Submitted by MARCOS LUCHIARI BARALDI (marcosbrld@yahoo.com.br) on 2018-09-12T03:42:53Z No. of bitstreams: 1 DISSERTAÇÃO-12.09.18.pdf: 3346423 bytes, checksum: a92ab36f4ef9b546a9685be711a2f4b5 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-09-12T13:24:07Z (GMT) No. of bitstreams: 1 baraldi_ml_me_sjrp.pdf: 3346423 bytes, checksum: a92ab36f4ef9b546a9685be711a2f4b5 (MD5) / Made available in DSpace on 2018-09-12T13:24:07Z (GMT). No. of bitstreams: 1 baraldi_ml_me_sjrp.pdf: 3346423 bytes, checksum: a92ab36f4ef9b546a9685be711a2f4b5 (MD5) Previous issue date: 2018-08-03 / Este trabalho apresenta uma verificação de uma das relações mais importantes da matemática elementar: a relação de Euler. Ela expressa uma relação entre o número vértices, arestas e faces de poliedros convexos, podendo ser estendida aos poliedros estrelados, particularmente aos de Kepler-Poinsot. Para analisar tal relação, a proposta é utilizar material concreto, como jujubas, canudos e varetas de fibra. A princípio é realizada a construção dos poliedros de Platão, canudos rígidos e coloridos, onde é possível verificar com facilidade a veracidade da Relação de Euler. Na sequência utilizam-se as varetas de fibra de vidro 1,4 mm que com a introdução nas arestas dos poliedros, verifica-se facilmente que apenas o dodecaedro e o icosaedro são passíveis da estrelação, por prolongamento das arestas obtendo assim, dois dos poliedros estrelados de Kepler-Poinsot. Por fim, é analisado que a Relação de Euler, também se verifica para esses estrelados. Com tal procedimento fica mais perceptível a não existência de outros poliedros estrelados, pois a partir de sua construção com canudos e a ampliação de suas arestas com varetas fica claro a não intersecção delas. Vale lembrar que tais atividades lúdicas são incentivadas no ensino da matemática e algumas já foram abordadas em dissertações do PROFMAT e em documentos oficiais de ensino no Brasil, como nos Parâmetros Curriculares Nacionais, no Currículo do Estado de São Paulo, matrizes de referências de avaliações tais como: Saresp (Sistema de avaliação de rendimento escolar do estado de São Paulo), Saeb (Sistema nacional de avaliação do ensino básico) e ENEM (Exame nacional do ensino médio). / This paper presents a verification of one of the most important relations of elementary mathematics: Euler's relation. It expresses a relation between the number of vertices, edges and faces of convex polyhedra, and can be extended to the starry polyhedra, particularly to those of Kepler-Poinsot. To analyze this relationship, the proposal is to use concrete material, such as jelly beans, straws and fiber rods. At first the construction of Plato's polyhedrons, rigid and colored straws, is carried out, where it is possible to verify with ease the veracity of the Euler Relation. The 1.4 mm glass fiber rods are then used which, with the introduction of polyhedron edges, can easily be verified that only the dodecahedron and the icosahedron are capable of staring by prolonging the edges, thus obtaining two of the polyhedra starring Kepler-Poinsot. Finally, it is analyzed that the relation of Euler, also is verified for these stars. With such a procedure it is more noticeable the existence of other starry polyhedra, since from its construction with straws and the enlargement of its edges with rods it is clear the nonintersection of them. It is worth remembering that such play activities are encouraged in the teaching of mathematics and some have already been addressed in PROFMAT dissertations and in official teaching documents in Brazil, such as in the National Curriculum Parameters, in the Curriculum of the State of São Paulo, references reference matrices such as: Saresp (System of evaluation of school performance of the state of São Paulo), Saeb (National system of evaluation of basic education) and ENEM (National High School Examination).

Made available in DSpace on 2015-03-03T15:36:11Z (GMT). No. of bitstreams: 1 ClesioRB_DISSERT.pdf: 808792 bytes, checksum: 2d1aa128ad7360c7d557a02b2b246fb8 (MD5) Previous issue date: 2013-05-03 / Universidade Estadual do Rio Grande do Norte / Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited / Atravessando os s?culos, a Matem?tica - como ci?ncia exata que ? - vem assumindo um papel determinante na vida do homem, que dela faz uso para suprir necessidades de sua vida di?ria. Com essa trajet?ria, fica caracterizada a import?ncia dessa ci?ncia como instrumento de valoriza??o n?o s? conteud?stica, mas tamb?m de um saber matem?tico que conduz o ser aprendiz a um processo din?mico de aprendizagem e - ciente, capaz de buscar solu??es para seus problemas reais. No entanto, necess?rio se faz compreender que o conhecimento matem?tico hoje requer um novo olhar daqueles que diretamente lidam com o processo ensino-aprendizagem, pois cabe a eles - professores de Matem?tica - desmistificarem a vers?o de que a Matem?tica, trabalhada na sala de aula, traz dificuldades para a compreens?o do alunado. Sobre esse prisma, buscou-se com este trabalho encontrar uma metodologia que auxilie os alunos a entenderem melhor as Fun??es Quadr?ticas e suas aplica??es no cotidiano. Fazendo-se uso dos conhecimentos etnomatem?ticos, contextualizando os problemas referentes ao conte?do e, ao mesmo tempo, manuseando o software GeoGebra, objetivando uma melhor visualiza??o do comportamento dos gr?ficos das citadas fun??es.

Mais tempo para os alunos nas escolas tem sido constante demanda na educação brasileira. A partir da Lei de Diretrizes e Bases da Educação Nacional (LDBEN) 9.394/96, artigo 34, que estabeleceu a progressiva ampliação da jornada escolar para os alunos do Ensino Fundamental, a Rede Pública de Ensino de Belo Horizonte, em Minas Gerais, propôs uma Educação em Tempo Integral. Para ampliar a jornada escolar de alunos regularmente matriculados, entre seis e 14-15 anos, foi implantado o Programa Escola Integrada (PEI) nas escolas do município mineiro no ano de 2007. Pesquisas realizadas apontam que o referido programa propicia a melhoria do desempenho escolar dos alunos. Em consonância com este contexto, a presente pesquisa, de caráter predominantemente qualitativo, investigou as atividades desenvolvidas no turno regular, nas aulas de Matemática do 3º. Ciclo do Ensino Fundamental, e no turno oposto às aulas regulares, nas oficinas do Projeto de Intervenção Pedagógica (PIP), buscando compreender como a atuação de professores de Matemática tem promovido a progressão da aprendizagem dos alunos, entendida aqui como fonte de ampliação dos conhecimentos e dos horizontes culturais. Este estudo desenvolvido durante todo o ano letivo de 2011 foi orientado pela seguinte questão de investigação: Que representações e que resultados a Educação em Tempo Integral suscita em professores de Matemática e alunos do 3º. Ciclo de duas escolas públicas da Rede de Ensino de Belo Horizonte? Com o intuito de identificar e analisar as representações mais marcantes de aprendizagem da matemática enunciadas por professores e alunos, a fundamentação na teoria das representações formulada por Henri Lefebvre foi utilizada por levar em consideração não apenas os discursos dos sujeitos, como também as ações que realizam. Os procedimentos metodológicos adotados envolveram observação do cotidiano escolar, entrevistas semi-estruturadas com professores de matemática, com alunos e seus pais além de análise documental como fonte de informação para contextualizar a escola antes e depois da implantação do PEI. Como resultado constata-se que a educação em tempo integral propôs reorganizar o trabalho pedagógico e instituir novos tempos da e na escola, no sentido de desconstruir os mecanismos de exclusão e seletividade produtores do fracasso escolar. As representações dos professores e dos alunos sobre essa problemática elucidam que o tempo escolar ampliado possibilitou a melhoria da aprendizagem em matemática que também foi verificada pelos resultados das avaliações escolares e sistêmicas. Embora professores e alunos afirmem que as práticas inovadoras propostas pelo PEI não estão suficientemente consolidadas, em seus depoimentos reconhecem que a ampliação do tempo de permanência na escola tem promovido mudanças no cotidiano escolar e na cotidianidade da comunidade, nas relações entre o tempo vivido e o tempo social; portanto, coerentes com a perspectiva de escola que se deseja democrática, cidadã e inclusiva na direção de uma Educação Integral. / More time for students in schools has been steady demand in Brazilian education. From the Law of Guidelines and Bases of National Education (LDBEN) 9.394/96, Article 34, which established the progressive expansion of the school day for elementary school students, the Public School of Belo Horizonte in Minas Gerais proposed a toward Full-time Education. To extend the school day for students enrolled between six and 14-15 years, was implemented Integrated School Program (PEI) in schools in the mining town in 2007. Researches indicate that the program promotes the improvement of students achievement. In line with this context, the present research predominantly qualitative, investigated the activities during the regular shift, in Mathematics classes in the 3rd. cycle of elementary school, and in opposite shift, to regular classes, in the workshops Pedagogical Intervention Project (PIP), seeking to understand how the performance of mathematics teachers has promoted the advancement of student learning, understood here as a source of expansion of knowledge and cultural horizons. This study, developed during the 2011 school year, was guided by the following research question : What representations and results in Full-time Education raises math teachers and students of the third cycle of the two public schools in Belo Horizonte? In order to identify and analyze the most striking representations of learning cited by mathematics teachers and students, the foundation of the theory of representations made by Henri Lefebvre was used by taking into account not only the discourses of the subject, as well as the actions they perform. The methodological procedures involved observation of the school routine, semi-structured interviews with mathematics teachers, with students and their parents, as well as document analysis as a source of information to contextualize the school before and after the implementation of the PEI. As a result, it appears that Full-time Education has proposed to reorganize the educational work and to institute new times at school in order to deconstruct the mechanisms of exclusion and selectivity that are producers of school failure. The representations of teachers and students about this problem elucidates that the extended school time enabled the improvement of learning mathematics that was also verified by the results of school evaluation and systemic. Although teachers and students claim that innovative practices proposed by PEI are not sufficiently consolidated, acknowledged in their testimonies recognize that increasing time spent in school has promoted changes in the school routine and daily life of the community, the relations between lived and social time, and therefore consistent with the perspective of school that want to democratic, citizenship and inclusive toward a Comprehensive Education.

The purpose of this document is to review the incorporation of technology into a math classroom. With technology becoming more a part of our growing society it is important for teachers and students to stay up with the times.

Much research supports that student mindset influences how well students do in school and that teacher actions influence student mindset. Research has also shown that just because a teacher has a growth mindset, it does not imply that their students will also have a growth mindset. This research looks closer as to why a teacher's mindset does not correlate with their students' mindset by further examining teacher mindset and the connection between teacher mindset and teacher actions. In summary, teachers' mindsets do not directly influence student mindset for a few reasons: secondary mathematics teachers have different mindsets towards honors and regular students, while they have heard about mindset, they do not understand mindset deeply, and mathematics teachers do not know how to help their students develop a growth mindset.

This study investigated the interaction of mathematics teachers with learners’ mathematical errors. The teachers’ verbal interaction with learners’ errors during learning periods and their written interaction in assessment tasks were explored. The study was contextualized in grade 9 secondary school classrooms in the Gauteng province of South Africa. The investigation was epistemologically underpinned by constructivism/socio-constructivism. The investigation was qualitatively approached through four case studies. Structured and semi-structured interviews, classroom observations and learners’ written assessment tasks were employed as sources of data. The participating teachers were described in terms of their beliefs about mathematics, their beliefs about learners’ mathematical errors, their observed prevalent teaching approach and their professed and enacted interaction with learners’ mathematical errors. Within-case and cross-case comparisons ensued. The findings proposed that when teachers believed that the value of learners’ errors was vested in the corrections thereof, rather than employing these opportunities for discussion, valuable opportunities for learners to develop and improve their meta-cognitive abilities might potentially be lost. The findings further indicated that a focus on the mere correction of learners’ errors probably denied learners opportunities to develop a mathematical discourse. The results of the investigation illuminated that an emphasis on achievement during assessment, together with a disapproving disposition towards errors among teachers and learners, were hindrances. They acted as barriers to engendering a socio-constructivist learning environment in which interactions with learners’ errors could enhance learning and establish a negotiating mathematical community. A concurrence between the teachers’ prevalent teaching approach and their mathematical beliefs was confirmed. However, in two of the four cases, a dissonance was revealed between their prevalent teaching approach and their interaction with learners’ errors. Interaction with learners’ mathematical errors was hence identified as a separate and discrete component of a teacher’s practice. The findings suggest the explicit inclusion of error-handling in reform-oriented teacher-training and professional development courses to utilize learners’ mathematical errors more constructively. / Dissertation (MEd)--University of Pretoria, 2010. / Science, Mathematics and Technology Education / unrestricted

Darbe nagrinėjamas informacinių technologijų fenomenas dabarties žinių visuomenėje, interneto technologijas siejant su mokymo(si) procesu. Pateikiama mokymosi proceso samprata technologinio kitimo amžiuje. Aptariamas konstruktyvizmu grindžiamo mokymosi aiškinimas (konstrukcionizmo pedagoginė teorija), atskleidžiami esminiai konektyvizmo principai ir užduotys, su kuriomis turi susidurti besimokantysis skaitmeninio amžiaus eroje. Pristatomi matematikos mokymo filosofijos (matematikos filosofijos) keliami klausimai. Galiausiai ieškoma atsakymų į klausimus: kokį vaidmenį kompiuterinės technologijos, pastarojo meto interneto tecnologijos ir paslaugos atlieka matematikos mokymo bei mokymosi proceso metu, kaip jį paliečia, kokias galimybes atveria, kaip keičia šį procesą. / This theme paper analyses the phenomenon of information technologies in relation with the present knowledge-based society and the Web technologies in the process of education. The concept of learning process is discussed in the age of technological change. The constructivism based learning (constructionism learning theory) is presented in this paper too. Besides this, the most essential principles and tasks of connectivism which a learner is supposed to deal with in the digital surroundings are being analysed as well. Moreover, the issues raised by the phylosophy of mathematics education (and the phylosophy of mathematics) are also introduced in this paper. Finally, the reply search to the following issues – what role do computer-based technologies, modern internet technologies and services play in the process of teaching and learning mathematics; how do the above mentioned factors influence a process of education; what are the perspectives of the mentioned processes; how do the discussed issues change the process of teaching and learning mathematics – is analysed in the paper.

The theoretical part deals with approaches to teaching, especially constructivistic, instructivistic and transmissive approach. The goal of this part is to compare the approaches and evaluate them considering the permanency of knowledge and active engagement of students. Simultaneously it aims at evaluating the approaches from the point of their of the mechanical knowledge. The charter dealing with inquiry based mathematics education is focused on teaching related to constructivistic approach. The next chapter describes tool called concept cartoons, which can be used as a mean to research. The theoretical part is focused on the topic of fraction, especially fraction interpretation and models and fraction representation. The second part of the thesis describes a survey realized at basic school. I narrowed the problem to fraction interpretation and representation according to survey of student's work. The next part of research is based on this analysis. Trying to accomplish the aims and find the answers to questions of the survey I chose strategy inspired by action research, because the main goal of the research was to improve and enhance my teaching knowledge and skills. The survey was processed qualitatively. The making of the thesis helped me make it clear, why the topic of fractions is so...

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.

O objetivo deste trabalho foi elaborar e aplicar um conjunto de atividades, na modalidade oficina, para uma turma de estudantes jovens e adultos do primeiro nível do ensino médio do Colégio de Aplicação da Universidade Federal do Rio Grande do Sul (CAp – UFRGS). As atividades foram elaboradas com a intenção de fazer uso de dados apresentados em mídias impressa e virtual no ensino da Matemática para contribuir na aprendizagem dos estudantes Jovens e Adultos. Essas mídias foram escolhidas por se constituírem em fontes de atualização acessíveis e possibilitarem a integração de várias áreas do conhecimento. Essas fontes de informações, além de se apresentarem como uma maneira de contextualizar os conteúdos específicos desta disciplina e valorizar os saberes e experiências dos aprendizes foram o ponto de partida deste trabalho. A análise dos dados permite concluirmos que a proposta representou uma contribuição tanto na aprendizagem de matemática dos estudantes quanto para as discussões e a consolidação de uma proposta de educação de jovens e adultos do CAp – UFRGS. / The aim of this work was to elaborate and implement a range of workshop-activity method for a class of young and adult students of the first level of education of Colégio de Aplicação at Federal University of Rio Grande do Sul (CAP - UFRGS). The activities were developed to use data submitted to printed and virtual media in the teaching process of mathematics to contribute with the learning of young and adult students. These media were chosen because they constitute an updated and accessible source. It allows the integration of several areas of knowledge. These sources of information, and present themselves as a way to contextualize the specific content of this discipline and enhancement of knowledge and experience of apprentices were the starting point for this work. Data analysis indicates that the proposal represented a contribution not only to the learning of mathematics of the students but also the discussion and consolidation of a proposal for education of young and adult at Cap. / El objetivo de este trabajo ha sido elaborar y aplicar un conjunto de actividades, en la modalidad de taller, para un grupo de estudiantes jóvenes y adultos del primer nivel de la Enseñanza Media del Colegio de Aplicação de la Universidad Federal de Río Grande do Sul (CAp – UFRGS). Las actividades se han elaborado con la intención de utilizar los datos presentados en los medios, impresos y virtual, en la enseñanza de Matemática para contribuir en el aprendizaje de los estudiantes jóvenes y adultos. Esos medios se han escogido porque se constituyen como fuentes de actualización accesibles y posibilitan la integración de varias áreas del conocimiento. Esas fuentes de información, además de presentarse como una forma de contextualizar los contenidos específicos de esta asignatura y de valorar los saberes y experiencias de los aprendices, han sido el punto de partida de este trabajo. El análisis de los datos permite que concluyamos que la propuesta ha representado una contribución tanto para el aprendizaje de Matemática de los estudiantes como para las discusiones y consolidación de una propuesta de educación de jóvenes y adultos del CAp – UFRGS.