Made available in DSpace on 2014-06-11T19:24:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-10-10Bitstream added on 2014-06-13T19:32:04Z : No. of bitstreams: 1 santos_mr_me_rcla.pdf: 1862429 bytes, checksum: 9a913eabe353c8ef2f077ba863df25ed (MD5) / Nesta pesquisa, investigamos Quais significados os professores de Matemática e de Arte atribuem ao trabalho com pavimentações do plano, envolvendo material manipulativo, em situação de ensino e aprendizagem de geometria?, em um curso de geometria. As atividades desenvolvidas nos encontros realizados com os professores-alunos de Matemática e Arte tiveram como pano de fundo o tema pavimentações do plano e estavam associadas a materiais didáticos manipuláveis. Foi apresentado um estudo referente aos conceitos e propriedades geométricas concernentes: às pavimentações uniformes, à visualização em caleidoscópios, aos tetraminós e às pavimentações de Penrose. Os encontros foram filmados, transcritos e analisados sob a perspectiva da análise fenomenológica. As análises e interpretações efetuadas permitiram identificar cenas que se mostraram significativas, as quais, mediante desdobramentos dos estudos interpretativos e efetuando as reduções sucessivas, levaram-nos a três categorias abertas: a primeira, construindo interdisciplinaridade aproximações e afastamentos, aborda os significados que surgiram nesse contexto multidisciplinar, e que avançam em direção à interdisciplinaridade, revelando disposições para as trocas possíveis. A segunda, a prática pedagógica dos professores-alunos, enfoca os significados que explicitam a presença de educadores que trazem consigo suas vivências da prática docente, a percepção que têm de seus alunos e suas expectativas em relação aos encontros. Por fim, construção de conhecimento trata das construções, desconstruções e reconstruções que ocorrem no ambiente dos encontros, em meio a uma atitude empática, evidenciando os humores e disposições dos professores-alunos para ampliarem seus horizontes de possibilidades. A análise dessas categorias permitiu a elaboração de uma síntese... / In this study, we investigate Which meanings the teachers of Mathematic and Art attribute to the work with tilling of the plan, with manipulative material, in teaching and learning of geometry?, in a geometry course. The activities developed in the encounters had as backdrop the theme tilling of the plan and were associated to didactic manipulative materials. A study was presented regarding the concepts and geometric properties, concerning: to the uniform tilling, to the visualization in kaleidoscopes, to the tetraminos and the tillings of Penrose. The encounters were filmed, transcribed and analyzed under the perspective of phenomenological analysis. The analyses and interpretations realized allowed to identify meaning scenes, the ones which, by the development of the interpretative studies and trough the successive reductions, took us to three open categories: the first, building interdisciplinarity - approaches and retrieves, analyses the meanings that appeared in that multidisciplinar context, and that move towards the interdisciplinarity, revealing dispositions for the possible changes. The second, the teacher-students pedagogic practice, focuses the meanings that shows the educators presence that bring their existence in the educational practice, the perception that have of their students and their expectations relative to the encounters. Finally, knowledge construction treats of the constructions, deconstructions and reconstructions that happen in the atmosphere of the encounters, trough an empathically attitude, evidencing the humors and dispositions for them to enlarge their horizons of possibilities. The analysis of these categories allowed the elaboration of a synthesis, in which we present considerations related to the use of manipulable materials... (Complete abstract, click electronic address below)

O objetivo deste trabalho e determinar a solução de algumas equações de coeficientes intervalares. Este estudo utiliza uma Teoria das Aproximações Intervalares, a qual foi descrita por [ACI91]. Nesta teoria a igualdade para intervalos e substituída pela relação de aproximação . Esta substituição deve-se ao fato da igualdade utilizada na Teoria Clássica dos Intervalos para resolução de equações de coeficientes intervalares não apresentar uma solução satisfatória, visto que a solução encontrada não contem todas as soluções das equações reais que compõe a equação intervalar. Pela substituição da igualdade intervalar por uma relação de aproximação é possível determinar a solução de equações de coeficientes intervalares, de maneira que esta solução contenha todas as possíveis soluções das equações reais pertencentes a equação intervalar. Apresenta-se alguns conceitos básicos, bem como analisa-se algumas propriedades no espaço solução ( /(R), +, •, C, 1). São representadas graficamente diferentes tipos de funções neste espaço intervalar, com os objetivos de obtenção da imagem, caracterização da solução e identificação gráfica da região de solução (ótima e externa), para cada tipo de função. Como a representação de intervalos de /(R) esta determinada num semiplano de eixos X - X+, onde X - representa o extremo inferior de cada intervalo e X+ representa o extremo superior dos intervalos, apresenta-se o espaço intervalar estendido /(R). Neste espaço intervalar estão definidos os intervalos não-regulares, representados no outro semi-piano de eixos X - X+ Em /(R) serão apresentados alguns conceitos fundamentais, assim como operações aritméticas e algumas considerações referentes aos intervalos não-regulares. No espaço intervalar /(R) e possível resolver equações de coeficientes intervalares de maneira análoga a resolução de equações reais no espaço real, pois este espaço intervalar possui a estrutura semelhante a de um corpo. Com isto apresenta-se a solução de equações de coeficientes intervalares lineares, obtida diretamente, assim como determina-se a Formula de Bascara Intervalar para resolução da Equação Quadrática Intervalar. Para funções que possuem grau maior que 2 apresenta-se alguns métodos iterativos intervalares, tais como o Método de Newton Intervalar, o Método da Secante Intervalar e o Método híbrido Intervalar, que permitem a obtenção do intervalo solução para funções intervalares. Por fim apresenta-se alguns conceitos básicos no espaço intervalar matricial M„,„(/(R)), bem como apresenta-se alguns métodos diretos para resolução de sistemas de equações lineares intervalares. / The aim of this work is to determine the solution set of some Equations of Interval Coefficients. The study use a Theory of Interval Approximation. The begining of this theory was described by [ACI91]. In this theory the equality for intervals is replaced by an approximation relation. When we make use of that relation to solve interval equations, it's possible to obtain an optimal solution, i.e., to get an interval solution that contain all of real solutions of the real equations envolved in the interval equation. By using the equality of Classical Interval Theory for solving interval equations we can not get an optimal solution, that is, the interval solution in the most of equations not consider some real solutions of real equations that belong to the interval equation. We present some basic concepts and analyse some properties at the interval space (1(R), E, -a x , 1). Different kind of functions are showed in this space in order to obtain the range, the solution caracterization and the graphic identification of the optimal and external solution region, for each kind of function. The representation of intervals in /(R) is determined in a half plane of axes X - , X+, where X - represent the lower endpoint and X+ represent the upper endpoint of the intervals. The nonregular intervals are defined in /(R), which are determined in an other half plane. In this interval space are presenting some specific concepts, as well as arithmetical operations and some remarks about nonregular intervals. The interval space (1(R), +, •, C, Ex , 1) have a similar structure to a field, so it's possible to solve interval coefficients equations analogously as to solve real equations in the real space. We present the solution of linear interval equations and we determine an interval formula to solve square interval equation. We present some intervals iterated methods for functions that have degree greater than 2 that allow to get an interval solution of interval functions. Finally we show some basic concepts about the interval matrix space Af,„„(IR)) and present direct methods for the resolution of linear interval sistems.

Resumo: Nesta pesquisa, investigamos Quais significados os professores de Matemática e de Arte atribuem ao trabalho com pavimentações do plano, envolvendo material manipulativo, em situação de ensino e aprendizagem de geometria?, em um curso de geometria. As atividades desenvolvidas nos encontros realizados com os professores-alunos de Matemática e Arte tiveram como pano de fundo o tema pavimentações do plano e estavam associadas a materiais didáticos manipuláveis. Foi apresentado um estudo referente aos conceitos e propriedades geométricas concernentes: às pavimentações uniformes, à visualização em caleidoscópios, aos tetraminós e às pavimentações de Penrose. Os encontros foram filmados, transcritos e analisados sob a perspectiva da análise fenomenológica. As análises e interpretações efetuadas permitiram identificar cenas que se mostraram significativas, as quais, mediante desdobramentos dos estudos interpretativos e efetuando as reduções sucessivas, levaram-nos a três categorias abertas: a primeira, construindo interdisciplinaridade aproximações e afastamentos, aborda os significados que surgiram nesse contexto multidisciplinar, e que avançam em direção à interdisciplinaridade, revelando disposições para as trocas possíveis. A segunda, a prática pedagógica dos professores-alunos, enfoca os significados que explicitam a presença de educadores que trazem consigo suas vivências da prática docente, a percepção que têm de seus alunos e suas expectativas em relação aos encontros. Por fim, construção de conhecimento trata das construções, desconstruções e reconstruções que ocorrem no ambiente dos encontros, em meio a uma atitude empática, evidenciando os humores e disposições dos professores-alunos para ampliarem seus horizontes de possibilidades. A análise dessas categorias permitiu a elaboração de uma síntese... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this study, we investigate "Which meanings the teachers of Mathematic and Art attribute to the work with tilling of the plan, with manipulative material, in teaching and learning of geometry?, in a geometry course. The activities developed in the encounters had as backdrop the theme tilling of the plan and were associated to didactic manipulative materials. A study was presented regarding the concepts and geometric properties, concerning: to the uniform tilling, to the visualization in kaleidoscopes, to the tetraminos and the tillings of Penrose. The encounters were filmed, transcribed and analyzed under the perspective of phenomenological analysis. The analyses and interpretations realized allowed to identify meaning scenes, the ones which, by the development of the interpretative studies and trough the successive reductions, took us to three open categories: the first, building interdisciplinarity - approaches and retrieves, analyses the meanings that appeared in that multidisciplinar context, and that move towards the interdisciplinarity, revealing dispositions for the possible changes. The second, the teacher-students pedagogic practice, focuses the meanings that shows the educators presence that bring their existence in the educational practice, the perception that have of their students and their expectations relative to the encounters. Finally, knowledge construction treats of the constructions, deconstructions and reconstructions that happen in the atmosphere of the encounters, trough an empathically attitude, evidencing the humors and dispositions for them to enlarge their horizons of possibilities. The analysis of these categories allowed the elaboration of a synthesis, in which we present considerations related to the use of manipulable materials... (Complete abstract, click electronic address below) / Orientador: Claudemir Murari / Coorientador: Maria Aparecida Viggiani Bicudo / Banca: Adlai Ralph Detoni / Banca: Geraldo Perez / Mestre

Syftet med studien är att få en djupare förståelse för begreppet utomhuspedagogik och ta reda på om utomhuspedagogik, som ett komplement till den traditionella undervisningen, är en undervisningsform som kan bidra till ökad förståelse inom ämnet matematik. Studien är en litteraturstudie där tidigare forskning har granskats och analyserats. Resultatet visar att utomhuspedagogik inom matematik inte bara ger direkt betydelsefull kunskap vid koppling av skola och samhället utan förbättrar även elevers hälsa, ökar elevers motivation till matematikämnet, elevers sociala förmågor utvecklas samt ger fler sinnen stimulans vilket gör elever mer alerta och mottagliga för inlärning. Mer tid till ämnet matematik och mer utbildning inom utomhuspedagogik är två avgörande faktorer för att lyckas integrera utomhuspedagogik i undervisningen.

This thesis is analyzing customers of Geocart CZ a.s. company. Thesis is presenting new models of evaluating of customers. Weight mathematic model is created in MS Excel software. In software fuzzyTECH and MATLAB are designed fuzzy models for evaluating of customers with application of fuzzy logic. This method of evaluating should eliminate risk of mistakes with choosing of customers and minimize opportunity costs.

Modifications to the quasistatic Carnot cycle are developed in order to formulate improved theoretical bounds on the thermal efficiency of certain refrigeration cycles that produce finite cooling power. The modified refrigeration cycle is based on the idealized endoreversible finite time cycle. Two of the four cycle branches are reversible adiabats, and the other two are the high and low temperature branches along which finite heat fluxes couple the refrigeration cycle with external heat reservoirs. This finite time model has been used to obtain the following results: First, the performance of a finite time Carnot refrigeration cycle (FTCRC) is examined. In the special case of equal heat transfer coefficients along heat transfer branches, it is found that by optimizing the FTCRC to maximize thermal efficiency and then evaluating the efficiency at peak cooling power, a new bound on the thermal efficiency of certain refrigeration cycles is given by $\epsilon\sb{m} = (\tilde\tau\sp2\sb{m}\ (T\sb{H}/T\sb{L}) - 1)\sp{-1},$ where $T\sb{H}$ and $T\sb{L}$ are the absolute high and low temperatures of the heat reservoirs, respectively, and $\tilde\tau\sb{m}=\sqrt{2}$ + 1 $\simeq$ 2.41 is the dimensionless cycle period at maximum cooling power. Second, a finite time refrigeration cycle (FTRC) is optimized to obtain four distinct optimal cycling modes that maximize efficiency and cooling power, and minimize power consumption and irreversible entropy production. It is found that to first order in cycling frequency and in the special symmetric case, the maximum efficiency and minimum irreversible entropy production modes are equally efficient. Additionally, simple analytic expressions are obtained for efficiencies at maximum cooling power within each optimal mode. Under certain limiting conditions the bounding efficiency at maximum cooling power shown above is obtained. Third, the problem of imperfect heat switches linking the working fluid of an FTRC to external heat reservoirs is studied. The maximum efficiency cycling mode is obtained by numerically optimizing the FTRC. Two distinct optimum cycling conditions exist: (1) operation at the global maximum in efficiency, and (2) operation at the frequency of maximum cooling power. The efficiency evaluated at maximum cooling power, and the global maximum efficiency may provide improved bench-mark bounds on thermal efficiencies of certain real irreversible refrigeration cycles.

Målet med vårt examensarbete var att ta reda på vad elever i grundskolans tidigare år har för attityd till matematik. Vi ville även veta varför och hur attityden förändras, om den förändras genom åren. Som bakgrund till undersökningen har vi använt oss av litte-ratur som handlar om elevers attityd och motivation till matematik. För att ta reda på vår problemställning besökte vi två olika skolor i södra Sverige där vi gjorde observationer och eleverna fick besvara enkäter. När vi sedan sammanställde resultaten och analyse-rade dem jämförde vi de svaren vi fått in genom våra enkäter med det vi såg när vi ob-serverade, samt de teorier vi använt oss av. Resultatet vi fick visade att elevers attityd och intresse för matematiken minskar både från skolår 2 till 4 och skolår 4 till 6. Det kan finnas flera olika anledningar till detta. Men en viktig del för att förhindra det är att som lärare vara flexibel i sin undervisning och vara noggrann med svårighetsgraden på uppgifter man ger eleverna.

I denna studie undersöker jag hur andraspråkselevers matematiska kunskaper bedöms, när matematikkunskaper ligger på högre nivå än de språkliga. Jag utgick från lärarens perspektiv gällande: vilka tillvägagångssätt en lärare använder för att bedöma eleverna, hur språket blir ett hinder och hur läraren gör för att undvika att språket ska vara ett hinder. För att besvara dessa frågor intervjuade jag två olika lärare på olika skolor som har även olika förutsättningar. Resultaten visar att lärare använder sig av kartläggning och matematikuppgifter, men de tar även hänsyn till att eleverna ännu inte har utvecklat språket genom att använda sig resurser som kan översätta och erbjuda andra uttrycksformer som ”plockisar”. / This study focuses on how second language pupils’ mathematical knowledge is accessed, when their mathematical knowledge is at a higher level than the linguistic knowledge. I focused on the teacher’s perpective regarding: What approaches a teacher uses to assess pupils, how the language becomes an obstacle and how the teacher does to avoid the language to be an obstacle. To answer these wuestions, i interviewed two different teachers at different schools who also have different conditions. The results show that teacheras use a survey and math problem, however they also take into account that pupils have not yet develop the language. Therefore they use  other resources for example a translater and other forms of expression such as ”plockisar”.

<p><p>The aim of this thesis is to investigate how some Proshika-teachers describe their mathematic teaching. Proshika is a non government organisation in Bangladesh. One of Proshika’s areas is to provide school attendance for children of poor households on the countryside. We chose to do a qualitative study, and interviewed teachers at six different Proshika-schools. We also made five observations in order to formulate relevant interview questions.</p><p>The result from the interviews shows that the teaching looks similar in the schools. The mathematic book has a dominating position in the teaching. The students calculate the same task at the same time and they calculate every task in the book. Group work exists and concrete materials are used as equipment in the teaching. To get better conditions in the teaching, the respondents want further education and cooperate with other teachers to improve their knowledge about different work methods and to develop their teaching. They also want more materials and breaks during the school day. Some of the teachers can think of having longer school days. Later in the thesis we reflect on how it is to collect data in another culture, how the researcher affects the result and how our theoretical framework can be relevant in this study.</p></p>

The aim of this thesis is to investigate how some Proshika-teachers describe their mathematic teaching. Proshika is a non government organisation in Bangladesh. One of Proshika’s areas is to provide school attendance for children of poor households on the countryside. We chose to do a qualitative study, and interviewed teachers at six different Proshika-schools. We also made five observations in order to formulate relevant interview questions. The result from the interviews shows that the teaching looks similar in the schools. The mathematic book has a dominating position in the teaching. The students calculate the same task at the same time and they calculate every task in the book. Group work exists and concrete materials are used as equipment in the teaching. To get better conditions in the teaching, the respondents want further education and cooperate with other teachers to improve their knowledge about different work methods and to develop their teaching. They also want more materials and breaks during the school day. Some of the teachers can think of having longer school days. Later in the thesis we reflect on how it is to collect data in another culture, how the researcher affects the result and how our theoretical framework can be relevant in this study.