Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-12-05T13:17:27Z No. of bitstreams: 1 Herica Cambraia Gomes.pdf: 5659818 bytes, checksum: bab407a2e9635d11c447b020893b9bad (MD5) / Made available in DSpace on 2017-12-05T13:17:27Z (GMT). No. of bitstreams: 1 Herica Cambraia Gomes.pdf: 5659818 bytes, checksum: bab407a2e9635d11c447b020893b9bad (MD5) Previous issue date: 2017-10-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / With the advancement of neuroscience, we find ourselves in a promising moment for inclusive mathematics, which has significant repercussion in the learning of the Decimal Numbering System, mainly in the associative aspects of mathematical cognition and psychomotor stimulation as inseparable in the body and mind relation. Musicality is presented as an innate process, in a construct of elements that encompass Corporeity, Rhythm and Sound, as a possibility of a new teaching strategy. Therefore, this investigation chose to identify teacher’s perception by elaborating, developing and analyzing teaching experiences of the Decimal Numbering System with Musicality in the first two years of Primary Education. The theoretical anchorage in composed of concepts that unfold into triads deriving from Neuroscience (SNARC effect, Numerical Route and Numerical Reasoning), Executive Functions (Voluntary Attention, Operational Memory and Inhibitory Control), Musicality (Corporeity/Watchful Hearing; Movements/Rhythms; and Qualities/Sound) and Teaching Mediation (Intentionality/Reciprocity. Meaning and Transcendence). The research, using a qualitative method, unfolds itself into practical activities, analyzed from the contributions of Musicality in the Decimal Numbering System teaching, into the curriculum and into teaching mediation. The results showed three improvements in teaching: 1) Voluntary Attention and Operational Memory brought by Musicality through watchful hearing projected in the Counting and in the Mental Calculation accomplished by the students, without distinction; 2) the development of the Corporeity and Musicality Scheme for Mental Calculation, in which the representation of the numerical writing comes from the Global Praxis, following systematized, coordinated, enlarged and ascending steps; and 3) the accomplishment of Mental Calculation during the Musicality activities that associate numbers and pulses, tones of musical instruments and mathematical operations, working as a process of evaluating Decimal Numbering System learning. The teacher’s self-evaluation elected studying practice, autonomy and creativity as the main influences of Musicality in the teaching performance; the teachers pointed out, also, the perspective of “error” as a boosting mechanism for the learning process and the respect of individual times as an inclusive practice of Mathematics Teaching / Com o avanço da neurociência, encontramo-nos em momento promissor na educação matemática inclusiva, com significativas repercussões na aprendizagem do Sistema de Numeração Decimal, sobretudo nos aspectos associativos da cognição matemática e estimulação psicomotora como indissociáveis na relação corpo-mente. A Musicalidade é apresentada como processo nato, em um constructo de elementos que envolvem Corporeidade, Ritmo e Som, como possibilidade de nova estratégia de ensino. Neste sentido, esta investigação optou por analisar as contribuições da Musicalidade no ensino do Sistema de Numeração Decimal por meio da identificação de percepções de professores nos dois anos iniciais do ensino fundamental, ao elaborarem, desenvolverem e analisarem experiências de ensino do Sistema de Numeração Decimal utilizando a Musicalidade. A ancoragem teórica é composta por conceitos, que se desdobram em tríades, advindos da Neurociência (Efeito SNARC, Rota Numérica e Senso Numérico), das Funções Executivas (Atenção Voluntária, Memória Operacional e Controle Inibitório), da Musicalidade (Corporeidade/Escuta Atenta; Movimentos/Ritmos; e Qualidades/Som) e da Mediação Docente (Intencionalidade/ Reciprocidade, Significado e Transcendência). A pesquisa, de abordagem qualitativa, exploratória e descritiva, configura-se com desdobramentos em atividades práticas, analisadas a partir de contribuições da Musicalidade no ensino do Sistema de Numeração Decimal, no Currículo e na Mediação Docente. Os resultados apontaram três evoluções no ensino: 1) a Atenção Voluntária e a Memória Operacional desencadeadas pela Musicalidade por meio da Escuta Atenta projetadas na Contagem e no Cálculo Mental realizados pelos alunos, sem distinção; 2) o desenvolvimento do Esquema de Corporeidade da Musicalidade para o Cálculo Mental, no qual a representação da escrita numérica parte da Praxia Global, obedecendo a etapas sistematizadas, coordenadas, ampliadas e ascendentes; e 3) a realização do Cálculo Mental durante as atividades de Musicalidade, que associam números e pulsos, timbres de instrumentos musicais e operações matemáticas, funcionando como processo de avaliação da aprendizagem do Sistema de Numeração Decimal. A autoavaliação das professoras elegeu a prática de estudos, a autonomia e a criatividade como principais influências da Musicalidade na performance docente; as docentes apontaram, também, a perspectiva do “erro” como mecanismo impulsionador do processo de aprendizagem e o respeito aos tempos individuais como prática inclusiva da educação matemática

Made available in DSpace on 2016-04-27T16:57:31Z (GMT). No. of bitstreams: 1 Silvana Ferreira de Lima.pdf: 3664030 bytes, checksum: 179f942da48e1137ee6520f842db36fd (MD5) Previous issue date: 2014-05-20 / This research aims to analyze how teachers working in the first years of elementary school at the State Network Paulista interpret and put into practice the different types of teaching guidelines, presented in curriculum materials to support the teacher and understand how to use these materials extend the numerical knowledge of their students. Given this goal, we turn our discussion to the curriculum proposed changes to the discipline of mathematics in the first years of elementary school, implemented by the Secretary of Education of São Paulo under the Project in Mathematics Education in Early Years ( EMAI ), started in 2012. This is a qualitative research based on the analysis of questionnaires, interviews and audio recordings of lessons four teachers, two teachers of the 3rd year and two in the 5th year in the first years of elementary school. We were able to identify the occurrence of different types of material usage by teachers, listed by Brown (2009 ), adaptation, reproduction and creation. To some extent, at different moments of the performance, they now reproduce, adapt and pray more rarely " create ". We consider the adaptation was more frequent use during practices observed being motivated by beliefs and conceptions that teachers have regarding the content and teaching of this discipline. The objectives in relation to learning of natural numbers and the decimal system were achieved with greater and lesser success according to knowledge of each to articulate/exploit the resources of material. The results show that it is not enough to recognize the existence of the relationship or the elements that shape, but it is necessary to emphasize that the material should be object/feature of these professionals, deepening both the mathematical content involved as didactic knowledge to thereto / A presente pesquisa tem como objetivo analisar como os professores que atuam nos Anos Iniciais do Ensino Fundamental da Rede Estadual Paulista interpretam e colocam em prática os diferentes tipos de orientações didáticas, apresentados nos materiais curriculares de apoio ao professor e entender, como utilizam esses materiais para ampliar os conhecimentos numéricos de seus alunos. Diante deste objetivo, voltamos nossas discussões às mudanças curriculares propostas para a disciplina de Matemática dos Anos Iniciais do Ensino Fundamental, implementadas pela Secretaria da Educação de São Paulo no âmbito do Projeto de Educação Matemática nos Anos Iniciais (EMAI), iniciado em 2012. Trata-se de uma pesquisa qualitativa, fundamentada na análise de questionários, depoimentos e áudio gravações de aulas de quatro professoras, sendo duas professoras do 3º ano e duas do 5º ano dos Anos Iniciais do Ensino Fundamental. Pudemos identificar a ocorrência de diferentes tipos de uso do material pelas professoras, elencados por Brown (2009), a adaptação, a reprodução e a criação. Em certa medida, em diferentes momentos da atuação, elas ora reproduzem, ora adaptam e mais raramente criam . Consideramos que a adaptação foi o uso mais frequente durante as práticas observadas sendo motivadas pelas crenças e concepções que as professoras possuem em relação ao conteúdo e ao ensino desta disciplina. Os objetivos em relação à aprendizagem dos números naturais e do sistema de númeração decimal foram alcançados com maior e menor êxito de acordo com conhecimentos de cada uma para articular/explorar os recursos do material. Os resultados apontam que, não basta reconhecer a existência da relação ou os elementos que a configuram, mas é necessário destacar que o material deve ser objeto/recurso de formação desses profissionais, aprofundando-se tanto os conteúdos matemáticos envolvidos como os conhecimentos didáticos a eles referentes

This thesis discusses inquiry-based education in mathematics aimed at the decimal system and large numbers in elementary school environment. Inquiry-based education is a form of education that uses exploration or verification of new findings by the students themselves. The principles and basic characteristics of inquiry-based education are discussed in the theoretical part. The practical section is based on qualitative research. Data collection and analysis of results in 5 experiments in two parallel 5th grade classes are used to determine the characteristics of inquiry-based education and to discover the possible problematic occurrences, which could be encountered with this kind of education. Based on this information, recommendations for practical use are formulated. Results have shown that inquiry-based education in mathematics classes is beneficial to the students. Although greater care in selecting the right exercise and rigorous preparation of the teachers and teaching aids is required, implementation of this education is worth the effort. It represents an untraditional variegation for the students, by which they can calmly educate themselves and consolidate their knowledge.

Vad denna utvärdering försökt få svar på är hur tillgängligheten för HBT-litteratur ser ut i de system som används hos privata och offentliga aktörer – internetbokhandlar och bibliotekskataloger tillgängliga via internet. Detta medförde ett antal mer praktiskta underliggande frågor om hur trädstrukturen är designad, vilket typ av språk som används och hur lätt det är att förstå, huruvida det finns särskilda kategorier för litteratur med HBT-innehåll och huruvida det finns direktlänkar mellan litteratur med HBT- innehåll. De system som testades var internetbokhandlarna Amazon (både den amerikanska versionen och det brittiska dotterbolaget), The Book Depository och Adlibris samt de klassificeringssystem som används av nationalbiblioteken i de länder där dessa bokhandlar har sitt säte (USA, Storbritannien och Sverige): Library of Congress Classification, Dewey Decimal Classification och Klassifikationssystem för svenska bibliotek. Två av bibliotekssystemen (LC och DDC) hade inte en trädstruktur som var tillgänglig för kunderna att se och navigera igenom, medan den tredje (SAB) erbjöd en struktur med både klassifikationskoden och svenska ord, även om det inte var optimalt konstruerade kategorier och förgreningar. Ingen av dem hade gott om länkar, om ens några, till annan litteratur med liknande innehåll. Internetbokhandlarna hade välutvecklade men inte för specifika trädstrukturer med lättförstådda namn och gott om länkar till annan litteratur. Två av dem (The Book Depository och Adlibris) hade inga huvudkategorier tillägnade HBT-material vilket däremot Amazon UK och Amazon US hade. Alla bibliotekssystemen skulle behöva omarbetas för att tillgängligheten för litteratur, och i synnerhet HBT-litteratur som var fokus i denna utvärdering, ska bli god. Library of Congress och British Library skulle behöva upprätta trädstrukturer för kunderna att använda sig av och alla tre behöver se till att en kategori där all HBT- litteratur samlas finns på den högsta nivån. Internetbokhandlarna å andra sidan behöver inte göra mycket för att tillgängligheten i deras system ska bli god: Adlibris och The Book Depository behöver precis som bibliotekssystemen upprätta en HBT-kategori i trädstrukturen men i övrigt är de privata aktörerna fullt godkända. De båda Amazon- filialerna var de aktörer visade sig ha den bästa tillgängligheten av alla. / What this investigation has tried to find out is how easily availabie LGBT literature is in the systems that are used by private companies and the public sector - online book shops and library catalogues available online (OPACs). This entailed a number of more practical underlying factors regarding the design of the tree structure, what kind of language is used and how easy it is to understand, whether or not there are special categories for LGBT-related literature and whether or not there are direct links between literature with LGBT content. The systems investigated were the online book shops Amazon (both the American version and the British subsidiary), The Book Depository and Adlibris along with the classification systems used by the national libraries in the countries where these book shops reside (the US, the UK and Sweden): Library of Congress Classification (LC), Dewey Decimal Classification (DDC) and Klassifikationssystem för svenska bibliotek (SAB). Two of the library systems (LC and DDC) did not have a tree structure available for the customers to see and navigate through, while the third one (SAB) offered a structure with both the classification code and Swedish words explaining what the codes meant, even if the categories and subdivisions were not optimally constructed. None of them had very many links to other literature. Two of them (The Book Depository and Adlibris) did not have main categories specifically for LGBT content which both Amazon US and Amazon UK did. All the library systems could use a revision to ensure that literature, and particularly LGBT literature as that was the focal point of this investigation, is easily available. The Library of Congress and the British Library need to establish a tree structure their clients could use and all three need to make sure they have a category where LGBT literature is collected and available at the root. The online book shops on the other hand do not need to do much to improve the availability of their systems: like the library systems, Adlibris and The Book Shop need to create a category of LGBT literature in the tree structure but besides that the private companies pass with credit. The systems used by the Amazon branches proved to have the greatest availability of all the systems investigated.

Den här licentiatuppsatsen handlar om hur en undervisning kan främja elevers förståelse av tiobassystemet genom att de bjuds in till en undervisning där de kan delta i ett kollektivt utforskande av bassystemet, som en övergripande nivå av tiobassystemet. Syftet är att exemplifiera och diskutera hur en undervisning, som främjar elevernas möjligheter att utveckla ett tänkande om tiobassystemet på en generell eller övergripande nivå, kan utformas. Vidare är syftet att studera vad i en undervisning, designad enligt principerna för lärandeverksamhet, som kan förstås som förebyggande i specialpedagogisk mening. Studien bygger på resultatet av två artiklar med följande frågeställningar: 1) Vilka aspekter i uppgifternas utformning och genomförande främjar elevers möjligheter att pröva relationen mellan olika bastal och övergång till successivt större respektive mindre talenheter? 2) Vad i elevernas resonemang och arbete med speciellt designade uppgifter kan ses som tecken på teoretiskt tänkande om bassystemet? Learning study har använts som forskningsramverk och genererat data för uppsatsens två artiklar. Learning studyn genomfördes i årskurs 4, tillsammans med tre matematiklärare. Design och analys är inspirerad av El’konins och Davydovs matematiska program och några principer från lärandeverksamhet. Analysen i de bägge artiklarna är genomförd med stöd av teoretiska principer för lärandeverksamhet. Datamaterialet består av videoinspelningar från tre lektioner (totalt cirka 420 minuter), transkriptioner och datasammanställningar av uppgifter, transkriptioner och anteckningar från utvärderingarna i det iterativa arbetet med lektionerna. Resultatet består av tre aspekter som behöver synliggöras genom uppgifternas utformning och genomförande för att eleverna ska kunna arbeta teoretiskt med bassystemets struktur: (1) Bastalet, (2) Tal som mätetal, och (3) Talenheternas representationer. Eleverna behöver urskilja aspekterna för att kunna identifiera att det fattas en lämplig talenhet och för att kunna pröva och reflektera över relationen mellan bastalet och övergången till successivt större respektive mindre talenheter i olika baser. Resultatet består också av ett antal exempel på tecken på teoretiskt tänkande inom tre identifierade kategorier: 1) basens funktion för det värde som siffrorna anger i talet, 2) positionsväxling, och (3 entalet som ett av en kvantitet. I analysen har Davydovs definition av teoretiskt tänkande, som något som kan komma till uttryck i form av teoretisk reflektion, analys och planering samt reproduktion av grundläggande principer för ett specifikt ämnesinnehåll, använts. Resultatet ger ett bidrag till den matematikdidaktiska forskningen och till den specialpedagogiska forskningen med inriktning mot matematik genom beskrivningar av de tre aspekterna och av tecken på teoretiskt tänkande. Vidare kan beskrivningarna av uppgifternas utformning och genomförande användas i undervisning och i fortsatta studier. I diskussionen behandlas hur en undervisning kan utformas som främjar elevernas möjligheter att utveckla ett teoretiskt tänkande om bassystemet. Diskussionen behandlar också vad i en undervisning designad enligt principerna för lärandeverksamhet som kan förstås som förebyggande i specialpedagogisk mening genom att skapa möjligheter för elever att redan tidigt i grundskolan kollektivt utforska och förstå hela positionssystemet som en struktur. Slutligen diskuteras implikationer för specialundervisning och studiens bidrag. / The subject of this licentiate thesis is about how a teaching can promote students' understanding of the base-ten system by inviting them to a teaching where they can collectively explore the base system, as an overall level of the base-ten system. The aim is to exemplify and discuss how teaching, which affords students opportunities to develop thinking about the base-ten system on a general or overall level, can be designed. Furthermore, the aim is to study teaching designed according to the principles of learning activity in terms of how it can be preventive from a special pedagogical perspective. The study is based on the results of two articles with the following questions: 1) Which aspects in the design and implementation of the tasks afford students opportunities to explore the relationship between different base numbers and the transition to successively larger and smaller number units? 2) What in the students' reasoning and work with specially designed tasks can be seen as signs of theoretical thinking about the base system? Learning study has been used as a research framework and generated data for the two articles. The learning study was carried out in year 4, together with three mathematics teachers. Design and analysis are inspired by El’konin’s and Davydov’s mathematical program and some principles from learning activity. The theoretical principles for learning activity were used as tools for analysis. Data consists of video recordings from three lessons (in total approximately 420 minutes), transcriptions and data compilations of tasks, transcriptions, and notes from the evaluations in the iterative work with the lessons. The results consist of three aspects that need to be made visible through the design and implementation of the tasks so that the students can work theoretically with the structure of the base system: (1) The base number, (2) Number as a measurement number, and (3) The representations of the number units. The students need to distinguish the aspects in order to discern that a bigger or smaller number unit is missing and to test and reflect on the relationship between the base number and the transition to successively larger and smaller number units, constructed in different bases. The result also includes several examples of signs of emerging theoretical thinking within three identified categories: 1) the bases function to the digits´ value in the number, 2) position switching, and (3) the unit as one of a quantity. In the analysis, Davydov's definition of theoretical thinking, as something that can be expressed in the form of theoretical reflection, analysis, and planning as well as the reproduction of fundamental principles for specific subject content, has been used. The results contribute to mathematics didactic research and to special educational research with a focus on mathematics through descriptions of the three aspects and signs of theoretical thinking. Further the descriptions of how tasks can be designed and carried out be used in teaching and continued research. The discussion deals with how teaching can be designed that afford student opportunities to develop theoretical thinking about the base system. The discussion also deals with what in a teaching designed according to the principles of learning activity can be understood as preventive in a special pedagogical perspective, by creating opportunities for students to collectively explore and understand the entire position system as a structure already early in elementary school. Finally, implications for special education and the contribution of the study are discussed. / <p>Sammanläggningen i Pdf innehåller båda artiklarna. </p>

Made available in DSpace on 2016-04-27T16:58:15Z (GMT). No. of bitstreams: 1 Elenice de Souza Lodron Zuin.pdf: 5274197 bytes, checksum: a63234162ca31e57f17e683cbb5f4f15 (MD5) Previous issue date: 2007-05-28 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This study fits into the field of the History of School Disciplines. Our objective is to find how the introduction of the metric system into Brazil and Portugal in the second half of the nineteenth century came about. This new knowledge had to be integrated into the general education system in order to adhere to the legislation of both countries. The renovation led to changes in school Arithmetic, not only due to the inclusion of a new system of weights and measurements, but also to other content, such as decimal numbers. Our main sources were Portuguese and Brazilian school printed material published in the eighteen hundreds. With regard to the methods used to incorporate the metric decimal system, we can affirm that the period of study constitutes a transition phase during which diverse publications and methodologies abounded in an attempt to establish a model. We show that incorporation of the new knowledge does not occur in the same manner in all schools, even though these may follow the same guidelines and didactic texts, nor does it occur straight away due to the fact that school culture needs time to adapt to the changes imposed, giving it new meaning. We conclude that during the period studied, certain bases were established for the disciplinarization of the metric decimal system and for the changes which took place in the teaching of Arithmetic in primary schools / Este estudo se enquadra no campo da Historia das Disciplinas Escolares. Objetivamos verificar como ocorreu a introdução do sistema métrico em Portugal e no Brasil na segunda metade do século XIX. Esse era um novo saber que deveria se integrar à formação geral para o cumprimento da legislação nos dois países. A reforma provocou alterações na Aritmética escolar, não só pela inclusão do novo sistema de pesos e medidas, mas, também, de outros conteúdos, como os números decimais. Nossas principais fontes foram os impressos escolares portugueses e brasileiros publicados nos Oitocentos. Em relação ao modo de incorporar o sistema métrico decimal, constatamos que, o período estudado constituiu-se em uma fase de transição, na qual diversas publicações e meto-dologias distintas circularam na tentativa de se fixar um modelo. Comprovamos que a incorporação de um saber não ocorre da mesma maneira em todas as escolas, ainda que sejam seguidos os mesmos textos didáticos e as mesmas orientações, e nem se dá de forma imediata, porque a cultura escolar necessita de um tempo para apropriar-se do que lhe é imposto, dando-lhe novos significados. Concluímos que, no período estudado, se estabeleceram algumas bases para a escolarização do sistema métrico decimal e para as alterações que deveriam ocorrer no ensino de Aritmética nas escolas primárias