In this paper we introduce a new model which we apply to Discrete Mathematics, but could be applied to other courses as well. The model uses homework, lectures and quizzes. The key factor and design is centered on the quizzes which are given daily. We also discuss how lectures and homework question sessions can be shortened slightly to allow for twenty-five minute quizzes without sacrificing content. The model assumes a course which meets two days a week lecture, each of which is ninety minutes with no recitations. A three hour lecture could also be applied to this model.

No description available.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (leaves 172-177).

Thesis (M. Ed(Curriculum studies)--University of Pretoria, 2004. / Includes bibliographical references.

Thesis (M.Ed.)--Memorial University of Newfoundland, 1975. / Typescript. Bibliography: leaves 74-77. Also available online.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

Orientador: Lourdes de la Rosa Onuchic / Banca: Geraldo Perez / Banca: Edna Maura Zuffi / Resumo: Esta dissertação tem como objetivo principal verificar se a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas constitui-se num bom caminho alternativo para a construção de conceitos e conteúdos trigonométricos pelos alunos do Ensino Médio. Dentro da Educação Matemática, atualmente, o ensinoaprendizagem- avaliação de Matemática através da resolução de problemas é visto como uma metodologia alternativa, que visa a um trabalho centrado no aluno, a partir de problemas geradores de novos conceitos e novos conteúdos matemáticos, levando-o a construir um conhecimento matemático através da resolução de problemas. Nessa metodologia, o aluno participa ativamente da construção do conhecimento com a orientação e supervisão do professor que, somente no final desse processo de construção, formaliza as idéias construídas, utilizando notação e terminologia corretas. As unidades temáticas trabalhadas com os alunos foram Conceitos básicos e Trigonometria no triângulo retângulo; A circunferência e arcos trigonométricos e Funções Trigonométricas e resolução de triângulos quaisquer. Constatei que, ao trabalhar com esta metodologia, em sala de aula houve um aumento na motivação, tanto da professora em ensinar quanto dos alunos em aprender. Além disso, em muitas oportunidades, foi possível observar os alunos relacionando suas atividades com alguns tópicos já trabalhados anteriormente. Todos esses fatos, retratados em minha aplicação, reforçam fortemente a relevância desse trabalho. A metodologia de pesquisa adotada neste trabalho é a Metodologia de Romberg. / Abstract: This thesis has as main goal the verification if the teaching-learning-assessment of Mathematics Methodology through the Problem Solving approach is a good alternative way to the construction of trigonometric concepts and contents by high school students. Currently, within Mathematics Education, teaching-learning-assessment of Mathematics through problems solving is seen as an alternative methodology, which aims to work in a student centered way, from problems that might produce new mathematics concepts and contents, leading them to construct mathematics knowledge through problem-solving. Within this methodology, students participate actively in the construction of knowledge with the teacher orientation and supervision who formalize the constructed ideas just at the end of this construction process, using right notation and terminology. The thematic units worked on with the students were: Basic concepts and trigonometry in the right-angled triangle; Circles and trigonometric arcs and Trigonometric functions and solution of problems involving general triangles. I have realized that, working with this methodology, there were a motivation increase in the classroom, both for the teacher to teach, and the students to learn. Furthermore, it was possible to see, in many opportunities, the students connecting their activities with some topics that had already been worked on. All those events happened in my research application, strongly reinforce the relevance of this work. The research methodology adopted in this work is the Romberg’s one. / Mestre

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-12-13Bitstream added on 2014-06-13T19:11:41Z : No. of bitstreams: 1 huamanhuanca_rr_me_rcla.pdf: 2747717 bytes, checksum: 524fc14b4631e834d79514b5267d0a67 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta dissertação tem como objetivo principal verificar se a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas constitui-se num bom caminho alternativo para a construção de conceitos e conteúdos trigonométricos pelos alunos do Ensino Médio. Dentro da Educação Matemática, atualmente, o ensinoaprendizagem- avaliação de Matemática através da resolução de problemas é visto como uma metodologia alternativa, que visa a um trabalho centrado no aluno, a partir de problemas geradores de novos conceitos e novos conteúdos matemáticos, levando-o a construir um conhecimento matemático através da resolução de problemas. Nessa metodologia, o aluno participa ativamente da construção do conhecimento com a orientação e supervisão do professor que, somente no final desse processo de construção, formaliza as idéias construídas, utilizando notação e terminologia corretas. As unidades temáticas trabalhadas com os alunos foram Conceitos básicos e Trigonometria no triângulo retângulo; A circunferência e arcos trigonométricos e Funções Trigonométricas e resolução de triângulos quaisquer. Constatei que, ao trabalhar com esta metodologia, em sala de aula houve um aumento na motivação, tanto da professora em ensinar quanto dos alunos em aprender. Além disso, em muitas oportunidades, foi possível observar os alunos relacionando suas atividades com alguns tópicos já trabalhados anteriormente. Todos esses fatos, retratados em minha aplicação, reforçam fortemente a relevância desse trabalho. A metodologia de pesquisa adotada neste trabalho é a Metodologia de Romberg. / This thesis has as main goal the verification if the teaching-learning-assessment of Mathematics Methodology through the Problem Solving approach is a good alternative way to the construction of trigonometric concepts and contents by high school students. Currently, within Mathematics Education, teaching-learning-assessment of Mathematics through problems solving is seen as an alternative methodology, which aims to work in a student centered way, from problems that might produce new mathematics concepts and contents, leading them to construct mathematics knowledge through problem-solving. Within this methodology, students participate actively in the construction of knowledge with the teacher orientation and supervision who formalize the constructed ideas just at the end of this construction process, using right notation and terminology. The thematic units worked on with the students were: Basic concepts and trigonometry in the right-angled triangle; Circles and trigonometric arcs and Trigonometric functions and solution of problems involving general triangles. I have realized that, working with this methodology, there were a motivation increase in the classroom, both for the teacher to teach, and the students to learn. Furthermore, it was possible to see, in many opportunities, the students connecting their activities with some topics that had already been worked on. All those events happened in my research application, strongly reinforce the relevance of this work. The research methodology adopted in this work is the Romberg s one.

This thesis explores the range of strategies used for educational provision for gifted children in mathematics in a group of schools in England. A review of literature relating to international theory and existing research in gifted education and empirical work into the teaching of gifted mathematicians were carried out. The literature review examined the dominant theories of intelligence and giftedness in general, including the historical background of definitions of giftedness and methods for its measurement, before specifically focusing on the concept of mathematical giftedness. The study was located in primary schools within Greater London, where schools are required to implement the ‘Gifted and Talented’ policy of the UK government. The research was conducted in two stages during the school years 2007-2008 and 2008-2009. The first stage involved a questionnaire survey sent to primary schools within five Local Educational Authorities. For the second stage of the research, which constituted the main study, a case study approach was used. The main methods of data collection employed within the case study were observations of mathematics lessons, semi-structured interviews with children nominated as able or gifted mathematicians and their teachers, as well as analysing documentary evidence (i.e., school policy, teacher’s planning, children’s assessment records and children’s written work). It was found that schools were responding to the policy in pragmatic terms, although no specific training was provided for practising teachers or school co-ordinators as part of the national training programme in making provision for mathematically gifted children. In practice, in classrooms, it was found that teachers’ level of confidence and expertise, the level of focused attention given to gifted children, the level of support and extension through higher-order questioning, as well as the size of the class and the nature of the work set were factors which affected the progress, perceptions and attitudes of children who were nominated to be able mathematicians. There is a paucity of research which has investigated aspects of provision for gifted and talented children, particularly in mathematics, in the UK. By specifically addressing this topic, this study makes a distinct contribution to current literature in both understanding aspects of mathematical giftedness and the range of provision used. This study makes a particular contribution to finding out how practising teachers in England are responding to a government initiative, which should be of interest to both policy-makers and practitioners. This thesis also presents examples for organising and teaching mathematics to gifted children at higher cognitive levels, within regular classrooms; this may be of interest to audiences internationally, including countries where there are no policies of provision for mathematically gifted children.

Nesta pesquisa, de abordagem qualitativa, discutimos o uso da Resolução de Problemas como metodologia de ensino em Matemática numa Perspectiva Metodológica a alunos do Ensino Médio. Tendo por objetivo geral contribuir para a melhoria do ensino-aprendizagem em Matemática. Durante três bimestres foram desenvolvidas atividades em três turmas da 2° série de uma escola publica da Rede Estadual de Ensino no município de Tremembé-SP. Essas atividades focalizavam os seguintes tópicos: as habilidades em que os alunos apresentavam defasagem, os diferentes tipos de problemas matemáticos sugeridos por Smole e Diniz (2001), a relação entre a Matemática e a Língua Materna e os processos cognitivos e metacognitivos. A coleta de dados deu-se por meio do diário de campo da professora-pesquisadora e dos registros produzidos pelos alunos ao longo das aulas. A análise dos dados aponta que na prática pedagógica, trabalhar com diferentes tipos de problemas aproxima a Matemática e a Língua Materna, ampliando a compreensão dos alunos, como também formular problemas ou parte dele embora se constitua uma tarefa desafiadora, contribui positivamente com o processo de resolução além de propiciar o início de reflexões de ordem metacognitiva. / In this qualitative research, we discuss the use of problems solving as a methodology of mathematics teaching in a methodologic perspective to high school students. With the general goal of contributing to the improvement of teaching-learning in mathematics, were developed activities in three classes of the second grade of a Public School of the State Teaching Network in the municipality of Tremembé-SP during three bimester. These activities focused on the following topics: the abilities in which the students presented lags, the different types of mathematical problems suggested by Smole and Diniz (2001), the relation between Mathematics and the Mother Language and the cognitive and metacognitive processes. The data collection was done through the teacher-researcher\'s field diary and the records produced by the students throughout the classes. The analysis of the data points out that in pedagogical practice, working with different types of problems brings the Mathematics and Mother Language closer, broadening the students comprehension, and formulating problems or part of it, although it is a challenging task, positively contributes to the resolution process beyond of propitiating the beginning of reflections of metacognitive order.