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O professor de matemática e seus saberes e suas necessidades em relação à sua disciplinaNeves, Marcos Rogério 11 May 2007 (has links)
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Previous issue date: 2007-05-11 / This work is a result of the research about the characteristics of the knowledge related to specific content of mathematics matter that a teacher is developing/reworking throughout his professional career. This is a case study, which the participant has the characteristics to be egress of the university course of the education of mathematics teachers; to have sought specific training in mathematics after three years of the professional practice and have a positive relationship with math and with their work. The design of teacher s knowledge that served as the basis emphasizes the social and discursive dimension of knowledge, proposing consider it as an expression of the practical reason, which belongs more to the fields of argument and the trial, than the fields of cognition and of information. We associate to the concept of knowledge the notion of relationship with knowledge, which guides us to consider the contexts and practices, in which the teacher is mobilizing to learn, or mobilize their knowledge in their interaction with students, the school team, with teaching materials and with the circumstances and demands of the profession. Through interviews, investigate how these contexts and practices influenced the construction of logical structure (requirements of rationality) of the teacher's way of thinking, over his career, especially considering the content of mathematics with which he works. Among the results of the research, we noticed that extent, the consistency, organization, the mechanisms for selection and improvement of knowledge of the teacher, concerning to the content of mathematics, are very influenced by the nature and function of their activity and, thus, for his practice in different situations and contexts linked to school. Throughout his career, he presents an authentic (and enviable) mobilization to learn that feeds the process of acquisition and updating of their knowledge, from their professional needs. However, in their experiences into the course of the education of mathematics teachers he found little support to reflect and improve their knowledge and their practices. Considering that the requirements of rationality are the conditions of intelligibility that a person need for the speech and its action their and the other make sense and are acceptable as evidence of a coherent dialogue, we noticed that the experiences of this subject in the universitary course little nurture the dialogue between the higher-level math and its knowledge, leaving, one hand, of to contribute in a meaningful way with their problem and thinking about the content, on the other, working to consolidate perspective in which their knowledge had been constructed to from their practice. / O presente trabalho é resultado da investigação sobre as características dos saberes relacionados aos conteúdos específicos da matéria de ensino que um professor de matemática vem elaborando/reelaborando ao longo de sua trajetória profissional. Trata-se de um estudo de caso, cujo participante tem como características ser egresso do curso de licenciatura em matemática; ter buscado uma formação específica em matemática após três anos de exercício da profissão; e ter uma relação positiva com a matemática e com seu trabalho. A concepção de saberes docentes que nos serviu de base ressalta a dimensão discursiva e social do saber, propondo considerá-lo como a expressão de uma razão prática, a qual pertence muito mais ao campo da argumentação e do julgamento do que ao campo da cognição e da informação. A ela associamos a noção de relação com o saber, que nos orienta a considerar os contextos e as práticas, nas quais o professor se mobiliza para aprender, ou mobiliza seus saberes na interação com seus alunos, com a equipe escolar, com materiais didáticos e com as circunstâncias e exigências da profissão. Através de entrevistas investigamos como estes contextos e práticas influenciaram a construção das lógicas estruturadoras (exigências de racionalidade) da maneira de pensar do professor, ao longo de sua carreira, principalmente considerando os conteúdos de matemática com os quais ele trabalha. Entre os resultados da pesquisa, constatamos que a amplitude, a consistência, a organização, os mecanismos de seleção e aperfeiçoamento dos saberes do professor, referentes aos conteúdos de matemática, são bastante influenciados pela natureza e pela função de sua atividade e, portanto, por sua prática em diversas situações e contextos ligados a escola. Ao longo de sua carreira, ele apresenta uma autêntica (e até invejável) mobilização para aprender que alimenta os processos de aquisição e atualização de seus saberes, a partir de suas necessidades profissionais. Contudo, em suas experiências no curso de licenciatura em matemática ele encontrou pouco suporte para refletir e aperfeiçoar seus saberes e suas práticas. Tendo em vista que as exigências de racionalidade constituem as condições de inteligibilidade que o próprio indivíduo impõe para que o discurso e a ação seu e do outro façam sentido e sejam aceitáveis como elementos de um diálogo coerente, notamos que as experiências deste sujeito no meio universitário pouco oportunizaram o diálogo entre a matemática de nível superior e seus saberes, deixando, por um lado, de contribuir de maneira significativa com sua problematização e reflexão acerca dos conteúdos, por outro, colaborando para consolidar a perspectiva na qual seus saberes docentes vinham sendo construídos a partir de sua prática.
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A needs analysis for the implementation of a complementary course in mathematics education for teachers of mathematics in Namibia: a case studyIlukena, Alex Mbonabi January 2009 (has links)
After the introduction of the Basic Education Teacher Diploma (BETD) in Namibia, a number of studies were conducted on how teachers, lecturers, stakeholders and the Namibian public perceived the BETD program and its implementation. However, very few studies focussed specifically on mathematics subject content knowledge and pedagogical content knowledge in the BETD. The purpose of this study was to investigate the need for a complementary course in mathematics education to address the lack of mathematical content and pedagogical knowledge in the Namibian BETD. The study involved five mathematics school teachers, two mathematics college lecturers in the Kavango educational region and a professor of mathematics education at the University of Namibia. These participants were purposefully selected because of their knowledge and experiences with various aspects of the BETD program. The motivation for conducting this study was to gain a better understanding of some of the issues that have been raised about the BETD program, particularly the perceived inadequacy of mathematical subject content and methodology since the inception of the program. The study adopts a qualitative approach in reporting participants’ reflections. The views of the focal educators and documents such as syllabi and course outlines were the main source of data. The findings indicate that despite the training that the three BETD mathematics graduates in this study received, the level of mathematics taught in a complementary course, such as an ACE, would clearly better equip mathematics teachers to teach proficiently and facilitate access to institutions of higher learning such as universities. The results of the study revealed that there was a need for the implementation of a complementary course to the BETD in mathematics education for teachers of mathematics in Namibia. This study also provided valuable insights into what such a course could look like.
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An investigation into understanding the experiences of the level 5-7 student teachers when teaching fractions in primary schools in Namibia: a case studyVatilifa, Ndamononghenda January 2013 (has links)
The Namibian government through the Ministry of Education seeks for teachers to meet the demands and rise to the challenges of the post-independence basic education system. Therefore the University of Namibia Education Faculty must ensure through the training of student teachers for both lower, upper primary and secondary school level that these demands are met. Research shows that one of the major challenges in teacher training programs, specifically in the mathematics education programmes, lies with the student teachers’ difficulties in dealing with various topics in mathematics, particularly fractions. The teaching of fractions is a challenging area at primary level and lays the foundation for understanding different topics in upper grades such as algebra, ratio and proportion, statistics and probability, to mention just a few. This study focused on an exploration of teaching fractions by five student teachers during their teaching practice.The main purpose was to gain an understanding of the experiences of the level 5-7 student teachers with regard to their practice of fraction teaching; their experience of the mathematics education course with respect to the teaching of fractions; and their prior experience related to fractions and fraction teaching at Grade 6 level. The findings from this research showed that student teachers viewed mathematics, specifically fractions, as just about doing calculations, doing drill and practice as in this way learners’ understanding of fractions is enhanced. The importance of using rules and procedures was emphasized as paving the way to mastering fractions. The data analysis also revealed that student teachers employed different teaching approaches when they considered learners’ prior knowledge. However, they misinterpreted the learner-centred approach in terms of group work and class discussion in their teaching of fractions. The data also revealed that some student teachers had an understanding of fractions as they managed to redirect their learners from applying some fraction misconceptions. The findings further showed that due to lack of understanding most of the participants experienced fear and anxiety in their fraction teaching; attempted an approach then reverted to old practices used in schools; taught fractions as symbolic representations where no meaning was involved; used incorrect terminologies such as ‘1 over 4’ or ‘1 out of 4’ instead of a ‘quarter’ or ‘one-fourth’. It is further revealed that the some student teachers viewed a fraction as a pair of two different whole numbers and can be broken apart. The findings of this study yielded one main implication for the teaching of mathematics: that the teacher training programs, specifically for mathematics teachers, must take into consideration the weaknesses and strengths of the student teachers shown in this study to properly train and prepare them to become effective mathematics teachers.
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A metodologia de resolução de problemas : concepções e práticas pedagógicas de professores de matemática do ensino fundamental /Redling, Julyette Priscila. January 2011 (has links)
Resumo: Atualmente, a tendência das propostas educacionais é promover, aos alunos a possibilidade de participar ativamente da construção do seu próprio conhecimento. E, dessa forma, o Ensino-Aprendizagem de Matemática através da resolução de problemas é concebido como uma metodologia alternativa, que visa a um trabalho centrado no aluno e, por isso, pode levá-lo a construir um conhecimento matemático através da resolução de problemas. Nesse processo, o papel do professor é o de orientar e supervisionar o trabalho dos alunos e formalizar as idéias construídas ao seu final. Nesse contexto, justifica-se o desenvolvimento da presente investigação, que teve por objetivo investigar e analisar a compreensão e a prática de professores de matemática do Ensino Fundamental II sobre resolução de problemas, sua importância no processo de ensino-aprendizagem da matemática e as ações de ensino-aprendizagem envolvendo resolução de problemas. A pesquisa qualitativa desenvolveu-se por meio de aplicação de questionário, realização de observações de aulas e entrevistas com os professores. Foi possível identificar que os professores verbalizam suas concepções e crenças de Ensino-Aprendizagem de Matemática através da resolução de problemas, com o foco num trabalho onde os alunos desenvolvem sua capacidade de aprendizagem autônoma. Contudo, suas ações apontam para uma realidade diferente, onde os conteúdos são formalizados previamente e os problemas são utilizados para finalizar os assuntos, fato que não caracteriza o uso da resolução de problemas enquanto metodologia de ensino-aprendizagem / Abstract: Currently, the trend of education proposals is to promote students, to participate actively in the construction of their own knowledge. An thus, the teaching-learning of mathematics through the problem solving , is designed as an alternative methodology, aimed at a student-centered work, and therefore can lead him to build a mathematical knowledge through solving problem. In the process, the teacher's role is to guide and supervise the work of students and formalize the ideas built to its end. In this context, explains the devolopment of this research, which aimed to investigate and analyze the understanding and practice of mathematics teachers of middle school about the problem solving its important in the process of teaching-learning of mathematics and teaching-learning actions involving solving problem. The qualitative research was development through a questionnaire, conducting interviews and observations of lessons with teachers. We were able to identify which teachers verbalize their ideias and beliefs of teaching-learning of mathematics through the problem solving, with the focus on work where students develop their capacity for independent learning. However, their actions suggest a different reality, where the contents are previolusly formalized and problems are used to finalize the issues, which did not characterize the use of problem solving as teaching-learning methodology / Orientador: Luciana Maria Lunardi Campos / Coorientador: Renata Cristina Geromel Meneghetti / Banca: Lourdes de La Rosa Onuchic / Banca: Nelson Antônio Pirola / Mestre
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An investigation into the prevalence and use of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia: a case studyShilamba, Julia Ndinoshisho January 2013 (has links)
This research report focuses on an investigation of the prevalence and nature of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia. The existence of code switching in these classrooms was established by administering a survey to all grade 8 teachers in the region, while the nature of these practices was explored by interviewing and observing selected teachers using a case study research methodology. The data from the survey was analysed quantitatively using descriptive statistics, while the qualitative data from the case study which comprised of audio and video transcripts was analysed within the framework of Probyn’s (2006) code switching categories. These categories looked at code switching in terms of: explaining concepts; clarifying statements or questions; emphasising points; making connections with learners’ own contexts and experiences; maintaining the learners’ attention with question tags; classroom management and maintaining discipline; and affective purposes. The study found that code switching is widespread in most of the grade 8 mathematics classrooms in the Ohangwena region. It also revealed that the teachers’ code switching practices aligned well with most of Probyn’s framework. The criterion of maintaining learner’s attention with question tags was however not found in this study. The results of the study showed that teachers code switch because the majority of the learners’ language proficiency is not good. Code switching is mostly used as a strategy to support and promote learners understanding in mathematics. The study recommends that it is high time that code switching is acknowledged as a legitimate practice and recognised as an important and meaningful teaching strategy to assist learners who are learning mathematics in their second language. Code switching needs to be de-stigmatised and teachers should be supported in using this practice effectively and efficiently.
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A critical investigation into the process of negotiating a mathematics education curriculum with pre-service teachersWestaway, Lise January 2005 (has links)
It's almost like a dinner party and a buffet. A dinner party you get dished up stuff and you eat it and a buffet you can choose what you want out of a range of stuff. I mean think about it when you go to a dinner party- they always dish up something you don't like and you don't want to eat it anyway. It's the same if you have a lecturer in the front that just dishes out what you're going to learn, ... you have to learn it. But in terms of the curriculum negotiation process, I've got to choose what I wanted to leam. (Melissa II 27/11/01: 3) This thesis focuses on the process of negotiating the curriculum with twelve pre-service teachers registered for the Bachelor of Education (Primary) Degree during their Mathematics Education Course in their third year of study. The research is presented methodologically as an action research located within two paradigmatic positions, interpretive and critical. The research attempted to understand, interpret and critique the process of curriculum negotiation within the context of teacher education in South Africa In order to understand the negotiated curriculum process, experiences of the participants are presented through the use of their voices within the thesis. The interpretation is based on the construction and reconstruction of meaning during the enactment of the negotiated curriculum process and during the writing and reviewing of this thesis. The critique is rooted in the historical, cultural and social contexts of both the students and the author. The main contention of this thesis is that curriculum negotiation is not necessarily a suitable vehicle for developing a critical pedagogy in pre-service teacher education when all the participants form a homogenous group in this case, white middle-class women. The democratic values promoted within the context of our curriculum negotiation were fraught with dilemmas and entrenched the values of western liberalism. At most, the curriculum negotiation process and the development of a democratic learning environment, promoted a conscientisation at an individual level, namely a ' transformation of consciousness' . The democratic values promoted in our pedagogy were not sufficient in bringing about social change, a 'transformation for social action'.
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An investigation into the pre-service training of secondary school mathematics teachers at colleges of education administered by the House of RepresentativesHendricks, Mogamat Armien January 1989 (has links)
This study involves an investigatioh into the nature and effectiveness of the pre-service training, where provided, of secondary school Mathematics teachers at the 11 colleges of education administered by the House of Representatives in the Republic of South Africa. The purpose of this study is to determine whether the HDE (Secondary) course offered at some of the aforementioned colleges of education is justified, In spite of the fact that it contravenes the requirements of the Education Act, No. 73 of 1969. Three different questionnaires were designed and during 1986 were sent to heads of Mathematics departments at the aforementioned colleges of education , to Mathematics teacher educators at these colleges and to beginning secondary school Mathematics teachers, teaching at schools administered by the House of Representatives in the Eastern Cape and Natal. The findings of this study show that the secondary course for Mathematics teachers is only offered at 5 of the 11 colleges of education and only a small percentage of students take this course. During 1986 most of the Mathematics teacher educators at the colleges of education were not suitably qualified. The study also shows that the Mathematics curriculum for the training of secondary school teachers is inadequate and a revision thereof is thus recommended. An obvious conclusion drawn from the findings is that the training of secondary school Mathematics teachers at these colleges of education is still in an early stage of development. One of the main recommendations of this study is that the training of secondary school Mathematics teachers at colleges of education administered by the House of Representatives should be terminated , in view of its ineffectiveness and In accordance with Education Act , No . 73 of 1969. On the other hand, in case this is not possible, suggestions are also made for the improvement of the pre-service training of secondary school mathematics teachers at these colleges of education.
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A formação continuada de professores de matemática : uma inserção tecnológica da plataforma khan academy na prática docenteMenegais, Denice Aparecida Fontana Nisxota January 2015 (has links)
Com a inserção das Tecnologias da Informação e Comunicação (TICs) na sala de aula, em especial a inclusão dos laptops e da internet, a formação continuada de professores constitui-se como uma das principais ações das políticas públicas em educação, conquistando espaço nas discussões acadêmicas, políticas e econômicas, com vistas à qualificação da educação brasileira. Justifica-se a escolha do tema a partir de experiências da professora-pesquisadora como formadora de professores em um curso de licenciatura em Matemática e ministrante de cursos de formação continuada, em que percebeu que, em geral, as formações não oferecem subsídios suficientes para a efetiva integração das tecnologias digitais no contexto escolar. A presente pesquisa tem como objetivo analisar como os professores de Matemática da educação básica, em processo de formação continuada, podem aprimorar sua prática docente, levando em consideração a realidade da nova cultura digital e o conhecimento do processo de desenvolvimento da inteligência e do raciocínio do estudante. Foi realizada, em um primeiro momento, uma análise da disciplina “Tecnologias Aplicadas ao Ensino de Matemática”, presente no Projeto Político-Pedagógico do Curso de Licenciatura em Matemática de uma universidade pública federal, à luz da Epistemologia Genética de Piaget, com a intenção de, posteriormente, compreender a influência das tecnologias na prática pedagógica dos professores. Em um segundo momento, um grupo de profissionais da área da Matemática atuantes da rede pública estadual da região de Bagé participou da pesquisa, que consistiu de entrevistas, observação em sala aula e utilização da plataforma Khan Academy. A metodologia de pesquisa-ação foi implementada visando à participação da pesquisadora, com observação e ação, a fim de alcançar os objetivos propostos para chegar à teorização sobre os resultados. Observou-se, a partir dos resultados, que o curso de formação continuada proposto favoreceu a integração de tecnologias digitais no contexto escolar, promovendo mudanças na prática docente e favorecendo a aprendizagem de conteúdos de Matemática. Os professores participantes, ao final do curso de formação, mostraram-se mais confiantes e melhor preparados para utilizar os recursos tecnológicos disponíveis nas escolas, além de sentirem-se encorajados a ampliar sua utilização. O uso da plataforma Khan Academy possibilitou essas mudanças e colaborou para que despontasse um novo paradigma de ensino e de aprendizagem, no qual os conhecimentos prévios dos estudantes, suas dificuldades e potencialidades, são valorizados e considerados como princípios da prática pedagógica. / With the inclusion of Information and Communication Technologies in the classroom, especially the inclusion of laptops and the Internet, continuing education of teachers constitutes one of the main actions of public policies in education, gaining ground in discussions academic, political and economic, with a view to qualifying the Brazilian education. The choice of theme is based on experiences of the teacher-researcher as training of teachers in a degree course in Mathematics and teacher of continuing education courses, when it was possible to realize that, in general, the formations do not provide sufficient subsidies for effective integration of digital technologies in the school context. This research aims to analyze how mathematics teachers of primary education, in continuing education process, can improve their teaching practice, taking into account the reality of the new digital culture and the knowledge of cognitive development process and reasoning of the student. It was held, at first, an analysis of the course "Technologies Applied to the Teaching of Mathematics", present in the political-pedagogical project of the Degree in Mathematics from a federal public university based on Genetic Epistemology of Piaget, with the intention thereafter to understand the influence of technology in pedagogical practices of teachers. In a second step, a group of professionals working in the field of Mathematics of the state public network Bage region participated in the survey, which consisted of interviews, observation in the classroom and use Khan Academy platform. The methodology of action research was implemented aiming at the participation of the researcher, with observation and action in order to achieve the proposed objectives to reach the theorizing about the results. It was observed from the results that the proposed course of continuing education favored the integration of digital technologies in the school context, promoting changes in teaching practice and encouraging people to learn mathematics content. The participating teachers, at the end of training course, proved to be more confident and better prepared to use available technological resources in schools, and they felt encouraged to expand its use. The use of Khan Academy platform enabled these changes and contributed to the debate on a new paradigm of teaching and learning, in which prior knowledge of the students, their difficulties and potential, are valued and considered as principles of pedagogical practice. / Con la inserción de las Tecnologías de Información y Comunicación (TICs) en el salón de clase, en especial la inclusión de los laptops y de la internet, la formación continuada de profesores se constituye como una de las principales acciones de las políticas públicas en educación, conquistando espacio en las discusiones académicas, políticas y económicas, con la mirada vuelta hacia la calificación de la educación brasileña. Se justifica la elección del tema a partir de experiencias de la profesora investigadora como formadora de profesores en un curso de licenciatura en Matemáticas y ministrante de cursos de formación continuada, en los que ha percibido que, en general, las formaciones no ofrecen subsidios suficientes para la efectiva integración de las tecnologías digitales en el contexto escolar. Esta investigación tiene como objetivo analizar como los profesores de Matemáticas de la educación básica, en proceso de formación continuada, pueden perfeccionar su práctica docente, llevando en cuenta la realidad de la nueva cultura digital y el conocimiento del proceso de desarrollo de la inteligencia y del raciocinio del estudiante. Se realizó, en un primer momento, un análisis de la asignatura “Tecnologías Aplicadas a la Enseñanza de Matemáticas”, presente en el Proyecto Político Pedagógico del Curso de Licenciatura en Matemáticas de una universidad pública federal, con base en la epistemología genética de Piaget, con la intención de, posteriormente, comprender la influencia de las tecnologías en la práctica pedagógica de los profesores. En un segundo momento, un grupo de profesionales del área de Matemáticas actuantes en la red pública estadual de la región de Bagé participó de la investigación, que consistió en entrevistas, observación en el salón de clase y utilización de la plataforma Khan Academy. La metodología de investigación acción ha sido implementada visando a la participación de la investigadora, con observación y acción, a fin de alcanzar los objetivos propuestos para llegar a la teorización sobre los resultados. Se observó, a partir de los resultados, que el curso de formación continuada propuesto ha favorecido la integración de las tecnologías digitales en el contexto escolar, promoviendo cambios en la práctica docente y favoreciendo el aprendizaje de contenidos de Matemáticas. Los profesores participantes, al final del curso de formación, se mostraron más confiantes y mejor preparados para utilizar los recursos tecnológicos disponibles en las escuelas, además de que se sientan entusiasmados a ampliar su utilización. El uso de la plataforma Khan Academy posibilitó esos cambios y colaboró para que surgiera un nuevo paradigma de enseñanza y de aprendizaje, en el que los conocimientos previos de los estudiantes, sus dificultades y potencialidades son valorados y considerados como principios de la práctica pedagógica.
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Geometrias Não Euclidianas : obstáculos epistemológicos na formação de licenciandos em matemáticaSantos Filho, Luiz Carlos dos January 2016 (has links)
Orientadora: Profa. Dra. Maria Beatriz Fagundes / Dissertação (mestrado) - Universidade Federal do ABC, Programa De Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2016. / O corpo de conhecimento das Geometrias Não Euclidianas redefiniu as fronteiras da matemática no campo da geometria e seu estabelecimento pode ser caracterizado como uma descontinuidade e ruptura no processo de desenvolvimento do conhecimento científico conformeevidenciada na epistemologia de Gaston Bachelard,para quem o conhecimento do real imediato,frequentemente,se constitui em um obstáculo epistemológicoao conhecimento científico. O conceito central no âmbito da pesquisa aqui proposta,de obstáculo epistemológico,é tratado principalmente em "A formação do espírito científico" (1937, primeira edição). Obra, na qual Bachelard descreve e analisa alguns obstáculos epistemológicosque surgiram no decorrer da história do pensamento científico,e que também setornouuma referência importante na área de ensino de ciências,conforme autoras como Barbosa e Bulcão (2011) e Lopes (1996),e em ensino de matemática (TRINDADE, 1996). Na pesquisapretende-se observar e analisar o papel de obstáculos epistemológicosquesurgem no contexto do ensino e da aprendizagem das Geometrias Não Euclidianas durante a formação inicial de licenciandos em matemática. Com tal objetivo, foirealizado um estudocomofoco na elaboração, realização e análise de um minicurso sobre Geometrias Não Euclidianas, para estudantes do último semestre do curso de licenciatura em matemática,em uma instituição de ensino superior da região da grande São Paulo. Os dados foramcoletados a partir de registros deaulas gravadasem vídeo e áudio e a análise dos dados foifeitacom base emtranscrições destas gravações, seguindo ospreceitos da Análise de Discurso conformea proposta de Orlandi (2015).Esta análise evidenciou o papel de obstáculos epistemológicos denominados:verbal; experiência primeira; substancialista e generalização abusiva, os quais ocorreram na formação dos licenciandos durante a construção de conceitos sobre Geometrias Não Euclidianas. / The body of knowledge of Non-Euclidean Geometry redefined the boundaries of mathematics on geometry field. Your arisecan be characterized as a discontinuity and rupture in scientific knowledge development process as evidenced in the epistemology of Gaston Bachelard, for whom the real immediate knowledge often constitutes an epistemological obstacle to scientific knowledge. The concept of epistemological obstacles, central within the research here proposed project, is mainly treated in "The formation of the scientific spirit" (1937, first edition). This work, in which Bachelard describes and analyzes some epistemological obstacles that have emerged during the history of scientific thought, has also become an important referencein the science education area as authors such as Barbosa and Bulcão (2011) and Lopes (1996) and also in mathematics education (Trinity, 1996). In research conducted in this master's work is intended to observe and analyze the role of epistemological obstacles that arise in the context of teaching and learning of Non-Euclidean Geometry during the initial training of undergraduates in mathematics. To achieve these goals, it conducted a study that focused on the development, implementation and analysis of a short course on Non-Euclidean Geometry, for students in their final semester of the degree in mathematics course in a higher education institution in the Greater São Paulo region. The datawere collected from records of videotaped lessons. The Data analysiswas made from transcripts of the recordings, according to the precepts of Discourse Analysis, following the proposal of Orlandi (2015). This analysis highlighted the role of some epistemological obstacles in training undergraduates during the constructionconcepts of Non-Euclidean Geometry.
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Perfil conceitual de equação e a sala de aula da educação básica : uma análise do conhecimento profissional docenteAlves, Karina Aguiar January 2017 (has links)
Orientador: Prof. Dr. Alessandro Jacques Ribeiro / Dissertação (mestrado) - Universidade Federal do ABC, Programa De Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2017. / Esta pesquisa discute aspectos da teoria dos perfis conceituais abordando o conceito de equação em aulas de matemática da educação básica. Para tanto, inicialmente realizou-se uma revisão sistemática da literatura, a qual contemplou três eixos estruturantes: Formação de Professores que Ensinam Matemática, Perfil Conceitual e Ensino de Álgebra. Considerando as lacunas encontradas na literatura e a necessidade de diferentes abordagens de ensino para o conceito de equação, traçou-se como objetivo de pesquisa identificar os conhecimentos dos professores da Educação Básica ao ensinarem equação fundamentados na abordagem dos perfis conceituais. A fim de abarcar esse objetivo, realizou-se uma investigação com professores participantes de um curso de extensão realizado na Universidade Federal do ABC, no ano de 2016. Foram planejados cinco encontros para apresentação, discussão e apropriação do modelo de Perfil Conceitual de Equação e, simultaneamente, foram elaborados e desenvolvidos dois planos de aulas para turmas do 9º ano do ensino fundamental e do 3º ano do ensino médio, cujo enfoque concentrava-se na exploração de abordagens diferenciadas do conceito de equação. Cabe ressaltar que tanto o desenvolvimento, a escolha e a avaliação dos planos de aula foram realizados com a colaboração dos professores participantes do curso de extensão. O desenvolvimento dos planos de aula escolhidos pelo grupo deu-se pela participação voluntária de dois professores e foram realizados em duas escolas públicas da região metropolitana de São Paulo. As aulas videogravadas foram analisadas sob dois enfoques: (i) levantar e mapear as dimensões do conhecimento docente que emergem dos professores ao ensinar equação na educação básica; (ii) compreender os diferentes significados do conceito de equação mobilizados pelos professores ao desenvolverem aulas fundamentadas na abordagem dos perfis conceituais. Os resultados dessa pesquisa nos informaram que a prática dialógica em aulas de matemática se traduz numa ferramenta desejável para uma abordagem de ensino baseada no Perfil Conceitual de Equação, assim como, que as dinâmicas de aula propostas pelos professores influenciam na mobilização das dimensões do conhecimento docente. A partir disso, acredita-se que esses resultados inauguram diferentes possibilidades de compreensão do modelo teórico do Perfil Conceitual de Equação e apresentam especificidades no que se refere às diferentes dimensões dos conhecimentos docentes. / This study discusses aspects of the conceptual profile theory and the concept of equations in elementary education mathematics classes. An initial review addresses three sets of literature: training of mathematics teachers, the conceptual profile theory, and algebra instruction. New approaches are required to address gaps found in literature. The present research identifies knowledge of elementary education teachers with respect to approaches to conceptual profiles of fundamental equations. Research was conducted with teachers of an extension course, Elementary Algebra, of the Federal University of ABC between September and December 2016. Five meetings involved the presentation, discussion and integration of the conceptual profile equation model. Subsequently, two lesson plans for the 9th grade level classes and 3rd grade level classes were developed to explore new approaches for the concept of equation. The development, selection and evaluation of lesson plans were conducted in co-collaboration with participating teachers of the extension course. Two volunteer teachers applied lesson plans in two public schools of the Sao Paulo metropolitan region. Video recordings of the classes were analyzed through two lenses: (i) the review and mapping of teacher knowledge dimensions based on teaching of equations in elementary education, and (ii) understanding the different meanings of the equation concept developed by teachers in classes involving conceptual profiles. The findings of this research inform the argument that dialogical practices in mathematics classes provide a desirable tool for approaching teaching based on the conceptual profile of equation. An additional associated finding was that dialogical practices influence the ways through which teachers mobilize knowledge concepts. These findings suggest that there are different ways of understanding the conceptual profile of equations theoretical model, including the relationship of this theory to the particular characteristics of the knowledge of teachers.
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