<p>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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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.</p>

The National Research Council (NRC) outlines an assessment design framework in Knowing What Students Know. This framework proposes the integration of three components in assessment design that can be represented by a triangle, with each corner representing: cognition, or model of student learning in the domain; observation, or evidence of competencies; and interpretation, or making sense of this evidence. This triangle representation signifies the idea of a need for interconnectedness, consistency, and integrated development of the three elements, as opposed to having them as isolated from each other. Based on the recommendations for research outlined in the NRC's assessment report, this dissertation aims to conduct a dimensionality analysis of Programme for International Student Assessment (PISA) mathematics items. PISA assesses 15-year olds' skills and competencies in reading, math, and science literacy, implementing an assessment every three years since 2000. PISA's mathematics assessment framework, as proposed by the Organisation for Economic Co-operation and Development (OECD), has a multidimensional structure: content, processes, and context, each having three to four sub-dimensions. The goal of this dissertation is to show how and to what extent this complex multidimensional nature of assessment framework is reflected on the actual tests by investigating the dimensional structure of the PISA 2003, 2006, and 2009 mathematics items through the student responses from all participating OECD countries, and analyzing the correspondence between the mathematics framework and the actual items change over time through these three implementation cycles. Focusing on the cognition and interpretation components of the assessment triangle and the relationship between the two, the results provide evidence addressing construct validity of PISA mathematics assessment. Confirmatory factor analysis (CFA) and structural equation modeling (SEM) were used for a dimensionality analysis of the PISA mathematics items in three different cycles: 2003, 2006, and 2009. Seven CFA models including a unidimensional model, three correlated factor (1-level) models, and three higher order factor (2-level) models were applied to the PISA mathematics items for each cycle. Although the results did not contradict the multidimensionality, stronger evidence was found to support the unidimensionality of the PISA mathematics items. The findings also showed that the dimensional structure of the PISA mathematics items were very stable across different cycles. / text

<p>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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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&nbsp / 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.</p>

The aim of this thesis is to elaborate a set of tasks that will have increasing difficulty and will lead pupils to the skill of solving problems designed for gifted students. The action research will focus on the student's work with the proposed tasks. In the theoretical part, attention will be paid to the available literature on the teaching of mathematics to exceptionally gifted pupils.

The aim of my work is to prove continuity of solving word problems in math within the context of reading and mathematical literacy. Ten word problems will be created with different mathematical content, with longer task for challenging reading literacy. For all problems will be stated the correct solution. In the practical part, the problems will be assigned to solve to selected pupils at selected schools. The results of their solution will then be analysed and published.

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.