Dissertations / Theses on the topic 'Teaching of matrices and determinants'

Este trabalho tem como objetivo apresentar os conteúdos de matrizes, determinantes e sistemas lineares aos professores de matemática que lecionam no ensino médio, ressaltando as situações-problema bem como suas aplicações, contextualizando através de problemas.
The goal of this work is to present an introduction to matrices, determinants, and linear systems to high school mathematics teachers highlighting some applications.

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It is presented in this work, the results of a qualitative research associated to the teaching of mathematics, in which it was adopted the methodology of teaching through the problem solving. Thus, the goal was to analyze the possibilities that the resolution of problems with matrices and determinants could provide for a meaningful learning of mathematical concepts. The methodological procedures used to gather data were: interview-type semi-structured with teachers from the school, questionnaires with pupils, the participant observation in the classroom and the daily field of the teacher-researcher. The survey was developed with 26 students from the 3º grade of high school at the Technical School José Cañellas of Frederico 8 Westhapen - R/S in the second semester of 2007. For the application and development of activities using the resolution of problems, were followed the steps suggested by Onuchic (1999), which are: 1) To form groups and deliver the activity, 2) The role of the teacher, 3) Results on board; 4) Plenary and analysis of results; 5) Consensus and formalization of activities. Based on theoretical and practical assumptions, it was noticed the importance and necessity of exercise at schools, the problem-solving, since it contemplate the skills and competences developed and proposals in the teaching of mathematics. For this, are vital that the lessons are more participatory, where the teacher is the mediator of the teaching-learning and the students the active subjects of this process. It was thus offer to learners the interpretation of problems as well as the remove of the requested information for later resolution, and by this way allowed to verifying the implementation of such content in several real-life situations. Therefore, the research supplied the understanding of the concepts of matrices and determinants easier, and significantly, since working with the methodology of problem solving awakened the interest and motivation of the students involved, leading them to more autonomy and construction of other problems from the studied ones.
Apresenta-se, nesse trabalho, os resultados de uma pesquisa qualitativa associada ao ensino da matemática, em que se adotou a metodologia de ensino por meio da resolução de problemas. Desse modo, o objetivo foi analisar as possibilidades que a resolução de problemas com matrizes e determinantes pode oferecer para uma aprendizagem significativa de conceitos matemáticos. Os procedimentos metodológicos utilizados para a coleta de dados foram: entrevista do tipo semi-estruturada com professores da escola, questionários com os alunos, a observação participante em sala de aula e o diário de campo da professora-pesquisadora. A pesquisa foi desenvolvida com 26 alunos do 3º ano do Ensino Médio da Escola Técnica José Cañellas de Frederico Westhapen R/S, no segundo semestre de 2007. Para a aplicação e o desenvolvimento das atividades utilizando a resolução de problemas, foram seguidos os passos sugeridos por Onuchic (1999), os quais são: 1) Formar grupos e entregar a atividade;2) O papel do professor; 3) Resultados na lousa; 4) Plenária e análise dos resultados; 5) Consenso e formalização das atividades. Com base nos pressupostos teóricos e práticos, percebeu-se a importância e a necessidade de que se exercite nas escolas a resolução de problemas, já que esta contempla as competências e as habilidades desenvolvidas e propostas no ensino de matemática. Para isso, são imprescindíveis que as aulas sejam mais participativas, em que o professor seja o mediador do processo de ensino-aprendizagem e os alunos os sujeitos ativos desse processo. Procurou-se assim, oportunizar aos educandos a interpretação de problemas, bem como a retirada das informações solicitadas, para posterior resolução. Dessa forma, possibilitou-se a verificação da aplicação desses conteúdos em várias situações da vida real. Portanto, a investigação oportunizou a compreensão dos conceitos de matrizes e determinantes com maior facilidade e de forma significativa, já que trabalhar com a metodologia de resolução de problemas despertou o interesse e a motivação dos educandos envolvidos, levando-os a maior autonomia na construção e resolução de outros problemas a partir dos estudados.

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility. In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility. The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more. The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.
Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.

The determinants that affect the financial performance of an insurance company are complicated due to the intangible nature of insurance products and the lack of transparency in the market. Consequently, the financial performance of insurance companies is important to various stakeholders such as policyholders, insurance intermediaries and policymakers. This study aims to investigate the determinants of financial performance of insurance companies based on their financial strength rating performance. The empirical data are drawn from A.M. Best Insurance Report Online: Non- US Database. The sample consists of 57 insurers in the United Kingdom over the period of 2006 to 2010. The analyses include eight firm-specific variables, which are leverage, profitability, liquidity, size, reinsurance, growth, type of business and organisational form. Rating transition matrices and regression models are employed in this study. Rating transition analysis demonstrates a significant degree of rating changes, as reflected in the rating fluctuations. Based on the empirical results, this study establishes that profitability, liquidity, size and organisational form are statistically significant determinants of financial performance of insurance companies in the United Kingdom. This study recommends an alternative to measure the size of an insurance company, which is based on the gross premium written. In addition, this study provides insights into the effects of the global financial crisis on the financial performance of the insurance companies.

The problem of this study was to describe and compare the relationship of learning style and leadership style upon the selection of instructional strategies by nursing educators in associate and baccalaureate degree nursing programs. Data were collected using Kolb's Learning Style Inventory, Hersey and Blanchard's Leader Effectiveness and Adaptability Description, a researcher-developed Instructional Strategies Inventory, and the Personal Data Form. It was found that leadership style was highly correlated between the associate degree and baccalaureate degree faculty groups. More of the associate degree faculty members had basic leadership styles of Low Relationship/Low Task and High Task/Low Relationship. Most of the baccalaureate faculty members had Low Relationship/Low Task leadership styles. The following conclusions were developed: (a) Nursing faculty in associate and baccalaureate degree programs have similar learning and leadership styles; (b) nursing faculty tend to use the traditional instructional strategies such as lecture, discussion, and case studies at the same frequency of use? and (c) the selection of instructional strategies in nursing education may be affected by variables other than the instructor's learning and leadership styles. In view of the findings of this study, the following recommendations for further study appear to be warranted, (a) Further research should be conducted to determine the effectiveness or ineffectiveness of identified instructional strategies in nursing education, and (b) more research should be done to identify creativity in the selection of instructional strategies in nursing education. The following implications are suggested from an analysis of the data: (a) Although faculty characteristics are rarely a determining factor in the design of a nursing curriculum, they must be taken into account when selecting instructional strategies, and (b) the apparent lack of diversity in instructional strategies utilized in the classroom setting emphasizes the need for faculty to expand their knowledge base in this area.

Este trabalho tem como objetivo central a elaboração, implementação e reflexão sobre uma sequência didática para o estudo de matrizes a partir de tranformações geométricas. A sequência didática pretende propiciar ao aluno um estudo que justifique as definições das operações entre matrizes e suas respectivas propriedades, a partir da observação e análise de algumas transformações geométricas, de modo a se refazer o processo histórico da definição e obtenção desses conceitos. Além disso apresenta algumas atividades de aplicação de matrizes, onde a composição e iteração de transformações geométricas no software Shapari geram algumas figuras fractais. Como metodologia de trabalho adotamos a engenharia didática para a elaboração, implementação e avaliação da didática proposta. O texto também apresenta a análise das referências sobre o ensino de matrizes e tranformações geométricas. Começando pelas orientações dos documentos oficiais e passando pela apresentação de diversos estudos sobre o tema delimitamos e justificamos a nossa proposta de ensino. Além disso, apresentamos um extrato sobre o conhecimento matemático envolvido no tema, de modo que sirva de base para o docente que implementar a seuência didática em sala de aula.
This work has as its main goal the formulation, implementation and contemplation of a didactie sequence to the study of matrices from geometric transformations. The didactic sequence intends to propitiate the student a study which justifies the definitions of operations between matrices and their respective properties, from the observation and analysis of some geometrie transformations, so that they are able to redo the historical process of the definition and the acquisition of these concepts. Besides that, it shows some activities to the application of matrices, in which the composition and interation of geometric transformations in the Shapari software generate some fractals. We have adopted Didactic Engineering as a methodology to the elaboration, implementation and evaluation of the proposed didactic sequence. The text also shows an analysis of the references about the teaching of matrices and the geometric transformations. We delimited and justified our teaching proposal by staring with orientations of official documents and showing a series of studies about the theme. Besides that, we show an excerpt about the mathematical knowledge involved in the theme, so that, it can be used as basis to the teacher who decides to implement the didactic sequence in the classroom.

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In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications
Neste trabalho, estudamos o m?todo apresentado no livro "Os nove cap?tulos sobre a arte matematica", escrito no s?culo I da era crist?, a em de revelar como a hist?ria pode ser uma motivadora na introdu??o de t?picos da matem?tica do ensino m?dio. Atrav?s de observa??es dos padr?es que se repetem no m?todo apresentado, fomos capazes de introduzir, de maneira natural, o conceito de equa??es lineares, sistema de equa??es lineares, solu??o de sistemas de equa??es lineares, determinantes e matrizes, al?m do desenvolvimento de Laplace para c?lculo de determinantes de matrizes quadradas de ordem maior que 3, considerando, em seguida, algumas de suas aplica??es gerais

The current study investigated the determinants of Internet services’ adoption and use among high school learners in the East London Education District, in the Eastern Cape. Underpinned by the Unified Theory of Acceptance and Use of Technology, the research questions included: (1) What is the effect of performance expectancy on the learner’s intention to adopt and use Internet services? (2) What degree of variation exists for effort expectancy on the learner’s intention to adopt and use Internet services? (3) How much of the determinants explain the usage of Internet services? (4) Which is (are) the best predictor(s) of Internet service usage given a set of determinants? (5) What is the effect of confounding variables (if any) on Internet services’ adoption and usage? (6) Which model can be designed based on the best predictor(s) of Internet services’ adoption and usage for secondary school learners? A quantitative approach based on the positivist paradigm was used to quantify the relationships among various factors that contribute to Internet services’ adoption and use. The research design used was a survey. Data were collected through structured questionnaires. Out of 286 questionnaires issued, the response rate was 40.6%. The study sample size was 116 high school learners using simple random sampling. The data was analysed using the multiple regression analysis technique, and Pearson correlations. Out of the four determinants from the UTAUT, performance expectancy was the strongest predictor of intention to adopt Internet services. Large positive correlations ranging from r = 0.638 up to r = 0.989 were found among performance expectancy and effort expectancy variables towards the intention to use Internet services, significant at p < 0.05. To enhance the efficiency of the UTAUT model, this study has designed the Adoption and Application of Technology for Learning (AATL) model, which added the price of Internet, persistent use of Internet, and perceptions about Internet use.

Research has generally demonstrated that students enrolled in developmental mathematics courses are leaving these courses without achieving conceptual understanding and transferrable knowledge and skills. Such outcomes have challenged educators to incorporate instructional strategies that have the most significant effect on the success of students in developmental education courses, in particular reform-based practices for the teaching of developmental mathematics courses based on constructivism. However, there is little or no empirical information on which of these instructional strategies and designs are being used (and by whom), as well as on the frequency of use, perceived value or importance to learning, and instructors' beliefs in their ability to use these best practices.

This cross-sectional study was intended to fill this gap by examining the role of personal teaching efficacy and perceived usefulness in determining the use of reform-based practices by instructors teaching developmental mathematics at the postsecondary level. Data was collected from 160 developmental or remedial mathematics instructors at two- and four-year regionally accredited postsecondary institutions in the United States who responded to a Web-based survey. Multiple statistical methods were applied to analyze the data, including correlation and multiple regression analyses.

Findings indicated that personal teaching efficacy and perceived usefulness each has a significant positive correlation with the use of reform-based practices, with personal teaching efficacy having the stronger correlation. In addition, only personal teaching efficacy was statistically significant for the regression model. These findings suggest that activities to support the use of reform-based practices include ways to increase instructors' beliefs in their ability to use reform-based practices. Directions for future research should continue to focus on instructors' beliefs and attitudes toward the use of reform-based practices as a means for improving developmental mathematics instruction.

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The objective of this study is to propose a different approach to teaching of matrices, seeking value the geometric aspect of them, and determinants. In fact, the matrices are important not only as a way to organize numerical data (tables), but also by the different properties of the operations that define the matrix algebra. However, the traditional way of teaching matrices and determinants in a secondary education, such as tables of numbers and a number associated with a matrix, respectively, the definitions of matrix operations and determinants, as well as their properties become quite unnatural. The Geometry not only turns these concepts more natural, but also develops our intuition about it. Furthermore, the geometrical aspects of the matrices and determinants are present in technological applications such as in Computer Graphics, for example. We begin this work by analyzing some textbooks adopted in secondary education, in order to see how the theory of matrices and determinants have been approached in classrooms, and to relate it to national education curriculum guidelines. Later, we explore the geometric content of matrices and determinants and propose a methodology for teaching, which brings out this aspect. This approach by middle of the Geometry is intended to stimulate the student to deduce properties and reflect on the results in operations with matrices, for example, addition, multiplication and also in the calculation of determinants. In proposing this methodology, we use the free software Geogebra, with the intent of providing a better view of the content for the student.
O objetivo deste estudo é propor uma abordagem diferente para o ensino das matrizes, buscando valorizar o aspecto geométrico delas, e dos determinantes. De fato, as matrizes são importantes não apenas como forma de organizar dados numéricos (tabelas), mas também pelas diversas propriedades das operações que definem a álgebra matricial. Todavia, na forma tradicional de ensinar matrizes e determinantes no ensino médio, como tabelas de números e um número associado a uma matriz, respectivamente, as definições das operações matriciais e determinantes, assim como as suas propriedades, tornam-se bastante artificiais. A Geometria não apenas ajuda a tornar estes conceitos mais naturais, como também desenvolve a nossa intuição sobre o assunto. Além disso, os aspectos geométricos das matrizes e determinantes estão presentes em aplicações tecnológicas tais como em Computação Gráfica, por exemplo. Começaremos este trabalho analisando alguns livros didáticos adotados no ensino médio, para verificar como a teoria de matrizes e determinantes vem sendo abordada em sala de aula; e relacionar essa teoria com os parâmetros curriculares nacionais do ensino médio. Posteriormente, exploraremos o conteúdo geométrico de matrizes e determinantes e proporemos uma metodologia para o seu ensino que valorize este aspecto. Esta abordagem por meio da geometria tem a finalidade de estimular o aluno a deduzir propriedades e refletir sobre os resultados obtidos nas operações realizadas com matrizes, por exemplo, a adição, a multiplicação e também, no cálculo de determinantes. Ao propor esta metodologia, faremos uso do software livre Geogebra, com o intento de propiciar uma melhor visualização do conteúdo pelo aluno.

Initiée dans les années 1960 par l’économiste américain Gary Becker, le développement de la théorie du capital humain a considérablement ouvert le champ d’investigation de la science économique. Au cours des deux dernières décennies, de nombreux travaux de recherche en économie de l'éducation ont cherché à identifier les caractéristiques du système ou de l’environnement scolaire qui permettent aux individus d’acquérir un maximum de compétences, de savoirs et d'informations au cours de leur scolarité. Cette thèse s’inscrit dans ce courant de recherche et étudie plus spécifiquement deux aspects de l’environnement scolaire qui ont retenu l’attention des économistes : la productivité des enseignants et l’influence des camarades de classe. Le premier chapitre de cette thèse étudie dans quelle mesure les pratiques pédagogiques des enseignants aux États-Unis permettent d’expliquer les différences de performances de leurs élèves en mathématiques. Dans un premier temps, nous montrons que chaque heure passée en classe à étudier les mathématiques engendre une progression significative des élèves dans cette discipline. Nous montrons ensuite que la productivité de l’heure d’enseignement est très fortement corrélée avec la mise en place de pratiques pédagogiques interactives, qui requièrent une participation active de la part des élèves. Plus spécifiquement, chaque heure passée avec un enseignant mettant l'accent sur ce type de pratiques est 2 à 3 fois plus productive qu'une heure passée avec un enseignant mettant l'accent sur des pratiques plus traditionnelles telles que le cours magistral.Le deuxième chapitre de cette thèse étudie l’impact d’une politique publique visant à améliorer les pratiques des enseignants, à savoir le système d’inspection individuelle des enseignants du second degré en France. Dans ce chapitre, nous montrons que les performances des élèves en maths au Diplôme National du Brevet (DNB) s’améliorent significativement à la suite d’une inspection de leur enseignant de mathématiques, non seulement pour les élèves assignés à l’enseignant l’année de l’inspection, mais également pour les élèves assignés à cet enseignant les années suivantes, suggérant une amélioration durable de ses compétences pédagogiques. De surcroît, l’inspection des enseignants de maths de 3ème produit des effets bénéfiques persistants chez les élèves, qui se traduisent par une augmentation de leur probabilité de choisir une filière scientifique en première et d’obtenir un baccalauréat scientifique au cours des années suivantes. Finalement, les effets bénéfiques d’une inspection sur les performances des élèves en maths et sur leur trajectoire scolaire sont particulièrement marqués pour les enseignants de l’éducation prioritaire, lesquels font face à des contextes d’enseignement plus difficiles.Le troisième et dernier chapitre de cette thèse étudie les effets du genre des camarades de classe de 3ème sur le parcours scolaire des élèves en France. Deux ensembles de résultats se dégagent de l’analyse. D’une part, l’influence des camarades de classes est persistante au cours du temps, puisque la proportion de filles parmi les camarades de classes en 3ème influence non seulement la réussite au brevet, mais également le taux de décrochage scolaire, le choix des filières après le collège et le taux d’obtention du baccalauréat. D’autre part, la proportion de filles parmi les camarades de classes en 3ème a des effets bénéfiques sur la scolarité des filles alors qu’elle a des effets négatifs sur celle des garçons. Plus spécifiquement, cette proportion réduit le taux de décrochage scolaire des filles après la 3ème et augmente leur taux d’obtention d’un baccalauréat général, particulièrement dans la filière scientifique. A l’inverse, elle augmente la proportion de garçons choisissant une filière technique après le collège et réduit leur taux d’obtention d’un baccalauréat général
The Human Capital Theory developed by Gary Becker in the 60's substantially widened the area of investigation of economics. Over the last two decades, many studies in the economics of education intended to identify the characteristics of an educational system which enable individuals to acquire as much skills, knowledge and information as possible. This thesis contribute to this literature by studying two aspects of the educational environment that has particularly attracted economists' attention over recent years: teacher productivity and peer effects in the classroom. The first chapter of this thesis investigate to what extent teaching practices implemented by math teachers in the US relate to their students' math performance. First, it shows that every single hour spent in the classroom studying mathematics generate a significant improvement in students' math performance. Second, it shows that the productivity of instructional time strongly relates to the implementation of interactive teaching practices, which require student active participation in the lesson. More precisely, each hour spent with a teacher putting a high weight on this kind of practices is 2 to 3 times more productive than an hour spent with a teacher putting a higher weight on traditional practices, such a teacher lecture. The second chapter of this thesis studies the impact of a public policy aimed at improving teachers' practices, namely the individual teacher evaluation system in French secondary education. In this chapter, we show that students' performance at the end-of-middle school national exam significantly improve after the evaluation of their math teacher, not only for students taught by an evaluated teacher the year of the evaluation, but also for students taught by the same teacher on subsequent years, suggesting a long-lasting improvement in teacher pedagogical skills. These positive effects persist over time for students, who not only perform better at the end-of-middle school exam but also choose more often and graduate more often from the science track in high school. In addition, the positive effects of teacher evaluation are particularly salient in education priority schools, in contexts where teaching is often very challenging.The third chapter of this thesis investigates the effect of school peers' gender on students' performance and educational careers in French middle schools. First, it shows that the proportion of female peers' in middle school has persistent effects on students' educational careers as it not only affects students' test score at the end-of-9th-grade national examination, but also influences their track choices and high school graduation rates several years later. Second, it shows that a larger share of girls in the classroom has positive effects for girls and negative effects for boys. More specifically, it reduces girls' dropout rates and increases their probability to graduate from an academic track in high school, especially in the scientific track, while it increases boys' probability to attend a vocational school after 9th grade and decreases their high school graduation rate

In schools in the Amathole District and throughout the rest of South Africa efforts are being made to encourage learners to pursue the Science and Applied Science curriculum stream in Grades 10 to 12. The aim of this study was both to determine and to explore those factors which, according to grade 9 learners, would either attract them to or deter them from following the Science and Applied Science curriculum stream from Grade 10 onwards. The study also sought to ascertain the views of teachers regarding the issues raised by the learners. A sample comprising 346 learners and 3 teachers were involved in the study. Using both quantitative and qualitative methods within the context of a post-positivist paradigm and utilising questionnaires and interviews, the study found that, consistent with existing research, there are both intrinsic and extrinsic related factors which play a role in the intention of learners to consider pursuing the Science and Applied Science curriculum stream. The intrinsic factors include learners‟ enjoyment of practical work and love for the Science and Applied Science. Extrinsic factors include perception that jobs in the field of Science and Applied Science compensate well. However, it was the intrinsic factors that pushed the learners to have the intention to follow the Science and Applied Science curriculum stream. Sociological, economic and personal dynamics seem to account for these patterns in the results. By contrast, two key sets of factors deterred the learners from the Science and Applied Science curriculum stream. One relates to factors in their internal loci of control, and the other to factors in learners‟ external loci of control. The internal locus of control factors had a greater influence, which suggests, according to attribution theorists, that the learners were inclined to look within themselves for the reasons that deterred them from the Science and Applied Science curriculum stream. In addition, a cluster analysis was conducted to ascertain whether the demographic profiles of the learners played a role in respect of their intention to pursue the Science and Applied Science curriculum stream. This cluster analysis revealed that, in terms of gender, males were more inclined than females to follow the Science and Applied Science stream. However, it was also significant that peer influence played an important role in attracting males to the Science and Applied Science curriculum stream, whereas it was career interest factors that attracted the females. In terms of ethnic groups, Indians and blacks were more inclined than coloureds and whites to follow the Science and Applied Science stream with whites being the least attracted to this stream. Career choice dynamics provide some explanations for these outcomes. The key contribution of this study lies in the fact that the study has shown that practical work as a teaching strategy may result in greater learner participation in the Science and Applied Science curriculum stream. The study recommends that, in order to promote greater participation in the Science and Applied Science curriculum stream in schools, strategies related to teaching in terms of which both genders are taken into consideration should be implemented. Other recommendations were also made. Nevertheless, it must be borne in mind that the study is a case study and that it is, therefore, not possible to generalise the findings.

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A melhoria na qualidade do ensino matemático resulta de diversos fatores como: qualificação dos professores, busca de novos modelos pedagógicos e inclusão da tecnologia aos processos de aprendizagem. Existe um grande distanciamento entre a tecnologia e a sala de aula, principalmente quando se fala em ensino público, e é nessa problemática que este trabalho busca contribuir com soluções alternativas. Aproveitando a enorme demanda dos aparelhos móveis e a forte influência que esses dispositivos detém sobre os jovens, buscou-se fundamentar o trabalho realizando pesquisas sobre os aspectos pedagógicos da aprendizagem móvel e, em virtude do fascínio exercido pelos jogos digitais, foram estudadas as técnicas de gamificação. Nesse contexto, foi desenvolvido um aplicativo tipo perguntas e respostas (QUIZ), de acordo com os preceitos da aprendizagem móvel e utilizando os recursos motivacionais da gamificação. Como tópico matemático, foi utilizado matrizes e determinantes devido a contemporaneidade do assunto e sua diversidade de aplicações. Com a finalidade de validar os objetivos, foi realizado um experimento com alunos do Ensino Médio do Colégio de Aplicação da Universidade Federal de Roraima, onde após a utilização do aplicativo foi distribuído um questionário a alunos e professores. E, com a tabulação dos resultados, foi realizada uma breve avaliação de alguns aspectos deste trabalho.
The improvement in the quality of mathematics teaching is the result of several factors such as the qualification of teachers, the search for new pedagogical models and the inclusion of technology to learning processes.There is a large gap between the technology and the classroom, especially when it comes in public education, and it is this problem that this work seeks to contribute to alternative solutions. Taking advantage of the huge demand of mobile phones and the strong influence that this device has on young people, we seek to support our application conducting research on the pedagogical aspects of mobile learning and, because of the fascination exerted by digital games, we studied the techniques of gamification. In this context, it was developed an application questions and answers (QUIZ), according to the precepts of mobile learning and using the motivational resources of gamification. As mathematical topic was used matrices and determinants due to this matter be current and its range of applications. For the purpose to validate the goals was carried out an experiment with high school students of the College Application of the Federal University of Roraima, where after using the application has distributed a questionnaire to students and teachers. And with the tabulation of results, there was a brief review of some aspects of this work.

CAPES
O estudo de matrizes no ensino médio é quase sempre centrado no ensino de técnicas operatórias, mesmo foco dado pelos materiais didáticos que abordam esse assunto nesse nível de ensino. O texto propõe uma visão diferenciada a essa prática de ensino, mostrando de forma simples, clara e de fácil compreensão para um aluno do ensino médio algumas aplicações de matrizes, usando para isso as transformações geométricas de translação, rotação e transformação de escala.
The study of matrices in high school is almost always centered on the teaching of operative techniques, same focus given by textbooks that address this issue at this level of education. This text proposes a different approach, showing in a clear and simple way some applications as translation, rotation and scaling.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico
This work describes an investigative experience related to High School Math teachers Studies, more precisely about their performance in relation to the use of technologies as mediators during their classes. Through a Math Educational Didactic and technological work- shop offered in the ambit of activities in the Programa de Estudos Pós-Graduados em Educação Matemática da PUC/SP (grupo TecMEM), where a group of teachers from Estado de São Paulo Public School were under observation in the realization in dynamic activities using the software WinMat as well as in the executions of tasks with traditional medias, all of them related to the theme "matrices and determinants". Through qualitative analysis of data, it was possible to verify several difficulties by these groups of researchers, conceptual and technical, but these difficulties could decrease as soon as this articulation was being reached between the interface technological domain and the recover of mathematics concepts involved. Besides, the teachers who are in this investigation have noticed the importance of pedagogical strategies in which mathematics technological classes should be included, more than the simple use of software or other artifact to the students use
Este trabalho relata uma experiência investigativa relacionada à formação continuada de professores de Matemática do Ensino Médio, mais precisamente no que tange ao preparo dos mesmos em relação ao uso de tecnologias como mediadoras em suas aulas. Através de uma Oficina Didática de Educação Matemática e Tecnologias, oferecida no âmbito das atividades do Programa de Estudos Pós-Graduados em Educação Matemática da PUC/SP (grupo TecMEM), um grupo de professores da rede pública do Estado de São Paulo foi acompanhado na realização de atividades dinâmicas com uso do software Winmat, bem como na consecução de tarefas em com mídias tradicionais, todas relacionadas ao tema matrizes e determinantes . Através de análise qualitativa dos dados, foi possível constatar diversas dificuldades por parte dos sujeitos da pesquisa, tanto conceituais quanto técnicas, que puderam ser minoradas à medida que se alcançava uma articulação entre o desenvolvimento do domínio tecnológico da interface e a recuperação dos conceitos matemáticos envolvidos. Além disso, os docentes envolvidos nesta investigação indicaram perceber a importância das estratégias pedagógicas que incluam tecnologias nas aulas de Matemática, muito além da mera inserção de softwares e ou artefatos para o uso de seus estudantes

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This work is a study of linear systems from the perspective of linear algebra. We will use the concepts of matrix, vector, linear combination, linear dependence and independence, vector space, basis and dimension. We will also calculate the determinants and implications. Our aim is to present the rudiments of Linear Algebra as helper tool in solving linear systems and display its geometry. We want it to manufacture a auxiliary text that can be explored by students and high school teachers, and so gently introducing this powerful mathematical tool. Throughout the text will be covered also some historical aspects.
Este trabalho é um estudo de sistemas lineares sob uma perspectiva da Álgebra Linear. Utilizaremos os conceitos de matriz, vetor, combinação linear, dependência e independência linear, espaço vetorial, base e dimensão. Faremos também o cálculo de determinantes e implicações. Nosso intuito é apresentar os rudimentos da álgebra linear como ferramenta auxiliadora na resolução de sistemas lineares e exibir a sua geometria. Queremos com isto confeccionar um texto auxiliar que possa ser explorado por estudantes e professores do Ensino Médio e, assim, suavemente introduzindo esta poderosa ferramenta da matemática. No decorrer do texto serão abordados também alguns aspectos históricos.

Background: The human secondary sex ratio has been the subject of long-standing medical, environmental and social scientific curiosity and research. A decline in male birth proportion in some industrialised countries is linked to endocrine disruption and is validated by some empirical studies. Increasing parental age and population stress and associated decreases in sex ratio have also been demonstrated. A thorough literature review of 123 relevant and diverse studies provides context for these assessments. Methods: A spatial-temporal investigation of birth sex ratio in Scotland and potential determinants of endocrine disruptor pollution, socio-economic factors including neighbourhood stress, deprivation, smoking, and maternal age, was conducted. This involved review of national and regional sex ratio time trends, and stratified/spatial analysis of such factors, including the use of GIS tools. Secondary data were sourced from Scottish Government web portals including Scottish Neighbourhood Statistics and the Scottish Environmental Protection Agency. Results: Regional differences in sex ratio between 1973 and 2010 are observed which likely lever the national male birth proportion downwards, with the region of poorest air quality from industrial emissions, the Forth Valley, displaying the greatest sex ratio reduction. Further analysis shows significant upwards skewing in sex ratio for the population cohort experiencing the least and 2nd most deprivation. Localised reductions in sex ratio for areas of high modelled endocrine disruptor pollution within the Central Region in Scotland are also displayed. Discussion: Limitations of the analyses include the danger of ecological fallacy in interpreting from area-based measurement and the simplified pollution modelling adopted. Despite this, and given elevated incidence of testicular cancer in Scottish regions mirrors the study’s results, tentative confirmation of the endocrine disruptor hypothesis can be substantiated. Further, elucidation on advanced parental age as a contributory factor to secondary sex ratio change is also given. Recommendations are made with respect to environmental monitoring and health protection, and preventative health strategies in Scotland.

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Os sistemas de equações lineares são muito úteis, pois podem modelar matematicamente diversos problemas em Estatística, Física, Química, Engenharia, Administração, Economia, enfim, em várias áreas do conhecimento. Historicamente, o cálculo de soluções desse tipo de sistema pelos chineses motivou o surgimento das matrizes, que, grosseiramente falando, são tabelas de elementos distribuídos em linhas e colunas. O uso de matrizes facilita o estudo e também a resolução de sistemas lineares, pois simplificam a notação e padronizam os procedimentos. O método do escalonamento de matrizes, por exemplo, é uma técnica que pode ser utilizada em sistemas lineares em geral, além de ser facilmente automatizada devido ao seu algoritmo. O objetivo deste trabalho é apresentar alguns conceitos e resultados sobre matrizes e sistemas lineares e abordar a relação entre eles, além de propor alguns problemas que podem ser resolvidos utilizando esses resultados. Professores do Ensino Médio podem utilizar tais problemas em sala de aula para trabalhar esse assunto com seus alunos.
The systems of linear equations are very useful because they can mathematically model several problems in Statistics, Physics, Chemistry, Engineering, Administration, Economics, and finally, in various areas of knowledge. Historically, the computation of solutions of this type of system by the Chinese motivated the emergence of matrices, which, roughly speaking, are tables of elements distributed in rows and columns. The use of matrices facilitates the study and the resolution of linear systems because they simplify the notation and standardize the procedures. The Echelonment method, for example, is a technique that can always be used in linear systems in general, besides being easily automated due to its algorithm. The objective of this work is to present some concepts and results about matrices and linear systems and to approach the relation between them, besides proposing some problems that can be solved using these results. High school teachers may use such problems in the classroom to work on this subject with their students.

Projeto de Graduação apresentado à Universidade Fernando Pessoa para obtenção do grau de Licenciada em Enfermagem
A adoção de estilos de vida (EV) saudáveis deve ser vista como uma oportunidade e um desafio da pessoa, família e comunidade, possibilitando uma atitude preventiva de saúde. A entrada no ensino clínico (EC) é um momento de mudança marcante na biografia do estudante. Consiste numa formação aglutinadora, mobilizando aprendizagens, permitindo a aquisição de competências ao futuro enfermeiro. Na transição para o EC o estudante deverá mobilizar recursos, desenvolvendo respostas adaptativas ao novo processo. Quando tal não acontece, reflete-se negativamente ao nível da saúde e do seu bem-estar. Este estudo teve como objetivos conhecer os EV dos estudantes de enfermagem em EC e promover a adoção de comportamentos promotores de saúde. É um estudo descritivo, transversal e quantitativo. Com uma população representada por todos os estudantes da licenciatura de enfermagem de uma Universidade do Norte do País. Amostra de conveniência, constituída por 39 estudantes de enfermagem em EC. O instrumento de colheita de dados foi o questionário “Estilos de Vida Fantástico”. Os dados foram tratados recorrendo a estatística descritiva e apresentados sobre a forma de gráficos e tabelas. Dos 39 estudantes 82% são género feminino e 18% do masculino. Situam-se numa média de idades de 23 anos. Destes 95% são solteiros e 5% são casados. Quanto aos fatores determinantes dos EV dos estudantes em EC, no item “família e amigos”, 95% referem ter com quem falar de assuntos importantes e 89,7% recebe carinho e afetos. Relativamente à “atividade física/associativismo” 51,3% dos inquiridos refere “quase nunca” participar em atividades associativas, 40,3% menciona andar cerca de 30 minutos diários, enquanto que 48,7% refere fazer atividade física 3 ou mais vezes por semana. Foram encontrados indicadores de comportamentos saudáveis nas dimensões “álcool e drogas”, “tabaco”, “comportamento sexual e saúde” e “outros comportamentos”. Quanto à “nutrição” e “sono e stress” deparamo-nos com comportamentos pouco consentâneos. Relativamente ao “trabalho/tipo de personalidade”, 71,8% diz sentir-se feliz, 54% refere sentir-se acelerado e/ou atarefado, 46% mencionam sentir-se tensos e/ou oprimidos e 30% triste ou deprimido. Os resultados confirmam comportamentos não tão saudáveis nas principais determinantes da saúde, havendo necessidade de intervenções especificas para a promoção de EV saudáveis. Durante esta transição, os hábitos saudáveis, são deixados de lado. A adoção de EV requer a proposição de estratégias que favoreçam a adesão e a participação dos estudantes na realização de ações de promoção de saúde.
The adoption of healthy lifestyles (EV) should be seen as an opportunity and a challenge for the person, family and community, enabling a preventive health attitude. The entry into clinical teaching (EC) is a moment of remarkable change in the student's biography. It consists of an agglutinative formation, mobilizing learning, allowing the acquisition of skills to the future nurse. In the transition to the EC the student must mobilize resources, developing adaptive responses to the new process. When this does not happen, it reflects negatively on the level of your health and well-being. This study aimed to know the EV of nursing students in CHD and to promote the adoption of health promoting behaviors. It is a descriptive, cross-sectional and quantitative study. With a population represented by all the students of the degree of nursing of a University of the North of the Country. Sample of convenience, made up of 39 nursing students in EC. The data collection instrument was the "Fantastic Lifestyles" questionnaire. The data were treated using descriptive statistics and presented in the form of graphs and tables. Of the 39 students 82% are female and 18% are male. They are located at an average age of 23 years. Of these 95% are single and 5% are married. Regarding the determinants of students' EVs in CS, in the item "family and friends", 95% refer to whom they talk about important matters and 89.7% receive affection and affection. Concerning "physical activity / association" 51.3% of respondents said "almost never" participate in associative activities, 40.3% said to walk about 30 minutes a day, while 48.7% referred to physical activity 3 or more times per week. Indicators of healthy behaviors were found in the dimensions "alcohol and drugs", "tobacco", "sexual behavior and health" and "other behaviors". As for "nutrition" and "sleep and stress" we are faced with inconsistent behaviors. Regarding "work / personality type", 71.8% said they felt happy, 54% reported feeling rushed and / or busy, 46% mentioned feeling tense and / or oppressed and 30% sad or depressed. The results confirm not so healthy behaviors in the main determinants of health, and there is a need for specific interventions to promote healthy VS. During this transition, healthy habits are left out. The adoption of EV requires the proposition of strategies that favor students' participation and participation in health promotion actions.
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ABSTRACT The shift in the nation’s political climate between 2016-2019 has exacerbated the longstanding pervasive issues of racism and discrimination against People of Color and those marginalized by societal inequity. This has serious implications for teaching and schooling, as it causes children to feel unsafe, question their sense of belonging, and internalize racial oppression. Indicators of inequitable school experiences for Students of Color and students from marginalized identity groups warrant attention to the socially determined facets of public education: specifically a sense of school belonging (SOSB) for Students of Color, the impact of racial trauma, the patterns of social engagement that shape their experiences, as well as the pedagogical practices teachers employ to support their social-emotional wellbeing. This qualitative case study seeks to illustrate how classroom teachers at Arday Elementary School support the social-emotional wellbeing of Students of Color by examining their understanding of racial trauma and SOSB and their use of equity literate pedagogies in the classroom to effectively support their Students of Color in a public elementary school in Northern New England. Findings include the hidden curriculum, teacher critical consciousness, cultural congruence, learning environment, racial trauma, and resistance. These findings point to a newly conceptualized framework, Equity Pedagogy for Social-Emotional Wellbeing (EPSEW), which applies a social determinants perspective to examinations of educational inequity and considers the social and community contexts that predetermine and influence inequitable outcomes. Keywords: equity pedagogy, equity literacy, social determinants, school belonging, racial trauma, internalized racism, social emotional well-being, critical pedagogy, anti-bias education

A research report submitted to the Faculty of Science, University of the Witwatersrand, in partial fulfillment of the degree of Master of Science.
The Toeplitz form is a most useful and important teo! in many areas of applied. mathematics today including signal processing, time-series analysis and prediction theory. It is even used in quantum mechanics in Ising model correlation functions. (Abbreviation abstract)
AC 2018

博士
國立政治大學
應用數學研究所
95
Classical and generalized Vandermonde matrices are ubiquitous in mathematics, and various studies on their determinants, inverses, explicit LU factorizations with applications are done recently by many authors. In this thesis we shall focus on two topics: One is generalized Vandermonde matrices revisited and the other is various decompositions of some generalized Vandermonde matrices. In the first topic, we prove the well-known determinant formulas of two types of generalized Vandermonde matrices using only mathematical induction, different from the proofs of Fulin Qian's and Flowe-Harris'. In the second topic, which constitutes the main results of this thesis, we devote ourself to two themes. Firstly, we study a special class which is the transpose of the generalized Vandermonde matrix of the first type and succeed in obtaining its LU factorization in an explicit form. Furthermore, we express the LU factorization into 1-banded factorizations and get the inverse explicitly. Secondly, we consider a totally positive(TP) generalized Vandermonde matrix and obtain its unique LU factorization without using Schur functions. The result is better than Demmel and Koev's which is involved Schur functions. As by-products, we gain the determinant and the inverse of the required matrix and express any Schur function in an explicit form. Basing on the above result, we obtain a way to calculate Kostka numbers by expanding Schur functions.

In this thesis, I present a small experiment of teaching the singular value decomposition (SVD) of matrices using a computational approach. The goal of the experiment was to check if students who completed the first two undergraduate linear algebra courses are prepared for this topic and if they would be satisfied with the computational approach. The experiment took place in the summer of 2011 and consisted in two sessions of lectures of four hours each, in a computer lab, on the premises of Concordia University. The same four students attended both sessions. The approach consisted in first introducing students to the general ideas and then gradually zooming into the details of the theory and the computational techniques and algorithms. In the instructional sessions, lecturing by the teacher alternated with participants’ exploring the theoretical results and algorithms using prepared Maple worksheets. Before the sessions started, participants were asked to respond to a questionnaire (Pre-test) that verified their knowledge of basic linear algebra concepts necessary for understanding the SVD theory. After the session, participants were asked to respond to another questionnaire (Post-test) addressing their understanding of SVD and their opinions about the teaching approach and the teaching of SVD in an undergraduate program. Participants’ responses to test questions were collected and analyzed. One of the immediate conclusions is that without a good understanding of the fundamental concepts of linear algebra the topic of singular value decomposition of matrices could prove challenging for even the top achieving undergraduate students. The participants showed interest in the teaching method, but mentioned that more time would be required to really benefit from learning about the numerical advantages and the vast applications of the singular value decomposition.

A dissertation submitted to the Faculty of Arts Unitrers:Ltyof the witwatersrand, Johannesburg for the degree ~f Master of Arts. Johannesburg, 1992.
This investigat:i.ondemonstrates that school-leavers" experience the greatest amount pf difficulty in answering comprehension questions that demand inferencing related to stylistic effects in written passages. It also demonstrates that the texts use,d in Transvaal Education Department written comprehension examinations and the questions