In this thesis I set out to explore the area of specific learning difficulties, an area of conflicting theories, understandings, policies and provision. The purpose of this comparative research in such a heavily debated area was to illuminate the commonalities and differences which can be observed across countries. Comparative research in a policy related area has a long tradition. However, Greece and Scotland provided two different cultural and educational backgrounds which made the comparisons particularly interesting. The nature of, as well as the provision for, specific learning difficulties is investigated in this research through the eyes of those involved. The perceptions of policy agents, head teachers, learning support teachers, mainstream teachers, parents and pupils, as well as the underlying constructs evident in policy documentation and literature in both countries, provided the data on which this thesis was based. This thesis seeks to compare current policies and provision in Scotland and Greece, to investigate the discrepancies between policy and provision, to highlight the differences in perceptions about the nature of specific learning difficulties among the different groups within and between the countries, and to identify factors which might have influenced these perceptions and the current provision. In addition, as both countries are members of the European Union, the impact that the EU had in forming the current policies or provision is also examined. The case-study schools were selected by policy agents in Scotland and from a list provided by the Ministry of Education in Greece. Case-study pupils were selected by the learning support teachers of the schools selected, or the head teachers using the learning support teachers files. The aim was that no preconceptions held by the researcher about the nature of specific learning difficulties influenced the selection of the case-study schools and/or pupils, consistent with the ethnographic principles of investigation. The data was gathered through semi-structured interview schedules which, although they maintaineda structure, allowed the respondents to play the leading role. The interviews were supported by observation of the case-study pupils, from which examples were drawn to use as exemplification during the interviews. Relevant policy documents and literature, not only those explicitly about specific learning difficulties but also those rather more generally about special educational needs were also studied and compared with the constructs held by professionals and consumers. The findings of this study indicated that culture, societal and educational context had influenced the perceptions of, and the provision for, specific learning difficulties. This was highlighted by the fact that the differences among the various groups within the same country were substantially less distinctive than those between Scotland and Greece. These differences highlighted the `inclusive' Scottish society, supporting the notion of `rights' of individuals, whilst in Greece the attitudes were focused on `exclusion' and the `protective' role of the family. The educational systems also played a significant role; the Greek system is heavily hierarchical, with a prescriptive curriculum based on knowledge and delivered by common-to-all books which focus on the `average' child. In contrast, the Scottish system has been characterised as task-oriented and able to differentiate according to children's needs. In addition, the Scottish curriculum is designed for all pupils, and includes guidelines for 'support for learning' targeted at those with special educational needs. The distinctiveness of the Greek and the Scottish societies and educational systems was reflected in the different understandings of special educational needs. In Scotland, they were seen as a continuum of needs including specific learning difficulties. In relation to specific learning difficulties the location of problems was perceived to be to a large extent within the learning environment and, in conjunction with the dominance of the `rights' discourse, responsibilities were placed explicitly on mainstream and head teachers as well as learning support. The latter's role was perceived as co-operative teaching and consultancy. In Greece, concerns were raised about the system itself and its limitations. Characteristics of this system were the lack of clear responsibility on the part of head teachers, and the lack of co-operation between learning support teachers (regarded as responsible for specific learning difficulties) and mainstream teachers. The construct of special educational needs as set of categories of impairment, the distinctive special and general education systems, the provision for specific learning difficulties in 'special classrooms' and the locus of the problem perceived to be within the child, all reflected the dominant position of the 'medical and charity' discourses in the society. In conclusion, although the aim of the education systems has been stated as being `inclusive' education in both Greece and Scotland, I argue that the two countries are at different points, closer or further apart, from their goal. However, the complexity of the various factors involved in the educational development of the two countries presented in this thesis makes a linear comparison a simplistic one, and hence unsuitable. Nevertheless, as both Greece and Scotland reiterate their objective towards "one school for all", a goal set also by the EU, the latter's impact in Greece is stronger. EU acts through its role as `expert' and co-ordinator of exchanges and by funding projects to support inclusive education. This comparative research has indicated how studies of this kind can raise the awareness of the impact of characteristics of national societies on an area of education which has common rhetoric ('inclusion') across countries but where practice and provision can look very different `on the ground'.

Made available in DSpace on 2016-07-27T13:53:56Z (GMT). No. of bitstreams: 1 MARIA GORETTI QUINTILIANO CARVALHO.pdf: 1872383 bytes, checksum: 1e5240852d34481d9e477c4cac22def3 (MD5) Previous issue date: 2007-08-23 / This dissertation argues the participation of the professor in the relation that the student diagnosised with learning difficulties establishes with the knowledge. It presents the historical about the difficulty of learning in the Brazilian pedagogical speech from the research of Tiballi (1998), Patto (1999), and Angellucci et alli (2004), and presents the concepts of learning and difficulty in learning according to geneticcognitive that Piaget has as his main exponent; social-cognitive, with Vygotsky as his main theorical and the cultural conception, that has Bernard Charlot as one of the scholars that, in the present time, makes an analysis on knowledge, the learning and the relation that the subject establishes with knowledge, adding some important elements for the understanding of the learning process. By empirical research done in the system of municipal public education in São Luís de Montes Belos, this dissertation identifies the conceptions of learning difficulty that mark out with buoys the pedagogical work of the professor in basic education, reflecting about what the professors think about learning difficulty and which elements constitute this conception, and, still what the professors and/or the school make to revert the situations of failure at school, beyond the criteria that the professors consider to identify the children who have learning difficulty. This reflection is based on the reformularizations of Charlot (2000, 2001, 2005, 2006) about learning, that considers the relation with knowledge, with learning, how the relation that the subject establishes with the world, with the other and with himself even when he is collated by the necessity in learning. / Esta dissertação discute a participação do professor na relação que o aluno diagnosticado com dificuldades de aprendizagem estabelece com o conhecimento. Apresenta o histórico sobre a dificuldade de aprendizagem presente no discurso pedagógico brasileiro a partir das pesquisas de Tiballi (1998), Patto (1999), e Angellucci et alli (2004) e os conceitos de aprendizagem e de dificuldade de aprendizagem segundo as concepções: genético-cognitiva, que tem Piaget como seu principal expoente; sócio-cognitiva, com Vygotsky como seu principal teórico e a concepção cultural, que tem Bernard Charlot como um dos estudiosos que, na atualidade, faz uma análise sobre o saber, a aprendizagem e a relação que o sujeito estabelece com o saber, acrescentando alguns elementos importantes para a compreensão do processo de aprendizagem. Por meio de pesquisa empírica realizada no sistema de ensino público municipal em São Luís de Montes Belos, esta dissertação identifica as concepções de dificuldade de aprendizagem que balizam o trabalho pedagógico do professor no ensino fundamental, refletindo sobre o que os professores pensam acerca da dificuldade de aprendizagem e quais elementos constituem essa sua concepção, e, ainda o que os professores e/ou a escola fazem para reverter situações de fracasso escolar, além dos critérios que os professores consideram para identificar as crianças que têm dificuldade de aprendizagem. Essa reflexão fundamenta-se nas reformulações de Charlot (2000, 2001, 2005, 2006) sobre a aprendizagem, que considera a relação com o saber, com o aprender, como a relação que o sujeito estabelece com o mundo, com o outro e consigo mesmo quando é confrontado pela necessidade de aprender.

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São notórias e bem evidentes as dificuldades de aprendizagem no ensino de Cálculo. Algumas tentativas de resolver, ou pelo menos, amenizar, este problema têm sido realizadas tanto no campo pedagógico quanto no âmbito da pesquisa. Muitas dessas ações, inseridas no próprio contexto do ensino superior de Cálculo, partem do pressuposto que essas dificuldades de aprendizagem são de natureza psicológica, internas ao sujeito aprendiz. No entanto, contrariando esta tendência, esta pesquisa pretende mostrar que parte significativa dos problemas de aprendizagem do atual ensino de Cálculo é de natureza essencialmente epistemológica, está além dos métodos e das técnicas de ensino, sendo inclusive anterior ao seu próprio tempo de realização. Diante disto, foram imaginadas duas ações inter-relacionadas, dois mapeamentos que visam ao levantamento e entendimento dessas dificuldades de natureza epistemológica no ensino de Cálculo: um mapeamento conceitual do Cálculo e de suas idéias e procedimentos básicos; em seguida, munido desses elementos, realizou-se efetivamente o mapeamento das dificuldades supracitadas. Assim, a partir do entrelaçamento dos fatos históricos e pedagógicos, e tendo como pano de fundo as dualidades essenciais e os mapas conceituais do Cálculo, foram explicitados e consubstanciados cinco macro-espaços de dificuldades de aprendizagem de natureza epistemológica, cinco eixos que estruturam o ensino de Cálculo, a saber: o eixo discreto/contínuo; o eixo variabilidade/permanência; o eixo finito/infinito; o eixo local/global; e o eixo sistematização/construção. Nesse esforço filosófico, foram estabelecidas relações entre os macro-espaços determinados com os mapas históricos e conceituais do Cálculo, e destes com o ensino de matemática em todos os níveis. Então, pôde-se perceber, em essência, um único lugar-matriz das dificuldades de aprendizagem de natureza epistemológica do ensino de Cálculo: o da omissão/evitação das idéias básicas e dos problemas construtores do Cálculo no ensino de Matemática em sentido amplo. Isto posto, para romper com o isolamento semântico, a subestimação da relevância das idéias e dos instrumentos característicos do Cálculo, propõem-se algumas intervenções didáticas relativas ao ensino básico de Matemática e ao ensino do próprio Cálculo. O que se pretende com isso é possibilitar ao Cálculo exercer no campo pedagógico a mesma função integradora que ele realizou no âmbito científico, no processo de construção do conhecimento matemático. / The difficulties in learning Calculus are noticeable and quite evident. Some attempts to solve, or at least, soften, this problem have been made both in the pedagogical field and in the scope of the research. Many of these actions, within the context of a higher teaching of Calculus itself, assume that such difficulties in learning are of a psychological nature, internal to the learner. However, contrary to this tendency, this research intends to show that a significant part of the problems of learning the current teaching of Calculus is of a nature essentially epistemological, it is beyond the methods and the techniques of teaching, being also prior to its own time of realization. With that in mind, there were imagined two actions interrelated, two mappings which aim the rising and understanding of these difficulties of an epistemological nature in the teaching of Calculus: a conceptual mapping of Calculus and of its ideas and basic procedures; next, having these instruments, the mapping of the previously mentioned difficulties was effectively done. Thus, from the interlacement of the historical and pedagogical facts, and having as background the essential dualities and the conceptual maps of Calculus, there were clarified and consubstantiated five macro spaces of the difficulties in learning of an epistemological nature, five axes which structure the teaching of Calculus, namely: the axis discreet/continuous; the axis variability/permanence; the axis finite/infinite; the axis local/global; and the axis systematization/construction. In this philosophical endeavour there were established relations between the macro spaces determined by the historical and conceptual maps of Calculus, and from these with the teaching of mathematics in all levels. Therefore, one can notice, essentially, a single point of origin in the difficulties in the learning of an epistemological nature in the teaching of Calculus: the omission/avoidance of the basic ideas and the construction problems of Calculus in the teaching of mathematics in an ample sense. So, to break up with the semantic isolation, the underestimation of the relevance of the ideas and of the instruments characteristics of Calculus, some didactic interventions are proposed in the field of the basic teaching of Mathematics and in the teaching of Calculus itself. What is expected from this is to allow Calculus to have in the pedagogical field the same function of integration that it had in the scientific field, in the process of building the mathematical knowledge.

Orientador : Anna Regina Lanner de Moura / Dissertação (mestrado) ¿ Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-09T12:44:29Z (GMT). No. of bitstreams: 1 Scarlassari_NathaliaTornisiello_M.pdf: 1150253 bytes, checksum: 3ff8a24b10e00322ae200a7208de6031 (MD5) Previous issue date: 2007 / Resumo: Esta pesquisa, de caráter qualitativo, tem como objetivo principal discutir Que tipo de dificuldades alunos da 6ª série do Ensino Fundamental apresentam em uma situação B de ensino de álgebra, comparativamente a alunos da mesma série que passaram por uma situação A de ensino de álgebra? As situações de ensino tiveram a seguintes características: A situação A ocorreu em uma escola da rede particular de ensino da cidade de Piracicaba, em 1999, em duas classes de 6ª série e constituiu-se fonte de dados para a nossa pesquisa de Iniciação Científica que versou sobre as dificuldades dos alunos em álgebra. Atuamos como observadoras das aulas de álgebra que foram desenvolvidas numa abordagem tradicional, pela manipulação simbólica, resolução e correção de listas de exercícios na lousa. Os dados foram provenientes das respostas dos alunos a uma lista de exercícios. Dessas respostas analisamos e categorizamos as dificuldades em álgebra, aí manifestas. A situação B de ensino de álgebra ocorreu em uma escola estadual da cidade de Campinas, em duas classes de 6ª série onde atuamos como pesquisadoras e professora das classes pesquisadas. Foram trabalhadas atividades que propunham o desenvolvimento dos nexos conceituais da álgebra elementar, tais como: fluência, variável, campo de variação, linguagem, operacionalidade e unidade. Após esse desenvolvimento solicitamos aos alunos responderem a mesma lista de exercício usada na situação A. Comparamos as dificuldades encontradas nas duas situações para os mesmos exercícios. Esta comparação indica que os alunos da situação B encontraram menos dificuldades para realizar as atividades e que a freqüência dos erros, nessa situação, foi menor. Este trabalho permitiu afirmar que a Situação B de ensino proporcionou uma aprendizagem mais significativa das idéias algébricas correspondentes aos exercícios solicitados do que a Situação A, de abordagem tradicional / Abstract: The main purpose of this research is to discuss under a qualitative aspect What kind of difficulties the sixth-grade students of Elementary school present with regard to the Algebra learning situation B in comparison with those students from the same grade who have experienced the Algebra learning situation A? The learning situations had the following characteristics: The situation A occurred in two sixth-grade classes of one private school located in the city of Piracicaba, Sao Paulo, in 1999, and it has constituted data source for the Undergraduate Research that discussed students' difficulties regarding algebra. We have been acting as observers in the algebra classes, which were prepared according to a traditional approach using symbolic manipulation, resolution, and correction of lists of exercises on the blackboard. The data was gathered from the answers given by the students to a list of exercises, from which we were able to analyze and categorize the difficulties in algebra. The algebra learning situation B happened in two sixth-grade classes of public school in the city of Campinas, São Paulo, where we have acted both as researchers and teachers on the researched classes. Working activities proposed the development of the conceptual nexus of elementary algebra, such as fluency, variable, variation field, language, operationability and unity. Afterwards we invited the students to answer the same list of exercises used in situation A. We compared the difficulties found in both situations considering the same exercises. This comparison shows that the students in situation B found less difficulty to solve this list and there was a fewer occurrence of mistakes compared to situation A. This research allowed us to affirm that the learning situation B has brought a more significant understanding of the algebraic ideas related to the given exercises than the situation A, which considered a traditional learning approach / Mestrado / Educação Matematica / Mestre em Educação

São notórias e bem evidentes as dificuldades de aprendizagem no ensino de Cálculo. Algumas tentativas de resolver, ou pelo menos, amenizar, este problema têm sido realizadas tanto no campo pedagógico quanto no âmbito da pesquisa. Muitas dessas ações, inseridas no próprio contexto do ensino superior de Cálculo, partem do pressuposto que essas dificuldades de aprendizagem são de natureza psicológica, internas ao sujeito aprendiz. No entanto, contrariando esta tendência, esta pesquisa pretende mostrar que parte significativa dos problemas de aprendizagem do atual ensino de Cálculo é de natureza essencialmente epistemológica, está além dos métodos e das técnicas de ensino, sendo inclusive anterior ao seu próprio tempo de realização. Diante disto, foram imaginadas duas ações inter-relacionadas, dois mapeamentos que visam ao levantamento e entendimento dessas dificuldades de natureza epistemológica no ensino de Cálculo: um mapeamento conceitual do Cálculo e de suas idéias e procedimentos básicos; em seguida, munido desses elementos, realizou-se efetivamente o mapeamento das dificuldades supracitadas. Assim, a partir do entrelaçamento dos fatos históricos e pedagógicos, e tendo como pano de fundo as dualidades essenciais e os mapas conceituais do Cálculo, foram explicitados e consubstanciados cinco macro-espaços de dificuldades de aprendizagem de natureza epistemológica, cinco eixos que estruturam o ensino de Cálculo, a saber: o eixo discreto/contínuo; o eixo variabilidade/permanência; o eixo finito/infinito; o eixo local/global; e o eixo sistematização/construção. Nesse esforço filosófico, foram estabelecidas relações entre os macro-espaços determinados com os mapas históricos e conceituais do Cálculo, e destes com o ensino de matemática em todos os níveis. Então, pôde-se perceber, em essência, um único lugar-matriz das dificuldades de aprendizagem de natureza epistemológica do ensino de Cálculo: o da omissão/evitação das idéias básicas e dos problemas construtores do Cálculo no ensino de Matemática em sentido amplo. Isto posto, para romper com o isolamento semântico, a subestimação da relevância das idéias e dos instrumentos característicos do Cálculo, propõem-se algumas intervenções didáticas relativas ao ensino básico de Matemática e ao ensino do próprio Cálculo. O que se pretende com isso é possibilitar ao Cálculo exercer no campo pedagógico a mesma função integradora que ele realizou no âmbito científico, no processo de construção do conhecimento matemático. / The difficulties in learning Calculus are noticeable and quite evident. Some attempts to solve, or at least, soften, this problem have been made both in the pedagogical field and in the scope of the research. Many of these actions, within the context of a higher teaching of Calculus itself, assume that such difficulties in learning are of a psychological nature, internal to the learner. However, contrary to this tendency, this research intends to show that a significant part of the problems of learning the current teaching of Calculus is of a nature essentially epistemological, it is beyond the methods and the techniques of teaching, being also prior to its own time of realization. With that in mind, there were imagined two actions interrelated, two mappings which aim the rising and understanding of these difficulties of an epistemological nature in the teaching of Calculus: a conceptual mapping of Calculus and of its ideas and basic procedures; next, having these instruments, the mapping of the previously mentioned difficulties was effectively done. Thus, from the interlacement of the historical and pedagogical facts, and having as background the essential dualities and the conceptual maps of Calculus, there were clarified and consubstantiated five macro spaces of the difficulties in learning of an epistemological nature, five axes which structure the teaching of Calculus, namely: the axis discreet/continuous; the axis variability/permanence; the axis finite/infinite; the axis local/global; and the axis systematization/construction. In this philosophical endeavour there were established relations between the macro spaces determined by the historical and conceptual maps of Calculus, and from these with the teaching of mathematics in all levels. Therefore, one can notice, essentially, a single point of origin in the difficulties in the learning of an epistemological nature in the teaching of Calculus: the omission/avoidance of the basic ideas and the construction problems of Calculus in the teaching of mathematics in an ample sense. So, to break up with the semantic isolation, the underestimation of the relevance of the ideas and of the instruments characteristics of Calculus, some didactic interventions are proposed in the field of the basic teaching of Mathematics and in the teaching of Calculus itself. What is expected from this is to allow Calculus to have in the pedagogical field the same function of integration that it had in the scientific field, in the process of building the mathematical knowledge.

Made available in DSpace on 2016-04-27T18:12:25Z (GMT). No. of bitstreams: 1 Daniella Sampaio Zorzi.pdf: 314112 bytes, checksum: 0247348e3a50c360b7b142fd75698c0d (MD5) Previous issue date: 2007-10-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Introduction: In recent years, the enormous demand of children and adolescents who present some type of problem in their learning process has configured as a public health issue. However, in the speech language pathology evaluations it was proven that most of the difficulties faced in these cases was not connected to a specific language disturb. It implies to say that the pedagogical performance, below the expected, it is more related to a restriction to the social uses of reading and the writing. In other words, related to a low degree of literacy. We talk about a multifaceted problematic that crosses the different sectors of the society, in special the health and the education. Having said that, a better approach of the health professionals with the school universe is necessary in order to lead us torwards the promotion of intersector intervention strategies and have the problematic confrontation more effective. Objective: to identify and to analyze how the educators of the Nuses and the professors of Elementary school of the public net in Jaguaré deal with the difficulties of learning in their classrooms. Method: For data survey the focal group technique was used. Two focal groups were developed, being one formed by four Nuse s educators (two from Nuse Santa Cruz and two from Nuse Bom Jesus) and another one formed by seven teachers of the same school, which possesss a significant number of pupils who also go to the Nuses. The discussion flow was semi-structured and the meeting had a two hour duration and was recorded in cassette for posterior transcription and analysis. Results: In general way, both groups relate the difficulties of learning with organic causes and perceive its existence through changes in the pupils behavior. The family and the current system of education in public schools have been cited as factors that influence directly in this problematic and were the main point of critical by the participants. In spite of mentioning and considering the condition of life of their pupils and the lack of access to cultural information they present, both groups did not relate such questions to the learning difficulties. Another relevant aspect taking into consideration was the lack of feedback on the part of the different professionals of the health area on the referrals carried through them, considered as determinant to guide their practical in classroom. It was also noticed the influence of speech language pathology assessorship developed in the Nuses by the educators answers and the way they faced the learning difficulties. Conclusion: The different sectors still function in disarticulated way, what restricts the reaching power of its action. The construction of partnerships between the different sectors is essential, in order to weave care and protection nets in the attempt of crossing the actions of learning difficulties confrontation, increasing their reach and potentiality / Introdução: Nos últimos anos, a grande demanda de crianças e adolescentes que apresentam algum tipo de problema em seus processos de aprendizagem tem se configurado como uma questão para a saúde pública. No entanto, nas avaliações fonoaudiológicas evidenciou-se que a maior parte das dificuldades enfrentadas nesses casos não estava atrelada a um distúrbio específico de linguagem. Isto implica dizer que o desempenho pedagógico abaixo do esperado pode ter mais relação com uma restrição referente aos usos e funções sociais da leitura e da escrita, ou seja, com um baixo grau de letramento. Trata-se de uma problemática multifacetada que perpassa os diferentes setores da sociedade, em especial a saúde e a educação. Visto isso, para que o enfrentamento de tal problemática seja mais efetivo, torna-se necessária uma aproximação maior dos profissionais da saúde com o universo escolar para que possamos caminhar em direção à promoção de estratégias de intervenção intersetoriais. Objetivo: Identificar e analisar como as educadoras dos Nuses e os professores do Ensino Fundamental I de uma escola da rede pública de ensino da região do Jaguaré, lidam com as dificuldades de aprendizagem em suas salas de aula. Método: Para levantamento dos dados foi utilizada a técnica do grupo focal. Foram desenvolvidos dois grupos focais, sendo um com as quatro educadoras dos Nuses (duas do Nuse Santa Cruz e duas do Nuse Bom Jesus) e outro com sete professoras de uma mesma escola da região, a qual possui um número significativo de alunos que também freqüentam os Nuses. O fluxo de debate foi semi-estruturado e o encontro teve duração aproximada de duas horas e gravado em fita cassete para posterior transcrição e análise. Resultados: De modo geral, ambos os grupos relacionam as dificuldades de aprendizagem com causas orgânicas e percebem sua existência por meio de mudanças de comportamento de seus alunos. A família e o atual sistema de ensino das escolas públicas foram citados como fatores que influenciam diretamente nessa problemática e foi alvo de críticas das participantes. Apesar de mencionar e considerar como dado relevante as condições de vida de seus alunos e a falta de acesso a meios culturais que muitos apresentam, nos dois grupos não relacionou-se tais questões às dificuldades de aprendizagem. Outro aspecto relevante levantado foi a falta de devolutiva por parte dos diferentes profissionais da área da saúde sobre os encaminhamentos realizados por elas, considerada como determinante para orientar suas práticas em sala de aula. Notou-se ainda a influência da assessoria fonoaudiológica desenvolvida nos Nuses nas respostas das educadoras e na forma de se posicionarem frente às dificuldades de aprendizagem. Conclusão: Os diferentes setores ainda funcionam de forma desarticulada, o que restringe o alcance de suas ações. É essencial a construção de parcerias entre os diferentes setores, tecendo redes de cuidado e de proteção na tentativa de se transversalizar as ações de enfrentamento das dificuldades de aprendizagem, aumentando seu alcance e sua potencialidade

As dificuldades de aprendizagem matemática constituem um campo bastante complexo e ainda relativamente pouco explorado. Pesquisas com síndromes associadas ao baixo desempenho matemático indicam que há diferentes perfis cognitivos subjacentes às dificuldades na matemática e nos mostram que nem toda dificuldade de aprendizagem matemática é originada da mesma maneira. Esta dissertação de mestrado apresenta dois estudos de caso: um realizado com estudante com Síndrome do X-Frágil e o outro com estudante com Síndrome de Prader-Willi. O objetivo foi investigar e compreender a aquisição dos princípios e procedimentos de contagem numérica e recuperação de fatos aditivos da memória em cada estudante. Os dados foram obtidos a partir de análise documental, observações em sala de aula e no espaço escolar e aplicação de tarefas para investigação do senso numérico, dos princípios e procedimentos de contagem e da recuperação de fatos aditivos da memória. Os resultados obtidos indicaram que os sujeitos pesquisados apresentam lentidão no processo de aprendizagem, especialmente na construção dos princípios da contagem numérica, falhas no desenvolvimento do senso numérico e não utilizaram recuperação dos fatos aditivos da memória. As implicações educacionais resultantes deste estudo, principalmente no que diz respeito à educação inclusiva, determinam a necessidade de um novo olhar para o processo de inclusão de estudantes com diferentes síndromes em salas de aulas regulares, pois suas características cognitivas e comportamentais indicam que a inclusão por si só não garante o sucesso escolar. / The difficulties in learning mathematics are a very complex field and still relatively unexplored. Researches of syndromes associated with low mathematical performance indicates that different cognitive profiles underlie math learning difficulties and show us that not all of these difficulties have the same origins. This dissertation presents two case studies: one with Fragile X Syndrome (FXS) and another with Prader-Willi Syndrome (PWS). The objective was to investigate and understand the acquisition of the principles and procedures of numerical count and recovery additive facts from memory in each student. The data obtained were from documental analysis, observations in the classroom and in the school playground and applying tasks to investigate the number sense, the principles and procedures of numerical count and recovery additive facts from memory. The results indicated that the subjects studied show slow learning process, especially in the construction of the principles of counting, flawed development of number sense and did not recovery additive facts from memory. The educational implications, particularly in inclusive educations, determine a new look at the process of students with different syndromes in regular classrooms because their cognitive behavioral characteristics indicate that the inclusion only does not guarantee school success.

The low grades that students score in some statistical units in Kenyan universities is of great concern and has evoked research interest in the teaching of some of the units and the students’ learning of the statistical content. The aim of the study was to investigate the difficulties undergraduate students experience in the learning of bivariate normal distribution in a Kenyan university. The research also aimed to answer the following research questions on the difficulties undergraduate students encounter in the learning of bivariate normal distribution. The first research question was based on the reasons why students find learning of bivariate normal distribution difficult and the second research question was to find the reasons why students experience such difficulties in learning bivariate normal distribution. The target population for this study included lecturers teaching statistics in the university, and second- and third- year students enrolled or who have previously completed the probability and statistics III unit, where the bivariate normal distribution content is covered. In selecting students for the study, the simple random sampling technique was employed while convenient sampling was used to select lecturers who participated in the study. A mixed methods design was adopted for this study where both quantitative and qualitative data was collected. A total of 175 students and six lecturers participated in this research study. All students who participated in the study did a bivariate normal distribution test (Appendix 1) designed by the researcher and then filled in a questionnaire (Appendix 2). The lecturers who participated in the study filled in an open-ended questionnaire (Appendix 3). The results showed that undergraduate students have difficulties in learning bivariate normal distribution. This is because most of them could neither state the bivariate normal distribution nor solve any of the application questions on the content. The students find it difficult to learn and comprehend the bivariate normal distribution equation with its many parameters and constants of the two random independent variables. The results also showed that students could not state the normal distribution equation nor could they solve questions on the normal distribution, which forms the foundational knowledge required for effective learning of the bivariate normal distribution content. ii Based on the results, the study recommended that emphasis should be placed on the basic and foundational knowledge of the normal distribution content and its applications before teaching bivariate normal distribution in probability and statistics III. In addition, it is recommended that all students should be involved in the learning of basic content to enable them to understand all parameters and constants in the equations and their applications. The study also recommends that lecturers revise the foundational knowledge and content related to the bivariate normal distribution before introducing and teaching the bivariate normal distribution content. This study also recommends that the university should consider a change of curriculum by teaching the bivariate normal distribution, as an introductory course to the unit under the multivariate distributions in statistics, in third year of the students’ studies. ; ; / Mathematics Education / M. Sc. (Mathematics Education)

Made available in DSpace on 2016-06-02T20:02:55Z (GMT). No. of bitstreams: 1 6206.pdf: 2317505 bytes, checksum: cb846c0c5d86493651d0c1474738386e (MD5) Previous issue date: 2013-12-16 / The demotivation observed in the students concerning Physics led to the searching for a theoretical referential which could guide this pedagogical work. So, one understands the importance of Science teaching that contributes to a full formation of a conscious citizen that knows how to use their scientific knowledge with social responsibility. One looked for understand the difficult presented in the process of teaching and learning of Physics, focusing mainly in its important relation with Mathematics. For this, supported by PCN, it was analyzed the relation existing between the abilities and competences used in Math and Physics teaching. One also considered in the research, the different stages existing in Science learning, from which one understood the necessity of reaching the multidimensional stage in our schools. From this view, and supported by bibliographic references, it was pointed the existence of four main difficulties presented in the learning process of this subject. They are the difficulties inherent to Physics teaching, which started with the exceeding, premature and almost exclusive use of Math. There are also difficulties arising from Math learning that affect the learning of Physics. The difficulties from Portuguese language domain presented by students when reading, writing and interpreting scientific texts, limit the qualitative understanding of the subject and consequently, its conceptual understanding can be impaired. The existence of epistemological barriers, which arise from the different approaches of its own conceptual body also influence negatively the teaching and learning process of Physics. Supported by this perspective, the following question was done: What should one has to learn to teach, so the classes of Science, Physics and its integration with Math can make the knowledge more significant and, so that, multidimensional stage could be reached? The bibliographic analysis led to work in a theoretical basis with The Mental Models from Johnson-Laird . Using this theoretical support, it was elaborated and applied a didactic sequence, which was developed considering the difficulties in learning that were analyzed in this work. It was looked for understanding qualitatively the results obtained with the application of this didactic sequence. This process led to the elaboration of some topics, which were considered to be relevant in the preparation of a pedagogical activity for the teaching and learning process to be really relevant and, thus, contribute with a full citizen formation and a truly significant learning. / A desmotivação observada nos alunos em relação ao ensino da Física conduziu a busca de um referencial teórico que pudesse orientar este trabalho pedagógico. Entende-se a necessidade e importância de um ensino de ciências que contribua para uma formação plena de um cidadão consciente e que saiba usar o seu conhecimento científico com responsabilidade social. Buscou-se, então, compreender as dificuldades apresentadas no processo de ensino-aprendizagem da disciplina de Física, tendo como foco principal sua importante relação com a Matemática. Para isso, com o amparo dos PCN, foi analisada a relação existente entre as habilidades e competências trabalhadas no ensino da Matemática e da Física. Também considerou-se nessa pesquisa os diferentes estágios existentes na aprendizagem de ciências, a partir dos quais foi possível compreender a necessidade de alcançar nas escolas o estágio multidimensional. Partindo desta ótica, e com base na referência bibliográfica, aponta-se a existência de quatro dificuldades principais presentes no processo ensino aprendizagem dessa disciplina. São dificuldades inerentes ao ensino da Física que se originam no demasiado uso precoce e quase exclusivo da Matemática no ensino. Também há dificuldades provenientes da Matemática, cuja transferência das dificuldades oriundas de sua aprendizagem para a aprendizagem em Física assume o papel principal. As dificuldades provenientes do domínio da Língua Portuguesa, apresentadas pelos alunos ao ler, escrever e interpretar textos científicos, limitam a compreensão qualitativa da matéria e, consequentemente, o entendimento conceitual da disciplina de Física fica comprometido. A existência de barreiras epistemológicas que surgem nas diferentes abordagens feitas no próprio corpo conceitual da Física também influenciam de forma negativa o seu processo ensino-aprendizagem. Apoiando-se nesta perspectiva, questionou-se o seguinte: O que se deve aprender a ensinar para que, de fato, as aulas de ciências exatas, a física e sua integração com a matemática, em particular, tornem o conhecimento mais significativo e o estágio multidimensional possa ser atingido? A análise bibliográfica conduziu a um trabalho tendo por base teórica principal Os Modelos Mentais de Johnson-Laird . Com o auxílio deste suporte teórico, elaborou-se e aplicou-se uma sequência didática que foi desenvolvida, considerando as dificuldades de aprendizagem citadas e analisadas neste trabalho. Buscou-se compreender qualitativamente os resultados obtidos com a aplicação dessa sequência didática. Esse processo conduziu à elaboração de alguns tópicos que se considerou serem de muita relevância na preparação de uma atividade pedagógica para que o processo de ensino-aprendizagem seja realmente relevante e venha contribuir com uma formação cidadã plena e uma aprendizagem realmente significativa.