Thesis (Ed.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The purpose of this study was to investigate how advanced mathematics students in the eighth, tenth and twelfth grades used inferential reasoning in the solution of problems that required knowledge of elementary number theory. Inferences were classified based on the level of ambiguity involved, simple or complex; the number of pieces of information used, single-item or combined-item; the type of inference, simple single-item, simple combined-item, complex single-item or complex combined-item; and the purpose of the inference (seventeen inference codes were identified). The use of inferences classified by type was of primary interest. Also investigated were the procedures subjects employed to obtain, maintain and control information. Each of the 18 subjects, 6 from each grade, solved ten different problems in two to three sessions. Each problem involved the identification of a "mystery" whole number in the range of 1 to 1000 on the basis of clues that were provided. As the subjects interacted with the computer program that presented the problems, they were asked to "think aloud." Using transcribed, typewritten protocols and all paper-pencil notations recorded by subjects, protocols were coded employing a coding scheme developed by the investigator [TRUNCATED] / 2031-01-02

Made available in DSpace on 2016-04-27T16:57:09Z (GMT). No. of bitstreams: 1 Andre Henrique Pizysieznig.pdf: 2148950 bytes, checksum: e98b671a3a07d9dee100a4a9d809f88a (MD5) Previous issue date: 2011-10-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work is part of the problem that questions the process of building major mathematical concepts from Elementary Number Theory for Basic Education. In this context, this study aimed to investigate the conception of divisibility of the K-5 students in School Elementary or through an approach with calculator. The main theoretical references were sought in Resende (2007) and Zazkis and Campbell (2002) regarding the Elementary Theory of Numbers and Sfard (1991) to cognitive processes, Silva et al (1990), Borba and Penteado (2007) and Bianchini and Machado (2010) served as reference to discuss the use of the calculator in the classroom. The qualitative research methodology is based mainly in the Engineering Curriculum. Two sessions with students from the 6th year of public schools in Sao Paulo concluded that among the four concepts focused on the proposed activities: multiple and divisor a natural number, prime numbers and operations division, the students also used a division the calculator and mental arithmetic, half the students showed an operational concept in the process of internalization of the conception of multiple , showed no students meet the mathematical meaning of the term divisor and mostly did not recognize a divisor given representation in prime factors an integer. The calculator was used for all the subjects to calculate and / or validate their responses, being used by some students uncritically, combining alternately with mental arithmetic and algorithmic / Este trabalho se insere na problemática que questiona o processo da construção dos principais conceitos matemáticos da Teoria Elementar dos Números durante a Educação Básica. Neste contexto, este estudo teve como objetivo investigar a concepção de divisibilidade de alunos do 6° ano do Ensino Fundamental por meio de uma abordagem com calculadora. Os principais referenciais teóricos foram buscados em Resende(2007) e em Zazkis e Campbell (2002) no que tange à Teoria Elementar dos Números e em Sfard (1991) para processos cognitivos; Silva et al (1990), Borba e Penteado (2007) e em Bianchini e Machado (2010) serviram de referência para discutir o uso da calculadora em sala de aula. A pesquisa de cunho qualitativo se embasou principalmente na metodologia da Engenharia Didática. Duas sessões com alunos do 6° ano da rede pública estadual de São Paulo permitiram concluir que dentre os quatro conceitos focalizados pelas atividades propostas: divisor e múltiplo de um número natural, números primos e operação de divisão, os alunos para realizar uma divisão recorrem igualmente a calculadora e ao cálculo mental, metade dos alunos mostraram uma concepção operacional em fase de interiorização do conceito de múltiplo , nenhum aluno mostrou conhecer o significado matemático do termo divisor e em sua maioria não reconheceu um divisor dada representação em fatores primos de um número inteiro. A calculadora foi utilizada por todos os sujeitos da pesquisa para calcular e/ou validar suas respostas, sendo utilizada por alguns alunos de forma acrítica, conciliando alternadamente com o cálculo mental e algorítmico

Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_eduardo_sad_costa.pdf: 3568903 bytes, checksum: 4e09f1b15f7714b64ad56708b0bd9974 (MD5) Previous issue date: 2007-05-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work involves a qualitative study about whether and how mathematics High-School teachers work with their students the trouble-situations regarding linear Diophantine equations. The study was performed by means of analyzing semi-structured interviews applied on six mathematics teachers from the states of São Paulo and Minas Gerais, teaching at high-school level. The Numbers Elementary Theory has been treated by several researchers on Mathematical Education, as Campbell e Zazkis (2002), Resende (2007), as an adequate subject for the introduction and development of fundamental Mathematical ideas in High- School. However, the results of such investigation show that, although the interviewed teachers affirmed that they did work with problems of discreet mathematics that can be modeled through linear Diophantine equations, none of them seemed to work with their students using the knowledge of these equations properties in order to decide whether they have solution, and what these solutions would be / Neste trabalho apresento um estudo qualitativo sobre se, e como, professores de Matemática do Ensino Médio trabalham com seus alunos situações-problema que recaem em equações diofantinas lineares. O estudo foi feito por meio da análise de entrevistas semi-estruturadas realizadas com seis professores de Matemática dos estados de São Paulo e Minas Gerais que lecionam no Ensino Médio. A Teoria Elementar dos Números vem sendo tratada por diversos pesquisadores de Educação Matemática, como Campbell & Zazkis (2002), Resende (2007), como assunto propício para a introdução e desenvolvimento de idéias Matemáticas fundamentais no Ensino Básico. No entanto os resultados desta investigação indicam que embora os professores entrevistados afirmassem trabalhar com problemas de matemática discreta modeláveis via equação diofantina linear, nenhum deles deu indícios de trabalhar com seus alunos utilizando conhecimentos das propriedades dessas equações para decidir se as mesmas tem solução e quais seriam essas soluções

Made available in DSpace on 2016-04-27T16:57:42Z (GMT). No. of bitstreams: 1 dissertacao_silvio_barbosa_oliveira.pdf: 371682 bytes, checksum: 4f27d9c132d5173732426c8e48699248 (MD5) Previous issue date: 2006-05-24 / This work involves a qualitative study of how the theme of linear Diophantine equations is approached in mathematics textbooks for high school students. Using the methods associated with content analysis (Bardin, 1977), I search for references, in both explicit and implicit forms, to these equations in two different sets of high school mathematics textbooks, both of which had been approved in the last PNLEM (a national project for the assessment of high school textbooks). Although elementary number theory has been highlighted by researchers in mathematics education, such as Campbell and Zazkis (2002), as a subject apt for the introduction and development of fundamental mathematical ideas in compulsory education, the results of this investigation indicate that it receives little attention in the textbooks analysed / Neste trabalho apresento um estudo qualitativo sobre a abordagem dada pelo livro didático do Ensino Médio ao tema equações diofantinas lineares . Por meio de uma análise de conteúdo, segundo Bardin (1977), busquei o assunto em sua forma explícita e implícita em duas coleções de Matemática para o Ensino Médio, aprovadas no último PNLEM. Embora a Teoria Elementar dos Números venha sendo tratada por pesquisadores de Educação Matemática, como Campbell e Zazkis (2002), como assunto propício para a introdução e desenvolvimento de idéias matemáticas fundamentais, no Ensino Básico, os resultados desta investigação indicam a pouca exploração do assunto por parte das coleções analisadas