Jogos e situações-problema podem ser utilizados para desafiar e estimular os alunos, podendo ser recursos úteis para uma aprendizagem diferenciada e significativa. Assim, a presente pesquisa teve como objetivo proporcionar a prática de dois jogos - o Kenken e o Feche a Caixa - em 10 oficinas para alunos da Escola Fundamental II. Nessas oficinas a pesquisadora observou como os alunos utilizavam seu raciocínio lógico-matemático para solucionar jogos e situações-problema, argumentavam suas respostas e lidavam com erros e acertos. A pesquisadora buscou compreender o que era jogo e o que era raciocínio lógico-matemático a partir do referencial teórico piagetiano. A análise dos dados foi feita com base no desempenho de cada participante nas diferentes atividades propostas, focando principalmente nas estratégias utilizadas, nos erros cometidos e no comportamento dos alunos frente aos desafios. Os resultados apontaram que os alunos aprenderam a jogar de acordo com as regras e objetivos e também desenvolveram algumas boas estratégias, mas não conseguiram dominar um dos jogos de forma lógica. Entretanto, foi possível inferir que esses jogos se mostraram bons instrumentos para fortalecer os processos de aprendizagem, pois envolviam conhecimentos matemáticos, aritméticos, geométricos e lógicos, além de serem bastante motivadores / Games and problem-situations can be used to challenge and stimulate students, being considered useful resources for a meaningful learning. Thus, the present study aimed to provide the practice of two games - Kenken and Shut the Box for Middle School students during 10 workshops. In these workshops the researcher observed how students used their logical-mathematical skills to play games and solve problem situations, and also how they argued their answers and dealt with their mistakes. The Piagetian theory was used by the researcher to understand what game and logical-mathematical thinking mean. Data analysis was based on the performance of each participant in all activities proposed, focusing mainly on the strategies used, the mistakes and the behavior of students facing the challenges. The results showed that students learned the rules and objectives and also developed some good strategies in both games but failed to logically dominate one of the games. However, it was possible to infer that these games are good tools to improve the learning processes because they involve mathematical, arithmetical, geometrical and logical knowledge, besides being quite motivating

The main thrust of this study, therefore, revolved around the "scale-up" of the Case Instructional Sequence into a classroom size application able to be implemented by instructors with little additional practice in employing thistype of instructional sequence. Specifically, the purpose of this study was to determine the effect of the Case type treatment on the performance of two successive ninth grade physical science classes at a private, college-preparatory, secondary school in northeast Florida. These groups were to be assessed using the Tobin and Capie Test of Logical Thinking, a measure which could help assess their respective Piagetian stage.

Un club de matemáticas se conforma por estudiantes principalmente de secundaria que desean reunirse para realizar actividades adecuadas, así como perfeccionar o adquirir conocimientos y destrezas en esta área. De acuerdo con la experiencia se sabe que el poseedor del conocimiento del lenguaje matemático y las competencias derivadas de esta disciplina tendrá algunas ventajas significativas de cara a su desempeño escolar y posteriormente a nivel técnico y profesional. Las nuevas metodologías de los procesos enseñanza-aprendizaje, hacen necesaria una integración entre las diversas áreas. Hemos visto como en muchas ocasiones se trabaja de manera independiente en cada una de ellas desaprovechando la oportunidad que se tiene de fortalecer los aprendizajes y de lograr unos mejores resultados en los estudiantes. Además, al dialogar con los estudiantes, observamos que les gusta la iniciativa de integrarse con estudiantes de otros grupos para compartir ideas, conocimientos, opiniones de diversos temas en general y en particular en lo relacionado con las matemáticas. A través de la vivencia en las clases de matemáticas hemos observado como en muchos de los estudiantes existe el interés por trabajar o profundizar en los temas que se presentan en esta materia, ya que las matemáticas son una herramienta fundamental para el desarrollo de muchos temas. Surge entonces la iniciativa de conformar un Club de Matemáticas que permita la integración de estudiantes de diversos grupos alrededor de esta área para que sirva como medio de intercambio de experiencias, mejoramiento académico y mecanismo de profundización y más aun con un nivel de preparación para participar en Olimpiadas de Matemática. / A math club is made up of mainly high school students who want to get together to carry out appropriate activities, as well as to perfect or acquire knowledge and skills in this area. According to experience, it is known that the possessor of the knowledge of mathematical language and the competences derived from this discipline will have some significant advantages regarding their academic performance and later at a technical and professional level. The new methodologies of the teaching-learning processes make an integration between the various areas necessary. We have seen how on many occasions they work independently in each one of them, wasting the opportunity they have to strengthen learning and achieve better results in students. In addition, when dialoguing with the students, we observed that they like the initiative of integrating with students from other groups to share ideas, knowledge, opinions on various topics in general and in particular in relation to mathematics. Through the experience in mathematics classes we have observed how in many of the students there is an interest in working or delving into the topics presented in this subject, since mathematics is a fundamental tool for the development of many topics. Then the initiative arises to form a Mathematics Club that allows the integration of students from different groups around this area to serve as a means of exchange of experiences, academic improvement and deepening mechanism and even more with a level of preparation to participate in Mathematical Olympics. / Trabajo de investigación

The purpose of this study was to investigate (a) the role of a yearlong geometry course on high school geometry students' logical thinking and proof construction abilities, (b) the linkage between students' logical thinking and proof construction abilities, and (c) the impact of dynamic geometry software on students' performance. In addition, this study also ventured to determine if the type of geometry course had any impact on students' logical thinking and proof construction achievement. The sample for the study consisted of 1,325 high school geometry students enrolled in regular, honors, and mastery courses in four high schools from the school district affiliated with the Local Education Agency (LEA) during the academic year 2004-2005. Geometer's Sketchpadä (GSP) was assumed to represent the dynamic geometry software. Responses of students on two pre-tests and two post-tests, each with one on logical thinking and one on proof, were analyzed to address the research questions. Results of the analyses indicated no significant effect of the yearlong geometry course on the performance of students on proof tests but a fairly significant effect on the tests of logical thinking. Use of GSP was found to have some impact on honors and mastery students' performance on proof post-tests. Honors students showed a higher logical thinking level than their regular and mastery counterparts in both GSP and non-GSP groups. There was a significant positive correlation between students' performance on the tests of logical thinking and proof.

Orientador: José Carlos Miguel / Banca: Cyntia Graziella Guizelim Simões Girotto / Banca: Paulo César de almeida Raboni / Resumo: Este trabalho teve como objetivos a análise das heurísticas envolvidas numa experiência de ensino por meio da perspectiva metodológica da resolução de problemas e a análise da relação dos alunos do Ensino Médio com a disciplina Matemática. À luz da Teoria Histórico-Cultural, este trabalho pode contribuir para análise da subjetividade dos processos de formação de conceitos, dos modos de pensar dos educandos face à aprendizagem Matemática, de sua criatividade e raciocínio lógico ao resolver problemas. A metodologia utilizada foi a pesquisa qualitativa. Os alunos, sujeitos da pesquisa, foram considerados ora como resolvedores, ora como propositores de problemas; os dados foram coletados, em aulas de Matemática, de Maio a Novembro de 2.007. Ao conhecer como a experiência e os conhecimentos específicos afetam a solução de um problema, analisei os resultados e conclui que a eficiência na sua resolução depende não somente da memória, das idéias prévias e estratégias, mas de todos esses processos enunciados que participam efetivamente da formação do conceito matemático. Também conclui que prevalece, ainda, entre os educandos, uma visão ingênua e marcada por mitos resistentes a respeito da Matemática, porém se mostraram criativos ao resolverem problemas e modificaram aspectos importantes na sua relação com esta disciplina após serem submetidos a aulas na perspectiva metodológica de resolução de problemas. Pode-se afirmar que a perspectiva mencionada anteriormente propicia o conhecimento da Matemática, conduz à formação dos conceitos e ao desenvolvimento da criatividade dos educandos. Em suma, faz-se necessária uma ampla revisão na prática pedagógica desenvolvida em Matemática, a fim de que esta contribua para que os educandos tornem-se sujeitos de transformações sociais. / Abstract: This paper had as the goal the analysis of heuristics involved in a teaching experience through the methodological perspective of the problems solving and the analysis of the relations from the high school students with the subject Mathematics. In the light the view of the Historical-Cultural Theory, this paper can contribute for the analysis of the subjectivity of the concept-formation processes, the learners’ ways of thinking when talking about the Math’s learning, their creativity and logical thinking while solving problems. The methodology applied was the qualitative research. The students, individuals of the research, were considered sometimes problem-solvers and other times problem-proposers; the data were collected, in Math classes, from May to November, 2.007. When we know how the experience and the specific knowledge affect the solving of a problem, I analyzed the results and concluded that the efficiency in this resolution depends not only memory, previous ideas and strategies, but through all these mentioned processes that effectively take part in the formation of the Math concept. I concluded that it prevails, yet, among the learners a naïve view and marked by resistant myths concerning to Math, but they showed themselves creative when solving problems and changed important aspects of their relation with this subject after being given classes in the methodological perspective of the problem solving. We can state that the perspective mentioned above provides the Math knowledge; it conducts to the formation of concepts and the development of the learners ׳ creativity. In short, it is necessary a large review on the pedagogical practice developed in Mathematics, so that this subject can contribute for the learners to become individuals from social transformations. / Mestre

The purpose of this study was to investigate the effects of conceptual change text oriented instruction accompanied by demonstrations in small groups (CCTI) on ninth grade students&rsquo / achievement and understanding levels of ecology, attitudes towards biology, and attitudes towards environment. The instruments used in this study were the Test of Ecological Concepts (TEC), the Attitude Scale towards Biology (ASB), the Attitude Scale towards Environment (ASE), and the Test of Logical Thinking (TOLT). All data were collected from the public high school in Balikesir in the Spring Semester of 2001-2002. 88 students from four classes and two teachers were included in this study. Two of the classes were called control group and two of them were called experimental group. While the TEC, ASE and ASB were administered to all of the students as pre- and post-tests, the TOLT were conducted as pre-test. Data related to the TEC, ASB, and ASE were analyzed by multivariate analysis of covariance (MANCOVA). The results of the MANCOVA showed that there was significant effect of the treatment which was the conceptual change texts oriented instruction accompanied by demonstrations in small groups on the TEC, while there were no significant effect of the treatment on the attitudes towards biology and attitudes towards environment.

The purposes of the study were / to investigate the effect of type of high school on spatial ability, to investigate the relationships between students&rsquo / mathematics achievements, logical thinking abilities and their spatial abilities and to investigate the effect of technical drawing course on the development of students&rsquo / spatial abilities. The study was conducted in Ankara with 251 9th-grade students who enrolled to general, Anatolian, foreign language, commercial vocational and industrial vocational high schools. Two measuring instruments were utilized: Spatial Ability Tests and Group Test of Logical Thinking. Spatial Ability Tests, which were developed by Ekstrom, consist of card rotation, cube comparison tests measuring the spatial orientation ability and paper folding and surface development tests measuring the spatial visualization ability. The tests were translated in to Turkish by Delialioglu, (1996). Group Test of Logical Thinking was developed by Roadrangka, Yeany, and Padilla and a Turkish version of GALT was developed by Aksu, Beberoglu and Payko&ccedil / (1990). In order to analyze the obtained data, one way ANOVA, correlation analysis and t-test were used. The results of the study indicated that / there is no significant effect of type of high school on students&rsquo / spatial abilities / there is a significant positive relationship between spatial ability and mathematics achievement / there is a significant positive relationship between spatial ability and logical thinking ability / there is a significant positive relationship between spatial ability and technical drawing achievement / and there is a significant development in the students&rsquo / spatial abilities of the students in the technical drawing course.

Made available in DSpace on 2016-06-02T20:02:57Z (GMT). No. of bitstreams: 1 6432.pdf: 3122043 bytes, checksum: 082819afaa3a0b58bb6c250635b34e25 (MD5) Previous issue date: 2014-11-10 / This research has as main objective making a manipulative material to work sequences of activities by introducing the notion of Combinatorial Analysis in an intuitive and natural way in elementary school final years. Without using formulas, it presents an encouragement to use the Multiplicative Principle, tree diagram and list of possibilities as an important tool for solving various problems. We started the research making a description of the current curriculum documents in the Department of Education of the State of São Paulo, followed by historical overview and theoretical foundation. The survey was developed with the implementation of three activities with students from the 5th grade - 6 year to 8th grade - 9th year of elementary school in a Public State School in the city of Sorocaba/SP. These activities were designed to find out the students difficulties in the development of problems involving Combinatorial reasoning and to propose manipulative materials at low cost and to help in the construction and understanding of that content, since a big part of students and teachers consider it difficult to understand. These manipulative materials represent the final product of this research and it is hoped that teachers use them in their classrooms to make their classes more dynamic, rich and arousing the interest of the students. / A presente pesquisa tem como objetivo principal a confecção de material manipulável para trabalhar sequências de atividades introduzindo de maneira intuitiva e natural a noção de Análise Combinatória no Ensino Fundamental Anos Finais sem a utilização de fórmulas, incentivando o uso do Princípio Multiplicativo, do diagrama de árvore e da enumeração das possibilidades como uma ferramenta importante para a resolução de vários problemas. Iniciamos a pesquisa fazendo uma descrição dos documentos curriculares vigentes na Secretaria da Educação do Estado de São de São Paulo, seguida por um panorama histórico e fundamentação teórica. A pesquisa foi desenvolvida com a aplicação de três atividades com alunos da 5ª série/6º ano a 8ª série/9º ano do Ensino Fundamental de uma Escola Pública Estadual da cidade de Sorocaba/SP. Essas atividades foram elaboradas com o objetivo de constatar as dificuldades dos alunos no desenvolvimento de problemas que envolvam o raciocínio combinatório e propor materiais manipulativos, de baixo custo, que auxiliem na construção e compreensão desse conteúdo, considerados de difícil entendimento por grande parte de alunos e professores. Esses materiais manipulativos representam o produto final dessa pesquisa e espera-se que os professores o utilizem em suas salas de aulas para tornar suas aulas mais ricas e dinâmicas despertando o interesse dos alunos.

A presente dissertação é um estudo realizado sobre as dificuldades apresentadas pelos alunos do 5º ano do Ensino Fundamental ao resolver problemas de Matemática. Tendo como referenciais teóricos Polya, Dante, Krulik, Onuchic e Allevato, Smole, dentre outros. A coleta de informações foi realizada em duas turmas do 5º ano, sendo uma da rede pública e outra da rede privada. Os instrumentos da pesquisa incluíram a aplicação de um teste diagnóstico, contendo quatro diferentes tipos de problemas de aritmética, e entrevista de explicitação registrada em áudio, baseada no método clínico de Piaget, com três alunos de cada turma. Como base foram identificadas no teste diagnóstico quatro categorias de análise: dificuldades para compreender o enunciado do problema, dificuldades em uma etapa do procedimento, dificuldades por desconhecimento do conteúdo e dificuldade conceitual das operações básicas. Através da análise dos dados foi possível identificar quais as dificuldades dos alunos para a resolução de problemas de matemática e também compreender como as crianças pensam e agem ao responder diferentes tipos de problemas.

This essay will address the introduction of programming as an element in the compulsory school curriculum and examine the extent to which teachers have been affected by the introduction of programming in curriculaand syllabi. The essay is based on two questions: "What difficulties and opportunities have arisen in the teaching after programming was implemented in the syllabus?" and "What forms of pedagogy can teachers use to best support the development of logical thinking, problem solving, creativity and a structured approach through programming skills?". The questions are answered using scientific literature and analysis of previous scientific research. The results of the study are, among other things, that there is a great deal of uncertainty in how programming should be implemented in the students' syllabi, but also how the teachers should feel comfortable in teaching such a new subject when there is a lack of proper training for the teachers. Another conclusion is that the biggest reason for the introduction of programming in schools is to strengthen students' digital skills as society becomes increasingly digital.