Submitted by Maicon Juliano Schmidt (maicons) on 2015-06-03T12:32:25Z No. of bitstreams: 1 Joâo Cândido Moraes Neves_.pdf: 1725890 bytes, checksum: 3ca8d300deeac94f8bd1dc3faf2e4d4a (MD5) / Made available in DSpace on 2015-06-03T12:32:25Z (GMT). No. of bitstreams: 1 Joâo Cândido Moraes Neves_.pdf: 1725890 bytes, checksum: 3ca8d300deeac94f8bd1dc3faf2e4d4a (MD5) Previous issue date: 2015-02-02 / IFRS - Instituto Federal do Rio Grande do Sul / A presente tese tem como objetivo problematizar um dos enunciados que integram o discurso da Educação Matemática Escolar: “Os alunos não aprendem Matemática por ‘falta de base”’. O estudo utiliza as seguintes noções foucaultianas: enunciado, discurso, verdade e regimes de verdade. O material de pesquisa analisado é constituído por enunciações de um grupo de bolsistas do Programa Institucional de Bolsa de Iniciação à Docência (Pibid), que emergiram de entrevistas, diário de campo e seus relatórios finais; e também por teses, dissertações e artigos acadêmicos do período de 1994 a 2013, disponíveis no portal da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e na mídia, que remetem ao enunciado objeto do estudo. A análise do material de pesquisa mostrou: 1) a recorrência de enunciações que vinculam a dificuldade em aprender matemática à “falta de base” dos estudantes; 2) O enunciado “Os alunos não aprendem Matemática por ‘falta de base’” está entrelaçado com dois outros enunciados presentes no discurso pedagógico: a) A matemática escolar é constituída por um conjunto hierarquizado de conhecimentos (que tem estreitos vínculos com o enunciado O conhecimento matemático apresenta-se hierarquizado); b) O currículo escolar é hierarquizado, isto é, segue uma ordenação linear. / This thesis aims to discuss one of the statements that is part of the discourse of School Mathematics Education: "The students do not learn Mathematics by 'lack of basic skills'”. The study uses the following Foucault’s notions: statement, discourse, truth and regimes of thruth. The research material analized consists of utterances of a college group of the Teacher Induction Program (Pibid), which emerged from interviews, field diary, and their final reports; and also for theses, dissertations and scholarly articles from the period of 1996 to 2014, available on the website of Coordination for the Improvement of Higher Education Personnel portal (CAPES) and the media, referring to the statement object of the study. The analysis of the research material showed: 1) the recurrence of utterances that link the difficulty in learning Mathematics to "lack of basic skills" of students; 2) The statement "The students do not learn Mathematics by 'lack of basic skills' " is interlaced with two other statements presented in the pedagogical discourse: a) The scholar Mathematics is consisted of a hierarchical set of knowledges (which has close ties with the statement - The mathematical knowledge is hierarchical); b) The school curriculum is hierarchical, thus, follows a linear ordering.

Made available in DSpace on 2016-04-27T16:57:38Z (GMT). No. of bitstreams: 1 Talita Carvalho Silva de Almeida.pdf: 3209474 bytes, checksum: c7199d8619e815e18cc31281d3c30c9a (MD5) Previous issue date: 2015-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research aims to identify the teaching knowledge mobilized for Archimedean solids are taught. Thus, the research question was: which knowledge base for the Archimedean solid education in basic school? To answer this question we resort to a bibliographical study developed based on material already prepared, consisting of books and scientific articles. The theoretical framework was based on Mathematical Knowledge for Teaching, in sense Ball, Thames and Phelps, and Technological Knowledge for Education, in sense Mishra and Koehler, both obtained with advances in the initial proposal of Shulman and colleagues about the knowledge base for teaching and the Anthropological Theory of Didactic Yves Chevallard. Such references were fundamental in the composition of a scene that showed that teaching knowledge are minimally involved in the Archimedean solids teaching process. The methodological choice for the literature contributed to the achievement of the desired goal, since it allowed us to find aspects of knowledge not evidenced in studies by Shulman. The choice of a mathematical procedure performed by Renaissance as Mathematics Reference Model Epistemological led us to an Mathematics Organization and a possible Didactic Organization for Archimedean solids helping us to realize that the teaching knowledge come from the interaction of three particular components of knowledge, mathematical knowledge, technological knowledge and didactic knowledge / O presente trabalho tem como objetivo identificar os saberes docentes mobilizados para que sólidos arquimedianos sejam ensinados. Assim, a pergunta de pesquisa foi: qual base de conhecimento para o ensino de sólidos arquimedianos na escola básica? Para responder a esta questão, recorremos a um estudo bibliográfico desenvolvido com base em material já elaborado, constituídos principalmente de artigos científicos. O referencial teórico baseou-se no Conhecimento Matemático para o Ensino, no sentido de Ball, Thames e Phelps, e no Conhecimento Tecnológico para o Ensino, no sentido de Mishra e Koehler, ambos obtidos com avanços na proposta inicial de Shulman, e colaboradores acerca da base de conhecimento para o ensino e na Teoria Antropológica do Didático de Yves Chevallard. Tais referenciais foram fundamentais para a composição de um cenário que evidenciasse quais saberes docentes estão minimamente envolvidos no processo de ensino de sólidos arquimedianos. A escolha metodológica pela pesquisa bibliográfica contribuiu para o alcance do objetivo desejado, visto que nos permitiu encontrar aspectos do conhecimento não evidenciados nos estudos de Shulman. A escolha de um procedimento matemático realizado por renascentistas como Modelo Epistemológico de Referência nos conduziu a uma Organização Matemática e uma possível Organização Didática para sólidos arquimedianos, nos ajudando a perceber que os saberes docentes são provenientes da interação de três componentes particulares de conhecimento, conhecimento matemático, conhecimento tecnológico e conhecimento didático

Orientador: Prof. Dr. Alessandro Jacques Ribeiro / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2014. / Essa é uma pesquisa a qual fora desenvolvida no programa de pós-graduação em Ensino, História e Filosofia das Ciências e Matemática na Universidade Federal do ABC, em Santo André, cujo título é: "Analisando a mobilização de conhecimentos algébricos de professores de educação básica: O momento de preparação de aulas sobre equações.". Os objetivos dessa pesquisa consistem em mapear, investigar e compreender quais os conhecimentos algébricos que são mobilizados por professores quando estão elaborando suas aulas sobre equações para a Educação Básica. Adotou-se uma abordagem qualitativa como metodologia de pesquisa e os dados foram obtidos através de questionários e da análise documental das aulas preparadas pelos professores dessa pesquisa; gravações em áudio dos encontros os quais os professores preparam suas aulas em duplas. Os seis sujeitos de pesquisa são pessoas que preparam aulas para a Educação Básica nos conteúdos matemáticos tanto para seu ofício como professor(a) efetivo ou contratado, quanto para o desenvolvimento de pesquisa associado aos projetos de formação inicial ou continuada. Com isso, para fundamentar essa pesquisa inclusive nas análises dos dados, foram utilizados os trabalhos de Shulman (1986 e 1987) e Ball e equipe (2008). Estes últimos autores sugerem o quadro teórico do "Conhecimento Matemático para o Ensino", que é o "conhecimento matemático necessário para realizar o trabalho de ensinar matemática", além da existência de dois subdomínios, a partir dos trabalhos de Shulman: (i) Conhecimento Comum do Conteúdo e Conhecimento Especializado do Conteúdo; e (ii) Conhecimento do Conteúdo e os Estudantes e Conhecimento do Conteúdo e o Ensino. Após analisarmos os dados, baseados na perspectiva do conhecimento matemático para o ensino, pudemos identificar, entre outros, os seguintes conhecimentos algébricos: Reconhecimento de que uma sentença matemática não é equação (Conhecimento Comum do Conteúdo); Compreensão dos multisignificados do símbolo "=" (Conhecimento Especializado do Conteúdo); Reconhecimento dos conteúdos prévios para que os alunos possam compreender e participar de uma aula sobre equações (Conhecimento do Conteúdo e os Estudantes); Utilização de uma abordagem etimológica das palavras "equação" e "igualdade", com o objetivo de promover uma discussão destes conteúdos em sala de aula (Conhecimento do Conteúdo e o Ensino) e, por fim, Reconhecer que o conteúdo de equação, em especial a equação polinomial de 1º grau, tem forte relação e importância para o conteúdo de inequações, funções e outros conteúdos mais avançados (Conhecimento Curricular). / This is a research which had been developed in Master¿s program in Teaching, History and Philosophy of Sciences and Mathematical at the Federal University of ABC, in Santo André, whose title is "Analyzing the mobilizations of algebraic knowledge from basic education teachers: The moment to prepare lessons about equations". The objectives of this research are to map, investigate and understand which algebraic knowledge that was mobilized by teachers when working out their classes about equations for Basic Education. We adopted a qualitative approach to research methodology and data were collected through questionnaires and documentary analysis of the lessons had been prepared by the teachers of this research; audio recorded in meetings when teachers had planned their lessons in pairs. Those six teachers are people who prepare lessons for Basic Education in mathematical content to their craft both as a teacher actual or engaged, and for the development of research projects associated with initial or continuing training. Thus, to support this research including data analysis, the work of Shulman (1986 and 1987) and Ball et al. (2008) were used. Ball et al. suggest the theoretical framework of "Mathematical Knowledge for Teaching" which is the "Mathematical Knowledge needed to perform the job of teaching math" beyond the existence of two subdomains, from the works of Shulman: (i) Common Content Knowledge and Specialized Content Knowledge; also (ii) Knowledge of Content and Students, and Knowledge of content and Teaching. After analyzing the data, based on the perspective of mathematical knowledge for teaching, we identified, among others, the following algebraic knowledge: Recognition of a mathematical sentence is not an equation (Common Content Knowledge); Multimeaning understanding of the "=" symbol (Specialized Content Knowledge); Recognition of prior knowledge, so that students can understand and participate in an equations class (Content Knowledge and Students); Use an etymological approach of the words "equation" and "equality" with the aim of promoting a discussion of such content in the classroom (Content Knowledge and Teaching) and, finally, recognize that the contents of the equation, especially linear polynomial equation, has a strong relationship and importance to the content of inequalities, functions and other more advanced contents (Curricular Knowledge).

Made available in DSpace on 2016-04-27T16:58:30Z (GMT). No. of bitstreams: 1 Julio Cesar Guimaraes Queiroz.pdf: 840643 bytes, checksum: 8510f01586ba2706e33cdbfeb75df9d1 (MD5) Previous issue date: 2007-12-06 / Secretaria da Educação do Estado de São Paulo / The aim of this research is to investigate the mathematical knowledge sources of a teachers group who teaches in a public elementary school, in the city of São Paulo . Firstly we checked the available mathematical knowledge sources and we did a complementary research about similar themes. We also checked the graduation and recognition of the teachers as professionals. We found in Tardif and collaborators the background for development of this research. In order to find out the answer for the research question, we applied a needs analysis with thirteen questions for sixteen teachers. According to the answers, we chose three questions for an interview with five of these teachers to becoming clear important points in their answers. The result gotten into the needs analysis shows that the main material used by these respondents is the didactic book and also the graduated Mathematics teachers that help them with their doubts. We also concluded that the knowledge valued by the respondents is the one that Tardif (2006) calls Experiential Knowledge, which comes from in their individual or group daily experiences / O objetivo desta pesquisa é investigar sobre fontes de saber matemático de um grupo de professores e professoras que lecionam nos anos iniciais do ensino fundamental (do primeiro ao quarto ano do ciclo I) em uma escola pública municipal paulista. Para isso, percorremos uma trajetória de investigação sobre as fontes de saber matemático disponíveis e procuramos fazer um levantamento de trabalhos sobre tema similar. Também estudamos sobre a formação e a profissionalização do professor. Buscamos o referencial para o desenvolvimento de nossa pesquisa em Tardif e colaboradores. Em busca de resposta à nossa questão de pesquisa, aplicamos um questionário para dezesseis professores, composto por treze questões, e realizamos entrevista com cinco desses professores, com três questões que julgamos que esclareceriam pontos importantes levantados a partir das respostas ao questionário. Ao analisarmos os dados obtidos por meio dos questionários e das entrevistas, verificamos que as fontes de saber mais utilizadas pelos sujeitos de nossa pesquisa são os livros didáticos e os colegas, incluindo os professores especialistas, com formação em Licenciatura em Matemática. Verificamos também que os saberes valorizados pelos sujeitos são os que Tardif (2006) chama de Saberes Experienciais, aqueles que emergem das experiências individuais ou coletivas no cotidiano escolar

Made available in DSpace on 2016-04-27T16:58:47Z (GMT). No. of bitstreams: 1 Rodrigo Mioto.pdf: 376232 bytes, checksum: d7697b61b803acd57ccbea26df1e7afe (MD5) Previous issue date: 2008-11-17 / Secretaria da Educação do Estado de São Paulo / This document aims to investigate the knowledge construction for teaching Mathematics in the initial series. It intends to bring contribution for the initial formation improvement of the initial series teachers, being the trainee a reference point. The perspective is to identify Mathematic knowledge that this future teacher purchases during your formation at the University and at the school that the stage was developed. Contacting a University that offers the Pedagogy course, was selected a student that realized the supervised stage, indicated by the professor of this subject. The teacher of the discipline 'Mathematics Content and Methodology' from the Pedagogy Course and the regent teacher with whom was realized the stage in the Basic Education school were part of the research. It was investigated the proposals of the educational project and the Supervised Stage Manual related to the formation of a critic, investigative and reflexive professional on Mathematics contents; the opportunities for investigation, reflection and critic moments about Mathematics teaching and learning process on stage activities and practices and the regent teacher's contribution to the construction of a educational mathematics knowledge for the future teacher of initial series. Based on the research of Tardif (2002) about teacher knowledge and professional formation, Pimenta (2008) about stage and teaching, Curi (2004) about initial series teachers formation, Shulman (2004) about knowledge base categories for the teacher and Alarcão (2008) about the reflection in teaching. The data were obtained through documentary analysis and half-structured with two teachers of a Pedagogy course, a student that realized the stage, and the regent teacher of the school. The distance between the university and the school, pointed by several researches, prevails in this investigation, and it's up to the trainee the responsibility to realize his stage, according to the documents of institution and guidance of the regent teacher. This responsibility should be discussed, reflected and investigated by the formation agents / O presente trabalho tem como objetivo investigar a formação de conhecimentos escolares matemáticos das séries iniciais nas atividades de Estágio Supervisionado e Prática como componente curricular. Pretende trazer contribuição para o aperfeiçoamento da formação inicial de professores das séries iniciais. A perspectiva é a de identificar possíveis contribuições para a formação de conhecimentos escolares matemáticos para o futuro professor durante sua formação na universidade, no curso de Pedagogia, e na escola onde desenvolve seu estágio, por meio de um estudo de caso. A partir de contato com uma Universidade que oferece Curso de Pedagogia, foi selecionada uma aluna que realizou a disciplina de Estágio Supervisionado, indicada pela professora dessa disciplina. O professor da disciplina de Conteúdo e Metodologia de Matemática do Curso de Pedagogia e a professora regente com a qual foi realizado o estágio na escola de Educação Básica também fizeram parte da pesquisa. Investigou-se as propostas do Projeto Pedagógico e do Manual de Estágio Supervisionado relacionadas à formação de um profissional crítico, investigativo e reflexivo em relação aos conteúdos escolares matemáticos; as oportunidades de momentos de investigação, reflexão e crítica sobre o processo de ensino e aprendizagem da Matemática nas atividades de estágio e prática e as contribuições da professora regente para a construção do conhecimento escolar matemático da futura professora das séries iniciais. Fundamenta-se nas pesquisas de Tardif (2002) sobre saberes docentes e formação profissional, Pimenta (2008) sobre estágio e docência, Curi (2004) sobre a formação de professores das séries iniciais, Shulman (2004) sobre categorias da base de conhecimentos para o professor e Alarcão (2008) sobre a reflexão na docência. Os dados foram obtidos por meio de análise documental e entrevistas semi-estruturadas com duas professoras de um Curso de Pedagogia, uma aluna que realizou estágio e a professora regente da escola campo de estágio. O distanciamento existente entre a universidade e a escola, apontado por diversas pesquisas, prevalece nessa investigação, cabendo à estagiária a responsabilidade por realizar seu estágio, segundo o que consta nos documentos da instituição e orientações da professora regente. Responsabilidade que deveria ser dialogada, refletida e investigada pelos agentes formadores

This study establishes a framework for the practice and the acquisition of mathematical knowledge. The natures of mathematics and rituals/ritual-like activities are examined compared and contrasted. Using a four-fold typology of core features, surface features, content features and functions of mathematics it is established that the nature of mathematics, its practice and the acquisition is typologically similar to that of rituals/ ritual-like activities. The practice of mathematics and its acquisition can hence be metaphorically compared to that of rituals/ritual-like activities and be enriched by the latter. A case study was conducted using the ritual metaphor at two levels to introduce and teach a topic within the current year eleven West Australian Geometry and Trigonometry course. In the first level, instructional materials were written using a ritual-like mentor-exemplar, exposition, replicate and extrapolate model (through the use of specially organised examples and exercises) based on the approaches of several mathematics text book authors as they attempted to introduce a topic new to the West Australian mathematics curriculum. / In the second level, the classroom instruction was organised using a ritual-like pattern with direct exemplar mentoring and exposition by the teacher followed by replication and extrapolation from the students. Embedded within this ritual-like process was the personal (and communal) engagement with each student vis-a-vis the establishment of the relationships between the referent concepts, procedures and skills. This resulted in the emergence of solution behaviours appropriate to specific tasks imitating and extrapolating the mentored solution behaviours of the teacher. In determining the extent to which the instruction, mentoring and acquisition was successful, each student's solution 'behaviour was compared "topographically" with the expected solution behaviour for the task at various critical points to determine the degree of congruence. Marks were allocated for congruence (or removed for incongruence), hence a percentage of congruence was established. The ritual-like model for the teaching and acquisition of mathematical knowledge required agreement with all stake-holders as to the purpose of the activity, expert knowledge on the part of the teacher, and within a classroom context requires students to possess similar levels of prerequisite mathematical knowledge. / This agreement and the presence of an expert practitioner, provides the affirmation and security that is inherent in the practice of rituals. The study concluded that there is evidence to suggest that some aspects of mathematical ability are wired into the cognitive structures of human beings providing support to the hypothesis that some aspects of mathematics are discovered rather than created. The physical origin of mathematical abilities and activities was one of the factors used in this study to establish an isomorphism between the nature and practice of mathematics with that of rituals. This isomorphism provides the teaching and learning of mathematics with a more robust framework that is more attuned to the social nature of human beings. The ritual metaphor for the teaching and learning of mathematics can then be used as a framework to determine the relative adequacies of mathematics curricula, mathematics textbooks and teaching approaches.

In this dissertation, I propose that network theory offers a useful frame for informing mathematics education. Mathematical understanding, like the discipline of formal mathematics within which it is subsumed, possesses attributes characteristic of complex systems. As the techniques of network theorists are often used to explore such forms, a network model provides a novel and productive way to interpret individual comprehension of mathematics. A network structure for mathematical understanding can be found in cognitive mechanisms presented in the theory of embodied mathematics described by Lakoff and Nez. Specifically, conceptual domains are taken as the nodes of a network and conceptual metaphors as the connections among them. Examination of this metaphoric network of mathematics reveals the scale-free topology common to complex systems. Patterns of connectivity in a network determine its dynamic behavior. Scale-free systems like mathematical understanding are inherently vulnerable, for cascading failures, where misunderstanding one concept can lead to the failure of many other ideas, may occur. Adding more connections to the metaphoric network decreases the likelihood of such a collapse in comprehension. I suggest that an individuals mathematical understanding may be made more robust by ensuring each concept is developed using metaphoric links that supply patterns of thought from a variety of domains. Ways of making this a focus of classroom instruction are put forth, as are implications for curriculum and professional development. A need for more knowledge of metaphoric connections in mathematics is highlighted. To exemplify how such research might be carried out, and with the intent of substantiating ideas presented in this dissertation, I explore a small part of the proposed metaphoric network around the concept of EXPONENTIATION. Using collaborative discussion, individual interviews and literature, a search for representations that provide varied ways of making sense of EXPONENTIATION is carried out. Examination of the physical and mathematical roots of these conceptualizations leads to the identification of domains that can be linked to EXPONENTIATION.

No description available.

This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.

Mathematical modelling problems are embedded in written, representational, and graphic text. For students to actively engage in the mathematical-modelling process, they require literacy. Of critical importance is the comprehension of the problems' text information, data, and goals. This design-research study investigated the application of top-level structuring; a literary, organisational, structuring strategy, to mathematical-modelling problems. The research documents how students' mathematical modelling was changed when two classes of Year 4 students were shown, through a series of lessons, how to apply top-level structure to two scientifically-based, mathematical-modelling problems. The methodology used a design-based research approach, which included five phases. During Phase One, consultations took place with the principal and participant teachers. As well, information on student numeracy and literacy skills was gathered from the Queensland Year 3 'Aspects of Numeracy' and 'Aspects of Literacy' tests. Phase Two was the initial implementation of top-level structure with one class of students. In Phase Three, the first mathematical-modelling problem was implemented with the two Year 4 classes. Data was collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. During Phase Four, the top-level structure strategy was implemented with the second Year 4 class. In Phase Five, the second mathematical-modelling problem was investigated by both classes, and data was again collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. The key finding was that top-level structure had a positive impact on students' mathematical modelling. Students were more focussed on mathematising, acquired key mathematical knowledge, and used high-level, mathematically-based peer questioning and responses after top-level structure instruction. This research is timely and pertinent to the needs of mathematics education today because of its recognition of the need for mathematical literacy. It reflects international concerns on the need for more research in problem solving. It is applicable to real-world problem solving because mathematical-modelling problems are focussed in real-world situations. Finally, it investigates the role literacy plays in the problem-solving process.