Showing papers in "Bolema in 2015"

Educação e tecnologias: o novo ritmo da informação

Abstract: Em seu livro, Vani Moreira Kenski aborda a relacao entre educacao e tecnologias utilizando uma linguagem acessivel para que, alem dos estudantes e profissionais da educacao, outros leitores de diferentes areas, interessados pelo tema, possam compreender conceitos e questoes relacionados a educacao e as tecnologias. A autora trata o tema

Insubordinação Criativa: um convite à reinvenção do educador matemático

Abstract: In this article we introduce the concept of creative insubordination with the goal of analyzing the contributions that this perspective can make in transforming the practices of mathematics educators. The discussion is grounded in considerations of the complexities of education, professional autonomy, reflective practice, and professional collaborations. Our intention is to incite reflections around the question of why the field should consider creative insubordination in reinterpreting the practices of mathematics educators. Critical theories of education and mathematics education, which envision democracy, social justice, ethics, and solidarity as goals of the educational process, are at the heart of our discussions. As such, we justify the need for the community to consider the reinvention of the practices of mathematics educators.

Una Propuesta para el Análisis de las Prácticas Matemáticas de Futuros Profesores sobre Derivadas

Abstract: En el presente trabajo se informa de los resultados obtenidos al analizar las practicas matematicas de una muestra de futuros profesores de secundaria/bachillerato a proposito de dos tareas sobre derivadas. Este analisis ejemplifica el uso y alcances de las nociones practicasmatematicas y configuracion de objetos y procesos, proporcionadas por el Enfoque Onto-Semiotico (EOS) del conocimiento matematico, para la caracterizacion de los conocimientos del profesorado de matematicas. Los resultados del analisis evidencian tanto una desconexion entre los distintos significados parciales de la derivada como la necesidad de potenciar el conocimiento del contenido. Este aprendizaje puede hacerse mediante actividades que favorezcan el uso e identificacion de objetos matematicos, sus significados y los procesos involucrados en la solucion de tareas matematicas.

Conocimiento Didáctico-Matemático del Profesorado de Educación Primaria sobre Probabilidad: diseño, construcción y validación de un instrumento de evaluación

Abstract: This article presents the process of developing and validating a questionnaire to evaluate aspects of active primary school teachers’ didactic-mathematical knowledge when teaching probability Even though some instruments have been elaborated to measure mathematical knowledge for teaching, very few evaluate and describe primary school teachers’ categories of didactic-mathematical knowledge, especially for teaching probability For this reason, an instrument has been developed to evaluate active primary school teachers’ didactic-mathematical knowledge when teaching probability The instrument provides evidence of commonly held knowledge of the content, extensive knowledge of the content and the specialised knowledge of those teachers from the perspective of the Didactic-Mathematical Knowledge Model proposed by Godino and collaborators

Potencialização da Aprendizagem Autorregulada de Bolsistas do PIBID/UFPel do curso de Licenciatura em Matemática através de Oficinas Pedagógicas

Abstract: Este artigo apresenta a sintese de uma pesquisa qualitativa do tipo estudo de caso, que analisou se as oficinas desenvolvidas no Projeto Institucional de Bolsa de Iniciacao a Docencia/PIBID, do curso de Licenciatura em Matematica, da Universidade Federal de Pelotas/UFPel, promoveram a aprendizagem autorregulada das bolsistas de Matematica, qualificando seus processos de aprender e ensinar. Os dados coletados advieram da analise documental realizada a partir do projeto, do relatorio das oficinas de Matematica desenvolvidas e das entrevistas semiestruturadas realizadas com tres bolsistas de Matematica, que atuaram nas oficinas. Os dados foram submetidos a analise de conteudo e dela emergiram as seguintes categorias: a) planejamento; b) execucao; c) avaliacao das oficinas de Matematica realizadas em uma acao colaborativa. Pelos dados analisados, inferiu-se que as bolsistas desenvolveram acoes que revelaram sua capacidade de organizar, planejar e programar tarefas a serem realizadas dentro de um prazo estabelecido.

Desenvolvimento da Identidade Profissional de Futuros Professores de Matemática no Âmbito da Orientação de Estágio

Abstract: The objective of the present study was to investigate the role of Lesson Planning for Student Teaching in the development of the pre-service professional identity of mathematics teachers. To meet this objective, a qualitative research was developed, using a semi-structured interview as an information collection instrument, with Math undergraduate students from a Math Teacher Education course. The prospective teachers revealed that, during the Lesson Planning for Student Teaching, they mobilized/develop elements related to the teacher professional identity, such as: beliefs about lesson planning; appropriation of theoretical professional value; critical sense in lesson planning; availability for work with peers; research skills; and the capacity to reflect before the experience. These results evidence that the interactions between interns and between interns and teacher educators allowed prospective teachers to develop a questioning attitude and reveal expectations for their future professional practice, anticipating challenges.

Estudos em Raciocínio Combinatório: investigações e práticas de ensino na Educação Básica

Abstract: This paper presents research carried out over the past five years, by the Grupo de Estudos em Raciocinio Combinatorio do Centro de Educacao da Universidade Federal de Pernambuco – Geracao. The group's research lines are presented in the paper, as well as the main theoretical references used. Investigation by the group on teaching resources are analysed, research results developed with students of different levels and types of education are presented and discussed, as well as studies with K-12 teachers. The set of results obtained enable reflections concerning how combinatorial reasoning develops, what are the difficulties to be overcome and how practices can be more effective in teaching Combinatorics.

A Negociação de Sinais em Libras como Possibilidade de Ensino e de Aprendizagem de Geometria

Abstract: The theme on the inclusion of people with special educational needs is increasingly present in the academic and school environment. This article discusses a process of negotiation of signs in Brazilian sign language, Libras, carried out with deaf students in the early years of a public elementary school. Among the different relevant aspects in this teaching activity within the classroom, the interaction concerning geometry as a central theme is highlighted. The first section of the article presents aspects related to deafness and to the education of deaf people. In the following are presented the contexts of activity as well as excerpts of conversations in which students make agreement on the signs for different geometric figures, which were absent in the dictionaries. The results indicate the importance of the negotiation process for the enlargement of the lexical field in Libras, as well as for the engagement of students in the activity, as this process offers an opportunity to explore mathematical properties. Finally, it is acknowledged that the inclusion of disabled students in the regular school seems to be well supported by legislation concerning the access, although more efforts are still needed in order to ensure learning spaces for everybody.

Conhecimento Matemático para o Ensino de Diferentes Significados do Sinal de Igualdade: um estudo desenvolvido com professores dos Anos Iniciais do Ensino Fundamental

Abstract: O objetivo deste artigo e apresentar os principais resultados da pesquisa de mestrado “Conhecimentos de professores dos Anos Iniciais do Ensino Fundamental para o ensino dos diferentes significados do sinal de igualdade”, que buscou compreender quai sconhecimentos os professores declaram e demonstram possuir acerca dos diferentes significados do sinal de igualdade. As analises foram desenvolvidas por meio da triangulacao de dados produzidos por questionarios, pela analise de documentos e por uma dinâmica de interacao coletiva. Os resultados revelam limitacoes dos professores para reconhecer diferentes significados matematicos do sinal de igualdade; perceber as implicacoes do ensino dos diferentes significados do sinal de igualdade no e/ou para o curriculo; justificar potencialidades do trabalho em pequenos grupos de alunos nas aulas de Matematica. Demonstram tambem que o estudo analitico dos componentes envolvidos no conhecimento profissional do professor de Matematica pode desvelar necessidades de formacao de professores que ensinam Matematica.

Ensino e Aprendizagem de Matemática Através da Resolução de Problemas Como Prática Sociointeracionista

Abstract: Neste artigo apresentamos uma experiencia efetivamente pratica e a abordagem do Ensino e da Aprendizagem de Matematica atraves da Resolucao de Problemas, como pratica sociointeracionista, desde suas constituicoes teorica e filosofica a sua pratica educacional em um curso do Programa Nacional de Acesso ao Ensino Tecnico e ao Emprego, dirigido pelo Instituto Federal de Sao Paulo – Campus Sertaozinho. Apresentamos um campo de estudo social, historico e cultural como proposta da Resolucao de Problemas, nao apenas como uma metodologia de ensino-aprendizagem, mas sim como um campo de estudos que mantem vivo o movimento de acao/reflexao/acao por meio de conceitos e problemas da obra de Vygotsky. Lancamos mao dos elementos da autorregulacao e metacognicao pelo pensar-em-alta-voz na construcao do conhecimento e na constituicao da aprendizagem, alem de alguns desdobramentos dessa pratica no âmbito escolar.

O uso de narrativas (auto)biográficas como uma possibilidade de pesquisa da prática de professores acerca da Educação (Matemática) Inclusiva

Abstract: This article aims to present some discussions about the use of (auto)biographical narratives as source to realize Mathematics Education's researches having, as background, considerations about Inclusive (Mathematics) Education. Throughout the article, these issues will be discussed from some memoir excerpts related to Rosa's (2013) master's research, expecting to outline how mathematics teachers approached the Inclusive (Mathematics) Education and some practices in specialized or inclusive classes.

A Utilização do Geogebra na Demonstração Matemática em Sala de Aula: o estudo da reta de Euler

Abstract: In this study, we adopt a perspective of proof as a particular form of argumentation in mathematics. The study involves an experiment developed with 9th grade students, in which activities related to the triangle and its centres were proposed and carried out. This study follows a qualitative methodology of interpretative nature. Data were collected through participant observation, audio and video recordings of classes, student productions with paper and pencil, and with computers and interviews. Starting with the construction of figures in Geogebra, students structured their mathematical reasoning and ideas and built argumentative chains, which led to proving. The data show that most students were able to explore and formulate conjectures as a path leading to proving. Students recognized the importance of Geogebra as motivating but mainly for allowing experimenting and manipulating figures. The results point to the importance of the activity with Geogebra in construction and manipulation as a springboard to proof.

Enunciados de Tarefas de Matemática Baseados na Perspectiva da Educação Matemática Realística

Abstract: The objective of this article is to present a study on Math tasks instructions based on the Realistic Mathematics Education perspective, which allows: a) the analysis of Math tasks regarding their classification, characteristics, potentialities and constitution; b) to know whether the task is carried out routinely or not, what type of situation is refers to, whether it promotes mathematization processes, whether the task is flexible, whether it allows different resolution strategies, what kind of competencies it promotes, and whether it is characterized as an exercise or problem. An underlying intention of this research is to work as a resource for Math teachers, helping them understand Math tasks, analyze their potentials and limitations, and use them in the context of assessment as an investigative practice.

Comunidade de Prática de Professores que Ensinam Matemática como Espaço de Negociações de Significados sobre a Resolução de Problemas

Abstract: This article presents results of a research that analyzed negotiation of meaning on Problem Solving that took place in a group of teachers and future mathematics teachers. We use the concept of Community of Practice (Wenger, 2001) to analyze as a group constituted how a teachers' Community of Practice can be configured as a space for negotiation of meaning, considering the interaction between participation and reification processes. Episodes of meetings, which explain discussions on the subject, were chosen and the analysis indicated that there were negotiation of meaning that contributed to the process of teacher education and education of future teachers, which addressed the role of the teacher and students, the development of activities, and conceptions of Problem Solving. The negotiations of meaning occurred in moments of discussion, reflection and sharing of experiences on classroom practices.

What is Mathematics, Really? Who Wants to Know?

Abstract: Famous physicists, like Einstein and Wigner have been wondering, why mathematical symbolism could play such an effective and decisive role in the development of physics. Since the days of Plato, there have been essentially two different answers to this question. To Plato mathematics was a science of the unity and order of this universe. Since Galilei people came to believe that mathematics does not describe the objective world, it is not a reflection of some metaphysical realism. It is rather a reflection of human activity in this world. Kant, by his “Copernican Revolution of Epistemology” seems to have been the first to realize this. For example, number, or more generally arithmetic, was to the Pythagoreans “a cosmology” (KLEIN, 1985, p. 45), to Dedekind it is a means to better distinguish between things. The paper sketches the transition from an ontological to a semiotic interpretation of mathematics.

Diseños Prehispánicos, Movimientos y Transformaciones en el Círculo y Formación Inicial de Profesores

Abstract: Initially, an analysis of the logic design was used on plates or cups of pre-Hispanic cultures of the Grass, or Quillacingas, located south of Colombia. The results of this approach led to the construction of some activities to classes under the heading of movements and transformations in the circle. The main objective was to raise a methodological proposal to adapt a pre-Hispanic designs school environment, regardless of the regional context of the designs, as well as the presentation of a new work proposal in circular regions of the movements, dilation and the friezes, different from traditionally presented in school textbooks. In general, it is part of a ethnomathematics research to finish in a classroom experience with math teachers in training located north of Colombia.

Conocimiento Especializado de un Profesor de Matemáticas de Educación Primaria al Enseñar los Números Racionales

Abstract: Describimos el conocimiento especializado de un profesor de matematicas experto de Educacion Primaria, que ensena el tema de los numeros racionales a estudiantes de 11 a 12 anos de edad. Realizamos un analisis de contenido de las transcripciones de las 21 sesiones de clase impartidas por el profesor, empleando un sistema de categorias de los subdominios de conocimiento del modelo de Conocimiento Especializado del Profesor de Matematicas (MTSK). Ello nos permitio apreciar los conocimientos manifestados por el docente en su practica, especialmente en tres subdominios, el conocimiento de los temas matematicos, de las caracteristicas del aprendizaje de las matematicas y de la ensenanza de las matematicas.

O ensino de frações via resolução de problemas na formação de futuras professoras de pedagogia

Abstract: Neste artigo, apresentamos uma pesquisa que teve como objetivo favorecer a compreensao do ensino de fracoes via resolucao de problemas a futuras professoras de Pedagogia Apos uma formacao realizada no inicio da disciplina de Metodologia de Ensino de Matematica, aplicamos uma situacao e, ao final da disciplina, outra situacao, a 25 licenciandas as quais deveriam apresentar explicacoes de como conduziriam o ensino de fracoes na abordagem da resolucao de problemas Para analisar essas explicacoes, foram elaboradas quatro categorias, caracterizadas como aspectos de referencia no ensino Os resultados mostraram que, inicialmente, 36% apresentaram uma conducao de aulas que contemplou esses quatro aspectos, sendo que, ao final, essa porcentagem aumentou para apenas 44% Alem disso, ao final, 40% nao propuseram o problema como ponto de partida Concluimos que, apesar da formacao proporcionada, tais aspectos foram pouco compreendidos pelas participantes, principalmente o de se propor o problema como ponto de partida

Caminhos do Significado em Atividades de Modelagem Matemática: um olhar sobre os interpretantes

Abstract: In this article, we present results of a research in which we investigate evidence of assignment of meaning in mathematical modeling activities. The research is based on theoretical assumptions of mathematical modeling and on Peircean Semiotic focusing on theory of the interpretants signs. The search for evidence related to the attribution of meaning is permeated by the analysis of the interpretants produced by a group of students of a course degree in mathematics during steps associated with the development of modeling activities. Through such interpretants signs, we infer about the attribution of meaning to the problem and to mathematics during the development of the modeling activity analyzed, describing meaning's routes.

A Teoria dos Campos Conceituais num Processo de Formação Continuada de Professores

Abstract: A Teoria dos Campos Conceituais visa fornecer quadros e alguns principios para o estudo do desenvolvimento e da aprendizagem de competencias complexas dos estudantes. Compreendendo a aprendizagem como um processo que pode ser desencadeado pelas acoes efetivadas no ensino, utilizamos essa teoria no desenvolvimento das acoes de pesquisa embrenhadas em processos e praticas de ensino. Assim, este artigo objetiva analisar as reflexoes dos professores a respeito da aplicacao da Teoria dos Campos Conceituais durante um processo de formacao continuada que abordou o trabalho com conceitos das Estruturas Aditivas nos anos iniciais. Trata-se de um recorte de uma pesquisa mais ampla, que tinha como objetivo principal desenvolver uma formacao colaborativa entre professores dos anos iniciais e pesquisadores. Para alcancar o objetivo proposto, foi analisado o relatorio final, respondido por quatro das professoras participantes do processo formativo. A analise das reflexoes feitas pelas professoras, no relatorio final, revela que, para elas, a aplicacao dessa teoria durante o processo formativo proporcionou reflexoes a respeito da forma de desenvolver o processo de ensino, alem de dar suporte para a construcao de atividades que dao sentido a operacao matematica, possibilitando compreender as relacoes envolvidas nos conceitos.

Tecnologias Digitais e a relação entre teoria e prática: uma análise da produção em trinta anos de BOLEMA

Abstract: This article presents an analysis of the research on the use of digital technologies in mathematics classes in Brazil. Our research was based on articles in BOLEMA that have addressed this issue over the past thirty years. Methodologically, we conducted an analysis of the texts seeking similarities between them, combining elements of literature review, state of the art, and meta-synthesis. We identified two types of relationships between theory and practice: the first one in which the authors started from some practical activities, ending with some theoretical results; and the second one in which the authors, based on research results, designed interventions in classroom or in other educational settings. The analysis suggests that, in the context of published articles about Digital Technologies, the research in mathematics education constantly contemplates theory and practice in a dynamic manner, avoiding the extremes of immediate pragmatism and pure theory.

O Uso das TIC nas Práticas dos Professores de Matemática da Rede Básica de Ensino: o projeto Mapeamento e seus desdobramentos

Abstract: Esse artigo tem o proposito de apresentar o projeto Mapeamento do uso das tecnologias de informacao nas aulas de Matematica do Estado de Sao Paulo, bem como os resultados oriundos do mosaico de pesquisas que constituem esse projeto. Alem disso, apresentamos e discutimos uma acao de formacao continuada que ocorreu no periodo de agosto a novembro de 2014 na cidade de Bauru, que se refere a um curso de extensao universitaria. Para tanto, dialogamos com uma literatura dentro da Educacao Matematica, que aponta que o uso das TIC pode potencializar os processos de ensino e aprendizagem, porem ha empecilhos que dificultam esse uso nas escolas. Em seguida, trazemos os resultados iniciais do projeto, frutos de pesquisas que o compoem, as quais seguem uma abordagem metodologica qualitativa. Diante disso, posicionamos esse curso de extensao universitaria, que por sua vez, teve o objetivo de fomentar o uso das TIC nas praticas de professores de Matematica da Educacao Basica. Finalmente, argumentamos que o desenvolvimento de projetos dessa natureza possibilita um trabalho colaborativo de pesquisa, que tem por consequencia o incentivo da articulacao entre posgraduacao, licenciaturas e escolas da rede publica de Educacao Basica.

Práticas Possíveis com a História Oral na Formação Inicial de Professores (de Matemática)

Abstract: This article deals with results and discussions of two related researches to a larger project entitled "Oral History, Narratives and Teacher Training: Research and intervention”. The first study aimed to elaborate an understanding of the contributions, limitations, and potential of Oral History as a didactic-pedagogic approach for the Brazilian Educational Policy discipline, from an intervention with this discipline on the undergraduate course in Mathematics of Unesp/Rio Claro. The second research has sought an understanding of how the narrative and Oral History approach can contribute in courses involving mathematics and its teaching in pedagogy courses, even in the work place, with student and teachers in situations that allow contact and discussions about the daily life of schools and mathematics teaching practices and, with this objective in mind, the chosen discipline was: Content, Methodology, and Practice Teaching of Mathematics, related to the course of Pedagogy of Unesp/Rio Claro. Broadly, such surveys indicate the approach to oral history, through the mobilization of its procedures, as an useful practice to support training processes destined to future teachers (of Mathematics), in that they allowed an application path of personal and professional background of undergraduate in history, bringing contributions to the development of critical understanding regarding the work of these future teachers.

As Concepções de Geometrias não Euclidianas de um Grupo de Professores de Matemática da Educação Básica

Abstract: Current research identified and analyzed the concepts of non-Euclidean geometries of a group of 27 primary school Math teachers who work in government schools in the state of Parana, Brazil. Knowledge, opinions, preferences, and ideas on the geometries of the participants were verified. The participants were chosen through a questionnaire and data collection was retrieved from a half-structured interview. Six teachers did not provide any ideas on the subject matter and one male teacher was not aware of the inclusion of non-Euclidean geometries in the curriculum. Thirteen teachers presented some ideas and opinions on non-Euclidean geometries. Results show that the insertion and the study of non-Euclidean geometries have not introduced new concepts since only eight teachers provided concepts based on results and concepts of these geometries.

Etnomatemática de una Artesanía Argentina: identificando etnomodelos de trenzado

Abstract: This investigation focuses on the study of the mathematics of an Argentine craftsmanship of making braids. The objective is to develop a situated mathematical interpretation for the modeling of the braiding practice from an emic perspective. We set out from the reorganization of the space through the universal mathematical activities to locate and design and a broad view of mathematics as a system that deal with the relational, quantitative, and spatial aspects of human experience (QRS-system). Through the key concept of ethnomodels, we describe the ways in which artisans organize the space and we describe the symbolic system which is the language they use to communicate.

Aprendizagens Expansivas Reveladas pela Pesquisa sobre a Atividade Matemática na Sala de Aula

Abstract: In this article we examine the theoretical and methodological possibilities offered by Expansive Learning theory to analyze learning resulting from a problem solving classroom activity. This activity involved the use of a school procedure, rule of three, and its subsequent unfolding when students' everyday situations were confronted with a school procedure. The field research, in two 8th-grade classes from a public school, revealed a range of learning instances not anticipated by the teacher related with the meaning expansion of a school procedure (rule of three) and with the different ways of solving a problem when everyday situations are introduced by means of a cultural artifact (water bill). It also showed how research in mathematics education may influence the subjects' learning.

Do Conceito à Prática da Autonomia do Professor de Matemática

Abstract: This paper presents theoretical and practical articulations of a concluded doctoral research. Our goal is to promote discussions about mathematics teachers possibilities related to the ‘autonomy’, the ‘self care’ according to Michel Foucault (2010). During the period of one year appropriating the method of cartography – mapping the human subjectivity – by weekly meetings with mathematics teachers of a public school in Sao Paulo state countryside, an intervention was made possible, which intends to map the force lines that circulated in this space of dialogue and, therefore, to discuss theirs process of subjectivation. Thus, we believe in the possibility of the concepts presented here producing new forms of visibilities at school, creating the possibility of establishing new ways of existence and possible spaces of freedom in the present.

Ethno)mathematics as discourse

Abstract: Interpreting mathematics as a discourse includes three claims: that there are forms of mathematics-reality transitions, that mathematics includes actions, and that mathematics includes a political dimension. Through a discussion of different mathematics-based discursive acts, I will substantiate the discursive interpretation of mathematics. Next, by reconsidering ethnomathematics-based discursive acts, I will argue that also ethnomathematics can be interpreted as a discourse. As in the case of mathematics, ethnomathematics-based discursive acts concern the formation of: possibilities, rationality, structures and artefacts, authority, and overlooking. Finally, I will provide a critical perspective on both mathematics and ethnomathematics through the claim that any kind of action is in need of critical reflections.

Envolvimento dos Alunos em Atividades de Modelagem Matemática: relação com o saber e possibilidades de ação

Abstract: In this paper, we present the results of an investigation that sought to understand the involvement of two students, members of a group, in a mathematical modelling activity, based on the relationship that they have established with mathematical knowledge. Supported by Bernard Charlot's theoretical framework – the relationship to knowledge – and using a qualitative approach, we analysed three episodes in which the group is developing a modelling project. Besides the episodes, interviews promoted a deep understanding of aspects related to the students’ involvement. Our analysis gave rise to the construction of the concept of possibilities of action. As a result, we noticed that the relationship of each student to mathematical knowledge plays a decisive role in his/her possibilities of action and that students’ involvement in modelling activities can be understood not only as the actions effectively performed by them, but also as the possibilities of action that they glimpse.

Reflexões sobre Relações entre Currículo, Avaliação e Formação de Professores na Área de Educação Matemática

Abstract: Our objective in this paper is to create some thoughts about the articulation of research on curriculum, assessment and teacher training in the area of mathematics education, particularly focused on how articulate the projects/actions that constitute public policies in Brazil are when considering this triad. These reflections are based on experiences in our research group, projects/actions of governmental reorganization curriculum, and teacher training. We emphasize the need to develop research on articulated curriculum, assessment, and teacher training and their results to be better publicized, in order to contribute effectively in the formulation of public policies. Even within projects/actions that constitute public policies in Brazil, it is observed that the proposed curriculum discussion, evaluation, and training of teachers do not correlate and are implemented as if they were self-sufficient, with visible dislocation.