet med detta arbete är att få kunskap om hur pedagoger i förskoleklass samt årskurserna 1-3 som har tillgång till iPads i sin matematikundervisning ser på användandet av dessa. Hur resonerar pedagoger när de använder iPadsen och finns det en tanke bakom hur iPadsen används när det gäller matematiska mål i Lgr 11? Metoden som användes för att få svar på frågeställningarna var dels en enkätundersökning för att nå ut till många pedagoger och därefter fördjupande intervjuer som baserade på enkätfrågornas resultat.

O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Investigação etnomatemática em contextos indígenas: caminhos para a reorientação da prática pedagógica

From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community

Ensino de matemática, história da matemática e artefatos: Possibilidade de interligar saberes em cursos de formação de professores da Educação Infantil e anos iniciais do Ensino Fundamental.

This work is located at the shield of research that defends the use of Mathematics History, based on the utilization of historical artifacts at teaching activities, at Mathematics classrooms, and at graduation courses for teachers of Elementary School and of the first grades of High School. The general objective is to examine the possibility of the use of historical artifacts, at teaching activities, at graduation courses for teachers of Elementary School and of the first grades of High School. Artifact, at this work, is comprehended as objects, documents, monuments, images and other kinds of materials that make sense to the Human actions at the past and that represent what have been said and done at the Human history. At the construction of the theoretical-methodological way of the research we have based ourselves upon the ideas of the authors that are engaged at the teachers formation; at researchers adherents to the use of Mathematics History (MH) as a methodological resource, and at studies accomplished that elucidate the role of the artifacts at the history and as a mediatory element of learning. We defend the thesis that the utilization of historical artifacts at teaching activities enables the increasing of the knowledge, the development of competencies and essential abilities to the teacher acting, as well as interact at different areas of the knowledge, that provides a conception of formation where the teacher improves his learning, learning-doing and learning-being. We have adopted a qualitative research approach with a theoretical and pratic study disposition about the elements that contribute to the teachers works at the classroom, emphasizing the role of the Mathematics history at the teacher s formation and as a pedagogical resource at the mathematics classroom; the knowledge, the competencies and abilities of the historical artifacts as an integrative link between the different areas of the knowledge. As result, we emphasize that the proposition of using the MH, through learning activities, at the course of teacher graduation is relevant, because it allows the investigation of ideas that originate the knowledge generated at every social context, considering the contribution of the social and cultural, political and economical aspects at this construction, making easy the dialog among the areas and inside of each one The historical artifact represents a research source that can be deciphered, comprehended, questioned, extracting from it information about knowledge of the past, trace and vestiges of the culture when it was created, consisting of a testimony of a period. These aspects grant to it consideration to be explored as a mediatory element of the learning. The artifacts incorporated at teaching activities of the graduation courses for teachers promote changes on the view about the Mathematics teaching, in view of to privilege the active participation of the student at the construction of his knowledge, at the reflection about the action that has been accomplished, promoting stimulus so the teachers can create their own artifacts, and offer, either, traces linking the Mathematics with others knowledge areas.

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Pelos caminhos das idéias e da existência: a propósito das cartografias de J. T. de Moura Filho

The present study aimed to investigate the intellectual, personal and professional tracjetory of José Tavares de Moura Filho. Civil engineer who devoted him self to cartographic cience, though not a cartographer, and to literature. At 65 years old, already with retirement, he devoted his attention to writing his books and see the world, as he said. There were nine books, five of poetry, prose and short stories, and four of cartographic nature. The published his books independently. He wrote and his wife Elza typed. Once ready, he would seek the graphics, later a publisher, to reproduce his writing. He liked to say he would rather to pay for your books than bay a new car, and did so. Died at age of 82 years, leaving a rich material for the young students, those who read, as he always did by dedicating his books. In order to achieve the objectives of this study, we used as a theoretical some authors dealing with historiography, oral history, intellectual intineraries and history of ideas, as Garnica, Nóvoa, Barros, Bosi, Le Goff among others. From this perspective, we constructed an archeology of ideas and the existence of Moura Filho, to point contributions of the teaching of mathematics from his work

Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

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

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention