This study aimed to develop a teaching and learning model, based on principles derived from the fields of constructivist theory, schema theory, critical literacy theory, and design theory, to inform the development of hypermedia-mediated learning environments that facilitate the construction of mathematical knowledge by secondary school students in Thailand. In this study, the participants were a group of three secondary school students from the Demonstration school attached to the Faculty of Education at Khon Kaen University (Thailand). In order to ascertain how mathematical learning could be facilitated by the process of designing a web page that could be used to introduce other students to analytic geometry, all three participants were asked to work collaboratively to design an analytic geometry web page. The process of designing the web page was informed by a theoretical model derived from an analysis and synthesis from the research literature on constructivist theory, schema theory, critical literacy theory, and design theory. Findings from the study indicated that the creation of a web page facilitated and enhanced the Thai students' learning about analytic geometry. The major outcomes from the study are a revised theoretical framework to inform the integration of the design of mathematical web pages into Thai mathematics classrooms and a conceptual map framework to assess qualitative and quantitative changes to students' repertoires of knowledge about analytic geometry that emerge during the process of designing a webpage.

Educators need clear, actionable data to help them understand students' current levels of performance and students' probable trajectory toward college- and career-readiness in math if they are to make informed programmatic decisions to shape that trajectory. This study explored the relation between CBM-math in Grade 7 as a one-point, teacher accessible measure of student math skill and the students' performance on the Grade 8 EXPLORE-math test, a large-scale achievement test linked to one set of college- and career-readiness benchmarks. Results indicated that a moderate positive correlation and predictive relation exist between CBM-math and EXPLORE-math. Information was disaggregated by gender and for subgroups, including students eligible for special education, free or reduced meals, and English language development services. No difference in means for male and female students on either measure was identified, but eligibility for special education or for free or reduced lunch was associated with lower performance on both measures. Insufficient numbers of ELD students hindered detailed analysis, but none of the ELD students included in the study achieved the EXPLORE benchmark or the CBM normalized cut score based on the 40th percentile. An ROC analysis showed that easyCBM consistently predicted students who did not meet the EXPLORE benchmark, although results indicated that a higher cut score on easyCBM may be a more consistent predictor. The study adds to validity research on CBM and may be useful for educators seeking to identify students at risk of missing achievement benchmarks and make programmatic decisions to ensure students are on track to be college- and career-ready in math.

Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.

Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.

Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.

Orientador: Antonio Miguel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-09T09:57:52Z (GMT). No. of bitstreams: 1 Vilela_DeniseSilva_D.pdf: 1524315 bytes, checksum: 9bbabd38825517fb6c7294587eeedc4c (MD5) Previous issue date: 2007 / Resumo: Como o termo matemática vem sendo usado na literatura acadêmica da Educação Matemática? Esta é a questão inicial que orienta este estudo investigativo realizado com base em publicações e pesquisas acadêmicas recentes em Educação Matemática. Com base nesses documentos, verificou-se a ocorrência, em freqüência significativa, de diversas adjetivações do termo matemática tais como: matemática escolar, matemática da rua, matemática acadêmica, matemática popular, matemática do cotidiano, etc. A partir da análise de alguns desses textos, constatou-se que as adjetivações, que ocorrem geralmente aos pares, apontam especificidades das matemáticas, tais como, diferenças em resultados, processos, valores, significados, conceitos, etc. A partir de uma visão de conjunto das especificidades apontadas nos textos pesquisados, as diversas adjetivações são interpretadas como jogos de linguagem que não possuiriam uma essência, mas apresentariam semelhanças de famílias, no sentido dado por Wittgenstein a este conceito. Para formular a questão acima, inspiramo-nos nos conceitos desse filósofo, bem como em sua concepção de filosofia, que possui uma perspectiva de ampliação dos significados alcançada mediante as descrições dos usos de um conceito, a qual possibilita dissolver a noção essencialista e referencial de significado A partir disso, para alcançar um sentido sociológico dessas adjetivações à interpretação filosófica é ampliada com conceitos da sociologia de Bourdieu, notadamente com o conceito de campo científico. As adjetivações expressariam uma tensão no campo das matemáticas: o reconhecimento da produção de conhecimentos matemáticos em diversas práticas que não só a dos matemáticos profissionais, mas também as dos professores, as de grupos profissionais, etc., e também o questionamento do monopólio da definição e atribuições do campo por matemáticos profissionais. Ou seja, as adjetivações são entendidas como objetivações de novos termos da gramática do campo das matemáticas. Além disso, são indicados elementos para uma compreensão das matemáticas como práticas sociais, não simplesmente como determinadas por estratégias racionais intencionais, e sim como práticas condicionadas pela própria estrutura da linguagem, que implica em regularidades as quais limitam e regulam as possibilidades de inteligibilidade e de desenvolvimento das matemáticas nas práticas especificas, mas que não constituem regulamentos que impediriam novos usos / Abstract: How used the term Mathematic in Mathematics Education literature has been? This is the main question that guides this investigation, supported by recent academic researches and publications in the field of Mathematics Education. Based on these writings, we have noticed the existence of several ways of adjetivizing the term mathematics such as: school mathematics, street mathematics, academic mathematics, popular mathematics, everyday mathematics, and so on. After analyzing some of these works, it can be seen that these adjectives, that often show up in pairs, point to mathematics specificities, such as difference in results, processes, values, meanings, concepts etc. From a global view of the specificities pointed in all researched texts, adjectives are understood as language-games that do not have an essence, but would present family resemblances, in the sense given by Wittgenstein to these concepts. To answer the question stated above, we were inspired by these Wittgenstein¿s concepts, as well as by his conception of philosophy, which has a tendency to broaden meanings through the use descriptions of a concept. This allows dissolving na essentialist notion of meaning as a last and universal reference. In order to search for a sociological sense for these adjectivize, our goal is to historically rescue this tendency to adjective in the current context of cultural studies in which modernity values are questioned. Thus, a philosophical explanation is broadened by concepts of Bourdieu's sociology, specially the concept of scientific field. The adjectives would express a struggle within the mathematics field, and the recognition that there is mathematical knowledge production in many practices beyond the professional mathematicians¿, like teachers¿, professional groups¿ etc. That is, adjectives are understood as objectivations for new terms of a grammar of mathematics fields. Besides, this work indicates elements for a understanding of mathematics as social practices, not merely determined by rational and intended strategies, but also as practices conditioned by language structures, which implies regularities that limit and adjust the possibilities of understanding and developmenting of mathematics within specific practices, but not representing regulations that could hinder new uses / Doutorado / Educação Matematica / Doutor em Educação

Este trabalho tem o objetivo de verificar como o logaritmo e a função logarítmica são abordados nos livros didáticos de Matemática do século XIX ao XXI, indicando a inserção desses conteúdos na Matemática Escolar brasileira. Baseamo-nos, dentre outros autores, em Choppin (2004), Valente (1999, 2004, 2005 e 2008) e Bittencourt (2004 e 2008) para identificarmos o livro didático como fonte de pesquisa da Matemática Escolar, a partir de suas formas conceituais, de enfoque didático ou referente à organização do saber. A fim de verificar relações entre o histórico dos logaritmos e da função logarítmica na Matemática e na Matemática Escolar, apresentamos a ideia dos logaritmos de Napier como facilitadores de cálculos, interpretamos sua definição geométrica por meio de um sistema de equações diferenciais ordinárias e, assim, mostramos um breve histórico sobre a inserção do logaritmo como função no Cálculo Integral. Os livros didáticos de Matemática analisados foram publicados entre os anos de 1879 e 2013. Nesta análise, consideramos o modo como os autores abordam ou tratam a Matemática, os tipos de atividades que são propostas, os tipos de explicações, definições, exemplos, gráficos, exercícios, aplicações e problemas associados aos logaritmos e à função logarítmica. Os resultados apontam que no século XIX os logaritmos eram tratados nos livros didáticos, quase sempre, por meio da Aritmética. A partir da década de 1890, eles são abordados, tanto no campo aritmético, pela associação à teoria das progressões, como no campo algébrico, sendo expoentes numa equação ou função. A partir da década de 1930 até os dias de hoje verificamos uma predominância da concepção algébrico-funcional dos logaritmos. Com base nas Orientações Curriculares para o Ensino Médio (2006), nos Parâmetros Curriculares Nacionais Ensino Médio (PCNs - 2000), nos Parâmetros Curriculares Nacionais+ Ensino Médio (PCNs+ Ensino Médio - 2002), no Exame Nacional do Ensino Médio e em livros didáticos recentes, verificamos que os logaritmos e a função logarítmica se inserem, atualmente, na Matemática Escolar brasileira, pela sua associação às aplicações, como por exemplo, juros compostos, dinâmica populacional, desintegração radioativa, potencial hidrogeniônico, Escala Richter, Escala de Magnitude de Momento (MMS) e nível de intensidade sonora. / This work aims to verify how the logarithm and logarithmic function are approached in the textbooks of Mathematics from the 19th to the 21st century, indicating the insertion of these contents in Brazilian School Mathematics. We are based, among other authors, in Choppin (2004), Valente (1999, 2004, 2005 and 2008) and Bittencourt (2004 and 2008) to identify the didactic book as a research source of School Mathematics, from its conceptual forms, of didactic approach or referring to the organization of knowledge. In order to verify relations between the logarithmic and logarithmic functions in Mathematics and School Mathematics, we present the idea of the logarithms of Napier as facilitators of calculations, we interpret their geometric definition by means of a system of ordinary differential equations and we show a brief history about the insertion of the logarithm as a function in the Integral Calculus. The mathematical textbooks analyzed were published between the years 1879 and 2013. In this analysis, we consider how authors approach or treat mathematics, the types of activities that are proposed, the types of explanations, definitions, examples, graphs, exercises, applications and problems associated with logarithms and logarithmic function. The results show that in the 19th century, logarithms were treated in textbooks, almost always, through Arithmetic. From the 1890s, they are approached, both in the arithmetic field, by association with the theory of progressions, and in the algebraic field, being exponents in an equation or function. From the 1930s to the present day we have found a predominance of the algebraic-functional conception of logarithms. Based on the Curriculum Guidelines for Secondary Education (2006), the National Curriculum Parameters - Secondary Education (PCN\'s - 2000), the National Curriculum Parameters + High School (PCN\'s + High School - 2002), the National High School Examination and textbooks recent, we have verified that the logarithms and the logarithmic function are currently inserted in Brazilian School Mathematics, by their association to the applications, such as compound interest, population dynamics, radioactive disintegration, hydrogen ionic potential, Richter Scale, Momentum Magnitude Scale (MMS) and level of sound intensity.

Orientador: Antonio Miguel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-27T00:11:35Z (GMT). No. of bitstreams: 1 FerreiradeSantana_DianaPatricia_D.pdf: 61557598 bytes, checksum: d70e3e9305614149df56a017a6270c4c (MD5) Previous issue date: 2015 / Resumo: O objetivo deste trabalho é fazer uma leitura das idéias de Ludwig Wittgenstein sobre a linguagem, tendo o silêncio como fio condutor das nossas considerações. Temos uma dupla finalidade: a primeira é identificar as formas de silêncio na vida e obra do filósofo austríaco como uma tentativa de compreender o autor e seu estilo idiossincrático, marcado por uma escrita assistemática e aforística; a segunda é identificar as formas de silêncio expressos na aprendizagem da matemática escolar a partir da afirmação feita por Michael Peters de que há um potencial pedagógico na forma como o filósofo empreende sua crítica. Procuramos, através de uma perspectiva não convencional "mostrada" por Wittgenstein, identificar o não-dito, mostrá-lo e desvelar o feitiço por meio da linguagem que ainda prevalece na aprendizagem da matemática escolar / Abstract: The aim of this work is to make a reading of Ludwig Wittgenstein¿s ideas onlanguage taking the silence as thread of our considerations. We have a dual purpose: the first is to identify the forms of silence in the life and work of Austrian philosopher as an attempt to understand the author and his idiosyncratic style marked by an unsystematic and aphoristic writing; the second is to identify the forms of silence expressed in the learning of school mathematics from the assertion made by Michael Peters that there are pedagogical potential in how the philosopher makes his criticism. We seek, through unconventional perspective "shown" by Wittgenstein, identify the unspoken, show it and unveil the bewitchment by language that still prevails in the learning of school mathematics / Doutorado / Ensino e Práticas Culturais / Doutora em Educação

One of the main reasons that students struggle as they transition from arithmetic to algebra in the middle grades is that they fail to develop the appropriate understanding of the equal sign. Previous research has suggested that students need to move past an operational understanding and develop a relational understanding of the equal sign in order to work with algebraic equations successfully. Other research has suggested that the way that we interpret and utilize the equal sign is based on three main factors: multiple meanings of the equal sign, equation types, and structural conventions. This study extends both areas of research by analyzing two middle grade curricula and looking for what meanings, equation types, and structural conventions appear in both teacher and student materials. The study confirms that students are exposed to three main meanings of the equal sign in the middle grades. The study also describes which meanings of the equal sign are associated with particular equation types and the frequency with which these equation types appear throughout the 7th and 8th grade curricula. Study findings can be used to inform instruction, as they delineate the factors that are attended to while making sense of the equal sign in the middle grades.

Research shows that students who take advanced mathematics courses perform better on measures of college readiness than students who take less rigorous courses. However, no clear effect has been shown on requiring all students to take more advanced courses. This study examined whether increases in the number and level of mathematics courses required for high school graduation have resulted in increased levels of college aspirations and preparedness. Specifically, twenty years of data from a rural school district in Texas were analyzed to determine whether the impact on college entrance exam-taking and performance differed by the mathematics requirements in effect for each class. Logistic and linear regression modeling revealed no statistically significant effect of higher requirements. And while overall results by gender and race mirrored previous research, with males tending to have higher scores than females and White students tending to score higher than African-American and Latinx students, the increased requirements were not associated with any mitigation in these inequities.