Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T14:29:24Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Alberto Soares - 2014.pdf: 3067775 bytes, checksum: 5f48b927a38578815e19f420ff1f1cd9 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T14:35:13Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Alberto Soares - 2014.pdf: 3067775 bytes, checksum: 5f48b927a38578815e19f420ff1f1cd9 (MD5) / Made available in DSpace on 2015-01-27T14:35:16Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Alberto Soares - 2014.pdf: 3067775 bytes, checksum: 5f48b927a38578815e19f420ff1f1cd9 (MD5) Previous issue date: 2014-08-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims to propose a different approach for teaching elementary functions in high school context, worrying about concepts understanding, definitions elementary functions characterizations. The didactic-pedagogic proposal presents a mathematical modeling from different regarding daily themes simulators from internet, which encourage students “to see”, hidden functions, and improve learning and teaching. In order to do math more interesting for student, it‟s necessary to experience the practical applications, simulating real nature situations and confronting results with theoretical calculations, to do sure those concepts and functions definitions have become a solid knowledge. / Este trabalho tem como objetivo principal propor uma abordagem diferenciada para o ensino das funções elementares no contexto do ensino médio, preocupando-se com a compreensão dos conceitos, definições e caracterizações das funções elementares. A proposta didático-pedagógica apresenta a modelagem matemática a partir de simuladores referentes a vários temas do cotidiano retirados da internet, o qual estimulam os alunos a “enxergarem” as funções escondidas, e melhorar o ensino aprendizagem. Com o intuito de tornar a matemática mais interessante para o aluno, faz se necessário vivenciar aplicações na prática, simulando situações reais da natureza e confrontando os cálculos com resultados teóricos, para se ter a certeza que os conceitos e definições das funções se tornaram um conhecimento sólido.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-07-13T20:13:32Z No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-07-14T13:28:30Z (GMT) No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-07-14T13:28:30Z (GMT). No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we will study a new strategy to minimize a convex function on a simplicial cone. This method consists in to obtain the solution of a minimization problem through the root of a semi-smooth equation associated to its optimality conditions. To nd this root, we use the semi-smooth version of the Newton's method, where the derivative of the function that de nes the semi-smooth equation is replaced by a convenient Clarke subgradient. For the case that the function is quadratic, we will see that it allows us to have weaker conditions for the convergence of the sequence generated by the semi-smooth Newton's method. Motivated by this new minimization strategy we will also use the semi-smooth Newton's method to nd roots of two special semi-smooth equations, one associated to x+ and the another one associated to jxj. / Neste trabalho, estudaremos uma nova estrat egia para minimizar uma fun c~ao convexa sobre um cone simplicial. Este m etodo consiste em obter a solu c~ao do problema de minimiza c~ao atrav es da raiz de uma equa c~ao semi-suave associada as suas condi c~oes de otimalidade. Para encontrar essa raiz, usaremos uma vers~ao semi-suave do m etodo de Newton, onde a derivada da fun c~ao que de ne a equa c~ao semi-suave e substitu da por um subgradiente de Clarke conveniente. Para o caso em que a fun c~ao e quadr atica, veremos que e poss vel obter condi c~oes mais fracas para a converg^encia da sequ^encia gerada pelo m etodo de Newton semi-suave. Motivados por esta nova estrat egia de minimiza c~ao tamb em usaremos o m etodo de Newton semi-suave para encontrar ra zes de dois tipos espec cos de equa c~oes semi-suaves, uma associada a x+ e a outra associada a jxj.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-03T14:04:36Z No. of bitstreams: 2 Dissertação - Francisco Fabio Monteiro de Ameida - 2016.pdf: 1329167 bytes, checksum: 102bfaddf62d4fafa436b4f868337d0d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-03T14:08:11Z (GMT) No. of bitstreams: 2 Dissertação - Francisco Fabio Monteiro de Ameida - 2016.pdf: 1329167 bytes, checksum: 102bfaddf62d4fafa436b4f868337d0d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-03T14:08:11Z (GMT). No. of bitstreams: 2 Dissertação - Francisco Fabio Monteiro de Ameida - 2016.pdf: 1329167 bytes, checksum: 102bfaddf62d4fafa436b4f868337d0d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-31 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The main goal of this work is to verify that we can assign the oblique launch a mathematical approach. To reach this conclusion, we address important issues of mathematics and physics, as linear functions and quadratic functions , and uniform and uniformly varied movements. These concepts were presented to facilitate understanding and implement an equation that allows to determine the moment of rise, the maximum height and horizontal reach, knowing an shot's angle, the initial velocity and gravity's acceleration. / O objetivo principal desse trabalho é veri car que podemos atribuir ao lançamento oblíquo uma abordagem matemática. Para chegarmos a esta conclusão, abordamos assuntos importantes da Matemática e da Física, como funções a m e quadrática, e movimentos uniforme e uniformemente variado. Tais conceitos foram apresentados para facilitar o entendimento e implementar uma equação que permita determinar o instante de subida, a altura máxima e o alcance horizontal, conhecendo um ângulo de tiro, a velocidade inicial e a aceleração da gravidade.

The study’s purpose was to explore the components of pedagogical content knowledge (PCK) for teaching quadratic function in Grade 10 mathematics classrooms in Mogalakwena district, Limpopo. The study was mainly guided by Shulman’s PCK and it was categorised as content knowledge, knowledge of the curriculum, knowledge of learners and knowledge of teaching strategies. The researcher employed a qualitative case study research design to explore the teaching of three purposefully selected Grade 10 mathematics teachers regarding their knowledge of quadratic function, strategies employed to teach quadratic function and knowledge of Grade 10 mathematics learners in quadratic function. In this study the researcher argued that PCK strands are interwoven, and in order to teach mathematical concepts, such as quadratic function, effectively teachers should employ components of PCK to complement one another. Data were gathered by lesson observation and interviews. Findings revealed that concepts of quadratic function are inefficiently addressed in Grade 10 due to teachers’ lack or inadequacy in some aspects of PCK. Therefore, there is need to develop mathematics teachers’ PCK in the Mogalakwena district to enhance their teaching of Grade 10 quadratic function. / Mathematics Education / M. Ed. (Mathematics Education)

Made available in DSpace on 2016-04-27T16:57:54Z (GMT). No. of bitstreams: 1 dissertacao_diana_maia.pdf: 2211549 bytes, checksum: 0b656e7207483294a3bdc1ff6f9fa699 (MD5) Previous issue date: 2007-05-17 / This research aims to supplement the studies that have already been conducted in regard to teaching quadratic functions as well as the utilization of software that support this teaching. It also aims to consider graphs of quadratic functions by making use of the global interpretation of the properties of images, as well as by adding a playful dynamic to initiate students into the notion of interval and function domain. The study has its theorectical roots based on the principles of Didactic Engineering and Raymond Duval´s Theory of Semiotic Representation Registers and Guy Brousseau s Theory of Didactical Situations. The didactic studies presents some brief analyses of some primary and middle school level didactic books and builds upon Benedetti s research (2003) about the utilization of graph software as well as Duval s research (1998) about the articulation problems between the graphical and algebraic registers. The computer-based tool used for the application of this study was Winplot. The study was carried out with private school students undergoing the 8th grade in the City of São Bernardo do Campo in the state of São Paulo. Data from four pairs that took part in seven research sessions were reviewed. Results reveal that an improvement was obtained and better retention was measured amongst students in regards of the square function concept, which was achieved by the articulation between visual variables and meaningful symbolic units / Esta pesquisa tem por objetivo, complementar estudos já realizados a respeito do ensino da função quadrática e da utilização de software para este fim. Com o intuito de abordar a questão da construção gráfica da função quadrática utilizando o procedimento de interpretação global das propriedades figurais e, ainda, inserir uma dinâmica lúdica para introduzir as noções de intervalo e domínio da função. Fundamentada nos princípios da Engenharia Didática e embasada na Teoria dos Registros de Representação Semiótica de Raymond Duval e na Teoria das Situações de Guy Brousseau. A seqüência didática apresentada orienta-se nas análises de alguns livros didáticos do Ensino Fundamental e Médio, nas pesquisas de Benedetti (2003), sobre a utilização de software gráficos e sobre o trabalho de Duval (1988) sobre a articulação entre os registros gráfico e algébrico. A ferramenta computacional utilizada na aplicação da seqüência foi o software Winplot, além do uso de papel e lápis. A seqüência foi aplicada com alunos da oitava série do Ensino Fundamental de uma escola particular na cidade de São Bernardo do Campo no estado de São Paulo. Foram analisados os protocolos de quatro duplas, que participaram das sete sessões. Os resultados obtidos levam a concluir que houve um avanço por parte dos alunos, na apreensão do conceito de função quadrática, propiciado pela compreensão e articulação entre as variáveis visuais e unidades simbólicas significativas

本研究旨在探討如何設計以建構主義為基礎的網際網路合作學習環境，以研發二次函數網際網路課程，並藉由實驗研究法分析在網際網路合作學習情境中，不同的學習型態與認知風格對於學習成效之影響，最後以質性研究法探討學生合作互動歷程之認知模式及相關影響因素，並分析學生學習二次函數易犯之錯誤類型。 本研究使用之研究方法包括學習軟體研發、實驗研究法、問卷調查法、晤談法、及內容分析法。研究者首先研發及評量「二次函數網際網路課程」，並隨機選擇國民中學二年級學生60名為研究對象，依學習型態及學生認知風格分成內控單獨組、外控單獨組、內控合作組、外控合作組、內外控混合合作組等五組進行教學實驗。俟教學實驗後進行紙筆測驗、問卷調查、及晤談，研究者並搜集學生在電子白板上的對話進行內容分析。根據研究結果分析，本研究主要之結論如下： 一、網際網路合作學習環境有助於學生學習數學二次函數概念在網際網路合作學習環境中，提供合作的視覺學習環境，協助學習者多重轉化代數表徵成為幾何表徵的動態網頁，使學習者在不同條件脈絡中進行比較、反思，以了解二次函數中代數與幾何的關係，已有具體的教學成效。 二、 在網路學習環中，不同認知風格的學生在個別學習效果上有差異存在在網際網路個別學習環境中，內控組的學習成效顯著優於外控組。即在網際網路學習環境中，採用個別學習策略，具外控取向特質的學習者，學習成效不佳；而具內控取向特質的學習者，有較佳的學習成效。 三、在網路學習環境中，不同認知風格的學生在合作學習效果上未有顯著差異存在在網際網路合作學習環境中，內控合作組、外控合作組、及內外控混合合作組的學習成效無顯著差異。研究顯示透過合作學習可提升外控取向學習者的學習成效，淡化認知風格對學習者的影響。 四、 網際網路合作學習互動歷程為個人建構、群體澄清、知識重構、群體重構的認知改變模式在網際網路合作學習互動歷程中，個人先形成自我的知識概念，並將個人建構的基模公開呈現與他人分享，當個體的認知概念間產生差異時，合作群體間即產生質疑，並提出澄清，經澄清後合作群體彼此協商，重構知識、統合意見並產生共識，即成為合作小組的認知概念。 五、 同儕模式的網際網路合作學習方式缺少高支持性鷹架結構以同儕為基礎的網際網路合作學習環境中，因學生的先備知識不足及溝通技巧的缺乏，容易產生錯誤概念的學習及習得片斷的知識。是以，針對年齡小或能力低的學習者所設計的網際網路合作學習課程，教師的參與討論與互動是必要的，以能提供學習者高支持性鷹架結構。 六、 在網際網路合作學習環境的互動歷程中，外控取向學習者佈題的行為多於內控取向學習者研究中發現外控取向學習者佈題的行為多於內控取向學習者，內控取向學習者解題的行為多於外控取向學習者。 根據研究結果，本研究提出下列建議，以供教學者、教學媒體設計者、教育行政單位、及後續研究者之參考： 一、應整合學科專家、教育專家、電腦網路程式設計師、美術專業人士以研發更符合學習者需求的網路課程。 二、宜針對學習者特性提供不同的網路教學策略，使建構的網際網路課程更符合學習者的需求。 三、在網際網路合作學習環境中，課程設計應以討論情境、分享知識、及解決問題為主，始能提升合作成效。 四、宜訂定網路界面設計標準及評鑑指標，以做為網路課程發展的依據。 五、在網際網路合作學習環境中，教師應適度參與學生的討論活動，提供鷹架支持的功能。 六、應加強國家整體網路基礎建設，使能改善網路教學品質，提高學習成效。 / The Purpose of this study is threefold.　One is to explore how to design a quadratic function internet curriculum in the internet computer-based collaborative learning environment, based on constructivism. Second, learning effects of different learning styles and cognitive styles in the internet collaborative learning context are analyzed through empirical research methods. Third, the students' cognitive modes and other relative factors in the collaborative learning interaction process, as well as the students' frequent error types in learning quadratic functions, are identified and analyzed through qualitative research methods. The research methods adopted in this study include the development of learning software, empirical research methods, questionnaires, interviews, and content analysis. The researcher first developed and assessed the "internet curriculum of quadratic functions", and selected 60 second graders of a junior high school as research subjects, according to the students' learning and cognitive styles, and categorizing them into the group of internal locus of control with individual learning, the group of external locus of control with individual learning, the group of internal locus of control collaborative learning, the group of external locus of control with collaborative learning, and the group of mixing internal-external locus of control with collaborative learning to implement teaching experiments. After the experiments were finished, the research conducted a written test, questionnaire surveys, and interviews. Besides, the students' dialogue data on Bulletin Board System was collected and analyzed. Based on the analysis results of this study, the main conclusionsare as follows: 1. Internet collaborative learning environment facilitates students learning the concepts of quadratic functions. In the environment of the internet collaborative learning, interactive web pages provide visualized collaborative learning context, assist learners to transform algebraic representation into geometric representation, and give learners opportunities to compare and rethink in different conditions about the relations of algebra and geometry in quadratic functions.　All of which have been proved to have concrete learning effects. 2. In the environment of the internet learning, individual learning effect differences exist among students of different cognitive learning styles. In the environment of the internet individual learning, learning effects of the external control group are better than those of the internal control group. In other words, learners with external locus of control, using individual learning strategies do not have good learning effects.　However, learners with internal locus of control have better learning effects. 3. In the environment of the internet learning, there is no significant differences among students with different cognitive styles. In the environment of the internet collaborative learning, the learning effects among the group of internal locus of control collaborative learning, the group of external locus of control with collaborative learning, and the group of mixing internal-external locus of control with collaborative learning show no significant differences.　This study shows collaborative learning help improve the learning effects of learners with external locus of control, and ease the impacts of cognitive styles on learners. 4. The interaction process of the internet collaborative learning is a cognitive revolution of individual construction, group clarification, knowledge reconstruction, and group reconstruction. In the interaction process of the internet collaborative learning, individuals form self knowledge concepts, and shares their self-constructed sckema with other people. When individual cognitive differences occur, there will be questioning, clarifying, negotiating, reconstructing the knowledge, integratingopinions, and reaching common agreements, which will become the cognitive concepts of the collaborative group. 5. Peer collaborative learning on the internet lacks highly-supportive scaffolding structures. In the context of peer collaborative internet learning, it is easy for students to learn incorrect concepts and incomplete knowledge content, owning to their insufficient prior knowledge and communication skills. Therefore, in designing the internet collaborative learning curriculum for young or incompetent learners, it is a must to involve the teachers to join the discussion and interaction, in order to provide learners highly-supportive scaffolding structures. 6. In the interaction process of the internet collaborative learning, learners with external locus of control have more problem posing behaviors than those with internal locus of control. The study finds that learners with external locus of control have more problem posing behaviors than those with internal locus of control. On the other hand, learners with internal locus of control have more problem solving behaviors than those with external locus of control. Based on the research results, this study proposes the following suggestion for the reference of teachers, educational media designers, education admonitions, and future researchers: 1. Discipline experts, education experts, internet engineers, computer programmers, art designers should cooperate to develop the internet curricula which meet learners' needs more perfectly. 2. Different internet teaching strategies should be provided based on learners' characteristics, in order to make the constructed internet curricula meet learners' needs more perfectly. 3. In the environment of internet collaborative learning, syllabus design should be mainly on discussing situations, sharing knowledge, and solving problems, in order to facilitate collaboration effects. 4. It is better to set the internet interface design standards and evaluation indexes to provide a basis for the internet curricular development. 5. In the environment of the internet collaborative learning, teachers should attend students' discussions when needed, functioning as scaffolding support. 6. National Information Infrastructure should be improved to have higher internet learning quality and thus to enhance learning effects.