The Long Division is a novel that applies some conventions and tropes of the noir fiction genre to tell a story from the points of view of five individuals whose fates are interconnected through the narrative. Jodie Larkin is an Atlanta housecleaner who, fed up with her thankless job, hits the road with stolen cash, desperate to reconnect with the son she gave up for adoption. That son is Calvin Nowak, a teenager eager to escape an adoptive family that he feels can never understand him. He and Jodie embark on a runaway quest to discover the source of his pain. Their journey will take them to small town New York, where Calvin’s biological father, Sam Hartwick, is secretly tracking the shooter in a double murder case that will test his reputation and his faith in redemption. That killer is Wynn Johnston, a college student gifted and tortured, who clings to his bright academic prospects while hunted by vengeful criminals, police, and his own demons. He strikes up a desperate relationship with Erika Hartwick, Sam Harwick’s legitimate daughter, just as Sam’s illegitimate son Calvin and one-time lover Jodie arrive in town and instigate a climactic confrontation between all the perspective characters. The novel explores the value of family and how it can be tested by extreme circumstances, especially in paradoxical or ironic context where family is founded on, or broken apart by, characters flaws that threaten the stability of family itself. Likewise, it explores whether certain family relationships can or should be repaired, and the motives and morality of individuals when they support or subvert family dynamics.

This is an action research study which focuses on a didactical model founded on base ten decomposition as an algorithm for performing division on naturals. Base ten decomposition is used to enhance the algebraic structure of division on naturals in an attempt to cross the cognitive divide that currently exists between arithmetic long division on naturals and algebraic long division on polynomials. The didactical model that is proposed and implemented comprises three different phases and was implemented over five one hour lessons. Learners’ work and responses which were monitored over a fiveday period is discussed in this report. The structure of the arithmetic long division on naturals formed the conceptual basis from which shorter methods of algebraic long division on polynomials were introduced. These methods were discussed in class and reported on in this study.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-05-03T17:56:24Z No. of bitstreams: 1 2016 - Eduardo Castro Brittes.pdf: 1568575 bytes, checksum: f11844cc4540daf8a36fe1a5dca0c9c6 (MD5) / Made available in DSpace on 2017-05-03T17:56:24Z (GMT). No. of bitstreams: 1 2016 - Eduardo Castro Brittes.pdf: 1568575 bytes, checksum: f11844cc4540daf8a36fe1a5dca0c9c6 (MD5) Previous issue date: 2016-08-31 / CAPES / In one of the public networks of teaching in which the author acts as a teacher, many students arrive at the beginning of the second segment of the elementary school without mastering the four basic arithmetic operations and, specifically, with many difficulties in multiplication and division of natural numbers. There is also the little interest of several of them for mathematical content in General. Considering this reality, noted a need to seek innovations, finding ways to stimulate this learning curriculum component. Over the years, researched some methods and algorithms to multiply and divide natural numbers. Testing several of them over the years, the classroom experience pointed out the Lattice and the Long Division with Estimation as potentially motivating algorithms for arithmetic operations, by format and for simplicity. The aim of this work was to carry out an action research in a class of sixth grade of elementary school, involving the use of these two algorithms, evaluating motivational aspects and learning during the trial. Initially, were applied in that class a test to evaluate the motivation for studying mathematics and a pre-test, where if asked to solve simple issues of multiplication and division of natural numbers, the way each student wanted. After this step, some activities were carried out, using the above algorithms. Finally, we conducted a post-test and was reapplied the test of motivation, which granted the necessary data to the conclusions of the research. The resemblance to the traditional "Tic-Tac-Toe", the Lattice was introduced as a handmade board game, which stimulated competition and generated a lot of interest in most. The long division with estimation already used in most movements, the subtraction, what is a content well assimilated by students in this age group and educational level, since, typically, these students have a better development of thought. So I received a lot of attention from students, who have improved their concepts of orders (units, tens, hundreds), to better carry out the algorithm. Based on the questionnaire assessed the motivation to study mathematics, it was possible to observe not only the improvement of the interest in the various activities involving Mathematical content, but also an increase of confidence and credibility in the relationship between teacher x student. The approach has yielded satisfactory results. This kind of experience can leave as a legacy to students for the abandonment of the initial bad impression you might have regarding the arithmetic and, often, removing the fear and disgust in having to do the math, replacing this feeling of security generated by the domain in a differentiated way to solve problems that require multiplication and division. Moreover this experience can increase the ability of the students to absorb the multiplicative principle, paving the way for it to deepen the learning in this field of knowledge. / Em uma das redes p?blicas de ensino em que o autor atua como professor, v?rios alunos chegam ao in?cio do segundo segmento do Ensino Fundamental sem dominar as quatro opera??es aritm?ticas b?sicas e, especificamente, com muitas dificuldades na multiplica??o e na divis?o de n?meros naturais. Verifica-se tamb?m o pouco interesse de v?rios deles por conte?dos de matem?tica de uma forma geral. Considerando essa realidade, notou-se uma necessidade de buscar inova??es, encontrando formas de estimular a aprendizagem deste componente curricular. Ao longo dos anos, pesquisaram-se alguns m?todos e algoritmos para multiplicar e para dividir n?meros naturais. Testando v?rios deles ao longo dos anos, a experi?ncia em sala de aula apontou a Gelosia e a Divis?o Americana como algoritmos potencialmente motivadores para o ensino de opera??es aritm?ticas, pelo formato e pela simplicidade. O objetivo deste trabalho foi realizar uma pesquisa-a??o numa turma do sexto ano do Ensino Fundamental, envolvendo o uso desses dois algoritmos, avaliando aspectos motivacionais e de aprendizagem durante a experi?ncia. Inicialmente, foram aplicados nessa turma um teste para avaliar a motiva??o para estudar matem?tica e um pr?-teste, onde se pedia para resolver quest?es simples de multiplica??o e divis?o de n?meros naturais, da forma como cada aluno desejasse. Depois dessa etapa, foram realizadas algumas atividades, usando os algoritmos supracitados. Finalmente, foi realizado um p?s-teste e foi reaplicado o teste de motiva??o, que concedeu os dados necess?rios para as conclus?es da pesquisa. Pela semelhan?a com o tradicional "Jogo da Velha", a Gelosia foi introduzida como um jogo de tabuleiro artesanal, o que estimulou a competi??o e gerou muito interesse na maioria. J? a divis?o americana usou, na maioria dos movimentos, a subtra??o, que ? um conte?do bem assimilado por alunos nesta faixa et?ria e de escolaridade, uma vez que, normalmente, esses alunos possuem um melhor desenvolvimento do pensamento aditivo. Por isso recebeu muita aten??o dos alunos, que aprimoraram seus conceitos de ordens (unidade, dezena, centena), para melhor desempenhar o algoritmo. Baseado no question?rio que avaliou a motiva??o para estudar Matem?tica, foi poss?vel n?o s? observar a melhora do interesse pelas diversas atividades que envolvem o conte?do de Matem?tica, como tamb?m um aumento de confian?a e credibilidade na rela??o professor x aluno. A abordagem rendeu resultados satisfat?rios. Esse tipo de experi?ncia pode deixar como legado para os alunos o abandono da impress?o inicial ruim que poderiam ter em rela??o ? Aritm?tica e, por muitas vezes, retirando o medo e repulsa em ter que fazer contas, substituindo este sentimento pela seguran?a gerada pelo dom?nio de uma forma diferenciada de resolver problemas que exigem multiplica??o e divis?o. Al?m disso, tal experi?ncia pode aumentar a capacidade dos alunos em absorver o princ?pio multiplicativo, abrindo caminho para que se aprofunde a aprendizagem neste campo de conhecimento.