This study examines the teaching and early learning of addition in primary classrooms. The relationship between teaching and learning is examined at the level of classroom interaction, in the completion of mathematical tasks. The mathematics lessons of two classes in each of two schools were observed over a period of six months, involving four teachers and the 4, 5 and 6 year old children in their classes. The mathematical focus of the study was the learning of addition, one of the first formal mathematical concepts taught in school. This formed a basis for exploring the factors involved in the teaching of mathematics to young children, and their learning. The methodology is qualitative, with participant observation the main method of data collection. Detailed fieldnotes were taken of all mathematics lessons observed; short unstructured interviews with teachers were carried out before and after the lessons. The children's understanding of number concepts and addition was assessed at both the beginning and the end of the observation period. The data was analysed using a grounded theory approach, which produced patterns of recurring variables. Analysis of these variables, influenced by the theoretical perspectives of the researcher, provided analytical pictures of teaching and learning, from which the findings emerged. The study highlights the complexity of the classroom for teachers and young children, where curriculum considerations, understanding of the mathematics concepts, social interaction and integration into the community of the classroom, vie for attention. It indicates that children are more likely to make sense of mathematics when the number curriculum is taught with a view to its complexity, rather than broken down into simple steps; the problems young children have learning to use mathematical symbols; and that the use of story is important in helping especially the youngest children understand mathematics. This was a small scale study, but provides a 'thick description' of teaching and early learning of addition, which can form a basis for future studies. Key Words: addition, early mathematical development, primary school, constructivism, socio-cultural theory, situated cognition, symbols, real world scripts, narrative.

Problem solving has received a great deal of attention in the past two decades. Much work has been carried out in the fields of cognitive psychology and education on the topic of problem solving. Psychologists mainly focused on the cognitive processes underlying problem-solving activities, while educators mainly focused on practical strategies to improve students’ problem-solving skills. The research studies carried out in these two fields were somewhat separate with different theoretical underpinnings. This thesis brings together the fields of cognitive psychology and education through the methodological advances of educational measurement developed to measure psychological constructs. More specifically, this thesis develops a theoretical framework for measuring problem-solving proficiencies, and applies item response theory to analyse students’ responses to the test items. (For complete abstract open document)

155 f. / Submitted by Suelen Reis (suziy.ellen@gmail.com) on 2013-05-06T17:06:04Z No. of bitstreams: 1 Dissertacao Robson Mattos.pdf: 755038 bytes, checksum: 9d4c08e94e86cb08fd9344b4cece3eb3 (MD5) / Approved for entry into archive by Maria Auxiliadora Lopes(silopes@ufba.br) on 2013-06-12T20:07:41Z (GMT) No. of bitstreams: 1 Dissertacao Robson Mattos.pdf: 755038 bytes, checksum: 9d4c08e94e86cb08fd9344b4cece3eb3 (MD5) / Made available in DSpace on 2013-06-12T20:07:41Z (GMT). No. of bitstreams: 1 Dissertacao Robson Mattos.pdf: 755038 bytes, checksum: 9d4c08e94e86cb08fd9344b4cece3eb3 (MD5) Previous issue date: 2009 / Este trabalho objetivou investigar, no cotidiano escolar de crianças de turmas do Ensino Fundamental I em uma escola da rede pública no município de Vitória da Conquista (BA), a relação dos Jogos com a construção dos conceitos Matemáticos. Este estudo de caráter qualitativo tem como respaldo teórico diversos autores, cujas produções trazem contribuições quanto aos Jogos e ao ensino da Matemática: Boyer (1974), Brenelli (1996), Brougère (2000), Chateau (1987), D‘Ambrósio (1998),Huizinga (2007), Kishimoto (2007), Kamii (2003a), Machado (1991a), Piaget (1975),Santos (2000), Vygotsky (1984), entre outros. Do ponto de vista metodológico, privilegiou-se a observação in loco, com registro fotográfico, entrevistas com as educadoras das turmas selecionadas para a pesquisa e um grupo focal, analisando como se estabelece a relação dos Jogos com o Ensino da Matemática. Destaca-se neste estudo a relação existente entre os Jogos e sua função pedagógica de aprendizagem no ensino da Matemática no contexto escolar, apresentando reflexões conceituais em torno desta relação. O estudo proporciona a compreensão da Matemática vivenciada em sala de aula, bem como possibilita a reflexão dessas educadoras sobre suas práticas pedagógicas. A análise dos achados da pesquisa possibilitou a identificação da importância pedagógica dos Jogos no Ensino da Matemática e sua contribuição na construção de conceitos nessa área, permitindo, também, a reflexão sobre a forma como os Jogos são trabalhados em sala de aula, onde, muitas vezes, são aplicados como jogos de exercícios e não como Jogos de construção. / Salvador

MATOS, Fernanda Cíntia Costa. O pedagogo e o ensino de matemática: uma análise da formação inicial. 2016. 143f. – Dissertação (Mestrado) – Universidade Federal do Ceará, Programa de Pós-graduação em Educação Brasileira, Fortaleza (CE), 2016. / Submitted by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2016-04-27T17:04:50Z No. of bitstreams: 1 2016_dis_fccmatos.pdf: 1350727 bytes, checksum: a99cc18251239d709017c3b9cd826065 (MD5) / Approved for entry into archive by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2016-05-04T11:31:10Z (GMT) No. of bitstreams: 1 2016_dis_fccmatos.pdf: 1350727 bytes, checksum: a99cc18251239d709017c3b9cd826065 (MD5) / Made available in DSpace on 2016-05-04T11:31:10Z (GMT). No. of bitstreams: 1 2016_dis_fccmatos.pdf: 1350727 bytes, checksum: a99cc18251239d709017c3b9cd826065 (MD5) Previous issue date: 2016 / Teacher training becomes ever more present in the field of educational research, it is by this professional requirement to present increasingly updated, either in relation to the content is the use of active methodologies. Therefore this study aimed to analyze the formation process of teachers for mathematics education in the early years of elementary school, presenting a development proposal, reflective training based on the Fedathi Sequence, the consolidation and improvement of such training. Our research locus were the classrooms of the subjects Mathematics Teaching during semester 2014.2, 2015.1 and 2015.2 and topics in mathematics education 2015.1 semester of Faculty of Education of the Federal University of Ceará (UFC). The subjects were the Faculty of Education students (evening-night), enrolled in these disciplines. As methodological resources use notes in the mentioned disciplines, as well as use of analysis of questionnaires and online forums. To support our studies we rely on studies of Nóvoa (1995) and (2009), Tardif (2002) and Gatti (2011). To help with inquiries and questions about the Teaching of Mathematics, we admitted him to Fiorentini (1995) and Lorenzato (2006) and Nacarato & Mengali (2009). As regards the formation of the teacher for teaching mathematics, we rely on the contributions of Curi (2004), Lima (2007) and Santos (2007), and finally, to support our proposal for extensive-reflective pedagogical training resort Sousa (2013). Indeed, we wish that the results contribute to a more solid formation with regard to undergraduate pedagogy, about the content and methods of mathematics in the early years of elementary school. / Os programas de formação de professor se faz cada vez mais presente no cenário das políticas públicas nacionais. Pesquisas educacionais, apontam a exigência desse profissional se apresentar cada vez mais atualizado, seja em relação aos conteúdos, ou nas metodologias ativas. Com efeito, o presente estudo teve como objetivo principal analisar o processo formativo dos pedagogos para o Ensino de Matemática nos anos iniciais do Ensino Fundamental, apresentando uma proposta de desenvolvimento da formação de forma reflexiva, fundamentada na metodologia de ensino Sequência Fedathi. Nosso lócus de pesquisa foram as salas de aulas das disciplinas Ensino de Matemática, durante os semestres 2014.2, 2015.1 e 2015.2 e Tópicos de Educação Matemática no semestre 2015.1 do curso de Pedagogia da Faculdade de Educação da Universidade Federal do Ceará-FACED/UFC. Os sujeitos da pesquisa foram os alunos do curso de Pedagogia (vespertino-noturno), regularmente matriculados nessas disciplinas. Como recursos metodológicos utilizamos observações nas disciplinas citadas, como também uso de análises de questionários e fóruns online. Para fundamentar nossos estudos nos apoiamos nos estudos de Nóvoa (1995) e (2009), Tardif (2002) e Gatti (2011). Para contribuir com indagações e questionamentos sobre o Ensino de Matemática, nos amparamos em Fiorentini, (1995) e Lorenzato, (2006) e Nacarato (2009). No que se refere à formação do pedagogo para o ensino da matemática, contamos com as contribuições de Curi (2004), Lima (2007) e Santos (2007), e, por fim, para fundamentar nossa proposta de formação pedagógica extensiva-reflexiva recorremos a Sousa (2013) e Souza (2015). Consideramos que os resultados encontrados contribuirão para uma formação mais sólida, no que se refere aos licenciandos de Pedagogia, acerca dos conteúdos e metodologias de Matemática para a melhoria do ensino nos anos iniciais do ensino fundamental.

Esta tese possui como tema a ética e a diferença na invenção de uma docência matemática em meio à vida, em uma perspectiva pós-estruturalista. Aproxima-se das contribuições teóricas de Deleuze, Foucault e autores afins para pensar a diferença a partir da repetição da escrita de si, tomada enquanto processo inventivo de uma docência. Durante os percursos da pesquisa, utiliza-se dos conceitos de univocidade em Deleuze para tratar da diferença e da ética em Foucault para desestabilizar prescrições das verdades das ciências da educação sobre a docência em matemática. Toma-se uma criação textual de autoria própria - o Vidário de Pendurela - composto por fragmentos escritos de uma docência em meio à vida, que se tornou corpo e produziu matéria de investigação para esta tese, a fim de realizar uma experimentação filosófica pela reescrita de si. O procedimento de pesquisa se deu de modo “amaneirado”, através de um movimento filosófico, uma experimentação de pensamento para pensar a singularidade produzida na escrita e na docência, que consistiu em reescritas de si a partir dos movimentos de recolhimento, colagem, raspagem e criação, ao repetir os escritos de Pendurela, em outro estilo de escrita, diferindo sentidos. Dessa maneira, mostrou-se a invenção de uma docência, utilizando os conceitos de devir, vontade de potência e univocidade para problematizar essa invenção pela reescrita. Ao colocar em funcionamento essa maneira de pesquisar, entendido como repetição da escrita de si, toma-se o mesmo como uma experimentação filosófica para pensar a singularidade produzida na escrita e na docência. / This thesis has as its theme the ethics and the difference in the invention of a mathematical teaching in midst of life, in a poststructuralist perspective. It draws on the theoretical contributions of Deleuze, Foucault and related authors to think about the difference from the repetition of self-writing, taken as an inventive process of teaching. During the course of the research, the concepts of univocity in Deleuze are used to deal with the difference and the ethics in Foucault to destabilize prescriptions of truths of education sciences about teaching mathematics. A textual creation of its own authorship – the Vidário de Pendurela - is taken composed of written fragments of a teaching in the midst of life, which became a structure and produced research material for this thesis in order to conduct a philosophical experimentation by self-rewriting. The research procedure happened in a “certain manner” through a philosophical movement, an experimentation of thinking about the singularity produced in writing and teaching. It consisted of self rewritings from the movements of recollection, collage, scraping and creation, repeating the writings of Pendurela, in another style of writing, differing senses. Thus, the invention of a teaching action is presented, using the concepts of becoming, willpower and univocity to problematize this invention by the rewriting. By putting this manner of searching into practice, recognized as repetition of self-writing, it is possible to understand this process as a philosophical experimentation to think the singularity produced in writing and teaching.

Submitted by MARINALDO ZAGO null (mzmarinaldozago@gmail.com) on 2016-02-24T01:20:19Z No. of bitstreams: 1 Dissertação Mestrado Marinaldo 2016 (Revista) (2).pdf: 1340836 bytes, checksum: ddd4c0614476082a2b54f2c78a5a9188 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-02-24T16:26:24Z (GMT) No. of bitstreams: 1 zago_m_me_sjrp.pdf: 1340836 bytes, checksum: ddd4c0614476082a2b54f2c78a5a9188 (MD5) / Made available in DSpace on 2016-02-24T16:26:24Z (GMT). No. of bitstreams: 1 zago_m_me_sjrp.pdf: 1340836 bytes, checksum: ddd4c0614476082a2b54f2c78a5a9188 (MD5) Previous issue date: 2016-01-29 / O ensino de Matemática vem passando por um grande conjunto de dificuldades. Isto pode ser comprovado com os resultados de alunos nas avaliações aplicadas em diferentes níveis e escalas, como o Saresp e o Enem.Um dos motivos que levaram a este quadro é o ensino de Matemática pautado por práticas tradicionais, pois, acaba sendo fator desmotivador para o ensino da disciplina. Uma metodologia alternativa, a Modelagem Matemática, pode ajudar a reverter este quadro, uma vez que trabalha com problemas reais, elencados do contexto dos próprios alunos, potencializando, deste modo, a motivação e o interesse, aguçando nos discentes a busca por soluções, mostrando as aplicações da Matemática no cotidiano. Neste trabalho foi realizada uma breve síntese das etapas envolvidas no processo de Modelagem Matemática, aplicada ao ensino de funções, seguido de seis propostas de atividades resolvidas para subsidiar o trabalho de professores pouco familiarizados com esta metodologia. Ainda, como forma de contribuir para uma importante atividade econômica do Município de Osvaldo Cruz-SP, foi realizada uma modelagem matemática com base em dados do setor de transportes, mais precisamente caminhões bitrens. Neste caso, trata-se da simulação de um exemplo mais complexo envolvendo o conceito de modelagem. Espera-se, por meio da divulgação desta pesquisa, contribuir para melhorar a qualidade do ensino de Matemática nas escolas públicas, tanto por meio de subsídio aos docentes, como pela proposição de metodologia com potencial de geração de envolvimento de alunos. / The teaching of mathematics has been experiencing a large set of difficulties. This can be proven by student results in assessments applied at different levels and scales, such as Saresp and Enem. One of the reasons that led to this situation is the teaching Mathematics guided by traditional practices, because it ends up being a demotivating factor to teach the subject. An alternative methodology, the Mathematical Modeling, may help change this situation, as it works with real problems, presented within students’ context, therefore increasing their motivation and interest, sharpening them in the search for solutions, showing the mathematics’ applications in everyday life. This work carried out a brief summary of the steps involved in the process of Mathematical Modeling, applied to teaching functions, followed by six proposals of solved activities to subsidize the work of teachers unfamiliar with this methodology. Also, in order to contribute to an important economic activity in Osvaldo Cruz-SP, mathematical modeling was carried out based on the transport industry data, more precisely b-train trucks. In this case, it was the simulation of a more complex example involving the concept of modeling. By this research we expect to help improve the quality of mathematics teaching in public schools, not only through subsidies to teachers, but also with the methodology proposition generating potential engagement of students.

Esta tese possui como tema a ética e a diferença na invenção de uma docência matemática em meio à vida, em uma perspectiva pós-estruturalista. Aproxima-se das contribuições teóricas de Deleuze, Foucault e autores afins para pensar a diferença a partir da repetição da escrita de si, tomada enquanto processo inventivo de uma docência. Durante os percursos da pesquisa, utiliza-se dos conceitos de univocidade em Deleuze para tratar da diferença e da ética em Foucault para desestabilizar prescrições das verdades das ciências da educação sobre a docência em matemática. Toma-se uma criação textual de autoria própria - o Vidário de Pendurela - composto por fragmentos escritos de uma docência em meio à vida, que se tornou corpo e produziu matéria de investigação para esta tese, a fim de realizar uma experimentação filosófica pela reescrita de si. O procedimento de pesquisa se deu de modo “amaneirado”, através de um movimento filosófico, uma experimentação de pensamento para pensar a singularidade produzida na escrita e na docência, que consistiu em reescritas de si a partir dos movimentos de recolhimento, colagem, raspagem e criação, ao repetir os escritos de Pendurela, em outro estilo de escrita, diferindo sentidos. Dessa maneira, mostrou-se a invenção de uma docência, utilizando os conceitos de devir, vontade de potência e univocidade para problematizar essa invenção pela reescrita. Ao colocar em funcionamento essa maneira de pesquisar, entendido como repetição da escrita de si, toma-se o mesmo como uma experimentação filosófica para pensar a singularidade produzida na escrita e na docência. / This thesis has as its theme the ethics and the difference in the invention of a mathematical teaching in midst of life, in a poststructuralist perspective. It draws on the theoretical contributions of Deleuze, Foucault and related authors to think about the difference from the repetition of self-writing, taken as an inventive process of teaching. During the course of the research, the concepts of univocity in Deleuze are used to deal with the difference and the ethics in Foucault to destabilize prescriptions of truths of education sciences about teaching mathematics. A textual creation of its own authorship – the Vidário de Pendurela - is taken composed of written fragments of a teaching in the midst of life, which became a structure and produced research material for this thesis in order to conduct a philosophical experimentation by self-rewriting. The research procedure happened in a “certain manner” through a philosophical movement, an experimentation of thinking about the singularity produced in writing and teaching. It consisted of self rewritings from the movements of recollection, collage, scraping and creation, repeating the writings of Pendurela, in another style of writing, differing senses. Thus, the invention of a teaching action is presented, using the concepts of becoming, willpower and univocity to problematize this invention by the rewriting. By putting this manner of searching into practice, recognized as repetition of self-writing, it is possible to understand this process as a philosophical experimentation to think the singularity produced in writing and teaching.

Title: Circumferences and areas of plane figures Author: Martin Šrámek Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This diploma thesis Circumferences and areas of plane figures is designed for teachers and high school students. Teachers might find some interesting tasks including various metric problems from the field of synthetic geometry as well as inference of mathematic equations for calculation circumferences and areas of plane figures which are taught at elementary schools and high schools. Pupils can appreciate solved tasks and their knowledge can be applied to other similar tasks. The ninth chapter includes more difficult tasks. There are many drawings exported from GeoGebra which can help students to understand the task better. Keywords: circumference, area, length, teaching of mathematics

Submitted to the Faculty of Education in fulfilment of the requirements for the degree of MASTER OF SCIENCE EDUCATION in the Department of Mathematics, Science and Technology (MSTE) at the University of Zululand, 2015. / This study set out to investigate beliefs held by pre service Bachelor of Education (B.Ed) students about the nature of science and science teaching and learning. The research sample comprised one hundred and eighty four (184) third and fourth year (B.Ed) students majoring in mathematics and physical sciences. Data on students’ epistemological beliefs about the nature of science and science teaching and Learning were collected using two questionnaires: The Nature of Science as Argument Questionnaire (NSAAQ) and Beliefs About Reformed Science Teaching and Learning (BARSTL). Furthermore the study sought to find out if those beliefs cohered with the beliefs espoused by the National Curriculum Statement (NCS) for Physical Sciences grades 10-12. The conceptual framework of this study was framed upon the preponderance of literature that carried the view that a teacher’s classroom practices are a consequence of two main dialectic influences: (a) the teacher’s epistemological beliefs about the nature of science, which may be either naïve or sophisticated; and (b) the teacher’s beliefs about teaching and learning, which may be either traditional or reformed. Accordingly, the conceptual framework guiding the study opined that teachers holding naïve beliefs about the nature of science, and those holding traditional notions of teaching and learning will be characterized by teacher-centred instructional approaches, while those holding sophisticated beliefs of the nature of science and a reformed view of teaching and learning will be associated with learner-centred instructional approaches. This study was a case study conducted at a South African university, and involved one hundred and eighty-four third and fourth year students registered for a four-year Bachelor of Education (B.Ed) degree for the Senior and Further Education and Training phase. During these two final years of the programme students are engaged in science enquiry practices in their Methods modules. The participants were registered in physical science and mathematics education. Intact groups were used, so there was no sampling undertaken to select participants. Data were collected by the use of (a) the Nature of Science as Argument Questionnaire (NSAAQ), to determine epistemological beliefs held by the participants about the nature of science, as well as the concurrence of those beliefs with the views about science teaching and learning espoused by the NCS; and (b) the Beliefs about Reformed Science Teaching and Learning (BARSTL) questionnaire, to determine the beliefs held by preservice education students about science teaching and learning. Data analysis involved the use of both descriptive statistical methods to decipher patterns and general trends regarding the epistemological beliefs about science held by participants, and their beliefs about science teaching and learning, as well as inferential statistics to test both a priori and a posteriori hypotheses. Similarly, statistical analysis was carried out to determine whether or not third- and fourth-year pre-service science education students held beliefs about science teaching and learning that were in agreement with the pedagogical content beliefs about science teaching and learning espoused by the NCS. The study found that pre service students held significantly more sophisticated epistemological beliefs about the nature of science at fourth year than at third year level. The results also showed that fourth year students demonstrated a significantly higher level of ‘reformed oriented teaching and learning beliefs’ about science than did the third year students. The results however showed that third and fourth year students held beliefs that were not in line with the beliefs espoused by the National Curriculum Statement (NCS). These results support studies which have found that student teachers become more sophisticated in their epistemological beliefs towards graduation. The findings also showed that the B.Ed programme is succeeding in developing both epistemological beliefs about the nature of science and teaching and learning. The degree to which the programme succeeded in developing these beliefs was however quite small. This study recommends that further investigations be done to determine whether students who hold sophisticated epistemological beliefs about the nature of science and ‘reformed beliefs about science teaching and learning’ also demonstrate superior science teaching skills

Diplomová práce se zabývá využitím programu GeoGebra ve výuce ma- tematiky, konkrétně v tématu konstrukce trojúhelník·. Cílem práce bylo na- vrhnout přípravu na hodiny výuky konstrukce trojúhelník· s využitím pro- gramu GeoGebra a následně ověřit, zda využití softwaru dynamické geometrie mělo vliv na zvládnutí nového učiva. Teoretická část obsahuje použité pojmy z planimetrie. V dalších dvou kapitolách se čtenář seznámí s programem GeoGebra a GeoTest a některými výzkumy, které jsou zaměřené na použití program· dynamické geometrie ve výuce matematiky. Následuje kapitola se- znamující s úlohami, které jsou v experimentu využity, a popisuje přípravu jednotlivých hodin. Poslední část je věnovaná pr·běhu experimentu, srovnání výsledk· žák· pomocí test· s kontrolní třídou. Získaná data jsou zpracována na základě pozorování a test·. Výsledky pozorování a analýzy potvrzují, že GeoGebra je vhodným doplňkem výuky konstrukce trojúhelník·. 1