The subject of the diploma thesis is the creation of study material relating the subject of theory of dividing for students trained to be teachers at primary school. In the first part of the thesis I am concentrating on theory of mentioned problem. The main target of the thesis in the second part is the collection of exercises for the students. In the third part of these I am checking the level of knowledge in the subject of divisions in natural numbers with ten years old autistics student that I take care during school instruction. The results of these tests are mentioned in the thesis.

The objective of this paper is to present a context in which mathematics can be glimpsed in a more attractive and dynamic way. For this, succinct but regular knowledge will be presented to the basic understanding of cryptography. We will cite examples of gures and how some of them work, in addition to some de nitions, theorems and demonstrations on topics such as divisibility, congruence, functions and arrays. Finally, we will make suggestions of a set of activities that provide the interconnection of mathematical and daily knowledge of the student, since this combination is an attractive factor for a better assimilation of content. However, the teacher has the insight to make choices and to judge what he thinks it's most interesting. / O objetivo deste trabalho é apresentar um contexto no qual a matemática pode ser vislumbrada de forma mais atrativa e dinâmica. Para isso, serão apresentados conhecimentos sucintos, mas regulares, para a compreensão básica da criptografia. Citaremos exemplos de cifras e de como funcionam algumas delas, mostraremos algumas definições, teoremas e demonstrações sobre assuntos, tais como, divisibilidade, congruência, funções e matrizes. Por fim, faremos sugestões de um conjunto de atividades que proporcionam a interligação de conhecimento matemático e conhecimento diário do aluno, visto que essa combinação é um fator atrativo para melhor assimilação do conteúdo. No entanto, o professor tem o discernimento para realizar escolhas e julgar o que achar mais interessante.

Made available in DSpace on 2015-05-15T11:46:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 885143 bytes, checksum: 948ed501e70f201fbd41ae588572c5bc (MD5) Previous issue date: 2010-08-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We present in this work a complete classification of the sublattices of (Zn,+, ≥) which are not groups of divisibility. Thus we provide a new class of ordered filtered groups of which are not groups of divisibility. The sublattices presented here generalize the exemples of P.Jaffard and G. G. Bastos / Apresentamos nesse trabalho uma classificação completa de sub-reticulados de (Zn,+, ≥) que não são grupos de divisibilidade. Deste modo, nós fornecemos uma nova classe de grupos ordenados que são filtrados, mas não são grupos de divisibilidade. Os sub-reticulados aqui apresentados generaliza os exemplos de P. Jaffard e G. G. Bastos.

The objective of this paper is to present a context in which mathematics can be glimpsed in a more attractive and dynamic way. For this, succinct but regular knowledge will be presented to the basic understanding of cryptography. We will cite examples of gures and how some of them work, in addition to some de nitions, theorems and demonstrations on topics such as divisibility, congruence, functions and arrays. Finally, we will make suggestions of a set of activities that provide the interconnection of mathematical and daily knowledge of the student, since this combination is an attractive factor for a better assimilation of content. However, the teacher has the insight to make choices and to judge what he thinks it's most interesting. / O objetivo deste trabalho é apresentar um contexto no qual a matemática pode ser vislumbrada de forma mais atrativa e dinâmica. Para isso, serão apresentados conhecimentos sucintos, mas regulares, para a compreensão básica da criptografia. Citaremos exemplos de cifras e de como funcionam algumas delas, mostraremos algumas definições, teoremas e demonstrações sobre assuntos, tais como, divisibilidade, congruência, funções e matrizes. Por fim, faremos sugestões de um conjunto de atividades que proporcionam a interligação de conhecimento matemático e conhecimento diário do aluno, visto que essa combinação é um fator atrativo para melhor assimilação do conteúdo. No entanto, o professor tem o discernimento para realizar escolhas e julgar o que achar mais interessante.

Orientador: Jose Plinio de Oliveira Santos / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T08:31:50Z (GMT). No. of bitstreams: 1 Reis_JacksonMartins_M.pdf: 998765 bytes, checksum: ea7248e69be4c892e184263be7050375 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho foram abordados tópicos de Teoria dos Números e alguns testes de primalidade. Mostramos propriedades dos números inteiros, bem como alguns critérios de divisibilidade. Apresentamos também, além das propriedades do Máximo Divisor Comum e Mínimo Múltiplo Comum, interpretações geométricas dos mesmos. Foram estudados Tópicos da Teoria de Congruências e por fim trabalhamos alguns Testes de Primalidade, com respectivos exemplos. / Abstract: In this work were discussed topics of the theory of numbers and some primality tests. We show properties of whole numbers, and some criteria for divisibility. We also present, beyond the properties of the Common Dividing Maximum and Minimum Common Multiple, geometric interpretations of the same ones. They had been study topics of theory of congruences and finally we work some of primality tests, whith respective applications. / Mestrado / Teoria dos Numeros / Mestre em Matemática

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-06-02T19:33:53Z No. of bitstreams: 2 Dissertação - Tânia Regina Rodrigues Franco - 2016.pdf: 2643450 bytes, checksum: c01355ce5ba1fb2524facde3704a3d8e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-03T12:44:18Z (GMT) No. of bitstreams: 2 Dissertação - Tânia Regina Rodrigues Franco - 2016.pdf: 2643450 bytes, checksum: c01355ce5ba1fb2524facde3704a3d8e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-06-03T12:44:18Z (GMT). No. of bitstreams: 2 Dissertação - Tânia Regina Rodrigues Franco - 2016.pdf: 2643450 bytes, checksum: c01355ce5ba1fb2524facde3704a3d8e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2016-03-30 / This essay begins with a theoretical foundation about the positional system, divisibility, Euclidean division, maximum common divisor, prime numbers and modular congruence. Through the concepts discussed, we show some applications, for elementary school students. The main main points of the theory and bring notions of applicability of arithmetic in daily situations. We will work solving Diophantine linear equations; we will determine some criteria of divisibility; by the relationship of modular congruence and arithmetic of the rest; even with modular congruence we will propose activities with codes and other existing numbers in our country, ending solving problem on calendars. These applications will serve of tools and methodologies of contextualized form, the teachers, will motivate their students to understand a little more about the concept of Modular Arithmetic, easy, fast and simple way. / Esta dissertação, inicia-se com uma fundamentação teórica acerca do sistema posicional, divisibilidade, divisão euclidiana, máximo divisor comum, números primos e congruência modular. Através dos conceitos abordados, apresentaremos algumas aplicações, para alunos do ensino fundamental. O principal objetivo é apresentar os principais pontos da teoria e trazer noções da aplicabilidade da aritmética em situações cotidianas. Trabalharemos a resolução de Equações Diofantinas Lineares; determinaremos alguns critérios de divisibilidade, através da relação de congruência modular e aritmética dos restos; ainda com congruência modular proporemos atividades com códigos e outras numerações existentes em nosso país, nalizando com a resolução de problemas sobre calendários. Essas aplicações servirão de ferramentas e metodologias para que de forma contextualizada, o professor, motive seu aluno a entender um pouco mais sobre o conceito de Aritmética Modular, de maneira fácil, rápida e simples.

This thesis evaluates traditional real estate diversification strategy by region and by property type. Additionally, it provides common risk measures - reduction of total risk and tracking error. The main contribution is twofold. First, it extends the coverage of common real estate research to the area of the Czech Republic and Slovakia. To our knowledge, this is the first study of this kind on the local market. Second, this thesis accounts for non-divisibility of ownership. This is a specific attribute of real estate, which may deteriorate investors' efforts for optimal allocation. Researchers' methods depart from Capital Asset Pricing Model. Evaluation techniques include efficient and pseudo-efficient frontiers, quantiles of total risk and tracking error, both as a function of portfolio size and portfolio value. Main findings include: (i) there is no strictly superior strategy, but there is a difference for specific subcategories, (ii) impartible ownership decreases risk-adjusted performance, this might be partially overcome by leverage, (iii) diversification is costly and index tracking is hardly possible. JEL Classification C22, C61, G12, R33 Keywords real estate diversification, direct investments, risk, ownership non-divisibility Title Traditional Real Estate Portfolio Diversification and...

My theses called Divisibility at second grade - textbooks and knowledge of the pupils is devoted to different aspects of schooling of this topic at elementary schools. This work is divided into three chapters. Whilst the first chapter is dedicated to the theory, the subject of two other chapters are two different researches conducted under the divisibility theme. Theoretical resources common to both parts of the research can be found in the first chapter. Among the topics mentioned in this chapter are for example the differences between formal and informal knowledge, constructivist and transmissive way of teaching or the process of solving word problems. The essence of my first research are the textbooks for elementary school concerned with the divisibility theme. Except the part devoted to a textbooks search (all the textbooks approved by the Ministry of Education, Youth and Sports which deal with divisibility), this chapter also contains the propaedeutics of divisibility and interviews with teachers, in which I have tried to cover the most important moments in the schooling of divisibility. Second part of my research is focused on checking of the pupils' knowledge of divisibility with a special emphasis on formal and informal knowledge. I have used the test to this purpose, which was...

The controversy around the inclusion of zero in the number system has been widely documented. Influential mathematicians in various ancient cultures did not accept zero as a number. The idea of the empty set was too abstract and they could not conceptualise division by zero. Surprisingly, understanding of the concept is still a matter of concern today. In spite of expansive reports on and recommendations for developing conceptualisation of the concept, learners and teachers still experience problems similar to those that ancient mathematicians struggled with. The study was initiated by an observation of Grade 7 learners' inability to solve the problems 4 × 0 and 0 ÷ 7 effectively or at all. I investigated why Grade 3 to 6 learners and mathematics teachers on a BEd (in-service) course and an accredited ACE course experience problems with the concept of zero. I was especially interested in the understanding of multiplication and division by zero. I investigated teachers' knowledge of zero's characteristics as a number, the history of zero and how they teach the concept, in order to support my assumptions. The data production process was performed over a period of two years. It involved a multi-case opportunity sample approach embedded in the empirical field that formed the backdrop of my involvement as mathematics education specialist in schools in the Western and Eastern Cape. The interpretative orientation of the study allowed me to conduct inquiries that served to confirm or challenge my assumptions and enabled me to construct generalisations that depict learners' and teachers' knowledge construction. The qualitative data analysis informed the presentation and discussion of the findings. The single most important message conveyed to readers of this study is that the value of zero as a number, its importance in the number system, its properties and its behaviour in calculations, should not be underrated. Teaching of this abstract concept requires competent teachers who are able to mediate understanding in the most effective and innovative manner. Professional development programmes should orchestrate this competence and curriculum developers and textbook authors should acknowledge the significance of learning and teaching the concept of zero.

Made available in DSpace on 2016-04-27T16:57:04Z (GMT). No. of bitstreams: 1 Rogerio Osvaldo Chaparin.pdf: 2644934 bytes, checksum: c8a8cb59aa59e9acbc623f18e66cbb61 (MD5) Previous issue date: 2010-10-08 / Secretaria da Educação do Estado de São Paulo / This study aims to investigate the students' conceptions of a first year high school on the concept of divisibility of natural numbers. The relevance of this study is the importance that, according to Campbell and Zazkis (1996) and Resende (2007), has the divisibility concepts relevant in the development of mathematical thinking, in research activities at any level of education, identification and pattern recognition, in the formulation of conjectures and especially in solving problems. To achieve this I used as the theoretical APOS Theory to analyze the protocols, Sfard in formulating the idea of design and research Rina Zazkis building activities. To collect the data I have chosen a didactic sequence consists of four activities performed in pairs of first year students of high school I teach at school. These survey results show that students had great difficulty in handling the operation of the division, designing mostly divisibility through actions, algorithms, and procedures. They did not know deduce relations, information, ie, mainly not understand that the representation in prime factors is a very important way to relate the concepts of multiple and divisor. The students were unable to apply the concepts mentioned above in a situation contextualized in a situation of daily life. Thus concludes that it is necessary to give greater emphasis to basic issues of the Elementary Theory of Numbers in the teaching of mathematics / Este trabalho tem como objetivo investigar quais as concepções dos alunos de um primeiro ano do ensino médio sobre o conceito de divisibilidade dos números naturais. A relevância deste estudo está na importância que, segundo Campbell e Zazkis (1996) e Resende (2007), tem os conceitos pertinentes a divisibilidade no desenvolvimento do pensamento matemático, nas atividades investigativas em qualquer nível de ensino, na identificação e reconhecimento de padrões, na formulação de conjecturas e principalmente na resolução de problemas. Para alcançar tal objetivo usei como aporte teórico a Teoria APOS para análise dos protocolos, Sfard na formulação da idéia de concepção e as pesquisas de Rina Zazkis na elaboração de atividades. Para a coleta de dados optei por uma sequência didática composta por 4 atividades realizada em duplas de alunos do primeiro ano do ensino médio na escola que leciono. Os resultados dessa pesquisa revelam que os alunos tiveram grande dificuldade na manipulação da operação da divisão, concebem na sua maioria a divisibilidade por meio de ações, algoritmos, procedimentos. Não souberam deduzir relações, informações, ou seja, principalmente não compreenderam que a representação em fatores primos é uma forma muito importante para relacionar os conceitos de múltiplo e divisor. Os sujeitos não conseguiram aplicar os conceitos citados acima numa situação contextualizada em uma situação do cotidiano. Desta forma conclui que é necessário dar uma ênfase maior para os assuntos básicos da Teoria Elementar dos Números no ensino da matemática