Arbetets syfte är att undersöka hur högstadieelever för matematiskt resonemang. De frågeställningar som studien inriktas på är vilka lösningsstrategier elever väljer då de resonerar matematiskt såväl som vad  det finns för skillnader och likheter mellan de yngre elevernas lösningar och de äldre elevernas lösningar. Undersökningen genomfördes i två klasser, den ena i årskurs 8 och den andra i årskurs 9, på en grundskola. Eleverna fick lösa uppgifter, vilka uppmanade dem att föra matematiskt resonemang, individuellt. Resultatet av studien visar att majoriteten av undersökta elever har valt att resonera deduktivt. Jämförelsen av elevers lösningar i två årskurser visar att årskurs 9 elevers resonemangsföring präglas av större förtrogenhet med den algebraiska demonstrationen. Resultatet visar även att elever med högre kunskaper om algebra oftare visar benägenheter till att vidaregeneralisera de givna påståendena. / The purpose of this study is to examine secondary school students’ strategies of reasoning. The study inquires into which strategies students choose when reasoning mathematically as well as differences and similarities between the younger students’ solutions and the older students’ solutions. The study was conducted in two classes, in years 8 and 9 respectively, at a secondary school. The students were asked to solve tasks, which encouraged them to reason mathematically, on individual basis. The study revealed that the majority of students had chosen to reason deductively. The comparison of students’ presented answers in two years showed that the ninth-graders’ solutions are characterized of greater skill when it comes to algebraic demonstrations. The results of the study also reveal that students with stronger algebraic abilities attempt more often to generalize the given mathematical statements further.

Проблематику алгоритмизации мышления и исследования в области создания систем искусственного интеллекта объединяет вопрос «Может ли машина мыслить?» Несмотря на то, что две данные области по-разному отвечают на вопрос о возможности мышления машины, результаты достигнутые в одной области могут повлиять на другую. Объектом исследования являются проблематика алгоритмизации мышления и интеллект в концепции Дж. Хокинса. Предметом исследования являются ограничения на алгоритмизацию в связи с моделью «память-предсказание». Цель исследования - рассмотреть проблематику алгоритмизации мышления в связи с концепцией Дж. Хокинса. Методы, применяемые в исследовании: концептуальный и логический анализ. Новизна данной диссертационной работы заключается в сопоставлении проблематики алгоритмизации мышления с современным исследование в области создания ИИ, концепцией Дж. Хокинса. В результате исследования установлено, что в основе интеллекта лежит модель «память-предсказание». Используя данную модель, становится возможным решить практически все проблемы, связанные с ограничениями на алгоритмизацию мышления. Выяснено, что концепт обозримости доказательства можно применить для оптимизации работы интеллектуальных систем. / The problem of algorithmizing thinking and research in the field of creating artificial intelligence systems unites the question "Can the machine think?" Although these two areas of knowledge respond differently to the question of the machine's thinking capabilities, the results achieved in one area can affect the other. The object of research work are problems of algorithmization of thinking and intellect in the theory of J. Hawkins. The subject of the research work are constraints on algorithmization in connection with the memory-prediction model. The purpose of the research work is to consider the problems of algorithmizing thinking in connection with the theory of J. Hawkins. Methods used in the research work: conceptual and logical analysis. The novelty of this research work is to compare the problems of algorithmizing thinking with modern research in the field of creating AI, the concept of J. Hawkins. As a result of the research it was established that the intellect is based on the memory-prediction model. Using this model, it becomes possible to solve almost all the problems associated with limitations on the algorithmization of thinking. It is clarified that the concept of surveyability of proof can be applied to optimize the operation of intelligent systems.

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Made available in DSpace on 2016-04-27T16:58:27Z (GMT). No. of bitstreams: 1 Antonio Carlos Eduardo.pdf: 25009681 bytes, checksum: 9704f78f02dc015433c456f384128734 (MD5) Previous issue date: 2007-10-15 / Secretaria da Educação do Estado de São Paulo / This research invests in the conception of learning environments aimed to contribute to the creation of a culture of argumentation, proving and proof in mathematics classrooms. It developed within the context of the project AProvaME as part of the exploration of how to initiate students into aspects of the proving process in relation to the topic of Arithmetic Progressions. In designing this learning environment, we sought contributions from the studies of Bordenave from the areas of the Communication Science and in the field of Mathematics Education, from research relatied to argumentation and in particular the work of Bolite Frant and Castro and of Maher. These contributions enabled the elaboration of an interactive environment for the mediation of mathematical ideas. One of the roles of mediation within the study focuses, in the light of Communication, on the action of the teacher during the negotiation of the mathematics presented in the classroom. Aspects related to socialisation, interaction and mediation were inspired by the constructionist proposal of Papert and other constructionist thinkers. On the basis of these studies, an approach was adopted to the use of technology involving the conception of visual objects embedded within activities aiming to support the development of certain habits of mathematical thinking delineated by Goldenberg. This qualitative study made use of didactic resources such as as the dynamic of games and the use of the computer to promote interaction and the emergence of scenarios for medication. The instruments used in the collection of data Blogs and video recordings valorised the interpretation of the dialogs which occurred within these scenarios. The use of Blogs, still not well documented in research in Mathematics Education, served to show the evolution of mathematical fluency in the arguments produced by the students and also acted as a parameter on the practice of the educator. Editing of the videos collected, permitted the formatting of fragments of registers from the dialogs in the form of cartoon strips, which came to represent a product with a wide range of possible uses both in the interpretation of dialogs and in reflections about the role of the teacher. The results obtained in this study led to recommendations for the creation of new contexts for argumentation / Esta pesquisa investe na proposição de ambiente de aprendizagem como possibilidade de criar uma cultura na sala de aula que promova / favoreça a argumentação. No transcorrer do projeto APROVAME1 surgiu a opção em explorar tópicos do conceito Progressão Aritmética para auxiliar no desenvolvimento de processos de iniciação à prova. Na implementação deste ambiente de aprendizagem buscamos contribuições advindas dos estudos de Ciência da Comunicação através de Bordenave, da Educação Matemática pelos estudos de alguns pesquisadores voltados à argumentação, dentre os quais: Bolite Frant e Castro, e estudos sobre desenvolvimento de provas de Maher. Estas contribuições possibilitaram a elaboração de um ambiente interativo e propício à prática da mediação. Um dos papéis de mediação exercido durante este estudo é apresentado à luz da Comunicação, focando na ação do professor durante a negociação matemática que se apresenta em sala de aula. Corroboram para estes aspectos socializáveis do ambiente, interação e mediação, a proposta construcionista de Papert, valorizada pela contribuição de outros estudiosos do construcionismo. Através desses estudos, um dos usos da tecnologia nesta pesquisa volta-se à elaboração de objetos visuais e possibilita o design das atividades sob a ótica do desenvolvimento de alguns hábitos de pensamento matemáticos, segundo Goldenberg. Este estudo qualitativo, emprega recursos didáticos como a dinâmica do jogo e o uso do computador, para promover a interação e o surgimento de cenários de mediação. Os instrumentos de coleta de dados vídeo e blog valorizam a interpretação dos diálogos surgidos nesses cenários. O uso do blog, ainda pouco difundido entre pesquisas da Educação Matemática, serve para mostrar a evolução da fluência matemática na argumentação dos alunos, e também atua como parâmetro da prática do educador. A edição do vídeo permitiu a formatação dos registros de fragmentos dos diálogos na forma de quadrinhos, o que veio a se constituir num produto com amplas possibilidades de uso, tanto no tocante à interpretação dos diálogos, quanto na reflexão sobre a postura do educador. Os resultados obtidos por este estudo recomendam a criação de novos Contextos para Argumentar