O presente estudo teve como objetivo geral compreender o processo de aprendizagem da matemática de estudantes durante o ciclo de alfabetização na cidade do Rio de Janeiro. Para isso, fez-se uso dos dados de uma pesquisa longitudinal, denominada Estudo Longitudinal da Geração Escolar 2005 GERES 2005. Esta Pesquisa consistiu em um estudo de painel que acompanhou ao longo de quatro anos consecutivos (de 2005 a 2008) uma amostra de estudantes do primeiro segmento do Ensino Fundamental (1 à 4 série e/ou 2 ao 5 ano) em cinco cidades brasileiras - Rio de Janeiro, Belo Horizonte, Campinas, Campo Grande e Salvador, por meio de testes de Matemática e Leitura aplicados aos estudantes e de questionários contextuais aplicados a seus professores, aos diretores das escolas, e aos pais. Especificamente o estudo concentrou-se sobre os dados referentes à rede municipal do Rio de Janeiro e mais especificamente ao período correspondente ao ciclo de alfabetização. Foram analisados os resultados médios em matemática dos estudantes nas três primeiras Ondas de avaliação e o percentual de acertos nos itens comuns a essas Ondas, com o intuito de verificar a evolução da aprendizagem em matemática ao longo do início da escolarização nos anos iniciais. Dentre os principais resultados da pesquisa foi possível perceber certa fragilidade na construção dos conceitos matemáticos básico dos anos iniciais, evidenciando que possivelmente a construção da linguagem matemática encontra-se aquém do esperado para os estudantes no início de sua formação matemática. Possivelmente, estes resultados reflitam uma prática comum nas escolas em que a ênfase do processo de aprendizagem esteja centrada em processos individuais, em contextos pouco familiares à criança, além da proposição de atividades que pouco exploram o raciocínio lógico e dedutivo do aluno, ou seja, o pensar sobre de forma lúdica e criativa. Tudo isso tem contribuído para aumentar a distância entre estudantes de diferentes classes sociais ou diferentes redes de ensino. / This research had as main objective to understand the process of learning mathematics students during literacy cycle in the city of Rio de Janeiro. For this, made use of data from a longitudinal research project, called "Generation School Longitudinal Study of 2005 - GERES 2005. This survey consisted of a panel study that followed over four consecutive years (2005-2008) a sample of students from the first upper elementary school (1st to and/or 2nd to 5th year 4th grade) in five Brazilian cities - Rio de Janeiro, Belo Horizonte, Campinas, Campo Grande and Salvador through math and reading tests administered to students and contextual questionnaires to their teachers, school principals, and parents. Specifically, the study focused on data concerning the municipal Rio de Janeiro and more specifically to the corresponding literacy cycle period. Average in mathematics of students in the first three waves of assessment results and the percentage of correct answers on common items such waves, in order to check the evolution of learning in mathematics throughout the beginning of schooling in the early years were analyzed. Among the main results of the research it was possible to perceive a certain fragility in the construction of the basic mathematical concepts of the early years, possibly indicating that the construction of mathematical language lies below expectations for students early in their mathematical training. Possibly, these results reflect a common practice in schools where the emphasis of the learning process is centered on individual processes in unfamiliar contexts the child, in addition to proposing activities that little exploit the logical and deductive reasoning of the student, "thinking about " a playful and creative way. All this has contributed to increase the distance between students from different social networks or different educational classes.

Submitted by JULIO CESAR AUGUSTUS DE PAULA SANTOS null (julio23@gmail.com) on 2016-04-07T03:20:01Z No. of bitstreams: 1 A ideia de número no ciclo de alfabetização matemática - o olhar do professor.pdf: 1340708 bytes, checksum: b0cb114e45a5b13e025ca4973ae4e528 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-04-07T17:55:22Z (GMT) No. of bitstreams: 1 santos_jcap_me_rcla.pdf: 1340708 bytes, checksum: b0cb114e45a5b13e025ca4973ae4e528 (MD5) / Made available in DSpace on 2016-04-07T17:55:22Z (GMT). No. of bitstreams: 1 santos_jcap_me_rcla.pdf: 1340708 bytes, checksum: b0cb114e45a5b13e025ca4973ae4e528 (MD5) Previous issue date: 2016-03-09 / O presente estudo tem o objetivo de investigar qual é a compreensão de número expressa por professores que ensinam matemática no ciclo de alfabetização (do 1º ao 3º ano do Ensino Fundamental). A pesquisa é qualitativa e desenvolvida em uma abordagem fenomenológica seguindo os procedimentos de produção e análise de dados conforme Bicudo (2011a, 2011b). Na trajetória percorrida, realizamos um estudo inicial da região de inquérito, o número no ciclo de alfabetização matemática, na perspectiva do Pacto Nacional pela Alfabetização na Idade Certa (PNAIC), trouxemos uma compreensão fenomenológica de número e procedemos à produção dos dados, entrevistando seis professores do ciclo de alfabetização (um professor do 1º ano, três professores do 2º ano e dois professores do 3º ano) de uma escola estadual da cidade de São Paulo (SP). A análise dos dados mostra que esses professores compreendem número ora como código, presentes em situações cotidianas, ora como quantidade, que emerge das situações de quantificação. / This study aims to research on what is the comprehension of number expressed by teachers who teach mathematics in the ciclo de alfabetização matemática (from 1st to 3rd year of elementary school). The research is qualitative and developed in a phenomenological approach following the production and data analysis procedure as in Bicudo (2011a, 2011b). In the path taken, we did an initial study of the investigation area, the concept of number in the ciclo de alfabetização matemática, in the view of the Pacto Nacional pela Alfabetização na Idade Certa (PNAIC), we brought a phenomenological comprehension of number and proceed to the data production, which consisted in interviewing six teachers of the ciclo de alfabetização matemática (one teacher from the 1st year, three teachers from the 2nd year and two teachers from the 3rd year) of a state school in the city of São Paulo (SP). The data analysis showed us that these teachers understand number sometimes as a code, which is highly noticed in daily situations and sometimes as a quantity, which comes from quantification situations.

Orientador: Maria Lúcia Lorenzetti Wodewotzki / Banca: Marcelo de Carvalho Borba / Banca: Marcus Vinicius Maltempi / Banca: Ole Skovsmose / Banca: Alexandrina Monteiro / Resumo: Com esta pesquisa busquei analisar as possibilidades de crescimento político dos estudantes, quando a modelagem matemática é adotada como estratégia de ensino-aprendizagem. Considero essas possibilidades como reflexões que se identificam com questionamentos, críticas, ações e transformações. Ao inserir este estudo no contexto da Educação Matemática Crítica baseei minha pesquisa bibliográfica em autores que se identificam com esse movimento. Adotei na pesquisa uma abordagem qualitativa e para a coleta de dados organizei três ambientes de aprendizagem, denominados cenários para investigação, com estudantes voluntários das séries iniciais dos Cursos de Matemática e de Engenharia de Computação, ambos da PUC-Campinas. A análise dos dados indica que o crescimento político dos atores nos cenários associa-se, de um lado, com a conscientização política resultante da sua atuação em investigações diretamente relacionadas com os temas dos projetos de modelagem, nas discussões que acompanham os resultados obtidos e no debate sobre o alcance desses resultados e sobre as conseqüências sociais do trabalho realizado. Do outro lado, esse crescimento associa-se com uma ação política que se concretiza por meio do envolvimento do estudante com a comunidade. Concluo este estudo indicando que o processo de crescimento político dos estudantes deve ser pensado como uma forma de alfabetização matemática, estreitamente relacionada com o núcleo de uma literacia matemática voltada para mudanças sociais. / Abstract: With this research I intended to analyze the possibilities of the students' political growth when the mathematical modelling is adopted as teaching-learning strategy. I consider those possibilities as reflections that identify with questioning, critics, actions and transformations. When inserting this study in the context of the Critical Mathematics Education I based my bibliographical research on authors that identify with this movement. The research was performed within a qualitative approach, starting from the construction of three learning environment, denominated scenarios to investigation, organized with voluntary students from the initial series of the courses of Mathematics and Engineering of Computation, both of PUC-Campinas University. The analysis of the data indicates that the actors' political growth in the sceneries associates, on a side, with the political awareness as a result of their involvement in investigations directly related with the themes of the modelling projects, in the discussions that accompany the obtained results and in the debate about the reach of those results, and about the social consequences of the accomplished work. On the other hand, that growth associates with a political action that is rendered through the student's involvement with the community. I conclude this study indicating that the process of the students' political growth should be thought as a form of mathematical literacy, strictly related with the nucleus of a mathematical literacy focused on social changes. / Doutor

O presente estudo teve como objetivo geral compreender o processo de aprendizagem da matemática de estudantes durante o ciclo de alfabetização na cidade do Rio de Janeiro. Para isso, fez-se uso dos dados de uma pesquisa longitudinal, denominada Estudo Longitudinal da Geração Escolar 2005 GERES 2005. Esta Pesquisa consistiu em um estudo de painel que acompanhou ao longo de quatro anos consecutivos (de 2005 a 2008) uma amostra de estudantes do primeiro segmento do Ensino Fundamental (1 à 4 série e/ou 2 ao 5 ano) em cinco cidades brasileiras - Rio de Janeiro, Belo Horizonte, Campinas, Campo Grande e Salvador, por meio de testes de Matemática e Leitura aplicados aos estudantes e de questionários contextuais aplicados a seus professores, aos diretores das escolas, e aos pais. Especificamente o estudo concentrou-se sobre os dados referentes à rede municipal do Rio de Janeiro e mais especificamente ao período correspondente ao ciclo de alfabetização. Foram analisados os resultados médios em matemática dos estudantes nas três primeiras Ondas de avaliação e o percentual de acertos nos itens comuns a essas Ondas, com o intuito de verificar a evolução da aprendizagem em matemática ao longo do início da escolarização nos anos iniciais. Dentre os principais resultados da pesquisa foi possível perceber certa fragilidade na construção dos conceitos matemáticos básico dos anos iniciais, evidenciando que possivelmente a construção da linguagem matemática encontra-se aquém do esperado para os estudantes no início de sua formação matemática. Possivelmente, estes resultados reflitam uma prática comum nas escolas em que a ênfase do processo de aprendizagem esteja centrada em processos individuais, em contextos pouco familiares à criança, além da proposição de atividades que pouco exploram o raciocínio lógico e dedutivo do aluno, ou seja, o pensar sobre de forma lúdica e criativa. Tudo isso tem contribuído para aumentar a distância entre estudantes de diferentes classes sociais ou diferentes redes de ensino. / This research had as main objective to understand the process of learning mathematics students during literacy cycle in the city of Rio de Janeiro. For this, made use of data from a longitudinal research project, called "Generation School Longitudinal Study of 2005 - GERES 2005. This survey consisted of a panel study that followed over four consecutive years (2005-2008) a sample of students from the first upper elementary school (1st to and/or 2nd to 5th year 4th grade) in five Brazilian cities - Rio de Janeiro, Belo Horizonte, Campinas, Campo Grande and Salvador through math and reading tests administered to students and contextual questionnaires to their teachers, school principals, and parents. Specifically, the study focused on data concerning the municipal Rio de Janeiro and more specifically to the corresponding literacy cycle period. Average in mathematics of students in the first three waves of assessment results and the percentage of correct answers on common items such waves, in order to check the evolution of learning in mathematics throughout the beginning of schooling in the early years were analyzed. Among the main results of the research it was possible to perceive a certain fragility in the construction of the basic mathematical concepts of the early years, possibly indicating that the construction of mathematical language lies below expectations for students early in their mathematical training. Possibly, these results reflect a common practice in schools where the emphasis of the learning process is centered on individual processes in unfamiliar contexts the child, in addition to proposing activities that little exploit the logical and deductive reasoning of the student, "thinking about " a playful and creative way. All this has contributed to increase the distance between students from different social networks or different educational classes.

Literacia matemática é a capacidade de identificar, compreender e utilizar noções quantitativas e matemáticas na vida prática. A falta dessa habilidade entre jornalistas é responsável por erros em reportagens e também pela limitação do trabalho de apuração. Esta pesquisa investiga a ocorrência e as formas como informações quantitativas são inseridas em notícias, e discute seu papel na a formação de estudantes de jornalismo, enfatizando a necessidade de pensar números em contexto e de compreender os conhecimentos matemáticos como uma ferramenta indispensável para o exercício da cidadania. Ao campo da pesquisa em Educação Matemática, o trabalho traz uma perspectiva voltada ao ensino de matemática em nível superior para carreiras não-afins. / Mathematical literacy is the ability to identify, understand and apply quantitative and mathematical knowledge in the everyday life. When lacking this ability, journalists not only make mistakes in reporting, but also become limited in their investigations. The present study researches how often and in which ways quantitative information is used in the news, and argues about its place in the journalism school, emphasizing the importance of thinking about numbers in their context and of understanding mathematical knowledge as an imperative tool for citizenship. To the Mathematics Education research field, this work provides a perspective on teaching Mathematics in higher education for careers outside of STEM.

Magister Educationis - MEd / The National Curriculum Statement introduced mathematical literacy officially in 2006. Learners in general perform poorly at mathematics in South Africa but there is strong belief that learners should graduate from schools sufficiently literate to deal with the mathematical issues they will encounter in out-of-school situations. Based on this, this study is an investigation of the contexts, which grades 8 - 10 learners would prefer to engage with mathematics. The aim of this study was thus to investigate mathematical literacy in relation to learners' motivations for the contexts they would prefer to deal with in mathematical literacy. The emphasis of the study is to concentrate on learners' written motivations for mathematical contexts. Data were collected using a questionnaire that deals with contexts for mathematics. / South Africa

Magister Educationis - MEd / The study explored the comparison of grade 8 to 10 urban and peri-urban learners' contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas; least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners. / South Africa

Philosophiae Doctor - PhD / Local and international pundits concur that education systems play a pivotal role in fostering and developing values in learners. In some countries, like South Africa, the values and rights enshrined in the Constitution and the Bill of Rights resonate in the Schools Act. As one of the concerns of education is nationbuilding, my study investigates if the integration of the values does achieve tolerance and co-operation in the classroom by examining how learners make sense of values in the Mathematical Literacy curriculum. While I firmly believe that educational institutions have a responsibility to integrate positive values into all aspects of the school curriculum, it is my contention that learners cannot fully benefit from values specifically related to the Mathematical Literacy curriculum itself on their own. All stakeholders in education need to come together to establish an informed understanding of policy documents and reconcile the complexities and challenges that surround the transmission of values, so that educators will be able to assist learners in a meaningful way. The classroom life of a learner is intricately woven with that of the teacher. In order to unearth the views and practices of learners and teachers, I adopted a participatory approach. The qualitative study that ensued was conducted in three Mathematics Literacy classrooms at secondary schools in Cape Town, South Africa. The observation sessions afforded me the opportunity to experience and appreciate how the teachers integrate values into the Mathematical Literacy lessons while observing learners‟ behaviour in the classroom. The interactions and interviews with both learners and teachers aided in further unravelling their understanding and implementation of values in the Mathematical Literacy lessons. For learners to develop into responsible, caring and morally just citizens who arecapable of critical thought, they equire an education that provides them with the necessary opportunities and tools to develop. Mathematical Literacy is able to provide learners with the relevant opportunities and thinking tools to construct meaning around moral concepts. I strongly believe that for learners to accomplish this goal, educators need to be appropriately capacitated to facilitate opportunities for their learners.I did not find any evidence in the literature that suggests a fail-safe theoretical approach to success in values education. I am of the opinion that for any measure of success in values education, a combination of these theories of learning and moral development has to be employed. / South Africa

Magister Educationis - MEd / The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in co~parison to those of other countries. Based on these observations, the present study is an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of this study was thus to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study pays more attention to mathematics education 111 real life situations. Data was collected using the ROSME questionnaire that deals with contexts preferred by students for mathematics education. A sample made up of over 1600 learners in grades 8 to 10 were randomly selected from 21 schools. Data collected from these learners was analysed using Kendall's W mean rank method in the SPSS 12.0 program since the data for this study were ordinal. The most important finding of this study was that, "Mathematics that entertains and surprises us" came up the highest ranked item. This indicates that mathematics education must be directed towards raising learners' interests. The lowest ranked item was, "Mathematics used to calculate the number of seats for parliament given to political parties after elections," and this might indicate among other things that political activity does not attract students' interest in a society where the concept of well-being is dominant. In general, Korean learners appear to favour learning mathematics in technological contexts and show less interest in political and agricultural contexts. In conclusion, this study suggests that teachers should use contexts that increase learners' interest in classroom activities. Korea has today become one of the strongest Information Technology countries. Therefore mathematics curricula and textbooks which are appropriate to this context must be provided for more efficient mathematics education. Thus, it becomes imperative that the Korean school system must develop a particular program for nurturing learners' mathematical power. Furthermore, mathematics education policy makers must reconsider whether the current education system, Pyungjunhwa Kyoyuk system, should be used or not.

Intensivundervisning i matematik - att vara eller icke vara. En problematisering av intensivundervisning i matematik. / Intensive education in mathematics - to be or not to beA problematization of intensive education in mathenatics