Quantitative reasoning permeates mathematical thinking, and mathematics education researchers have taken a quantitative reasoning approach to examining and modeling students' mathematical thinking and development in various domains. From this approach, secondary and post-secondary researchers have focused on students' ability to reason about how two quantities vary together (covariational reasoning). However, little is known about how covariational reasoning develops from, or connects with, arithmetic and algebraic reasoning. This study begins to bridge the gap in this knowledge. Originally this study was designed to examine middle grade students' units coordination in covariational reasoning across stages and consider the cognitive limiting factor of working memory. In this case study of Daniel, an advanced Stage 2 middle-grade algebra student, I examined the role his units coordinating structures played in his covariational reasoning in non-graphing and algebra tasks. I considered three main components in covariational reasoning (type of quantity, modality of change, and role of time) when analyzing covariational reasoning and capturing the underlying mental units and actions. I found type of quantity and time were the two biggest factors when determining Daniel's covariational reasoning. Daniel also used his units coordinating structures in various ways in the different covariation tasks, generating three different types of change units that were cognitively structurally different. These findings suggest cognitive connections between the types of units a student assimilates with, and the types of covariational reasoning they engage in, are interconnected and warrant future study. / Doctor of Philosophy / This study examines connections between middle-grade students' arithmetic reasoning and algebraic reasoning in their conceptualization of how two quantities vary together (covariation). I interviewed 6 cognitively diverse middle-grade students to investigate these connections and determine at the level of mental action level the types of quantities and actions students use in covariation. After collecting data on the 6 students and reflecting on the richness of each case, I elected to focus on one student for a fine-grain analysis. From this case study of Daniel, an algebra student, I found he used his arithmetic unit structures in unique ways depending on what quantities a task asked him to work with. I also found that Daniel's use of time as a measured quantity in his covariational reasoning influenced how he conceptualized two quantities changing together.

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Made available in DSpace on 2017-07-21T20:31:48Z (GMT). No. of bitstreams: 1 Patriciaad.pdf: 658891 bytes, checksum: 470ee20f3b92cc259e6d51a017684204 (MD5) Previous issue date: 2006-12-07 / This term paper proposes to argue and to analyze aspects of the Mathematical Modeling in the scope of the Mathematical Education, the teaching and learning of the Mathematics in the Basic Education s context. It presents as its central objective the analysis of the Mathematical Modeling while a differentiated educative practice for the teaching and as an investigation s leading question it seeks to identify the favored aspects of the Modeling whereas a practice that comes from the group or student s interest? By hypothesis, the disinterest for the taught subject in Mathematics provokes a deficient learning in the student s. The paper presents a general view of Mathematical Education and its perspectives for the teaching in the Basic Education facing the National Guidelines for the Elementary and High School system. It approaches the Modeling since the Pre-history until the Contemporary Age. For the central objective s achievement and other elect objectives of this investigation, it was used the explorative researches to provide a greater familiarity with the subjects that treats the Mathematical Education and Modeling. Furthermore, to become aware about the initial works characteristics of descriptive research. To get the knowledge about these initial works with the Modeling, it was used material produced by the first experiences participators in the specialization courses which were carried through in 1983/1984. It consists in the quantity of Education Laboratory of Education and Mathematical Education research LEPEM . It presents and analyzes the lived experiences with Modeling (in a public and in a private school), trying to identify aspects that constitute it as a differentiated practice developing and following the steps considered by Burak (1998/2004). The results of the experiences point to new teaching perspectives of the Mathematical Education. Word-Keys: Teaching and Learning, Modeling Mathematics, Mathematical Education, Interdisciplinary, Contextualization / This term paper proposes to argue and to analyze aspects of the Mathematical Modeling in the scope of the Mathematical Education, the teaching and learning of the Mathematics in the Basic Education s context. It presents as its central objective the analysis of the Mathematical Modeling while a differentiated educative practice for the teaching and as an investigation s leading question it seeks to identify the favored aspects of the Modeling whereas a practice that comes from the group or student s interest? By hypothesis, the disinterest for the taught subject in Mathematics provokes a deficient learning in the student s. The paper presents a general view of Mathematical Education and its perspectives for the teaching in the Basic Education facing the National Guidelines for the Elementary and High School system. It approaches the Modeling since the Pre-history until the Contemporary Age. For the central objective s achievement and other elect objectives of this investigation, it was used the explorative researches to provide a greater familiarity with the subjects that treats the Mathematical Education and Modeling. Furthermore, to become aware about the initial works characteristics of descriptive research. To get the knowledge about these initial works with the Modeling, it was used material produced by the first experiences participators in the specialization courses which were carried through in 1983/1984. It consists in the quantity of Education Laboratory of Education and Mathematical Education research LEPEM . It presents and analyzes the lived experiences with Modeling (in a public and in a private school), trying to identify aspects that constitute it as a differentiated practice developing and following the steps considered by Burak (1998/2004). The results of the experiences point to new teaching perspectives of the Mathematical Education. Word-Keys: Teaching and Learning, Modeling Mathematics, Mathematical Education, Interdisciplinary, Contextualization / Este trabalho propõe-se a discutir e analisar aspectos da Modelagem Matemática no âmbito da Educação Básica e também o ensino e a aprendizagem da disciplina nesse contexto. Apresenta como objetivo central a análise da Modelagem Matemática enquanto uma prática educativa diferenciada para o ensino de Matemática e como questão norteadora da investigação busca identificar: quais os aspectos favorecidos pela Modelagem enquanto uma prática que parte do interesse do grupo ou do aluno? Por hipótese, o desinteresse pelo assunto a ser ensinado em Matemática provoca um aprendizado deficiente no aluno. O trabalho apresenta uma visão geral da Educação Matemática e suas perspectivas para o ensino na Educação Básica frente às Diretrizes Nacionais para o Ensino Fundamental e Médio. Faz uma abordagem da Modelagem desde a Pré-história até a Idade Contemporânea. Para a consecução do objetivo central e de outros objetivos eleitos para a investigação valeu-se das pesquisas exploratórias para proporcionar maior familiaridade com os temas tratados sobre a Educação Matemática e a Modelagem Matemática e para conhecer as características dos trabalhos iniciais com a Modelagem valeu-se de algumas características das pesquisas descritivas. Para tomar ciência dos trabalhos iniciais com a Modelagem utilizou-se do material produzido pelos participantes das primeiras experiências com a Modelagem nos cursos de especialização realizado em 1983/1984, que consta no acervo da Unicentro no Laboratório de Ensino e Pesquisa em Educação Matemática - LEPEM. Apresenta e analisa as experiências vividas com a Modelagem Matemática buscando identificar aspectos que a constituam como prática diferenciada. A parte prática do trabalho consta de experiências vivenciadas no âmbito de duas escolas, uma pública e outra particular, desenvolvida seguindo os passos propostos por Burak (1998/2004). Os resultados das experiências apontam para novas perspectivas do ensino de Matemática na Educação. / Este trabalho propõe-se a discutir e analisar aspectos da Modelagem Matemática no âmbito da Educação Básica e também o ensino e a aprendizagem da disciplina nesse contexto. Apresenta como objetivo central a análise da Modelagem Matemática enquanto uma prática educativa diferenciada para o ensino de Matemática e como questão norteadora da investigação busca identificar: quais os aspectos favorecidos pela Modelagem enquanto uma prática que parte do interesse do grupo ou do aluno? Por hipótese, o desinteresse pelo assunto a ser ensinado em Matemática provoca um aprendizado deficiente no aluno. O trabalho apresenta uma visão geral da Educação Matemática e suas perspectivas para o ensino na Educação Básica frente às Diretrizes Nacionais para o Ensino Fundamental e Médio. Faz uma abordagem da Modelagem desde a Pré-história até a Idade Contemporânea. Para a consecução do objetivo central e de outros objetivos eleitos para a investigação valeu-se das pesquisas exploratórias para proporcionar maior familiaridade com os temas tratados sobre a Educação Matemática e a Modelagem Matemática e para conhecer as características dos trabalhos iniciais com a Modelagem valeu-se de algumas características das pesquisas descritivas. Para tomar ciência dos trabalhos iniciais com a Modelagem utilizou-se do material produzido pelos participantes das primeiras experiências com a Modelagem nos cursos de especialização realizado em 1983/1984, que consta no acervo da Unicentro no Laboratório de Ensino e Pesquisa em Educação Matemática - LEPEM. Apresenta e analisa as experiências vividas com a Modelagem Matemática buscando identificar aspectos que a constituam como prática diferenciada. A parte prática do trabalho consta de experiências vivenciadas no âmbito de duas escolas, uma pública e outra particular, desenvolvida seguindo os passos propostos por Burak (1998/2004). Os resultados das experiências apontam para novas perspectivas do ensino de Matemática na Educação.

The purpose of the present study was to investigate the effects of socioeconomic status, school factors (classroom climate, classroom activities) and affective variables (motivation, self-efficacy, mathematics anxiety, beliefs about the nature of mathematics and teaching of mathematics, students&rsquo / perceptions of their teachers and parents&rsquo / attitudes toward them) on mathematics achievement with 9th grade students in Ankara. For this purpose, structural equation modeling techniques were used. In the study, there were two research problems: &ldquo / What was the general model explaining the effects of socioeconomic status, affective and school factors on students&rsquo / mathematics achievement?&rdquo / and &ldquo / how the proposed model explained mathematics achievement in three school types (Anatolian, general and vocational high schools)?&rdquo / Some of the results of the analyses conducted in the study are the followings: In the main study, socioeconomic status had strong effect on mathematics achievement. In addition, while student-centered activities generally affected students&rsquo / mathematics achievement in a positive way but indirectly, teacher-centered activities had negative effects on affective variables. But for Anatolian and vocational high schools, this negative effect turned positive on mathematics achievement. In the main study, classroom climate had positive direct effects on self-efficacy and motivation toward mathematics as well as on mathematics achievement. Generally, affective variables had positive effects on mathematics achievement. But mathematics anxiety had no significant effect on it except general high school. The results of present study indicated that students&rsquo / perceptions of their parents and teachers&rsquo / attitudes and expectations toward them had positive indirect effects on mathematics achievement.

Made available in DSpace on 2014-12-17T15:04:59Z (GMT). No. of bitstreams: 1 PabloJSL_DISSERT.pdf: 2748711 bytes, checksum: 25bd52a895ba4efa08fa7fde9c4d4718 (MD5) Previous issue date: 2012-08-10 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice / Este trabalho discute aspectos relacionados ? linguagem matem?tica e ? sua compreens?o, em especial, por estudantes dos anos finais do Ensino Fundamental. Nesse sentido, objetivamos elaborar uma proposta de ensino consubstanciada por atividades de modelagem matem?tica e de leitura, que oportunize ao aluno do Ensino Fundamental uma melhor compreens?o da linguagem matem?tica inerente ao conte?do de propor??o. Visamos tamb?m construir/propor par?metros para a avalia??o da profici?ncia leitora desta linguagem por parte do estudante e analisar no processo de modelagem, a sua capacidade de desenvolver/aprimorar/potencializar esta profici?ncia. Para isso, desenvolvemos uma pesquisa de cunho qualitativo, com procedimentos de uma pesquisa-a??o, cuja an?lise dos dados se configura como An?lise de Conte?do. Referenciamo-nos epistemologicamente e didaticamente, nos estudos de: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo e Garnica (2006), Smole e Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin e Reyes (2010), dentre outros. Entendemos que para adquirir um novo conhecimento ? preciso aprender a l?-lo e ler para aprend?-lo, este processo ? indispens?vel para o desenvolvimento da profici?ncia leitora de um sujeito. A modelagem, por sua vez, ? um processo que possibilita o contato com distintas formas de leitura, oferecendo elementos favor?veis ao desenvolvimento ora mencionado. Os par?metros avaliativos que utilizamos para analisar o n?vel de profici?ncia leitora da linguagem matem?tica mostrou-se eficaz e, portanto, um valioso instrumento que permite ao professor uma avalia??o eficiente e cujos resultados podem orient?-lo melhor no planejamento e execu??o de sua pr?tica