This doctoral research was concerned with the role of language and its implications for the learning, teaching and assessment of mathematics for children aged 4-9 years. Earlier research by the author had established language and assessment as bridges enabling learning although they had the potential to increase the divide between teacher and learner. Reflection raised the question on how children achieved in mathematics despite potential difficulties with language and assessment. Review of the literature concluded that resources and sociocultural norms were also bridges between learner and teacher. A model was established of the relationships and processes between all perceived variables that provided an external, theoretical structure to be evaluated against structuralist, pragmatic and integrational linguistic approaches and empirical outcomes. The overarching approaches adopted were institutional ethnography and case study. An appropriate methodology was devised whereby sophisticated ICT equipment captured all visual and speech events during classroom interactions. Frequency analysis at word level, content analysis at utterance level and discourse analysis at total speech level triangulated with content analysis of interviews and evaluation of documentation completed the empirical research. Data analysis revealed five registers of children’s talk. Evidence suggested that the peer-peer ‘conditioned talk’ used in focused group work was the most effective for learning as it enabled them to discern the small steps in the inferential leaps in discourse made by their teachers, work out problems together, inform their peers, share findings and reinforce each others’ learning. Learners’ language showed aspects of structural, pragmatic and integrational linguistics, confirming a conclusion of the literature review that the various linguistic approaches discussed should be used to support and not exclude each other. The contribution made to knowledge is the ethnomethodology provided by the model, ICT resource and the five registers of talk revealed by the linguistic approach to discourse analysis. Teachers would be able to understand nuances of language used by their pupils and acquire essential skills and tools to put into effect the personalised learning agenda. Peer-peer observation of teachers would be an appropriate platform for the observation of the different registers used by learners, the resources that generate those registers, and their most effective use to close the gap between natural language and the subject specific language of mathematics.

Visi mokiniai, nepriklausomai nuo jų gabumų, polinkių ar mokymosi ypatumų turėtų pajusti matematikos praktinę naudą. Pagrindinėje mokykloje kiekvienas mokinys turi patirti sėkmę mokydamasis matematikos, o matematikos ugdymo turinys, jo perteikimo būdai ir tam naudojami metodai turi padėti mokiniui susiformuoti į mokymosi sėkmę. Atlikus tyrimą apie moksleivių ir mokytojų požiūrį į esamų mokomųjų kompiuterinių priemonių panaudojimą mokantis skaičiuoti įvairų trikampių plotus 7-oje klasėje, buvo kuriama interaktyvi mokymo priemonė „Trikampių plotai“. Šiame darbe pristatoma mokymo priemonė „Trikampių plotai“, kuri padeda mokyti(s) įvairių gebėjimų mokiniams matematikos pagrindų. Mokomoji priemonė sukurta Imagine Logo pagalba (Logo programavimo kalba). Mokomosios kompiuterinės programos „Trikampių plotai“ interaktyvi ir teorinė, ir praktinė dalis. Produktas buvo pristatytas Ukmergės Dukstynos pagrindinės mokyklos 7-os klasės moksleiviams ir matematikos mokytojams. Pagal atliktą matematikos mokytojų ir mokinių apklausą (tyrimą), mokomoji kompiuterinė priemonė yra patraukli, lengvai valdoma, suprantama, padedanti interaktyviai mokyti(s) skaičiuoti trikampio plotą įvairių gebėjimų mokinimas. / All pupils independent of their learning skills, abilities and peculiarity have to notice the practical advantage of mathematics. In Basic school every pupil has to delight in learning mathematics. The training content, its means of impart and used methods have to help pupil to form its attitude to learn successfully. The development of interactive learning tool “The Area of Triangles” was based on the results of the of research the attitude of pupils and teachers towards the use of exiting educational teaching computer courses in learning how to calculate the area of triangles in the 7th classes. In this work you can find the attractive visual, simple in use teaching aid “The Area of Triangles” which helps to teach/ learn the essentials of mathematics for pupils with different abilities. Teaching aid was created with the help of Image Logo (Logo computerese). Teaching computer aid “The Area of Triangles” include interactive theoretical and practical parts. The course was introduced to the pupils of 7th classes and teachers of mathematics. According to the results of the research the teaching aid is attractive and easy to use, comprehensible and instrumental to teach/learn interactively to calculate the area of triangles for pupils with different abilities.

Early in 2009 it became apparent from articles in the newspapers that first year mathematics students were not performing as well as the students of previous years. There was great concern regarding the insufficient transition from secondary to tertiary mathematics, as well as the preparedness of first year students for university studies. This research focuses on the different factors that are potential causes of the underachievement of first year mathematics students. Students‟ and lecturers‟ beliefs are shaped by their experiences, the impact of continuous perceptions from the world around them, the present dominant paradigm, as well as the beliefs of their teachers. The different views of the nature of school mathematics show how a worldview has an effect on these views and the implications of this on the teaching of mathematics in secondary, as well as tertiary institutions. The paradigm shift from the modern era to the post-modern era caused an awareness of and interest in the construction of meaningful mathematical understanding. The gap between first year students‟ and lecturers‟ beliefs regarding the nature of mathematics and how mathematics is learned became apparent. The changes in the thoughts about the structure of mathematics were investigated and a better understanding of the processes through which mathematical understanding develops emerged. This brought insight into the gap between the reasoning abilities of incoming students from secondary schools and the reasoning needed to succeed in university mathematics. The theoretical study of the global theories of Piaget and Van Hiele gave insight into conceptual development through different stages and that a person should be on an appropriate conceptual level to make sense of what they learn. If not, then rote learning is likely to occur. The local theory of Tall implies that to facilitate understanding of a concept in mathematics, one should go through three worlds of mathematics: the embodied world, symbolic world and the formal world. The embodied view helps someone to give deep meaning to a concept, otherwise one can be trapped in the symbolic world and not be able to move on to the formal world of mathematical thinking. The theoretical investigations led to an empirical study in three phases. Phase 1 was an investigation into the views of mathematics held by the students and the lecturers. In phase 2 an investigation was done to establish the students‟ preferences on how they learn mathematics and how mathematics should be taught, using the Index of Learning Styles (ILS) questionnaire of Felder and Silverman. The results were compared with the way lecturers want their students to learn and how they themselves prefer to teach. Phase 3 included a classification of the questions in the first mathematics test written at tertiary level and subsequent analysis of the answers of students to obtain information on the type of reasoning required from students at tertiary level, as well as the reasoning abilities of the students. The empirical study assisted in understanding the problematic transition from secondary to tertiary mathematics with regard to the nature of mathematics, the beliefs on teaching and learning of mathematics, as well as the reasoning skills that the students possess when entering university. / Thesis (Ph.D. (Natural Sciences Education))--North-West University, Potchefstroom Campus, 2013

Early in 2009 it became apparent from articles in the newspapers that first year mathematics students were not performing as well as the students of previous years. There was great concern regarding the insufficient transition from secondary to tertiary mathematics, as well as the preparedness of first year students for university studies. This research focuses on the different factors that are potential causes of the underachievement of first year mathematics students. Students‟ and lecturers‟ beliefs are shaped by their experiences, the impact of continuous perceptions from the world around them, the present dominant paradigm, as well as the beliefs of their teachers. The different views of the nature of school mathematics show how a worldview has an effect on these views and the implications of this on the teaching of mathematics in secondary, as well as tertiary institutions. The paradigm shift from the modern era to the post-modern era caused an awareness of and interest in the construction of meaningful mathematical understanding. The gap between first year students‟ and lecturers‟ beliefs regarding the nature of mathematics and how mathematics is learned became apparent. The changes in the thoughts about the structure of mathematics were investigated and a better understanding of the processes through which mathematical understanding develops emerged. This brought insight into the gap between the reasoning abilities of incoming students from secondary schools and the reasoning needed to succeed in university mathematics. The theoretical study of the global theories of Piaget and Van Hiele gave insight into conceptual development through different stages and that a person should be on an appropriate conceptual level to make sense of what they learn. If not, then rote learning is likely to occur. The local theory of Tall implies that to facilitate understanding of a concept in mathematics, one should go through three worlds of mathematics: the embodied world, symbolic world and the formal world. The embodied view helps someone to give deep meaning to a concept, otherwise one can be trapped in the symbolic world and not be able to move on to the formal world of mathematical thinking. The theoretical investigations led to an empirical study in three phases. Phase 1 was an investigation into the views of mathematics held by the students and the lecturers. In phase 2 an investigation was done to establish the students‟ preferences on how they learn mathematics and how mathematics should be taught, using the Index of Learning Styles (ILS) questionnaire of Felder and Silverman. The results were compared with the way lecturers want their students to learn and how they themselves prefer to teach. Phase 3 included a classification of the questions in the first mathematics test written at tertiary level and subsequent analysis of the answers of students to obtain information on the type of reasoning required from students at tertiary level, as well as the reasoning abilities of the students. The empirical study assisted in understanding the problematic transition from secondary to tertiary mathematics with regard to the nature of mathematics, the beliefs on teaching and learning of mathematics, as well as the reasoning skills that the students possess when entering university. / Thesis (Ph.D. (Natural Sciences Education))--North-West University, Potchefstroom Campus, 2013

The purpose of the study was to investigate second language learner‟s proficiency in mathematical language. The study was conducted using the Grade 12 learners in a senior secondary school in the district of Mthatha, Eastern Cape. The researcher used a case study approach and a questionnaire was used to investigate whether or not learners understood the language rather than to assess their mathematical ability. English was the language in question and used as the medium of instruction (MOI). In this study, aspects of the language used for mathematics are highlighted, the importance of mathematical vocabulary is discussed and reference is made to some recent research concerned with the understanding of mathematical language. The importance of language as a factor in the learning of mathematics is established through a consideration of bilingualism and the writer‟s own research into the understanding of mathematical language. Perhaps the most obvious educational difficulty which students encounter is that of language. Teachers and curriculum planners need to assess whether this is desirable, and to attempt to find ways in which learners in bilingual education programmes can learn mathematics in a meaningful way. Theories on the interaction between language and mathematical thinking, as well as the studies conducted with bilingual students can inform one‟s thinking about this issue. These ideas have important implications for teaching, texts and curriculum development. The study examined some of the above aspects in the context of South African Education.

Instituto de Apoio ao Desenvolvimento da Universidade Estadual Vale do Acaraà - UVA / O presente estudo à uma investigaÃÃo sobre os saberes e prÃticas das professoras do 5 ano em Sobral â CearÃ, em relaÃÃo à matemÃtica. Teve como objetivo verificar como estes saberes e prÃticas se transformam em aprendizagem das crianÃas, tendo como referÃncia os dados do Saeb/Prova Brasil, expressos nos dados do IDEB no perÃodo de 2005 a 2009. Està fundamentado nas obras de Perrenoud, Gauthier, Tardif, Lessard e Jacques Therrien. Trata-se de uma pesquisa qualitativa, sendo um estudo de caso mÃltiplo, realizado com duas professores do municÃpio de Sobral, que trabalharam em turmas do 5 ano, o maior tempo possÃvel no perÃodo de 2005 a 2009 e cujas escolas apresentaram evoluÃÃo significativa nos resultados de matemÃtica do Saeb/Prova Brasil, expressos nos dados do IDEB neste perÃodo. Os dados foram coletados atravÃs de anÃlise documental, entrevista semi estruturada e observaÃÃo de sala de aula, utilizando-se o Roteiro de observaÃÃo e o Quadro de observaÃÃo diÃria de sala de aula. A partir da anÃlise e comparaÃÃo dos dados coletados chegou-se a alguns resultados. Estes resultados demonstram que de fato os saberes e as prÃticas das professoras pesquisadas, referenciados por uma formaÃÃo permanente qualificada e focada na aprendizagem dos estudantes, com clareza dos objetivos educacionais e com metas estabelecidas e condiÃÃes adequadas, pode sim ser fator determinante na aquisiÃÃo da aprendizagem matemÃtica que se expressa nos dados do IDEB, mas que à necessÃrio um olhar mais qualificado para alguns elementos presentes neste processo, como a reduÃÃo de atividades com outros conteÃdos curriculares, tempo necessÃrio para que escolas e professoras se apropriem efetivamente dos resultados das avaliaÃÃes e de suas anÃlises e de uma formaÃÃo permanente que possibilite Ãs professoras, um aprofundamento das questÃes teÃricas presentes no processo de educaÃÃo-aprendizagem das crianÃas. O entendimento que fica ao final desta pesquisa à que a rede municipal de Sobral, as escolas e as professoras pesquisadas, indicam um caminho para ser observado, estudado, resignificado e porque nÃo seguido, com as devidas correÃÃes, adaptaÃÃes e melhoramentos, para que efetivamente os Ãndices expressos no IDEB, representem melhores estudantes, com melhores possibilidades do exercÃcio pleno da cidadania, a qual sem uma educaÃÃo de qualidade, à mero discurso, sem sentido social efetivo e mudanÃas efetivas na sociedade.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-16T10:34:37Z No. of bitstreams: 1 robsonluisthome.pdf: 1427745 bytes, checksum: e479bcae7fa50b924eba378700b20706 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T14:14:00Z (GMT) No. of bitstreams: 1 robsonluisthome.pdf: 1427745 bytes, checksum: e479bcae7fa50b924eba378700b20706 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T14:14:12Z (GMT) No. of bitstreams: 1 robsonluisthome.pdf: 1427745 bytes, checksum: e479bcae7fa50b924eba378700b20706 (MD5) / Made available in DSpace on 2017-02-07T14:14:12Z (GMT). No. of bitstreams: 1 robsonluisthome.pdf: 1427745 bytes, checksum: e479bcae7fa50b924eba378700b20706 (MD5) Previous issue date: 2016-11-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho tem o objetivo de divulgar e incentivar o incremento de ferramentas auxiliadoras no aprendizado da matemática associadas às inovadoras tecnologias educacionais. A motivação para a escolha desse tema está baseada nos bons resultados obtidos e na oferta de sistemas e ferramentas eficazes que propõem o fortalecimento e a motivação do aprendizado. Inicialmente abordamos o sistema educacional do ponto de vista histórico, tanto no mundo quanto no Brasil, sob uma perspectiva evolutiva, ligadas aos interesses e fatos que transformaram a Educação. Nesse contexto, identificamos sobre tudo os interesses políticos, religiosos e econômicos como fatores preponderantes no rumo do sistema educacional. A evolução tecnológica e suas consequências na área educacional são apresentadas e abordadas como elo da sintonia entre a tecnologia e a educação, identificada principalmente pela disseminação dos sistemas computacionais e por propostas pedagógicas diferenciadas e atuantes. Finalizando, apresentamos a robótica e algumas das principais e mais conceituadas plataformas educacionais on-line existentes e disponíveis no Brasil. Detalhamos o conceito das plataformas, mostrando suas operacionalidades, segmentos de atuação e avanços no desenvolvimento do aprendizado. Nesse trabalho, identificamos o potencial e o alcance que as plataformas oferecem e o quanto a associação “tecnologia e educação” estão presentes e insolúveis no processo da educação contemporânea, consolidando-se assim uma ferramenta valiosa identificada pela dinamização e eficiência. / The objective of this work is to promote and increase the use of helper tools in learning mathematics associated this tools to innovative educational technologies. The motivation for choosing this theme is based on the good results achieved and the provision of effective systems and tools that proposes strengthening and learning motivation. At first we approached the educational system from the historical point of view both in the world and in Brazil under an evolutionary perspective connected to the interests and facts that transform education. In this context, we have identified political, religious and economic interests as major factors in the direction of the educational system. Technological developments and their consequences in education are presented and discussed as a link in the line between technology and education, mainly identified by different and active pedagogical proposals and the dissemination of computer systems. To complete we present the robotics and some of the main and most prestigious educational online platforms existing in Brazil. We detail the concept of platforms, showing their operability, business segments and advances in the development of learning. This work identified the potential that platforms can offer and how the association – technology and education – are present and insoluble in the contemporary education process, thereby consolidating a valuable tool identified by the dynamism and efficiency of itself.

No description available.

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.

Made available in DSpace on 2016-04-28T20:56:44Z (GMT). No. of bitstreams: 1 Daniele de Lima Kramm.pdf: 6003171 bytes, checksum: ea246714b04ad3a53bc0c7f9b2b2ea62 (MD5) Previous issue date: 2014-04-16 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / In education, there has been concern in developing problem-solving behavior as one of the responsibilities of the school, whose task includes that of providing students with procedures to enable them to meet the challenges of contemporary life. The present study had problem solving as its central theme and aimed at identifying and understanding possible relationships between performance on tasks involving logical thinking and mathematics performance. To this end, subjects were 12 children aged 8 and 9 years old which attended the third year of elementary school - of a public school in the city of São Paulo. The instrument for data gathering was composed by12 questions involving problems without number, 12 problems with and without possible solution, 36 problems with some sort of logical violation (12involvingcausal violations, 12 implied temporal violations and 12 consisted of general violations). The subjects responded to the 60 problems whose correctness criterion required that the answer was in the predicted direction and was accompanied by proper justification, obtained by the inquiry provoked by the researcher. The following procedures for data analysis were performed by: 1. Individual performance on each problem; 2.Analysis of the relative difficulty of each question in each type of problem (depending on the number of hits obtained in them); 3.Analysis of the justifications; 4.Analysis of performance for classification of students (previously classified as strong or weak performers on mathematics), and 5. Performing Statistical using Minitab Statistical Software testing. It was possible to identify relationship between mathematics performance and behavior in solving logical problems / Na educação, constata-se a preocupação em desenvolver o comportamento de solucionar problemas como uma das responsabilidades da escola, à qual caberia a tarefa de prover os estudantes com procedimentos para que sejam capazes de responder aos desafios da vida contemporânea. O presente estudo teve como tema central a resolução de problemas, buscando identificar e compreender possíveis relações entre o desempenho em tarefas envolvendo raciocínio lógico e o desempenho em matemática. Para tanto, foram avaliadas 12 crianças de 8 e 9 anos de idade, frequentando o 3o ano do ensino fundamental de uma escola da rede pública de ensino na cidade de São Paulo. O instrumento para a realização deste estudo continha 12 questões que envolviam problemas sem número, 12 problemas com e sem solução possível e 36 problemas com algum tipo de violação lógica, sendo que 12 delas abordavam violações causais, 12 implicavam violações temporais e 12 eram compostas por violações gerais. Os sujeitos responderam aos 60 problemas, cujo critério de acerto implicava que a resposta estivesse na direção prevista e que fosse acompanhada da justificativa correta, obtida mediante inquérito da pesquisadora. Foram realizados os seguintes procedimentos para a análise dos dados: 1. Análise do desempenho individual em cada problema; 2. Análise da dificuldade relativa de cada questão em cada tipo de problema (em função do número de acertos obtidos neles); 3. Classificação das justificativas; 4. Análise do desempenho por classificação dos alunos (fortes e fracos); 5. Realização de testes estatísticos por meio do Minitab Statistical Software. Os resultados possibilitaram identificar a relação entre o desempenho em matemática e o comportamento de resolver problemas lógicos, sugerindo haver relação entre estes raciocínios