Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-09-08T13:54:27Z No. of bitstreams: 1 PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-09-09T18:51:21Z (GMT) No. of bitstreams: 1 PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5) / Made available in DSpace on 2016-09-09T18:55:06Z (GMT). No. of bitstreams: 1 PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5) Previous issue date: 2015-12-14 / In this work discuss optimization problems involving polynomial functions of de- gree greater than or equal to 2, where use the rate of variation to obtain the extremes, that can bemaximum orminimum. The proposal is to insert in high school the derived as rate of variation and from there to solve optimization problems, without defining the derivative formally. The problems proposed in this work meets the dynamic in the classroom, concrete problems, with some occurrence in our daily lives, may also include the areas of economics, engineering and physics. / No presente trabalho abordaremos problemas de otimização envolvendo funções polinomiais de grau maior ou igual a 2, onde utilizamos a taxa de variação na obtenção de extremos, que podem ser máximos ou mínimos relativos. A proposta é inserir no ensino médio a derivada como taxa de variação e a partir daí resolver problemas de otimização, sem definir a derivada de maneira formal. Os problemas propostos neste trabalho atende à dinâmica de sala de aula, sendo problemas concretos,com certa ocorrência no nosso cotidiano, podendo ainda abranger as áreas de economia, engenharia e física.

Advanced pulse width modulation (PWM) techniques such as space vector PWM, active zero state PWM, discontinuous PWM, and near state PWM methods are used in three-phase AC motor drives for the purpose of obtaining low PWM current ripple, wide voltage linearity range, and reduced common mode voltage (CMV). In some applications, a filter is inserted between the inverter and the motor for the purpose of reducing the stresses in the motor. The motor current PWM ripple components, terminal voltage overshoots, shaft voltage, and bearing currents, etc. can all be reduced by means of PWM techniques and passive filters. Various PWM techniques and passive filter types exist. This thesis studies the combinations of PWM techniques and filters and evaluates the performance of the motor drive in terms of the discussed stresses in the motor. PWM techniques are reviewed, a generalized algorithm for the implementation of PWM techniques is developed, and implementation on a 4 kW rated drive is demonstrated. Filter types are studied, among them the common mode inductor and the pure sine filter (PSF) configurations are investigated in detail. Filters are designed and their laboratory performance is evaluated. In the final stage the advanced PWM techniques and filters are combined, the incompatibility problem of discontinuous PWM methods with the PSF is illustrated. A cure based on rate of change limiter is proposed and its feasibility proven in the laboratory experiments. With the use of the proposed PWM algorithm and PSF, a motor drive with ideal DC to AC conversion stage (DC to pure sine) is achieved and its performance is demonstrated in the laboratory.

This research is a study of the relationship of the organizational characteristic of technology to rate of change in a human services organization. The first operation, directed to the technology construct, collected data and analyzed statistical differences on each of the separate indices of task difficulty and task variability and on the combined indices of the two dimensions. A second operation, directed to the rate of change construct, collected data and ranked the five social services programs. This research indicates that multiple technologies do exist among programs within the corporate structure of a single human services organization, and that programs differ in the rate at which rule changes occur. This research, however, indicates that technology is not related to change. The definition of change used in this study considered only one form of organizational adaptation: rate of change in program policies and procedures. Technology, however, may be related to other measures of change such as new programs, reorganizations, and staff increases.

abstract: This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change. The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development. The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items. The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions. Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2016

The shift towards collegiality is a new setting for many teachers. Most teachers work alone, in isolation from their colleagues and collegial collaboration requires organisational structures. The aim of the study is to describe and analyse upper secondary mathematics teachers’ collective practice,developed in a professional development initiative. This study is a case study and the empirical data is generated through observations and an interview of a group of four teachers at a school who met on a weekly basis throughout a term. Their discussions focused on the mathematical concept of slope in a setting of learning study. This thesis is the case of when mathematics teachers focus discussions on slope and draws on Wenger’s Communities of Practice Perspective, as a unitof analysis, and addresses the question: What are the characteristics of practice when upper secondary mathematics teachers focus discussions on slope in the setting of a learning study? The analysis accounts for characteristics of the aspects of practice, through the coherence of mutual engagement, joint enterprise and shared repertoire in the community of practice. The teachers are engaged around finding small changes in their teaching that could give major effect in students learning. They negotiate what the students need to know in order to understand the relation between Δy and Δx. The characteristic of practice is a conceptual mapping of the concept of slope. It reveals students’ partial understanding of related concepts due to how they were given meaning through previous teaching. The conceptual mapping of slope goes back as far as to the student’s partial understanding of the meaning of subtraction. However, what emerges is in relation to the teachers’ experience of avoiding students’ difficulties with negative difference when teaching slope. It turns out to be a negotiation and a renegotiation of teaching slope for instrumental understanding or conceptual understanding. An overall characteristic of practice is that it develops in a present teaching culture.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2017-07-14T18:26:15Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertaçao_César Thiago José da Silva.pdf: 4270293 bytes, checksum: c27eb9fe56f7dbe2e23b306df8911e96 (MD5) / Made available in DSpace on 2017-07-14T18:26:16Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertaçao_César Thiago José da Silva.pdf: 4270293 bytes, checksum: c27eb9fe56f7dbe2e23b306df8911e96 (MD5) Previous issue date: 2016-06-29 / Esta pesquisa teve como objetivo elicitar requisitos, prototipar e validar um software para abordar a taxa de variação de funções em uma abordagem variacional. A prototipação do software adotou um Modelo de Processo de Software desenvolvido com base na Engenharia Didático-informática (EDI), que alia aspectos da Engenharia Didática à Engenharia de Software e, que foi desenvolvida por Ricardo Tibúrcio em sua pesquisa de mestrado, paralela a esta. Tal processo é constituído de cinco fases: (i) Análises Preliminares, nas quais o conceito matemático foi situado em relação aos aspectos cognitivos, epistemológicos, didáticos e informáticos, (ii) Análise de Requisitos, na qual os resultados das Análises Preliminares foram traduzidos em requisitos do sistema, (iii) Análise à priori e Prototipação, nas quais o protótipo foi desenvolvido considerando-se as situações de uso a serem abordadas, (iv) Experimentação, na qual o software foi testado com os estudantes e (v) Análise à Posteriori e Validação, nas quais foi analisado se o protótipo atendeu aos objetivos especificados na sua concepção. Além da EDI, articularam-se na fundamentação uma sistematização da utilização das tecnologias digitais na Educação Matemática e um quadro de referência para analisar a contribuição do protótipo na abordagem de taxa de variação - o Quadro de Ações Mentais no Raciocínio Covariacional, de Marilyn Carlson e colaboradores. A validação foi realizada por meio da experimentação com uma dupla de estudantes da Licenciatura em Matemática da UFPE, que realizaram duas atividades com o uso do software, que foi chamado de Function Studium, para que fossem analisados os benefícios e limitações do seu uso na abordagem da taxa de variação das funções afim e quadrática. Os resultados da validação apontaram que: (a) Os benefícios do uso do software para a abordagem da taxa de variação fundamentaram-se, principalmente, na conexão entre os aspectos do objeto matemático levantados nas Análises Preliminares e os recursos do software Function Studium, requisitados e implementados com base nas necessidades apontadas, (b) A conexão simultânea e dinâmica das ações sobre as notações no software, contribuíram para a análise do comportamento da taxa de variação em função da variável independente e para relacionar a taxa instantânea com aspectos do gráfico como pontos de inflexão e concavidade e (c) Dificuldades emergidas no experimento, revelaram a necessidade da experimentação de versões parciais do software na Prototipação, o que sugere a participação dos estudantes e uma melhor discussão sobre a operacionalização da Análise à Priori. / This research aimed to elicit requirements, prototype and validate an educational software to explore the rate of change of functions in a variational approach. The prototyping process adopted a Model of Software development based on Didactic-Informatics engineering (EDI), which combines aspects of Didactic and Software Engineering, and was developed in parallel with this research in Ricardo Tibúrcio's dissertation. This Process comprises five steps: (i) Preliminary Analysis, in which the mathematical concept was analyzed in relation to cognitive, epistemological, didactic and computational aspects (ii) Requirements Analysis, in which the results of the Preliminary Analysis were translated into system requirements, (iii) A priori Analysis and Prototyping process, in which the prototype was developed considering the situations of use to be approached, (iv) Experimentation, in which the software was tried out with students and (v) A posteriori analysis and Validation, in which it was examined whether the prototype met the aims specified in its conception. In addition to EDI, a systematization of the aspects of digital technologies in Mathematics Education and a referential framework to analyze the contribution of the prototype in the approach of the rate of change were articulated into the foundation: The Framework of Mental Actions in Covariational Reasoning, from Marilyn Carlson and collaborators. The validation process was done within an experiment undertaken by a pair of students of Mathematics Teacher Training course from a Brazilian state university. They performed two activities using the software called Function Studium, so that the benefits and limitations of its use in the approach of the rate of change of linear and quadratic functions were analyzed. The validation process results showed that: (a) The benefits of software used to approach the rate of change were based mainly on the connection between the aspects of the mathematical object gathered in the Preliminary Analyzes and the Function Studium software tools required and implemented based on identified needs, (b) The simultaneous and dynamic links of the actions on the notations in the software contributed to the analysis of the characteristics of the rate of change as a function of the independent variable and to relate instantaneous rate to the aspects of the graph such as inflection points and concavity and (c) Difficulties emerged in the experiment revealed the need for trying out partial versions of the software in the prototyping phase, suggesting the participation of students and a better discussion on the operationalization of A Priori Analysis.

Made available in DSpace on 2016-04-27T16:58:19Z (GMT). No. of bitstreams: 1 eugenio.pdf: 984600 bytes, checksum: e418bb88c201ea98edc58db64ac89cd4 (MD5) Previous issue date: 2001-11-06 / The purpose of this work is to study the process by which students following a university-level course in the exact sciences acquire/construct the notion of average rate of change. An understanding of this notion could assist students in interpreting the meaning of the derivative as the average rate of change of a point. A didactic sequence was elaborated, inspired by Vergnaud (1994), who considers that the teaching and learning of mathematical notions and concepts should be approached by an exploration of problems, that is, by developing problem situations which favour new conceptualisations in their resolution. Eighteen pairs of students from a first year chemistry course worked on the sequence which lasted 1.440 minutes. The results indicated that the students advanced their understandings of average rate of change, as well as their ability to interpret graphs, for example, identifying intervals in which the function increases or decreases and describing the meaning of points where the function intersects the axes of the graph / Este trabalho tem por objetivo estudar o processo de aquisição/construção da noção de taxa de variação média de uma função, por alunos que ingressaram em um curso superior na área de exatas. A compreensão dessa noção pode favorecer a interpretação do significado da derivada como taxa de variação num ponto. Para tanto, foi elaborada uma seqüência didática inspirada nas concepções de Vergnaud (1994), que considera que o processo de ensino e aprendizagem de noções e conceitos matemáticos devem ser abordados mediante a exploração de problemas, ou seja, de situações em que os alunos precisem desenvolver algum tipo de estratégia para resolvê-las. Essa seqüência foi desenvolvida por 18 duplas de alunos do 1° ano de um curso de Química, ao longo de 1.440 minutos. Os resultados obtidos revelam que houve bom aproveitamento destes alunos na construção da taxa de variação média e também no desenvolvimento de competências para a interpretação de gráficos, como a identificação de intervalos de crescimento e decrescimento e na atribuição de significados aos pontos de intersecção com os eixos coordenados

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-01-23T11:30:24Z No. of bitstreams: 1 Edson Rodrigues da Silva.pdf: 3496477 bytes, checksum: 345c415e59b188dddb4a253bf2dffd17 (MD5) / Made available in DSpace on 2018-01-23T11:30:24Z (GMT). No. of bitstreams: 1 Edson Rodrigues da Silva.pdf: 3496477 bytes, checksum: 345c415e59b188dddb4a253bf2dffd17 (MD5) Previous issue date: 2017-11-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present research aims to build a knowledge base for the teaching of rate of change in Basic Education. For this, and in order to guide our research, we have established the following research question: What knowledge base is required for the teaching of rate of change in Basic Education? To answer this question, we used a bibliographical study as a methodological contribution, in which the sources of investigation consisted of researches that deal with the processes of teaching and learning of the rate of change in Basic Education, of the official documents that guide and organize the teaching of Mathematics in Brazil and in most Brazilian states, of the didactic materials used in different periods in Basic Education and scientific articles. The theoretical framework was based on the Knowledge Base Theory for Teaching, specifically in the conceptions of Shulman, Mishra and Koehler, Lima and Silva and Ball, Thames and Phelps and in the Anthropological Theory of Didactics of Chevallard. These theories helped us to compose a scenario that evidences the know that, when studied, conditions the construction of the necessary knowledge for the teaching of rate of change in Basic Education. There are four categories of teaching knowledge of fundamental and for the teaching of rate of change in Basic Education mediated by technologies: content knowledge, didactic knowledge, technological knowledge and pedagogical knowledge, in which their different interactions meet the conception of knowledge as a network of meanings and that, for us, constitute a knowledge base for the teaching of rate of change in this level of schooling. The construction of an Epistemological Model of Reference for the teaching of rate of change in Basic Education evidenced a Mathematical Organization that includes the know that, when studied, condition the construction of content knowledge for this teaching. The didactic knowledge for the teaching of rate of change includes the range of knowledge concerning the Theory of Didactical Situations, the Theory of Registers of Semiotic Representation, the Theory of Conceptual Fields, the Anthropological Theory of the Didactics, Didactic Engineering, the notion of Didactic Contract And the notion of Obstacle. The technological knowledge for the teaching of rate of change comprises the knowledge about the interface, functionality and characteristics of dynamic mathematical software that can be used in favor of the teaching and learning of this notion. The pedagogical knowledge for rate of change teaching comprises the range of knowledge that the teacher needs to mobilize to prepare, structure and assess tasks, to motivate and support student autonomy, to organize the different materials available, to manage the classroom, to deal with subjectivity and heterogeneity in the classroom, with the cognitive time of each student, with diverse groups, etc / A presente pesquisa tem por objetivo construir uma base de conhecimentos para o ensino de taxa de variação na Educação Básica. Para isso, e de modo a guiar nossa investigação, estabelecemos a seguinte questão de pesquisa: Qual base de conhecimentos é necessária para o ensino de taxa de variação na Educação Básica? Para responder essa questão recorremos a um estudo bibliográfico como aporte metodológico, em que as fontes de investigação constituíram-se de pesquisas que versam a respeito dos processos de ensino e de aprendizagem de taxa de variação na Educação Básica, dos documentos oficiais que direcionam e organizam o ensino de Matemática no Brasil e na maioria dos estados brasileiros, de materiais didáticos utilizados em diferentes períodos na Educação Básica e de artigos científicos. O referencial teórico baseou-se na Teoria da Base de Conhecimentos para o Ensino, especificamente nas concepções de Shulman, Mishra e Koehler, Lima e Silva e Ball, Thames e Phelps e na Teoria Antropológica do Didático de Chevallard. Essas teorias nos auxiliaram a compor um cenário que evidenciasse os saberes que, quando estudados, condicionam a construção dos conhecimentos necessários para o ensino de taxa de variação na Educação Básica. São quatro categorias de conhecimentos docentes fundamentais e necessárias para o ensino de taxa de variação na Educação Básica mediado por tecnologias: conhecimento do conteúdo, conhecimento didático, conhecimento tecnológico e conhecimento pedagógico, em que suas diferentes interações vão ao encontro da concepção de conhecimento como uma rede de significados e que, para nós, constituem uma base de conhecimentos para o ensino de taxa de variação nesse nível de escolaridade. A construção de um Modelo Epistemológico de Referência para o ensino de taxa de variação na Educação Básica evidenciou uma Organização Matemática que compreende os saberes que, quando estudados, condicionam a construção dos conhecimentos do conteúdo para este ensino. Os conhecimentos didáticos para o ensino de taxa de variação compreendem a gama de conhecimentos referentes a Teoria das Situações Didáticas, a Teoria de Registros de Representação Semiótica, a Teoria dos Campos Conceituais, a Teoria Antropológica do Didático, a Engenharia Didática, a noção de Contrato Didático e a noção de Obstáculo. O conhecimento tecnológico para o ensino de taxa de variação compreende os conhecimentos acerca da interface, funcionalidade e características de softwares dinâmicos de Matemática que podem ser usados em favor dos processos de ensino e de aprendizagem dessa noção. O conhecimento pedagógico para o ensino de taxa de variação compreende a gama de conhecimentos que o professor precisa mobilizar para preparar, estruturar e avaliar tarefas, motivar e apoiar a autonomia dos estudantes, organizar os diferentes materiais disponíveis, gerenciar a sala de aula, lidar com a subjetividade e a heterogeneidade em sala de aula, com o tempo cognitivo de cada aluno, com grupos diversificados, etc

Spatial analyses of shoreline recession and accretion, and future shoreline position predictions in coastal countries have considerable importance due to engineering, planning, management and environmental concerns. In spite of this importance, there are only a few studies in Turkey. The aim of this thesis are to determine the shoreline rate-of-change of B&uuml / y&uuml / k Menderes Delta, by geographical information systems for the last fifty-year period, in order to approximate future shoreline position of B&uuml / y&uuml / k Menderes Delta shoreline, and to evaluate appropriate models while predicting the future shoreline position. To achieve the purpose of the study time series shoreline position data is extracted from three sets of topographic maps belonging to 1954-1957, 1977-1978 and 1993 aerial photographs and two sets of high resolution satellite imageries (January 2002 Ikonos, August 2004 QuickBird). Then Coastal script of TNTMips, which uses some statistical shoreline analyses methods, that are End Point Rate (EPR), Average of Rates (AOR), Linear Regression (LR) and Jackknifing (JK) is edited so that it can locate the future shoreline positions on the map. Suitable baselines are created and appropriate transect intervals are decided to analyze the shoreline. Finally, some additional analyses that are Backward Analysis and Oscillation Analysis are done to obtain most suitable future shoreline position with rate-of-changes. The results showed that, shorelines having different geomorphologic characteristics needed to be analyzed separately and the linear methods to model the future shoreline position differ from one geomorphologic region to another.

It was the purpose of this design study to explore the Geometer’s Sketchpad dynamic mathematics software as a tool to model the derivative in introductory calculus in a manner that would foster a deeper conceptual understanding of the concept – developing domain specific understanding. Sketchpad’s transformation capabilities have been proved useful in the exploration of mathematical concepts by younger learners, college students and professors. The prospect of an open-ended exploration of mathematical concepts motivated the author to pursue the possibility of representing the concept of derivative in dynamic forms. Contemporary CAS studies have predominantly dwelt on static algebraic, graphical and numeric representations and the connections that students are expected to make between them. The dynamic features of Sketchpad and such like software, have not been elaborately examined in so far as they have the potential to bridge the gap between actions, processes and concepts on the one hand and between representations on the other. In this study Sketchpad model-eliciting activities were designed, piloted and revised before a final implementation phase with undergraduate non-math major science students enrolled for an introductory calculus course. Although most of these students had some pre-calculus and calculus background, their performance in the introductory course remained dismal and their grasp of the derivative slippery. The dual meaning of the derivative as the instantaneous rate of change and as the rate of change function was modeled in Sketchpad’s multiple representational capabilities. Six forms of representation were identified: static symbolic, static graphic, static numeric, dynamic graphic, dynamic numeric and occasionally dynamic symbolic. The activities enabled students to establish conceptual links between these representations. Students were able to switch systematically from one form of (foreground or background) representation to another leading to a unique qualitative understanding of the derivative as the invariant concept across the representations. Experimental students scored significantly higher in the posttest than in the pretest. However, in comparison with control group students the experimental students performed significantly better than control students in non-routine problems. A cyclical model of developing a deeper concept image of the derivative is therefore proposed in this study. / Educational Studies / D. Ed. (Education)