Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-08-25T20:33:11Z No. of bitstreams: 1 AlbertoAlencar.pdf: 2383717 bytes, checksum: 42a9fe0ddc23c12470c5b689922cfd5a (MD5) / Made available in DSpace on 2017-08-25T20:33:11Z (GMT). No. of bitstreams: 1 AlbertoAlencar.pdf: 2383717 bytes, checksum: 42a9fe0ddc23c12470c5b689922cfd5a (MD5) Previous issue date: 2017-03-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this work we tray to analyze functions in light of the semiotic Raymond Duval theory´s of. We show how content is presented to high school students. We also show the importance of adopting a different approach to this subject. A richer approach to symbols and signs for better learning. / Este trabalho versa sobre como a teoria dos registros de representações semióticas de Raymond Duval pode auxiliar no aprendizado de funções. Mostra como o conte´udo de funções é abordado nos livros didáticos e como tem sido transmitido para os alunos. Mostra também a importância de ser adotada uma nova abordagem para tal assunto, de modo que seu aproveitamento esteja à altura de sua importância.

A pesquisa investigou as potencialidades da Fotografia para o ensino de Geometria, em especial para o estudo do conceito de proporções, a partir de atividades desenvolvidas com um grupo de estudantes das turmas de 8° ano e 8ª série/9° ano, de uma escola do Campo, localizada no município de Herveiras (RS). Os objetivos foram identificar e reconhecer a realidade destes estudantes, que se caracterizam como estudantes de uma escola do Campo; elaborar e aplicar uma sequência de atividades que explorem as potencialidades da Fotografia como recurso didático para o ensino de Geometria e Proporção; e analisar as conexões que os estudantes de uma escola do Campo estabeleceram entre Fotografia e Matemática, a partir das atividades desenvolvidas. Pelo fato de a Educação do Campo ser pouco discutida por quem está distante do cenário da vida do Campo, tornou-se relevante um breve e panorâmico estudo sobre a Educação do Campo, de modo que fosse possível uma análise do contexto histórico e cultural da escola e da comunidade em que os participantes estão inseridos. A pesquisa enfatiza interfaces entre a Educação Matemática, a Educação do Campo e a Fotografia, de modo a possibilitar situações de ensino que estimulem a aprendizagem da Matemática escolar, até porque são poucos os estudos que tomam como objeto as interfaces entre a Fotografia e a Educação Matemática. As atividades desenvolvidas que subsidiaram as análises aconteceram ao longo do segundo semestre do ano de 2014, em 6 encontros, totalizando 22 horas de atividades práticas realizadas com 11 estudantes participantes. A documentação produzida é constituída de registros fotográficos produzidos pelos estudantes e pela professora-pesquisadora, além de registros escritos e filmagens. As análises dos dados são centradas em três categorias: a) o olhar dos estudantes fotógrafos para as paisagens. Essa categoria é elencada em quatro subcategorias, que são: a beleza e a harmonia do Campo, a destruição do Campo, sinais de Modernização no processo produtivo e da vida do Campo e as moradias dos estudantes - modos de viver; b) potencialidades da Fotografia para o ensino de Geometria e proporção. Nessa categoria são elencadas quatro subcategorias, sendo elas: técnica do olhar - perspectiva, visualização de formas geométricas nas fotografias: o bidimensional e o tridimensional, Razão e Proporção e Geometria das Transformações Isométricas. Por meio da análise das atividades, foi possível evidenciar que a sequência de atividades com Fotografias contribuiu, dentre outros aspectos, para a construção de um outro olhar sobre a Fotografia, seja na percepção da presença da Geometria, assim como no processo de elaboração conceitual de proporção e nas relações entre os diferentes registros do cotidiano. Como produto da pesquisa, foi elaborado um livro do tipo paradidático para subsidiar professores de Matemática no trabalho em sala de aula, a fim de ampliar e aprimorar o leque de conhecimentos no processo de aprendizagem destes conteúdos de forma mais dinâmica. / The research investigated the potential of Photography for teaching geometry, in special for the study the concept of proportions, from developed activities out with a group of students of classes the 8° year and 8ª grade/9º year, a school of countryside, localized in the municipality of de Herveiras (RS). The objectives were to identify and recognize the reality of these students, which is characterized as students of a school of countryside; develop and implement a sequence of activities what explore the potential of Photography as didactic resource for teaching of Geometry and Proportion; and analyze the connections that the students of a school of countryside established between Photography and Mathematics, from the developed activities. Because of the education of countryside to be little discussed by who it is distant the scenery of life in the countryside, has became relevant a short and panoramic study about the education of countryside, so that it was possible an analysis of the historical context and cultural of the school and the community whereupon the participants they are inserted. The research enfatizar interfaces between the Mathematics Education, the rural Education and the Photography, so enoble situations of teaching than stimulate the learning of school mathematics, because there are tehe studies that take as object the interfaces between the Photography and the mathematics education. The developed activities that subsidized the analyzes happened along of second semester of the year 2014, in, 6 meetings, totaling 22 hours of practical activities performed with 11 students participating. The documentation produced it is made of photographic records produced by students and by teacher-researcher, as well as written records and footage. The analysis of data they are centered in three categories: a) the look of students for landscapes. This category is elencada into four subcategories, that are: the beauty and harmony of the countryside, the destruction of the countryside, signs of Modernization in the productive process and the life of the field and the villas of students - ways of living; b) Photograph potential for teaching geometry and proportion. Potential the photography for learning of geometry and proportion. In that category are listed four subcategories, being them: technical look - perspective visualization of geometric shapes at the photographs: the two-dimensional and the three-dimensional, ratio and proportion and geometry of Isometric Transformations. Through analyzing the activities, was possible evidence that sequence of activities with photographs contributed, among other things, to construted another look on Photography, is the perception of the presence of Geometry, as well as the conceptual elaboration process of proportion and in relations between the different records of everyday. As the investigational product, It has crafted a book type paradidactic for subsidize teachers of Mathematics in the work in the Classroom, in order to enlarge and improve the range of knowledge in the process of learning process of these contents more dynamically.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-10-20T18:03:47Z No. of bitstreams: 1 2016 - C?ssius Marques.pdf: 3648508 bytes, checksum: 749f035bd888f4b4e273b950b79d79f0 (MD5) / Made available in DSpace on 2017-10-20T18:03:47Z (GMT). No. of bitstreams: 1 2016 - C?ssius Marques.pdf: 3648508 bytes, checksum: 749f035bd888f4b4e273b950b79d79f0 (MD5) Previous issue date: 2016-08-31 / CAPES / The teaching of mathematics changes slowly while the students' profile changes every generation. The I.T. labs set up in public schools, which are high cost investments, often get forgotten and become obsolete. Nowadays, with technology evolution and the appearance of smartphones and tablets, new educational apps are being developed for these tools. Many discussions have been held regarding the real applicability of such tools, if they can really help or simply distract the student, but it is a known fact that they are present all the time and that it is worthy to use them in order to improve the learning experience. Sketchometry is a dynamic geometry app with basic commands that could help students with geometry and mathematical functions. The moving of constructions, usually made by gestures and with the imagination of teachers, can now be done with the touch of fingers on the screens of mobile phones and tablets, making visualization easier. Teachers, however, still have difficulties implementing such tools in their classes. This essay attempted to evaluate the opinion of students of primary school, undergraduates, masters degree students and masters on the usage of smartphones/tablets in class. Activities with Sketchometry were shown, followed by an evaluation questionnaire for the research. The results obtained indicate that some of the reasons provided not to use the tools, are the number of students per classroom, the lack of structure in schools and the lack of skill of teachers. When it comes to licentiates, master's degree students and graduates from UFRRJ's PROFMAT, the majority of teachers and soon to be teachers believe in the usage of the tools, that the students are interested in using them and that there are indeed obstacles but they are not insuperable. / O ensino da Matem?tica muda lentamente, enquanto o perfil dos alunos muda a cada gera??o. Os laborat?rios de inform?tica montados nas escolas p?blicas, investimento de alto custo, muitas vezes ficam abandonados e se tornam obsoletos. Atualmente, com a evolu??o da inform?tica e o surgimento de celulares e tablets com tecnologia touchscreen, novos aplicativos educativos t?m sido desenvolvidos para essas ferramentas. Muito se tem discutido acerca da real aplicabilidade desses equipamentos, se podem realmente auxiliar na aprendizagem ou se apenas distraem o aluno, mas o certo ? que eles est?o presentes a todo momento e que vale a pena se valer disso para buscar melhorar o aprendizado. O Sketchometry ? um aplicativo de geometria din?mica, com comandos simples, que pode ajudar o estudante no estudo da geometria e de fun??es Matem?ticas. A movimenta??o das constru??es, antes feita com gestos e imagina??o por tantos professores, hoje pode ser realizada com o toque dos dedos nas telas de celulares e tablets, facilitando a visualiza??o. Os professores, no entanto, ainda t?m dificuldades em implementar esse tipo de ferramenta em suas aulas. Este estudo buscou avaliar a opini?o de estudantes do ensino fundamental, graduandos, mestrandos e mestres acerca da utiliza??o de celulares/tablets em sala de aula. Atividades com o Sketchometry foram realizadas e, em seguida, um question?rio de avalia??o para a pesquisa foi aplicado. Nos resultados obtidos, observou-se que entre os motivos citados para a n?o utiliza??o dessas ferramentas, est?o o n?mero de alunos por sala, a falta de estrutura nas escolas, o despreparo do pr?prio professor, entre outros. Com rela??o aos licenciandos, mestrandos e egressos do PROFMAT da UFRRJ, a maioria dos professores e futuros professores acredita na utiliza??o desse tipo de ferramenta, e que existe interesse dos alunos para que sejam utilizadas, que os obst?culos existem mas n?o s?o intranspon?veis.

Orientador: Raquel Gomes de Oliveira / Banca: Ana Maria Roque Dias Bovista / Banca: Leny Rodrigues Martins Teixeira / Resumo: Este estudo, vinculado à linha de pesquisa "Práticas e Processos Formativos em Educação" do Programa de Pós-Graduação em Educação da FCT/UNESP, relata os resultados de uma pesquisa que tem por objetivo analisar a compreensão que professores de Matemática têm da Resolução de Problemas como metodologia de ensino, como eles têm tomado conhecimento desta proposta metodológica e se há relação entre o entendimento sobre Resolução de Problemas e a prática pedagógica declarada pelo docente. A pesquisa, de abordagem qualitativa e natureza exploratória, utilizou como instrumentos de coleta de dados um questionário e análise documental. O questionário era composto por questões abertas e fechadas que formavam categorias de análise respectivamente à Formação Docente e a Resolução de Problemas, ao Entendimento do Professor de Matemática sobre Resolução de Problemas e à relação entre o entendimento docente sobre Resolução de Problemas e a prática pedagógica. Responderam ao questionário 31 professores com aulas atribuídas de Matemática no ano de 2017, no Ensino Fundamental II e/ou Ensino Médio, das 26 escolas no munícipio de Presidente Prudente, sendo um professor por escola, com algumas escolas tendo mais de um professor respondente. Para a análise dos dados utilizou-se a técnica de análise de conteúdo para as questões abertas do questionário e para a análise das questões fechadas foram consideradas as frequências de respostas. A análise documental foi realizada nos documentos prescritos qu... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This study, bound to the research line of "Practices and Formative Processes in Education" of the Post-Graduation Program in Education of FCT/UNESP, reports the results of a research which aims analyzing the comprehension that Mathematics teachers have about the Problem Solving as a teaching methodology, how they became aware of this methodological proposal and if there is a connection between their understanding about the Problem Solving and the pedagogical practice they state. The research, which was constituted of qualitative approach and exploratory nature, used as collecting tools a questionnaire and document analysis. The questionnaire was composed of open and closed questions which formed categories of analysis respectively to Teacher Education and Problem Solving, to the Understanding of Mathematics Teachers about Problem Solving and to the relation between the teaching understanding about Problem Solving and the pedagogical practice. 31 teachers with regular classes in 2017, in Elementary school and/or High School, from 26 schools in the city of Presidente Prudente answered to the questionnaire, being one teacher for school, and some schools accounting for more than one teacher. For data analysis, it was used the content analysis technique to the open questions in the questionnaire, and to analyze the closed questions it was taken into account the frequency of the answers. The document analysis was carried out in the prescribed documents that direct the teaching work... (Complete abstract click electronic access below) / Mestre

O presente trabalho tem como objetivo trazer uma proposta de aplicação de uma sequência didática para o ensino de frações no fundamental II, utilizando uma narrativa com elementos históricos para motivar os alunos a participarem da sequência. Apresentamos tambem algumas discussões sobre a pertinência do ensino das frações na atualidade, tendo como argumentos de partida alguns trabalhos apresentados por matemáticos, como Peter Hilton e Carlos Roberto Vianna. que discutiram existir a possibilidade da retirada das frações do currículo escolar. Utilizaremos uma abordagem histórica e conceitual das frações, através de duas dimesões temporais, a historiográfica e a dos tempos atuais, mostrando assim sua importância histórica. Baseamo-nos nos diferentes significados das frações: parte-todo, medida, quociente e operador multiplicativo. Por fim, oferecemos uma estratégia para que a aprendizagem de frações aconteça de forma conceitual e significativa. Tal estratégia foi elaborada através da análise teórica e da construção de uma sequência didática (SD), baseada nos princípios das situações didáticas de Guy Brousseau (Teoria da Situação Didática). A sequência foi utilizada em turmas do 6º ano do ensino básico. Buscamos, com isso, criar um ambiente de motivação para aprendizagem da matemática e, ao mesmo tempo, conceder significado aos conhecimentos relacionados às frações. / The present work aims to bring a proposal for the application of a didactic sequence for the teaching of fractions in the fundamental II segment, using a narrative with historical elements to motivate the students to participate in the sequence. We present some discussions about the pertinence of the teaching of fractions in the present time, starting with research presented by mathematicians such as Peter Hilton and Carlos Roberto Vianna, who discussed the possibility of the removal of fractions from the school curriculum. We will use a historical and conceptual approach of the fractions, through two temporal dimensions, the historiographic one and the one of the present times, thus showing its historical importance. We are based on the different meanings of fractions: part-whole, measure, quotient and multiplicative operator. Finally, we offer a strategy for the learning of fractions to happen in a conceptual and meaningful way, being so that such strategy was elaborated through the theoretical analysis and elaboration of a didactic sequence (SD) based on the principles of didactic situations offered by Guy Brousseau (Theory of Didactic Situation). The sequence was used in classes of the 6th grade of the elementary school.. We seek to create a motivational environment for learning mathematics, at the same time giving meaning to the knowledge related to fractions.

Thesis (M.Ed. (Mathematics Education)) -- UNiversity of Limpopo, 2013 / In this study, I presented the exploration of Mpho’s growth in mathematical understanding. Mpho is a grade 10 mathematics learner. To fulfil such, a qualitative research method was employed. I explored her growth in understandings in the context of co-ordinate geometry, exponents, and functions. Data generation, management and representation were guided by the notion of teaching experiments. Analysis was done through mapping learner’s growth of mathematical understanding using Pirie-Kieren’s (1994) model. Findings suggest that learner’s growth in mathematical understanding can be observed, mapped and improved with the aid of probing questions.

Thesis (M.A. (Mathematics Education)) --University of Limpopo, 2006 / Traditionally, mathematics has been perceived as objective, abstract, absolute and universal subject that is devoid of social and cultural influences. However, the new perspective has led to the perceptions that mathematics is a human endeavour, and therefore it is culture-bound and context-bound. Mathematics is viewed as a human activity and therefore fallible. This research was set out to explore geometrical concepts involved in the traditional circular buildings in Mopani district of Limpopo Province and relate them to the classroom learning in grade 11 classes. The study was conducted in a very remote place and a sample of two traditional circular houses from Xitsonga and Sepedi cultures was chosen for comparison purposes because of their cultural diversity. The questions that guided my exploration were: • Which geometrical concepts are involved in the design of the traditional circular buildings and mural decorations in Mopani district of the Limpopo Province?. How do the geometrical concepts in the traditional circular buildings relate to the learning of circle geometry in grade 11 class?. The data were gathered through my observations and the learners’ observations, my interviews with the builders and with the learners, and the grade 11 learners’ interaction with their parents or builders about the construction and decorations of the traditional circular houses. I used narrative configurations to analyse the collected data. Inductive analysis, discovery and interim analysis in the field were employed during data analysis. From my own analysis and interpretations, I found that there are many geometrical concepts such as circle, diameter, semi-circle, radius, centre of the circle etc. that are involved in the design of the traditional circular buildings. In the construction of these houses, these concepts are involved from the foundation of the building to the roof level. All these geometrical concepts can be used by both educators and learners to enhance the teaching and learning of circle geometry. Further evidence emerged that teaching with meaning and by relating abstract world to the real world makes mathematics more relevant and more useful.

Thesis (M.A. (Mathematics Education)) --University of Limpopo, 2013 / This study intended to improve Grade 9 learners’ mathematical processes of solving word problems. It was an action research study in my own classroom consisting of 64 Grade 9 learners. Learners were given learning activities on word problems to carry out as part of their normal classroom mathematics’ lessons. Data were collected in two stages: first, through passive observation, that is, without my intervention, and later through participant observation thus provoking their thinking as they attempt the given questions. The learners’ responses were analyzed through checking the mathematical processes they used without my intervention. Learners also submitted their post-intervention responses for analysis of progress after interventions. The scripts were reviewed based on four problem- solving stages adopted from George Polya (1945). Those stages are, namely understanding the problem, devising the plan, carrying out the plan and looking back. It became evident from the findings that learners attempt solving word problems with no understanding. Communication, reasoning and recording processes appear to be key factors in assisting learners to make sense of word problems and, finally, proceeding towards an adequate solution.

Från och med hösten 2018 blev programmering en obligatorisk del av matematikundervisningen.Som framtida lärare är det intressant att få inblick i hur implementeringen av programmering harlandat i skolan efter att det har funnits som centralt innehåll i matematikämnet. Syftet med studienvar att skapa förståelse för vilken kunskap inom programmering lärare har visat och undersöka hurderas kunskap inom programmering har påverkat deras implementering av verktyget. Datan somhar analyserats och kategoriserats i studien har plockats fram från sju semistrukturerade intervjuer.Verktyget som användes vid analys och kategorisering var Mathematical Knowledge for Teaching.Resultatet visade att lärarna med lägre grad av programmeringskunskap visade också på en lägregrad av implementering av programmering i matematikundervisning. Slutsatsen som kunde dras varatt ämneskunskap inom programmering var avgörande oavsett vilken kunskapskategori det gällde.Andra slutsatser som kunde dras var att lärarlaget hade påverkan gällande lärares implementeringav verktyget och att det krävdes kunskaper utöver ämneskunskap i programmering för attimplementera verktyget i högre utsträckning. / Since fall 2018, programming has been a mandatory part of mathematics classes in Sweden. As afuture teacher I have found it interesting to see how far the implementation process of programmingas part of mathematics has proceeded. The purpose of this essay/thesis is to provide a betterunderstanding of – to what extent the teachers knowledge within programming have affected theimplementation of programming within their mathematics classes as well as to highlight whatdevelopment of programming capabilities/skills can be observed a year after the implementation.The study conducted semi-structured interviews with seven teachers, the data provided was lateranalyzed and categorized using the Mathematical Knowledge for Teaching approach. The resultsshows that teachers with lesser knowledge of programming also showed a lower degree ofimplementation of programming in their math classes. Hence the conclusion can be drawn that –knowledge within the specific topic is one determining factor of to what extent a successfulimplementation can be expected. Further conclusions entail that the teachers team had significantinfluence over the teachers implementation of the tool and that genuine knowledge within the fieldwas required for a successful/satisfying implementation.

This thesis describes a one-year study of 120 fifth grade students whose teachers participated in a program entitled Project SMILE (Science and Mathematics Integrated with Literary Experiences). The purpose of the study was to investigate the extent to which the classroom implementation of Project SMILE positively influenced the classroom environment and student attitudes toward reading, writing and mathematics. This was accomplished by, first, facilitating a series of five professional development workshops with the teachers and, subsequently, asking these teachers to use the strategies with their students. Because Project CRISS (CReating Independence through Student-owned Strategies), the foundation of SMILE, had already proven to be successful nationwide for secondary students, this study focused on elementary (K-5) school students and their teachers. My evaluation of this unique program, that integrates children's literature and mathematics, focused on student attitudes and the nature of the classroom learning environment. My research represents one of the relatively few studies that have employed learning environment dimensions with students in the elementary school mathematics classroom as criteria of effectiveness in the evaluation of educational innovations. The My Class Inventory (MCI) and an adaptation of the 1988 NAEP (National Assessment of Educational Progress) Attitude Survey were administered to a sample of 120 Grade 5 students as measures of students' perceptions of the classroom learning environment and their attitudes. Qualitative data were composed of student and teacher interviews, classroom observations and work samples. Methodologically, my study supports previous research that successfully combined qualitative and quantitative methods of data collection. / The learning environment and attitude scales exhibited satisfactory internal consistency reliability and discriminant validity; additionally, the actual form of most learning environment scales was capable of differentiating between the perceptions of students in different classrooms. The implementation of SMILE was found to have a positive impact on the students and classes of the teachers who participated in the inservice program. In particular, students' attitudes to mathematics and reading improved, and there was congruence between students' actual and preferred classroom environment on the scales of satisfaction and difficulty. Therefore, others can implement SMILE with confidence. As well, prior research was replicated in that students' satisfaction was greater in classrooms with a more positive learning environment, especially in terms of student cohesiveness.