Thesis (Ph. D.)--University of Wisconsin--Madison, 1972. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 522-533).

Thesis (M. Ed.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 123-130).

Thesis (M.Ed.)--University of Hong Kong, 1998. / Includes bibliographical references (leaves 123-130). Also available in print.

A Metodologia de Projetos tem sido uma estratégia de ensino e aprendizagem que vem ganhando espaço na educação ao longo dos anos. Muitos, porém, trabalham com essa metodologia de forma equivocada, acreditando que contextualizar é usar o meio em que o aluno está inserido como cenário dos exercícios dados em sala de aula, como futebol ou atividade com coleção de figurinhas. O resultado significativo da utilização desta metodologia de ensino acontece quando o aluno vive o problema que deve resolver, ou seja, quando se torna o protagonista da sua resolução. Desta forma, o projeto desenvolvido por alunos do 6º ano do Ensino Fundamental de um colégio particular de uma cidade localizada no Vale do Paraíba, interior de São Paulo, foi resolver problemas de matemática com o fim de arrecadar verba para o Asilo, instituição da mesma cidade. Além de trabalhar a resolução de problemas matemáticos reais para a arrecadação, conviveram com idosos, e estabeleceram com eles uma questão de cunho social, que desenvolveu a cidadania entre eles. Assim, a pergunta que direciona a pesquisa é: \"A Metodologia de Projetos, como estratégia de ensino, favorece a aprendizagem de matemática de forma efetiva?\". Durante todo percurso do projeto observou-se que os alunos desenvolveram habilidades de interpretação e resolução de problemas de matemática, e ainda pôde-se notar o amadurecimento de atitudes de cidadania e respeito entre eles. / The Project Methodology has been a strategy of teaching and learning that has been gaining space in education over the years more and more. However, many works with this methodology are in the wrong way, believing that contextualizing is to use the student\'s environment as the setting for classroom exercises, such as football or a collection of cards. The significant result of the use of this teaching methodology happens when the student lives the problem that must solve, that is, when he becomes the protagonist of the problem solving. In this way, the project developed by students of the 6th year of elementary school of a private school in the city located in the Paraíba Valley, São Paulo, was to solve problems of mathematics in order to raise money for the Asylum, institution of the same city. In addition to working to solve real mathematical problems for collection, they had the experience of working with the elderly, a social issue, which developed citizenship among them. Thus, the research question is: \"Does the Project Methodology, as a teaching strategy, favor the learning of mathematics effectively?\". Throughout the course of the project it was observed that students have been able to develop mathematical problem solving and problem solving skills, and the maturity of citizenship attitudes and respect among them can be noted.

The purpose of this study is to examine the relationship between 6th grade students&rsquo / problem solving achievement scores after completing instruction on problem solving and their mathematics achievement mean scores related to Least Common Multiple (LCM), Greatest Common Factor (GCF), Sets and Whole Numbers topics obtained throughout the semester. In addition, the relationship between 6th grade students&rsquo / problem solving achievement scores after completing instruction on problem solving and their actual mathematics net scores obtained from Level Determination Exam (SBS) was investigated. In total, 170 sixth grade students from a private school in Istanbul participated in the study. The data were collected via three sources namely / Problem Solving Achievement Tests (PSATs), Mathematics Achievement Tests (MATs) and SBS exam. Quantitative methods were utilized to examine the research questions and a correlational design was used. The results of the statistical analysis showed that there was a significant positive correlation between students&rsquo / problem solving achievement scores after completing instruction on problem solving and their mathematics achievement mean scores obtained through out the semester related to LCM, GCF, Sets and Whole Numbers Topics. In addition, the findings of the analysis showed that there was a significant large positive correlation between the problem solving achievement scores after completing instruction on problem solving and students&rsquo / actual mathematics net scores obtained from SBS.

Made available in DSpace on 2018-06-27T19:13:12Z (GMT). No. of bitstreams: 2 Stefane Layana Gaffuri.pdf: 3250223 bytes, checksum: 40260452a0ff9143b4f594fc6e6b27d2 (MD5) Stefane Layana Gaffuri.pdf.jpg: 3528 bytes, checksum: 11cc3f59597b71de2e0048f1f80ad421 (MD5) Previous issue date: 2012-11-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work´s aimed to analyze the contributions that the Teaching-Learning-Assessment methodology through Problem Solving provides learning in early Probability concepts. The research subjects were students from one third semester class, from the Administration course, in the Statistics subject, from Centro Universitário Franciscano UNIFRA, in Santa Maria RS. In the theoretical chapter, we address the Probability and its different approaches, the research starts with a historical introduction, followed by an analysis of its applications and concepts, and also for the search of works from other authors who had referred to teaching and learning this content. The research was a qualitative type and the collected dada was based on the participant observation during the development of the activities developed by the students in groups, registered in the researcher and the students ´ field diary. The activities developed in the classroom followed the steps of Problem Solving method, suggested by Onuchic and Allevato (2009): problem preparation, individual reading of the problem, group reading, problem solving, observation and encouraging, solving record on the blackboard, plenary, search of agreement and formalization of the content. The activities developed in the classroom were organized in learning sessions, aiming the concept building of Probability. The research linked the use of manipulative to solve problems, it providing visualization, questioning, reflection and construction of knowledge by students. The results indicated that in front of an unknown math concept, the students tried to mean it by means of their conceptual images which already exist and the new ones built during the activities. It was possible to identify, also, the difficulty to group in creating strategies, argue and formulate mathematical ideas. Also, the results of the research indicate the importance of problem solving as a teaching strategy, which can provide the students the building of their knowledge. / O presente trabalho teve por objetivo analisar as contribuições que a metodologia de Ensino-Aprendizagem-Avaliação através da Resolução de Problemas proporciona à aprendizagem de conceitos iniciais de Probabilidade. Os sujeitos da pesquisa foram alunos de uma turma do terceiro semestre do curso de Administração, na disciplina de Estatística, do Centro Universitário Franciscano - UNIFRA, em Santa Maria RS. Na fundamentação teórica, a Probabilidade e seus diferentes enfoques são abordados, iniciando-se a pesquisa com uma introdução histórica, seguida por uma análise de suas aplicações e seus conceitos, e pela busca de trabalhos de outros autores que se referiam ao ensino e à aprendizagem desse conteúdo. A pesquisa é de natureza qualitativa e teve como instrumentos de coleta de dados, a observação participante, durante o desenvolvimento das atividades realizadas pelos alunos, e registradas no diário de campo da pesquisadora e dos alunos. As atividades em sala de aula seguiram os passos da metodologia de resolução de problemas, sugeridos por Onuchic e Allevato (2009): preparação do problema; leitura individual do problema; leitura em conjunto; resolução do problema; observar e incentivar; registro das resoluções na lousa; plenária; busca do consenso e formalização do conteúdo. Essas atividades foram organizadas em sessões de ensino, e agrupadas visando à construção dos conceitos inicias de Probabilidade. A pesquisa atrelou o uso de materiais concretos com a resolução de problemas, propiciando à visualização, o questionamento, a reflexão e a construção do conhecimento por parte dos alunos. Os resultados indicaram que frente a um conceito matemático desconhecido, os alunos buscaram exprimi-lo por meio dos conceitos já conhecidos e os novos construídos no decorrer das atividades. Verificou-se, também, a dificuldade do grupo em criar estratégias, argumentar e formalizar ideias matemáticas. Os resultados da pesquisa apontam, também, para a importância da inclusão da resolução de problemas como estratégia de ensino, a qual pode proporcionar aos alunos a construção do próprio conhecimento.

A Metodologia de Projetos tem sido uma estratégia de ensino e aprendizagem que vem ganhando espaço na educação ao longo dos anos. Muitos, porém, trabalham com essa metodologia de forma equivocada, acreditando que contextualizar é usar o meio em que o aluno está inserido como cenário dos exercícios dados em sala de aula, como futebol ou atividade com coleção de figurinhas. O resultado significativo da utilização desta metodologia de ensino acontece quando o aluno vive o problema que deve resolver, ou seja, quando se torna o protagonista da sua resolução. Desta forma, o projeto desenvolvido por alunos do 6º ano do Ensino Fundamental de um colégio particular de uma cidade localizada no Vale do Paraíba, interior de São Paulo, foi resolver problemas de matemática com o fim de arrecadar verba para o Asilo, instituição da mesma cidade. Além de trabalhar a resolução de problemas matemáticos reais para a arrecadação, conviveram com idosos, e estabeleceram com eles uma questão de cunho social, que desenvolveu a cidadania entre eles. Assim, a pergunta que direciona a pesquisa é: \"A Metodologia de Projetos, como estratégia de ensino, favorece a aprendizagem de matemática de forma efetiva?\". Durante todo percurso do projeto observou-se que os alunos desenvolveram habilidades de interpretação e resolução de problemas de matemática, e ainda pôde-se notar o amadurecimento de atitudes de cidadania e respeito entre eles. / The Project Methodology has been a strategy of teaching and learning that has been gaining space in education over the years more and more. However, many works with this methodology are in the wrong way, believing that contextualizing is to use the student\'s environment as the setting for classroom exercises, such as football or a collection of cards. The significant result of the use of this teaching methodology happens when the student lives the problem that must solve, that is, when he becomes the protagonist of the problem solving. In this way, the project developed by students of the 6th year of elementary school of a private school in the city located in the Paraíba Valley, São Paulo, was to solve problems of mathematics in order to raise money for the Asylum, institution of the same city. In addition to working to solve real mathematical problems for collection, they had the experience of working with the elderly, a social issue, which developed citizenship among them. Thus, the research question is: \"Does the Project Methodology, as a teaching strategy, favor the learning of mathematics effectively?\". Throughout the course of the project it was observed that students have been able to develop mathematical problem solving and problem solving skills, and the maturity of citizenship attitudes and respect among them can be noted.

By manipulating constraints and goals, this study had generated some ill-posed problems in "Fractions" which were packed into 2 mathematical tasks for teacher uses in an intended exploration of their perceived effectiveness of teaching mathematical problem-solving against their student responses through the lens of the theory of formative assessment. Each ill-posed problem was characterized by certain descriptive "instability" that users would have to define own sets of mathematical assumptions for problem-solving inquiries. 3 highly qualified, experienced, and trained mathematics teachers were purposefully recruited, and instructed to acquire and mark student responses without any prior teaching and intervention. Each of these teachers' perceptions of ill-posed problems was acquired through a semi-structured clinical case-interview. All teachers in common demonstrated only individual singular mathematical problem-solving inquiries as major instructional adjustments during evaluation, even though individuals had ample opportunities in manipulating the described intention of each problem. Although some could realize inquiries from students being alternative to own used, not all would intend to change initial instructional plans of each problem and could design dedicated tasks in extending given problem-solving contexts for subsequent teaching and maintaining the described problem-solving intentions merely because of evaluation purposes. The resulting thick teacher perceptions were then analyzed by the Mayring's (2015) Qualitative Content Analysis (QCA) method for exploring particularly those who could intend to influence and get influenced by students' used mathematical assumptions in interviews. Certain unanticipated uses of assumptions of student individuals and groups were evidently found to have influenced cognitively some teachers' further problem-solving inquiries at some interview instants and stimulated their perception changes. In the lack of subject implementation in mathematics education for the theory of "formative" assessment (Black & Wiliam, 2009), based on its definition, these instants should be put as their potential creations of and/or capitalizations upon certain asynchronous moments of contingency according to their planning of instructional adjustments for more comprehensive learning and definite growths of mathematical inquiries of students according to individuals' needs of problem-solving. Due to QCA, these perception changes might be characterized by four certain inductively formed categories of scenarios of perceptions, which were summarized as 1) Evaluation Perception, 2) Assumption Expansion Perception, 3) Assumption Collection Perception, and 4) Intention Indecision Perception. These scenarios of perceptions might be used to explore teachers' intentions, actions, and coherency in accounting for students' used assumptions in mathematical inquiries for given problem-solving contexts and extensions of given intentions of mathematical inquiries, particularly in their designs of mathematical tasks. Teacher uses of ill-posed problems were shown to have provided certain evidences in implementing formative assessments which should substantiate a subject implementation of its theory in the discipline of mathematics education. Methodologically, the current study also substantiate how theory-guided designs of ill-posed problems as well as generic plain text analysis through QCA have facilitate effectiveness comparisons of instructional adjustments within a teacher, across different teachers, decided prior knowledge, students of prior mathematical learning experiences, and students in different levels of schooling and class size.

In this workshop, we present a model of problem that we call Research Situation for the Classroom (RSC). The aim of a RSC is to put students in a role close to a mathematical researcher in order to make them work on mathematical thinking/skills. A RSC has some characteristics : the problem is close to a research one, the statement is an easy understandable question, school knowledge are elementary, there is no end, a solved question postponed to new questions... The most important characteristic of a RSC is that students can manage their research by fixing themselves some variable of the problem. So, a RSC is completely different from a problem that students usually do in France. For short : there is no final answer, students can try to resolve their own questions : a RSC is a large open field where many sub-problems exist; the goal for the students is not to apply a technique: the goal is, as for a researcher, to search. These type of situations are particularly interesting to develop problem solving skills and mathematical thinking. They can also let students discover that mathematics are “alive” and “realistic”. This workshop will be split into two parts. First, we propose to put people in the situation of solving a RSC to make them discover practically what is it. After, we present the model of a RSC and some results of our experimentations.