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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Sobre possibilidades de ensino e aprendizagem dos números irracionais no 8º ano do Ensino Fundamental / Learning and teaching possibilities towards irrational numbers in the 8th grade of Elementary School

Nobre, Ronaldo Bezerra 11 December 2017 (has links)
Esta dissertação apresenta um trabalho didático desenvolvido com turmas de 8º ano do Ensino Fundamental visando uma introdução significativa aos números irracionais, tanto quanto ao enfrentamento de dificuldades conceituais inerentes ao tema, como quanto ao envolvimento ativo dos estudantes no seu próprio aprendizado. Para elaborar, aplicar e analisar as atividades didáticas foram utilizados como embasamentos teóricos principais: a tese de doutorado de Olga Corbo (CORBO, O., 2012) sobre os conhecimentos necessários para a exploração de noções relativas aos números irracionais na Educação Básica e textos sobre investigações matemáticas de pesquisadores portugueses, sob a coordenação de João Pedro da Ponte (PONTE, J. P., et al., 1998 e ABRANTES, P. et al., 1999). As atividades foram planejadas visando abordagens dos conteúdos ricas em significados e acessíveis à faixa etária alvo. Estudantes de 8º ano realizaram pesquisas e apresentações em grupos sobre o número de ouro e atividades investigativas para explorar propriedades características dos números racionais e irracionais: representação decimal, associação à medida de segmentos de reta, localização na reta numerada, infinidade e densidade nesta reta. Em 2017, novas turmas desenvolveram atividades investigativas ampliando os objetivos para incluir a noção de comensurabilidade de segmentos de forma a viabilizar um debate participativo sobre a demonstração da incomensurabilidade entre o lado e a diagonal de um quadrado elaborada na Grécia antiga. Tudo isso contribuiu para que os estudantes concebessem, de maneira significativa para eles, a necessidade de uma infinidade de novos números para além dos racionais. / This dissertation presents a didactical work developed with 8th grade classes of Elementary School aiming a significant introduction to the irrational numbers in the sense that it confronts the conceptual difficulties related to the theme, as well the observation of the stimulating involvement of students in their learning process. In order to elaborate, apply and analyze the didactical activities, we considered as the main theoretical basis the doctoral thesis of Olga Corbo (CORBO,O., 2012) about the fundamental knowledge necessary for the exploration of irrational numbers in Basic Education and texts on mathematical investigations written by portuguese researchers and coordinated by João Pedro da Ponte (PONTE, JP, et al., 1998 and ABRANTES, P. et al., 1999). The activities were planned aiming to make the content approaches meaningful and accessible to the target age group. Eighth-grade students conducted researches and group presentations on the golden number and investigative activities to assess specific characteristics of rational and irrational numbers as: decimal representation, association to the measurement of straight segments, location in the numbered line, infinity, and density in this line. In 2017, new groups developed researches broadening the objectives to include the notion of commensurability of segments, in order to enable a debate in classroom about the demonstration of the incommensurability between the side and the diagonal of a square elaborated in ancient Greece. All of these steps contributed to the students understanding of the need for a multitude of new numbers besides rational ones.
2

Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness

Bailey, Judith (Judy) Lyn January 2004 (has links)
Over a period of twenty months a mathematics teacher educator uses narrative inquiry, a form of story-telling, to investigate her professional practice in working alongside pre-service primary teachers. Two main themes emerge in this research. The first of these centres around the use of mathematical investigations as a vehicle for supporting pre-service primary teachers to consider what the learning and teaching of mathematics may entail. As part of this process the author personally undertook several mathematical investigations. This resulted in significant learning about previously unrecognised personal beliefs about the nature and learning of mathematics. These beliefs were discovered to include ideas that 'real' mathematicians solve problems quickly, do so on their own and do not get stuck. Surprisingly, all of these subconscious assumptions were contrary to what the author espoused in the classroom. A consequence of this learning included some changed beliefs and teaching practices. One such change has been moving from a conception of mathematics as a separate body of 'correct' mathematical ideas, and where the emphasis when doing mathematics was on attaining the correct answer, to now viewing mathematics as a sense-making activity involving discovering, doing and communicating in situations involving numbers, patterns, shape and space. Thus, mathematics is now perceived to primarily be found in the 'doing' rather than existing as a predetermined body of knowledge. As such one's interpretations of a mathematical problem are important to consider. Changes in teaching include using mathematical investigations as a teaching approach with the belief that students can effectively learn mathematical ideas using this approach; an acceptance that this may involve periods of being 'stuck' and that this does not mean that the teacher needs to immediately support the students in becoming 'unstuck'; more in-depth interactions, including questioning, to support this mathematical learning; and an acceptance that mathematics can be learned by people working in a collaborative manner. The second theme encountered in this narrative inquiry involves the exploration of narrative as a powerful means with which to pursue professional development. Narrative inquiry, including a mention of differing forms of narrative writing, is described. Issues also considered include the place of reflection in narrative; the notion of multiple perspectives that are encountered in qualitative research such as this; issues of validity and authenticity; a consideration of what the products of narrative research might be and who may benefit from such research; a brief mention of collaboration; and the place of emotion in qualitative research. The concept of change occurring within a narrative inquiry is not seen to imply an initial deficit position. Rather the research process is regarded as the building of a narrative layer that supports and grows alongside the writer's life as it occurs (Brown Jones, 2001). Thus there is not a seeking of perfection or an ideal, but a greater awareness of one's professional practice. The results of narrative research therefore, are not definitive statements or generalisations about an aspect of that which is being researched (e.g., Winkler, 2003). As such, a definitive statement about how to be a teacher of pre-service students learning mathematics is not offered. Rather, a story is shared that may connect with the stories of the reader.
3

Investiga??o hist?rica na forma??o de professores de matem?tica: um estudo centrado no conceito de fun??o

Rocha, S?nia Maria Cavalcanti da 26 February 2008 (has links)
Made available in DSpace on 2014-12-17T15:04:50Z (GMT). No. of bitstreams: 1 SoniaMCR.pdf: 790974 bytes, checksum: 4b61f8a978ca87798933256ab674ed1d (MD5) Previous issue date: 2008-02-26 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought / Neste estudo analisamos o desenvolvimento de uma experi?ncia de ensino, envolvendo alunos da licenciatura em matem?tica da UFRN, que tomou como base a hist?ria da matem?tica e as investiga??es matem?ticas com vistas a contribuir para a melhoria do ensino-aprendizagem da matem?tica. Foram planejadas e aplicadas tarefas de investiga??o hist?rica em sala de aula enfocando o pensamento funcional. Descrevemos e avaliamos os resultados obtidos durante a experi?ncia, ? luz de autores que sustentam o pressuposto da investiga??o e da hist?ria como alternativa para a aprendizagem da matem?tica. Destacamos que o material de an?lise constituiu-se de di?rio de campo, grava??es em ?udio, question?rios com depoimento dos alunos envolvidos, bem como da avalia??o do professor da disciplina. Em rela??o ao conte?do matem?tico, o estudo se limitou ao conceito de fun??o, formas de representa??o e nota??o. Ficou evidenciado que os alunos avan?aram bastante no que se refere ? formaliza??o necess?ria dos conte?dos matem?ticos focalizados, como tamb?m, ao envolvimento ativo dos alunos nas diferentes etapas do estudo. Podemos afirmar que o estudo desenvolvido certamente representa contribui??es para uma abordagem significativa no ensino-aprendizagem do pensamento funcional
4

Sobre possibilidades de ensino e aprendizagem dos números irracionais no 8º ano do Ensino Fundamental / Learning and teaching possibilities towards irrational numbers in the 8th grade of Elementary School

Ronaldo Bezerra Nobre 11 December 2017 (has links)
Esta dissertação apresenta um trabalho didático desenvolvido com turmas de 8º ano do Ensino Fundamental visando uma introdução significativa aos números irracionais, tanto quanto ao enfrentamento de dificuldades conceituais inerentes ao tema, como quanto ao envolvimento ativo dos estudantes no seu próprio aprendizado. Para elaborar, aplicar e analisar as atividades didáticas foram utilizados como embasamentos teóricos principais: a tese de doutorado de Olga Corbo (CORBO, O., 2012) sobre os conhecimentos necessários para a exploração de noções relativas aos números irracionais na Educação Básica e textos sobre investigações matemáticas de pesquisadores portugueses, sob a coordenação de João Pedro da Ponte (PONTE, J. P., et al., 1998 e ABRANTES, P. et al., 1999). As atividades foram planejadas visando abordagens dos conteúdos ricas em significados e acessíveis à faixa etária alvo. Estudantes de 8º ano realizaram pesquisas e apresentações em grupos sobre o número de ouro e atividades investigativas para explorar propriedades características dos números racionais e irracionais: representação decimal, associação à medida de segmentos de reta, localização na reta numerada, infinidade e densidade nesta reta. Em 2017, novas turmas desenvolveram atividades investigativas ampliando os objetivos para incluir a noção de comensurabilidade de segmentos de forma a viabilizar um debate participativo sobre a demonstração da incomensurabilidade entre o lado e a diagonal de um quadrado elaborada na Grécia antiga. Tudo isso contribuiu para que os estudantes concebessem, de maneira significativa para eles, a necessidade de uma infinidade de novos números para além dos racionais. / This dissertation presents a didactical work developed with 8th grade classes of Elementary School aiming a significant introduction to the irrational numbers in the sense that it confronts the conceptual difficulties related to the theme, as well the observation of the stimulating involvement of students in their learning process. In order to elaborate, apply and analyze the didactical activities, we considered as the main theoretical basis the doctoral thesis of Olga Corbo (CORBO,O., 2012) about the fundamental knowledge necessary for the exploration of irrational numbers in Basic Education and texts on mathematical investigations written by portuguese researchers and coordinated by João Pedro da Ponte (PONTE, JP, et al., 1998 and ABRANTES, P. et al., 1999). The activities were planned aiming to make the content approaches meaningful and accessible to the target age group. Eighth-grade students conducted researches and group presentations on the golden number and investigative activities to assess specific characteristics of rational and irrational numbers as: decimal representation, association to the measurement of straight segments, location in the numbered line, infinity, and density in this line. In 2017, new groups developed researches broadening the objectives to include the notion of commensurability of segments, in order to enable a debate in classroom about the demonstration of the incommensurability between the side and the diagonal of a square elaborated in ancient Greece. All of these steps contributed to the students understanding of the need for a multitude of new numbers besides rational ones.
5

EDUCAÃÃO MATEMÃTICA: Favorecendo investigaÃÃes matemÃticas atravÃs do computador. / MATHEMATICAL EDUCATION: Favoring mathematical inquiries through the computer

Josà RogÃrio Santana 12 April 2006 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Os recursos computacionais representam novas perspectivas e problemas na Ãrea educacional com respeito ao ensino de matemÃtica. Um dos questionamentos presentes, consiste em compreender como ferramentas computacionais podem favorecer o trabalho docente e a aprendizagem discente. Neste aspecto, um fenÃmeno comum consiste na abordagem que favorece a passagem do Velho PC (Papel Caneta) ao Novo PC (Personal Computer), entretanto, este tipo de postura recaiu sobre a perspectiva do tipo âimplementou no computador, funcionou, acabouâ. Neste sentido atividades para formaÃÃo matemÃtica escolar em ambientes informatizados se tornam pouco reflexivas e acabam por valorizar manipulaÃÃes e simulaÃÃes em detrimento do mÃtodo matemÃtico atravÃs de provas e refutaÃÃes. Tomando estes problemas como base, neste trabalho, investigo a passagem do Novo PC ao Velho PC como possibilidade metodolÃgica em termos educacionais para dimensionar o uso do computador no ensino de matemÃtica favorecendo o processo investigativo. A pesquisa consistiu em compreender aÃÃes inesperadas em software educativo de matemÃtica nomeado por situaÃÃes surpresa. A partir destas, decorrentes de restriÃÃes computacionais, a idÃia consiste em viabilizar conjecturas que exigiam a argumentaÃÃo matemÃtica ou o processo de validaÃÃo por demonstraÃÃo. Para compreender a dinÃmica deste trabalho se investigou e caracterizou: i) As situaÃÃes surpresa; ii) Os procedimentos heurÃsticos e dedutivos na validaÃÃo matemÃtica na passagem do Novo PC ao Velho PC em termos docentes/discentes; iii) Que contribuiÃÃes a passagem do Novo PC ao Velho PC poderia oferecer ao desenvolvimento e uso de software educativo de matemÃtica. A pesquisa fez uso da engenharia didÃtica enquanto para favorecer a preparaÃÃo docente no contexto das situaÃÃes didÃticas, e para a postura do professor-investigador se fez uso da SeqÃÃncia Fedathi. A pesquisa de campo no ambiente escolar ocorreu em 3 etapas que consistiram na formaÃÃo de professores no ColÃgio Militar de Fortaleza, formaÃÃo de alunos de 6a sÃrie da EMEF Monteiro de Moraes em Fortaleza, e etapa final com estudantes de 8a sÃrie do CMF. Foram realizadas 40 horas/aula nestas 3 etapas. E pela transcriÃÃo de filmagens, questionÃrios entre outros dados, foi possÃvel compreender aspectos da passagem do Novo PC ao Velho PC como metodologia educacional que favorece investigaÃÃes matemÃticas atravÃs do computador. Foram consideradas situaÃÃes de experimentaÃÃo e desenvolvimento em software educativo de matemÃtica. ApÃs transcriÃÃo dos dados se obteve 18 situaÃÃes surpresa, houve dados decorrentes de experimentaÃÃo na manipulaÃÃo de software educativo de matemÃtica, e relato sobre experiÃncia no desenvolvimento do software GeoMeios. Os resultados mostraram que as situaÃÃes surpresa podem decorrer de limitaÃÃes computacionais, mas tambÃm resulta da aÃÃo-instrumental realizada na interaÃÃo homem-computador-saber. TambÃm foi possÃvel realizar a passagem do Novo PC ao Velho PC de forma reflexiva e crÃtica junto aos docentes e discentes, e por fim, foi se compreendeu que as aÃÃes instrumentais e as limitaÃÃes computacionais relativas a divergÃncias conceituais saber matemÃtico por parte dos desenvolvedores sÃo fatores que exigem maior consideraÃÃo na perspectiva da engenharia de software em termos educacionais. / The computerized resourses represents new perspectives and problems in the educational area with regard to the mathematics teaching. One of the present questions, consist in understanding as computer tools can favor the educational work and the learning studant. In this aspect, a common phenomenon consist in approach that favors the passage of the Old PC (PenCil) to the New PC (Personal Computer), however, this posture type relapses on the perspective of the type "it implemented in the computer, it worked, it ended". In this sense activities for school mathematical formation in computerized atmospheres turn not very reflexive and they end for valuing manipulations and simulations in detriment of the mathematical method through proofs and refutations. Taking these problems as base, in this work, I investigate the passage of the New PC to the Old PC as methodological possibility in educational terms for dimensioning the use of the computer in the mathematics teaching favoring the investigate process. The research consiste of understanding unexpected actions in educational software of mathematics, named by situation surprise. Starting from these, current of computacional restrictions, the idea consist of making possible structures you conjecture that demanded the mathematical argument or the validation process for demonstration. To understand the dinamical of this work it was investigated and it caracterized: i) situation surprise; ii) The procedures heuristics and deductive in the mathematical validation in the passage of the New PC to the Old PC in terms of teacher/studant; iii) That contributions the passage of the New PC to the Old PC could offer to the development and use of educational software of mathematics. The research made use of the didatic engineering while to favor the educational preparation in the context of the didatic situations, and for the posture of the researcher-teacher that used of the FedathiÂs Sequence. The field research in the school atmosphere happened in 3 stages that consisted of the teachers formation in the Military School of Fortaleza (CMF), formation how studants of 6a series of "EMEF Monteiro de Moraes", and final stage with studants of 8a series of CMF. The formations haved 40 hours/class was acomplished in these 3 stages. And for the transcription of video and questionnaries among other datas, it was possible to understand aspects of the passage of the New PC to the Old PC how an educational metodology that favors mathematical investigations through the computer. Experimentation situations and development were considered in educational software of mathematics. After transcription of the data was obtained 18 situations surprise, had given current of experimentation in the manipulation of educational in software of mathematics, and I tell about experience in the development of software GeoMeios. The results slowed that the situations suprise can elapse if computers limitations, but they also result of the action-instrumental accomplish the passage of the New PC to the Old PC in a reflexive and critical way the the educational ones and studants, and finaly, it was it was understood that the instrumental actions and the limatations relative of the computers to conceptual divergences to know mathmatical on the part of the developments they are actors that demand larger consideration in the perspective of the software engineening in educational terms.

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