To be numerate is to have the ability to understand numbers and be confident with numeric information presented in day-to-day situations. The way numeracy is defined varies between researchers; however, most agree that having skills in numeracy is essential to function in the world. In order to provide students with the opportunity for exposure to basic numeracy skills, McMaster University’s course Math 2UU3 – “Numbers for Life” is offered to non-mathematics major students in second year or above. To measure the effectiveness of this course, and to determine whether students retain the numeracy skills and knowledge acquired in the course, we developed a series of assessments with questions based on content learned throughout the semester. Students were tested three times – once before completing the course, once after completing the course, and once again a year later. This study focuses in on the logical reasoning aspect of numeracy which includes understanding logical structures and being able to work through problems rationally and systematically. The results from the study reveal that students who took the course and participated in completing the given assessments showed improvement with their logical reasoning skills significantly. / Thesis / Master of Science (MSc)

The present research aims to evaluate the extent of deaf children’s delay in mathematics, identifying the moderators of this delay and determine the longitudinal predictors of their mathematical achievement. For five decades, studies have reported that deaf children lag behind their hearing peers in mathematics (Gottardis, Nunes and Lunt, 2011). Background factors such as age, degree of hearing loss, presence of cochlear implant and types of educational provision were previously hypothesised to be moderators of the extent of this delay but, up to now, they have not been tested. Pagliaro (2010) argued that number knowledge, working memory and degree of hearing loss could be possible causes of deaf children’s difficulties in mathematics but no clear conclusions were reached. The present investigation aims to provide insight into the causes of deaf children’s delay in mathematics. The survey study addressed the first aim of the present study. The maths test of the Performance Indicators for Primary School (PIPS) was used as outcome measure. Factors related to deaf children (degree of hearing loss, age, years in education, presence of cochlear implant, gender, causes of deafness) and background factors (highest maternal education, language used at home, type of educational provision) were assessed as possible predictors and moderators of the extent of deaf children’s delay in mathematics. The overall extent of deaf children’s delay in mathematics was of -1.76 SDs. The older the children get and the more years they spend in special schools for the deaf or in units for hearing impaired, the wider is their gap in mathematics achievement compared with their hearing peers. It is, therefore, necessary to intervene in their mathematical learning in the early years of schooling in order to create pathways for improvement. The second aim of the present study was addressed through a longitudinal design. Logical-mathematical reasoning, working memory and counting ability were chosen as predictors of deaf children’s mathematical attainment on the basis of theoretical framework, evidence from longitudinal studies and from the analysis of the difficulties that deaf children have in these factors compared with hearing peers. Hierarchical regression analyses were used to assess the independence of the contributions of logical-mathematical reasoning, working memory and counting ability to the prediction of deaf children’s mathematical achievement measured through the PIPS. Age, years in education, type of educational provision and non-verbal intelligence were used as controls. Counting ability and working memory did make independent contributions to the prediction of deaf children’s mathematical success but logical mathematical reasoning was by far the strongest predictor. When the predictors were entered in the model, none of the control variables predicted significantly deaf children’s mathematical achievement. This study makes several empirical contributions. First, it established age, years in education and types of educational provision as moderators of the extent of deaf children’s delay in mathematics. Second, it determined the plausibility of a causal link between logical-mathematical reasoning, counting ability, working memory and deaf children’s mathematical achievement. The implication is that schools must explicitly plan to improve deaf children’s mathematical reasoning, counting ability and working memory when they are in kindergarten and in the first years of school in order to help the children’s mathematical development.

Esta pesquisa se dedicou à introdução dos jogos lógicos na sala de aula, em específico, ela busca a investigação das dificuldades encontradas pelos alunos com os diferentes estilos de jogos apresentados e quais são os raciocínios lógicos utilizados para a resolução dos problemas propostos. Buscamos os benefícios que estes jogos podem trazer para o ensino e a aprendizagem na sala de aula. Aliado a isso também trabalhamos a parte geométrica dos tabuleiros, e com isso os alunos utilizaram como ferramentas a régua e o compasso para a construção dos tabuleiros apresentados.. Para tanto, a metodologia de pesquisa escolhida foi o Estudo de Caso, de acordo com Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). O referencial teórico é baseado nos trabalhos de Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), bem como os PCNs e outros artigos/livros relacionados aos jogos lógicos e as construções geométricas com a régua e o compasso. As atividades foram desenvolvidas com uma turma do 9º ano do Ensino Fundamental de em uma Escola Municipal de Porto Alegre, no ano de 2015. Em especial sugerimos que é possível a inserção desses materiais a fim de serem usados como ferramentas de auxílio no ensino aprendizagem de matemática contribuindo positivamente para a formação dos alunos. Os registros coletados no estudo de caso possibilitaram a validação da proposta. / The present research has focused on the introduction of the logical games in the class. It aims to pin point difficulties presented by the students on the different styles of games proposed and a logical ratiocination is required to solve the tasks proposed. The benefits of the games along with the teaching and learning in the classroom was the goal. Additionally, the geometric segment of board games have been investigated and students used tools as ruler and compass to the construction of the boards presented. Therefore, the chosen researching methodology was the Case Study, according to Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). The theoretical referential is based on Works from Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), along with the PCNs and others articles/books related to logical games and geometric constructions with a ruler and a compass. The activities were performed by a 9th grade group of the Elementary School in a Municipal School in Porto Alegre, in 2015. We showed in particular that is possible the insertion of these materials in order to be used as a sustenance tool on Mathematics Learning contributing positively to students formation. The data collected in the case study enabled the authentication of the proposal.

The purpose of the study was to develop a revision of the logical reasoning section of the California Test of Mental Maturity which increases its discriminative ability while maintaining an acceptable measure of reliability. Subjects were 102 students of general psychology classes at North Texas State University. All were administered the Logical Reasoning section of the California Test of Mental Maturity in its original form and an experimental revision of it (LRTR). The Wesman Personnel Classification Test was administered at the same time to demonstrate the tests' construct validity. Pearson product-moment correlations, item and homogeneity analyses were run. Results indicated that the revised test correlated significantly with the original test and the WPCT. Internal validity of the revised test was satisfactory, showing an improvement over the original test in terms of clarity, reliability and homogeneity.

Submitted by Ricardo Pessoa Dos Santos null (ricopessoa@gmail.com) on 2017-12-14T17:35:33Z No. of bitstreams: 1 Dissertação.pdf: 4489608 bytes, checksum: 2c9d751844c4b178546f2154b0718705 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2017-12-14T18:53:30Z (GMT) No. of bitstreams: 1 santos_rp_me_sjrp.pdf: 4489608 bytes, checksum: 2c9d751844c4b178546f2154b0718705 (MD5) / Made available in DSpace on 2017-12-14T18:53:30Z (GMT). No. of bitstreams: 1 santos_rp_me_sjrp.pdf: 4489608 bytes, checksum: 2c9d751844c4b178546f2154b0718705 (MD5) Previous issue date: 2017-11-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Iremos apresentar a um grupo de alunos do Ensino Médio da rede pública de Ensino do Estado de São Paulo, o mundialmente conhecido quebra cabeças Sudoku, e realizar com eles várias atividades buscando apresentá-lo como subsídio didático na aprendizagem de conceitos matemáticos importantes, além de proporcionar oportunidades de aprimorar a concentração e o raciocínio lógico. Iremos explorar conceitos matemáticos ocultos por trás de suas linhas, colunas e blocos, partindo de uma das primeiras perguntas que podem ser feitas: Qual é a quantidade total de jogos válidos existentes? Para responde-la, será proposto a realização de diversas atividades, primeiramente com um Shidoku (matriz 4 × 4), em seguida iremos calcular o total desses jogos. O tamanho reduzido dessa grade, facilita os cálculos manuais, permitindo visualizar e compreender o processo utilizado, aproveitando para introduzir o princípio fundamental da contagem. A discussão principal desse trabalho, concentra-se na exploração de um método para se determinar a quantidade de jogos válidos existentes para um Sudoku, e para isso, utilizaremos as demonstrações de Bertrand Felgenhauer e Frazer Jarvis. Também apresentaremos um método capaz de gerar uma grade completa de Sudoku, partindo de uma matriz quadrada de ordem 3, que em seguida, será utilizada para gerar uma solução de Sudoku ortogonal. Finalizando, iremos apresentar e explorar algumas formas diferenciadas para os quebra cabeças Sudoku, mostrando variações no formato dos blocos, no tamanho das grades e uma variação que utiliza formas geométricas em suas pistas (Shapedoku). Como desafio de leitura, pesquisa e aprofundamento, será proposto o problema ainda em aberto do número mínimo de dados iniciais para se ter um jogo válido. Podemos afirmar que um dos objetivos esperados, é que tal atividade venha interferir na concentração e raciocínio, auxiliando nas atividades propostas nesse trabalho e que possam ser utilizadas em outros problemas do cotidiano. / We will present to a group of high school students of the public Education of Sao Paulo state, the world-known puzzle Sudoku, and perform with them several activities seeking to present it as a didactic subsidy in the learning important mathematical concepts, besides opportunities to enhance concentration and logical reasoning. We will explore hidden mathematical concepts behind their lines, columns and blocks, starting from one of the rst questions that can be asked: What is the total number of valid games in existence? To answer this question, it will be proposed to perform several activities, rst with a Shidoku (4 × 4 matrix), then we will calculate the total of these games. The reduced size of this grid facilitates manual calculations, allowing to visualize and understand the process used, taking advantage to introduce the fundamental principle of counting. The main discussion of this paper focuses on the exploration of a method to determine the amount of valid games existing for a Sudoku, and for that, we will use the demonstrations of Bertrand Felgenhauer and Frazer Jarvis. We will also present a method capable of generating a complete Sudoku grid, starting from a square matrix of order 3, which will then be used to generate an orthogonal Sudoku solution. Finally, we will introduce and explore some di erent shapes for the Sudoku puzzle, showing variations in the shape of the blocks, the size of the grids and a variation that uses geometric forms in their tracks (Shapedoku). As a challenge for reading, searching and deepening, the open problem of the minimum number of initial data to have a valid game will be proposed. We can say that one of the expected objectives is that such activity will interfere in concentration and reasoning, helping in the activities proposed in this paper and that can be used in other daily problems. / 3107510001F5

Esta pesquisa se dedicou à introdução dos jogos lógicos na sala de aula, em específico, ela busca a investigação das dificuldades encontradas pelos alunos com os diferentes estilos de jogos apresentados e quais são os raciocínios lógicos utilizados para a resolução dos problemas propostos. Buscamos os benefícios que estes jogos podem trazer para o ensino e a aprendizagem na sala de aula. Aliado a isso também trabalhamos a parte geométrica dos tabuleiros, e com isso os alunos utilizaram como ferramentas a régua e o compasso para a construção dos tabuleiros apresentados.. Para tanto, a metodologia de pesquisa escolhida foi o Estudo de Caso, de acordo com Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). O referencial teórico é baseado nos trabalhos de Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), bem como os PCNs e outros artigos/livros relacionados aos jogos lógicos e as construções geométricas com a régua e o compasso. As atividades foram desenvolvidas com uma turma do 9º ano do Ensino Fundamental de em uma Escola Municipal de Porto Alegre, no ano de 2015. Em especial sugerimos que é possível a inserção desses materiais a fim de serem usados como ferramentas de auxílio no ensino aprendizagem de matemática contribuindo positivamente para a formação dos alunos. Os registros coletados no estudo de caso possibilitaram a validação da proposta. / The present research has focused on the introduction of the logical games in the class. It aims to pin point difficulties presented by the students on the different styles of games proposed and a logical ratiocination is required to solve the tasks proposed. The benefits of the games along with the teaching and learning in the classroom was the goal. Additionally, the geometric segment of board games have been investigated and students used tools as ruler and compass to the construction of the boards presented. Therefore, the chosen researching methodology was the Case Study, according to Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). The theoretical referential is based on Works from Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), along with the PCNs and others articles/books related to logical games and geometric constructions with a ruler and a compass. The activities were performed by a 9th grade group of the Elementary School in a Municipal School in Porto Alegre, in 2015. We showed in particular that is possible the insertion of these materials in order to be used as a sustenance tool on Mathematics Learning contributing positively to students formation. The data collected in the case study enabled the authentication of the proposal.

Esta pesquisa se dedicou à introdução dos jogos lógicos na sala de aula, em específico, ela busca a investigação das dificuldades encontradas pelos alunos com os diferentes estilos de jogos apresentados e quais são os raciocínios lógicos utilizados para a resolução dos problemas propostos. Buscamos os benefícios que estes jogos podem trazer para o ensino e a aprendizagem na sala de aula. Aliado a isso também trabalhamos a parte geométrica dos tabuleiros, e com isso os alunos utilizaram como ferramentas a régua e o compasso para a construção dos tabuleiros apresentados.. Para tanto, a metodologia de pesquisa escolhida foi o Estudo de Caso, de acordo com Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). O referencial teórico é baseado nos trabalhos de Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), bem como os PCNs e outros artigos/livros relacionados aos jogos lógicos e as construções geométricas com a régua e o compasso. As atividades foram desenvolvidas com uma turma do 9º ano do Ensino Fundamental de em uma Escola Municipal de Porto Alegre, no ano de 2015. Em especial sugerimos que é possível a inserção desses materiais a fim de serem usados como ferramentas de auxílio no ensino aprendizagem de matemática contribuindo positivamente para a formação dos alunos. Os registros coletados no estudo de caso possibilitaram a validação da proposta. / The present research has focused on the introduction of the logical games in the class. It aims to pin point difficulties presented by the students on the different styles of games proposed and a logical ratiocination is required to solve the tasks proposed. The benefits of the games along with the teaching and learning in the classroom was the goal. Additionally, the geometric segment of board games have been investigated and students used tools as ruler and compass to the construction of the boards presented. Therefore, the chosen researching methodology was the Case Study, according to Fiorentini e Lorenzato (2006), Ventura (2007) e Gil (2002). The theoretical referential is based on Works from Macedo (2007), Grando (2011), Skovsmose (2000), Huizinga (2000), Kishimoto (2006), Zuin (2001), along with the PCNs and others articles/books related to logical games and geometric constructions with a ruler and a compass. The activities were performed by a 9th grade group of the Elementary School in a Municipal School in Porto Alegre, in 2015. We showed in particular that is possible the insertion of these materials in order to be used as a sustenance tool on Mathematics Learning contributing positively to students formation. The data collected in the case study enabled the authentication of the proposal.

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-04-11T14:06:58Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Nilton M. Silva.pdf: 2876212 bytes, checksum: f9ec311d7e39d91817f915d9a4f92caf (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-04-11T14:07:09Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Nilton M. Silva.pdf: 2876212 bytes, checksum: f9ec311d7e39d91817f915d9a4f92caf (MD5) / Made available in DSpace on 2018-04-11T14:07:09Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Nilton M. Silva.pdf: 2876212 bytes, checksum: f9ec311d7e39d91817f915d9a4f92caf (MD5) Previous issue date: 2018-02-15 / D'Ambrósio (1996, p.29) points out “that Mathematic programs are often outdated, obsolete and out of context. Due to this more and more students find it difficult to be motivated about this crystallized science.” In the present work, we seek to present proposals for challenging activities, where students are encouraged to think in an autonomous way. To create, to experiment, to establish strategies and to reach solutions. Different from the classroom, where one usually presents ready and finished work, making it only a copy of the method or the technique. / D’Ambrósio (1996, p.29) aponta que “os programas de Matemática consistem em coisas acabadas, mortas e absolutamente fora do contexto e com isso, torna-se casa vez mais difícil motivar alunos para uma ciência tão cristalizada.” No presente trabalho, buscamos apresentar propostas de atividades desafiadoras, em que os alunos são encorajados a pensar de maneira autônoma, a criar, a experimentar, a estabelecer as estratégias para chegar às soluções. Diferente da sala de aula onde, normalmente, se apresenta conhecimentos prontos e acabados, tornando-o apenas reprodutor de métodos e técnicas.

This thesis focuses on thinking and reasoning in preschool children in the mathematical education and deals with the development of thinking in this group. This thesis is based on the fact that preschool education is indispensable. The theoretical part is focused on development, stimulate thinking and types of preschool age child. The practical part is to stimulate thinking processes reduced to thinking and reasoning, or the possibility of stimulation in the form of worksheets. This thesis presents thirteen original worksheets, whose suitability was tested on twenty children aged 5-6 years in one kindergarten.

Com maiores publicações no início do século XXI, o tema superimitação, ou overimitation, tem despertado interesse de alguns psicólogos e biólogos por se tratar de um possível mecanismo social que leva os humanos a copiarem comportamentos irrelevantes na resolução de uma situação problema a partir de um modelo. Neste contexto, a presente dissertação de mestrado objetivou uma análise do comportamento de superimitação com mecanismos das funções executivas e cognição social de crianças da educação infantil, de 4 a 5 anos de idade. Participaram 36 crianças da educação infantil selecionadas de uma EMEI em São Paulo, segundo critérios pré-estabelecidos, avaliadas com os testes: superimitação (resolução da caixa problemas), teoria da mente - ToM (teste de falsa crença), testes para funções executivas de memória operacional (Missing Test), flexibilidade mental (DCCS), e raciocínio lógico (Teste de Matrizes Coloridas Progressivas de Raven). Os resultados indicaram que a superimitação não apresentou correlação com as funções executivas examinadas. Foram verificados indícios de tratar-se de uma atividade social, por consequência da associação com a função de teoria da mente, em detrimento a uma atividade isolada de resolução de problema cognitivo / Having experienced a growth in number of studies at the beginning of the 21st century, the subject of overimitation has caught the interest of psychologists and biologists in referring to a possible social mechanism that makes humans copy irrelevant behavior during the resolution of problem situations from a model. In that context, the present dissertation has as its objective an analysis of the overimitation behavior in relation to executive function and social cognition mechanisms in preschool children, 4 to 5 years of age. Thirty-six children participated in the study. They wereselected from a public municipal school (EMEI) in São Paulo, Brazil, according to preestablished criteria and evaluated using the problem box resolution task (overimitation), false belief test (ToM), and tests for executive functions of working memory (Missing Test), mental flexibility (DCCS), and logical thinking (Ravens Progressive Matrices Test). The results indicate that overimitation presented no significant correlation to executive functions. The findings provide evidence that overimitation is a result of social activity, since it showed possible association to theory of mind, instead of signs of an isolated activity cognitive problem solving