The aim of this case study was to examine, analyze and report on the findings of the experiences of selected mathematics teachers when they used the van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected mathematics teachers from the school where the researcher teaches. This school is located in the Oshikoto Education Region in Namibia. The school serves a multicultural group of 759 learners from a middle-class economic background. The site and participants were selected conveniently as the researcher had unrestricted access to both the facilities and the participants. This research takes the form of a case study and is underpinned by the interpretive paradigm. Data for this research was collected using a variety of techniques such as interviews, classroom observation and document analysis. This facilitated easy triangulation of the data. The findings of this research make four claims with regard to the experiences of the mathematics teachers with designing and implementing the circle geometry teaching programme using the five van Hiele phases of instruction as a conceptual framework. The findings revealed that firstly, all three participating mathematics teachers used and implemented all the five van Hiele phases of instruction in their lessons I observed. Secondly, the teachers navigated quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Thirdly, the teachers saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. Fourthly, the majority of the learners followed the instructions and seemed to obtain the answers faster than expected. The lesson presentations were lively and both teachers and learners communicated at length to discover angle properties of circles while developing and nurturing the technical language of geometry.

Orientador: Wilson Massashiro Yonezawa / Banca: André Koscianski / Banca: José Remo Ferreira Brega / Resumo: A baixa utilização de tecnologias para o apoio individualizado aos alunos, e as dificuldades enfrentadas por por professores e alunos no ensino e na aprendizagem dos números racionais foram os fatores motivadores da pesquisa. Foi realizada uma revisão de literatura sobre game design para o desenvolvimento de um jogo digital com características de motivação, imersão e conhecimento. Este jogo é baseado nas teorias do game design, com tecnologias HTML5 e Javascript, para que o jogo fosse multiplataforma. O jogo contempla três elementos básicos: a interface do aluno, composta por elementos jogáveis: a interface do professor, composta por elementos de análise em tempo real; e o servidor de transmissão e armazenamento dos dados. O jogo foi aplicado para seis alunos de uma turma de nono ano em uma escola estadual do município de Jaboticabal. Optou-se pela interpretação dos dados por meio de abordagens qualitativas. Os resultados indicam que o jogo digital proposto gera informações suficientes para que o professor identifique as características de seus alunos em relação a conteúdos de matemática, melhorando seu processo de ensino / Abstract: The low use of technology for the individual support to students and the difficulties faced by teachers in teaching and learning of rational numbers were the factors which motivated this research. It was performed a review of the literature about game design to the development of a digital game with characteristics of motivation, immersion and knowledge, this game is based on theories of game design, with technology HTML5 and JavaScrip so that the game was multiplatform. The game contemplates three basic elements: the student's interface, composed by playable elements; the teacher's interface composed by elements of real time analysis; and the server of transmission and storing of data. The game was applied to six students of a group of ninth year of a public school in the city of Jaboticabal. We opted by interpretation of data through qualitative approaches. The results indicate that the proposed digital games generates enough information in order the teacher can identify the characteristics of his/her students related to contents of mathematics, improving his/her teaching process / Mestre

Text in Afrikaans / 'n Leerling se wiskunde-selfkonsep wys heen na die konsep wat hy van homself op wiskundige vakgebied het. Die kwaliteit van hierdie konsep word bepaal deur die kwaliteit van sy eie betrokkenheid by, belewing van en sin- en betekenisgewing aan wiskundige vakinhoud. Wanneer die kwaliteit van 'n leerling se wiskunde-selfkonsep ontoereikend is, word sy onvermoe om op daardie tydstip sukses op wiskundige vakgebied te behaal, geopenbaar. Dit plaas die opvoeder voor die opgawe om bemoeienis met die leerling te maak en hom ten aansien van sy probleem te help. In die lig hiervan is 'n hulpverleningsprogram ter bevordering van die wiskunde-selfkonsep ontwerp. Aangesien leerlinge in Suid-Afrikaanse skole tans gedurende die st.7-skooljaar die besluit neem om die studie van wiskunde te staak of daarmee voort te gaan, is die inhoud van die program derhalwe op die st.7-leerling van toepassing gemaak. Spesifieke doelsteilings wat in die ontwerp van die program nagestreef is, is die volgende: Om die leerling te begelei tot insig in en die begryp van die kwaliteit van sy eie wiskunde-selfkonsep en grondliggende oorsake vir die vorming daarvan, ten einde hom in staat te stel om sy eie situasie in perspektief te plaas. Om die leerling te begelei tot die ontwikkeling van spesifieke vaardighede aan die hand waarvan hy homself op 'n meer selfstandige wyse kan handhaaf ten aansien van die begripmatige bemeestering van wiskunde as vak. By wyse van 'n loodsondersoek is die toepasbaarheid van die onderhawige program ondersoek. Uit die terugvoergesprekke met die leerlinge tydens die groepsessies en die inligtingstukke wat hulle voltooi het, blyk dit dat hulle baat gevind het by hulle deelname aan die program. Met die oog op moontlike toekomstige navorsing is spesifieke leemtes ten opsigte van die onderhawige studie uitgelig en aanbevelings gedoen wat as verdere riglyne geimplementeer kan word. / A pupil's mathematical self-concept is the concept a pupil has of himself in the sphere of Mathematics as a subject. The quality of this concept is determined by the quality of his own involvement in, live-experiencing of, and significance attribution in respect of mathematical subject content. When the quality of a pupil's mathematical self-concept is inadequate, his inability is manifested in his failure to master Mathematics as a subject. This confronts the educator with the task of becoming involved with the pupil and helping him with his problem. In view of this, an aid programme was designed to improve the mathematical self-concept. Owing to the fact that, at present, pupils in South African schools have to decide during their Std 7 school year whether they are going to continue with their study of Mathematics or discontinue these studies, the content of the programme was aimed at the Std 7 age group. The following are the specific aims that were pursued in the designing of the programme: To guide the pupil to insight in and understanding of the quality of his own mathematical self-concept and its underlying causes, in order to enable him to place his own situation in perspective. To guide the pupil in the development of specific skills to help him cope more independently with the successful mastery of Mathematics as a subject. The possibility of implementing such a programme in practice was established by means of a pilot investigation. From feedback discussions with the sample group during group sessions and from questionnaires they filled in, it appears that they benefited from their participation in the programme. With a view to possible future research, specific shortcomings with respect to the investigation were highlighted and recommendations made which can be implemented as further guidelines. / Psychology of Education / M. Ed. (Sielkundige Opvoedkunde)

The fundamental purpose of this research is to establish whether mathematics can be taught effectively with the use of appropriate media and to further establish the possible effects of media in the teaching of mathematics. The research touched on the principles and guidelines of media selection and the various methods that could be utilized in conjunction with media in the teaching of mathematics in the pre-primary and primary schools. In media selection, the emphasis was that media must be chosen objectively rather than on the basis of personal preference and that the effectiveness of media is dependent on the suitability of the physical conditions surrounding it. The overall findings regarding media utilization is that most educators believe that media used in conjunction with a suitable or appropriate method should help to actualize what is expected from the learner. The research method in this study can be divided into a literature study and an empirical investigation. The literature study was done with a view to support the introductory orientation of this study. The focus was on learning as an active process, it also highlighted how the young learners acquire knowledge and how their interaction with their environment impacts on their cognitive development. The research also dealt with concept formation with special reference to the variety of concepts such as physical sensory concepts, action-function concepts, evaluative concepts and abstract concepts. The questionnaire was used to gather data from seventy (70) educators about media integration in the teaching of mathematics in the pre-primary and primary schools. An observation guide was also used during the observation of the presentation of twelve (12) lessons by eight (8) teachers from the pre-primary and primary schools. The lessons included the nature and characteristics of media employed in the lessons. The following factors were taken into account: (a) lesson plan layout (b) specific outcomes (c) contact accuracy and relevance (d) learner variables and interest (e) the learning environment and (ij the mediation capabilities of the educator (g) availability of media in schools The discussion of data collected was followed by the data analysis and interpretation. The statistical techniques were used to put the researcher in a position to either reject or accept the null hypothesis. The techniques used were the Wilcoxon Signed Ranks Test, the Pearson Correlation coefficient, the NPar Test and Friedman Test. On the basis of the findings the researcher has sufficient, concrete evidence to conclude that the results invalidate the null hypothesis tested. Therefore the researcher's conclusion is that: (a) there is a possible effect of media in the teaching of mathematics lessons in the preprimary and primary schools. (b) there is a possible effect of media selection and integration of media in mathematics lessons. / Psychology of Education / D. Ed. (Psychology of Education)

Made available in DSpace on 2016-01-13T13:28:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-06-25. Added 1 bitstream(s) on 2016-01-13T13:33:44Z : No. of bitstreams: 1 000855694.pdf: 2118256 bytes, checksum: 88ce18178223f38eb361a3785f76721a (MD5) / Associação Universitária Iberoamericana de pós-grado (AUIP) / Analisamos as práticas algébricas constituídas por um grupo de alunos enquanto desenvolviam atividades de modelagem. Os participantes eram alunos de uma disciplina de Matemática Aplicada para os cursos de Biologia e Ecologia da UNESP, campus de Rio Claro, que foram convidados a produzir um projeto de modelagem sobre algum tema de seu próprio interesse como parte de uma das tarefas da referida disciplina. Trata-se de uma pesquisa de cunho qualitativo, cujos dados foram produzidos e analisados sob a perspectiva histórico-cultural da Teoria da Atividade, que apresenta o conceito de atividade prática como princípio explicativo do desenvolvimento humano e foca a atenção principalmente em três aspectos: a mediação de artefatos culturais, as relações intersubjetivas e as condições de legitimação das ações desenvolvidas. De acordo com os padrões de relacionamento materializados nos modelos matemáticos utilizados, foi possível concluir que, entre as vertentes discutidas de práticas matemáticas relacionadas com o conhecimento algébrico, as constituídas pelos alunos configuraram modos de ação que tomam o conceito de variação conjunta entre diferentes quantidades (covariação), como principal unidade de análise; isto é, adotam o enfoque variacional ou funcional como princípio de desenvolvimento. Embora este tipo de prática matemática trate com algum nível de generalidade, enfatizamos a necessidade de gerar processos de separação espaço-temporal do contexto do qual surgiram para poder ingressar no campo de significação do conhecimento algébrico. Isso significa que as quantidades significativas devem passar por um processo de des-temporalização e desespacialização, para que sejam institucionalizadas no campo das práticas algébricas; isto é, para que os modos de ação dos sujeitos estejam orientados a operar analiticamente com relações gerais entre quantidades indeterminadas (variáveis,... / We analyzed the algebraic practices constructed by a group of students while they were developing modeling activities. The participants were students from a course of the Applied Mathematics program for Biology and Ecology of the UNESP - Rio Claro campus, that were invited to make a modeling project in any topic of their own interest as a part of the assignments of the course. This is a qualitative research where data were produced and analyzed from the historical and cultural perspective of the Theory of Activity, that presents the concept of practical activity as an explicative principle of the human development and focuses its attention mainly in three aspects: the mediation of cultural artifacts, the intersubjective relations and the conditions of the legitimation of the developed actions. According to the relationship patterns materialized in the mathematic models used, it was possible to conclude that among the discussed strands of mathematical practices related with the algebraic knowledge, the ones constituted by the students configured modes of action that take the concept of combined variation between different quantities (covariance), as principal unit analysis; that is, they adopt the variational or functional approach as a development principle. Although this type of mathematical practice deals with some level of generality, we emphasize in the need to generate actions for the spatiotemporal separation of the context in which they appeared, to be able to enter the field of the meaning of the algebraic knowledge. This means that the significant quantities have to go through a de-timing and despacialisation process, for them to be institutionalized in algebraic practice field; that is, for the modes of action of the subjects to be oriented to operate analytically with general relations among indeterminate amounts (variables, unknowns, parameters and generalized numbers). The results indicate that the processes of ...

Made available in DSpace on 2016-04-01T17:55:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-10-16. Added 1 bitstream(s) on 2016-04-01T18:00:56Z : No. of bitstreams: 1 000858451.pdf: 2274233 bytes, checksum: 4a0375362eb44bf856277c8bb85f484f (MD5) / Em nossa excursão literária, observamos o que permeia o movimento de ensino e aprendizagem em Matemática de alguns licenciandos, em seu devir professores de Matemática, sujeitos estes que foram capturados pelo processo de ensino de Matemática e estão agora na postura de professores, trazendo para a sala de aula suas concepções a respeito de si, do que os circunda e, em particular, da Matemática. Com isso observamos os discursos que os impregnam, as linhas de força que os perpassam, os territórios que habitam, assim como os dispositivos em que estão inseridos, tendo o projeto de extensão, elaborado por nós, como um dispositivo que funcionou como base para a nossa investigação. Para isso, adotamos a Cartografia Existencial como metodologia de pesquisa, sendo a Filosofia da Diferença um dos principais aportes teóricos para o desenvolvimento desta pesquisa. Como cartógrafos adentramos os mais variados territórios existenciais dos sujeitos, fazendo conexões entre eles e utilizando fontes variadas: notas de campos, questionários, carta, conversas informais e mapas narrativos. Escolhemos a narrativa como maneira de expressar os movimentos que nos afetou, sem nos preocuparmos em buscar A resposta a uma pergunta específica, pois cada sujeito que compõe nossa rede educacional não apenas um, mas uns / En nuestro recorrido literario, observamos lo que permea el movimiento de enseñanza y aprendizaje de las matemáticas de alumnos de una licenciatura en matemática, en su devenir como profesores, sujetos éstos que han sido capturados por el proceso de enseñanza de la matemática y ahora están en el lugar de docentes que traen para sus aulas de clase concepciones al respecto de sí mismos, situaciones que les circundan y en particular nociones sobre la misma matemática. Observamos los discursos que los impregnan, las líneas de fuga que los traspasan, los territorios que habitan, así como los dispositivos en los que están sumergidos. Tomamos un proyecto de extensión desarrollado por nosotros como dispositivo para la producción de la información, adoptando como metodología de investigación la Cartografía Existencial cuyas bases se encuentran en la filosofía de la diferencia y que asumimos como uno de los principales aportes teóricos para el desarrollo de esta investigación. Como cartógrafos nos adentramos a los más variados territorios existenciales de los sujetos, haciendo conexiones entre ellos por medio de diferentes fuentes: notas de campo, cuestionarios, cartas, conversaciones informales y mapas narrativos. Elegimos la narrativa como una forma de expresar los movimientos que nos afectaron sin preocuparnos en buscar la respuesta a una pregunta específica, pues entendimos que cada sujeto que compuso nuestra red educativa no era apenas uno, sino unos

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-11-22Bitstream added on 2014-06-13T18:52:59Z : No. of bitstreams: 1 pires_amm_me_rcla.pdf: 669984 bytes, checksum: 4395900a3293740fce2abfd7082df0d8 (MD5) / Nesta dissertação, viso a apresentar a investigação que realizei junto ao Grupo de Pesquisa-Ação em Educação Matemática, na Universidade Paulista, campus de Rio Claro (GPA-RC). Na investigação, trato o fracasso do ensino e da aprendizagem em Matemática, por meio de ação diferencial auto-regulada, própria da linha de investigação adotada pelo GPA-RC: análise dos condicionantes da sala de aula e intervenção pedagógica. Tomo minha prática como objeto de pesquisa e busco as conseqüências de uma tentativa de combate ao fracasso escolar de alunos universitários através da estratégia de Grupo de Estudos. A descoberta, realizada no GPA-RC, provoca mudança em meu olhar e adoção de aporte teórico sobre grupos operativos. / This dissertation aims at presenting the research made within the Group of Action Research in Mathematical Education at the Universidade Paulista on the Rio Claro campus (GPA-RC). This project investigates the failure of the teaching and learning of Mathematics through the self-regulated differential action approach, which is adopted by the GPA- RC, and includes the analysis of the conditioning factors in the classroom and of pedagogical intervention. My research is based on my own teaching practice and I look at the consequences of an attempt to combat the failure of university students using the Group-Work strategy. The findings, which took place at the GPA-RC, have brought about changes in my perception and the adoption of the operative group-work theoretical framework.

Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-09-10Bitstream added on 2014-06-13T19:21:01Z : No. of bitstreams: 1 paulette_w_dr_rcla.pdf: 2523632 bytes, checksum: 3500dd6f416ea1545817b682741bab3f (MD5) / Quando começamos a lecionar a disciplina Matemática para o Curso de Administração de Empresas da Unip-Campus Vergueiro, percebemos que o ensino tradicional, com aulas expositivas dialogadas, não criava um ambiente propício para uma boa aprendizagem de matemática. Inconformados, fomos em busca de uma nova forma de ensino-aprendizagem para essa disciplina. Adotamos a Metodologia de Pesquisa de Romberg como guia para nossa pesquisa. Por meio de uma seleção de estratégias e procedimentos, passamos a conhecer: a) o perfil do Administrador Profissional: dessa forma, verificamos quais são os conhecimentos, as atitudes e as habilidades de um bom administrador; b) o perfil do Corpo Discente: assim passamos a conhecer suas tendências, suas aptidões e seus conhecimentos matemáticos; c) o perfil do Corpo Docente que leciona matemática e dos da área profissionalizante, que utilizam matemática e que tópicos são mais utilizados; d) a realidade do ensino de matemática nas últimas décadas. De posse dessas informações, fomos em busca de uma nova metodologia de ensino-aprendizagem que atendesse ao perfil exigido pelo MEC, pelo CFA e pela Unip. A metodologia que passamos a adotar foi a Metodologia de Ensino-Aprendizagem de Matemática via Resolução de Problemas. Com essa metodologia propusemos mudanças na ementa e conteúdo programático, aplicando-a durante o ano de 2001 para alguns tópicos do programa. Com a experiência obtida, preparamos e aplicamos, no ano de 2002, um cronograma que continha 40 semanas de aula, apresentando, para cada semana, o título do conteúdo programático, os objetivos a alcançar e o conteúdo matemático a ser trabalhado. Nesse modelo de ensino-aprendizagem, os conceitos matemáticos foram construídos a partir de situações-problema retiradas do cotidiano do Curso de Administração de Empresas e em concordância com o novo conteúdo programático...

Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-01-23Bitstream added on 2014-06-13T21:03:09Z : No. of bitstreams: 1 maio_w_dr_rcla.pdf: 6728503 bytes, checksum: 431b5f127d6916250db2e7f4a0bc772f (MD5) / A partir da década de 90, com o advento de aparelhos que permitem o estudo do cérebro humano in vivo, começamos a determinar experimentalmente as regiões do cérebro, quais suas funções, como e onde as memórias são arquivadas, quais as suas estruturas básicas e como tudo isso se interliga. As interações com o meio, onde o ser se situa, são feitas pelos receptores sensoriais, os órgãos dos sentidos e todas são transformadas em impulsos bioelétricos e registros bioquímicos, gerando sinapses entre os neurônios e as memórias de primeira e segunda ordem. A função das sinapses, nas interações internas, é determinada, sendo fundamental na e para a aquisição do conhecimento, a ponto de dizermos hoje: há sinapse, há conhecimento. As representações simbólicas das linguagens, dos códigos das ciências e sociais, são associações feitas pelo cérebro através de suas interações com o meio ambiente e com as estruturas sociais. Estes conhecimentos neurofisiológicos, entre outros, mudaram a visão do Homem, que deixa de ser Cartesiana e passa a ser Sistêmica. A análise feita no texto incorpora esta visão numa interdisciplinariedade com as demais ciências. O Homem passa a fazer parte do Universo e deve estar sujeito às suas leis, inclusive o seu cérebro. A pesquisa relata as estruturas básicas que fundamentam as ciências ditas da Física, analisa os últimos resultados obtidos pela Neurofisiologia, integrando-os com as estruturas matemáticas. O papel importantíssimo das sinapses no aprendizado é enfatizado. Mostramos num primeiro momento que o cérebro possui, em si, a capacidade de formar classes a partir de registros sensórios, memórias de primeira ordem, gerando as memórias de segunda ordem, que ficam ligados, entre si, por sinapses, de maneira análoga à geração de grupos quocientes e das estruturas Físicas do nosso Universo... / From the decade of 90, with the advent of devices that permit the study of the human brain in alive, we begin determine experimentally the regions of the brain, which theirs functions, as and where the memories are filed, which theirs basic structures and as everything that themselves link. The interactions with the environment, where the self situates, is done by the sensorial receivers, the sensorial organs and all are transformed in bioelectrical impulses and biochemical records, generating synapses between the neurons and the memories of first and second order. To function of the synapses, in the internal interactions, is determined, being fundamental in the and for the acquisition of the knowledge, to such point that we will say today: there is synapse, there is knowledge. The symbolic representations of the languages, of the codes of the sciences and social, associations deeds by the brain thru his interactions with the environment and with the social structures. These neurofisiological knowledge, among others, they changed the vision of the Man, no more being Cartesian, but rather being Systemic The analysis made in the text incorporates this vision in an interdisciplinary besides the other sciences. The Man passes be part of it the Universe and should be subject to its laws, including his brain. The research relates the basic structures that substantiate the sciences said the Physical ones, analyzes the last results obtained by the neurofisiology, integrating them with the mathematical structures. The very important role of the synapses in the learning is emphasized. We show in a first moment that the brain possesses in itself the capacity to form classes from records sensorial, memories of first order, generating the Second order memories, that stayed connected, between themselves, by synapses, in an analogous way to the quotient groups generation and of the structures...(Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:31:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-09-09Bitstream added on 2014-06-13T19:21:06Z : No. of bitstreams: 1 silva_nma_dr_rcla.pdf: 1210875 bytes, checksum: 434340db19d35a17506253a73c9f88eb (MD5) / É uma investigação sobre fundamentos da Educação Matemática a partir de práticas imersas na totalidade escolar. Deriva da implementação de um projeto de extensão universitária em um dado contexto escolar e tem como norteadora a seguinte questão: Tornar consciente o pressuposto da totalidade e compreender o todo através de suas inter-relações pode favorecer o sujeito na organização de seu conhecimento matemático e, conseqüentemente em seu processo de auto-educação? As tensões individuais e coletivas identificadas através das práticas pela manifestação das diversas totalidades individuais foram textualizadas e identificadas como Nervuras do Real. As nervuras, como reentrâncias na prática, e a organização do texto, como momentos da reflexão, denotam movimento e ação, justificando a metodologia empregada na pesquisa. A pluralidade teórica empregada norteia-se pela totalidade, um pressuposto sentido e buscado interativamente pelos envolvidos no processo. São discutidas interconexões de especificidades, tomando a totalidade como algo fluido e dinâmico, e a Educação Matemática como um conjunto de práticas imersas nessa totalidade. As totalidades abordadas e pressupostas visam contribuir com a Educação Matemática por apresentá-la no cotidiano do mundo vivido e compartilhado por sujeitos (que agem) no espaço-tempo da finitude humana, uns-com-os-outros (educação) e consigo-próprios (auto-educação) / Study is an investigation concerning the foundations of the Mathematical Education starting from practices immerged in the school totality. It derives of the development of a project of university extension in a specific school context and he has as a guideline the following question: To turn conscious the presupposition of the totality and to understand the whole through its interrelations can favor the individual in the organization of its mathematical knowledge and, consequently in the process of educating himself? The individual and tensions identified through the practices for the manifestation of the several individual totalities were transformed in text and identified as Reentrance's Real. The re-entrances in the practice, and the organization of the text, as moments of the reflection, denote movement and action, justifying the methodology of the research. The adopted theoretical plurality has as a guideline of the totality, a presupposed perceived and sought for by the interaction of the individuals involved in the process. Specificity connections are discussed, taking the totality as something fluid and dynamic, and the Mathematical Education as a entirety of practices immersed in this concrete totality. The approached and presupposed totalities seek to contribute with the Mathematical Education for presenting it in the quotidian of the lived and shared world by individuals (who act) in the space-time of the human finiteness, one with the other ones (education) and with itself (education of itself)