The Common Core State Standards for mathematics and English language arts were released in June of 2010 and have been adopted by a majority of U.S. states. The authors of these standards have claimed that they are internationally benchmarked -- that is, that they are as rigorous, focused, and coherent as the standards and expectations used in high-performing countries -- but have not provided evidence to back up these claims. Singapore, whose students have scored at the top of recent international assessments, is frequently touted as a leader in mathematics education. To test the claims of international benchmarking for the Common Core, this paper uses the methodology of the Surveys of Enacted Curriculum to compare the Common Core State Standards for Mathematics to the Singapore Mathematics Framework in terms of rigor, focus, and coherence. The Common Core State Standards and the Singapore Mathematics Framework do call for similar levels of conceptual understanding, mathematical reasoning, and problem-solving. However, the content expectations outlined by the Common Core are somewhat more rigorous than those outlined by the Singapore Mathematics Framework. / text

The importance of mathematics instruction including "real life" contexts relevant to students’ lives and experiences is widely acknowledged (Common Core State Standards Initiative, 2010; National Council of Teachers of Mathematics, 2000; 2006; 2009), however questions about why contextualized mathematics is beneficial and how different types of contextualization impact problem solving have yet to be fully addressed by research. Common justifications for contextualized mathematics include the idea that relevant contexts may help students to apply what they learn in school to out-of-school situations, and that relevant contexts may scaffold learning by providing a bridge between what students understand and the content they are trying to learn. The present study investigates these justifications, as well as students' beliefs and problem-solving methods, using story problems on linear functions. A situated cognition theoretical framework (Greeno, 2006) is used to interpret student behavior in the complex, social system of "school mathematics." In a series of interviews, students from a low-performing urban school were presented with algebra problems. Some problems were personalized to the ways in which they described using mathematics in their everyday lives, while others were normal story problems, story problems with equations, or abstract symbolic equations. Results showed that students rarely explicitly used situational knowledge when solving story problems, had consistent issues with verbal interpretation of stories, and engaged in non-coordinative reasoning where they bypassed the intermediate step of understanding the given situation before trying to solve the problem. After completing most of Algebra I, students still had considerable difficulty with symbolic representations, and struggled to coordinate formal and informal mathematical reasoning. Problems with the same mathematical structure with different amounts of verbal and symbolic support elicited different strategies from students, with personalized problems having high response rates and high use of informal strategies. This suggests that students can use sophisticated, situation-based reasoning on contextualized problems, and that different problem framings may scaffold learning. However, results also demonstrated that the culture of schooling, and story problems as an artifact of this culture, undermines many of the justifications for contextualizing mathematics, and that students need more authentic ways to develop their mathematical reasoning. / text

Student performance in the area of mathematics is a topic of national concern in the United States, with several reports documenting the need for effective instruction to boost student achievement. However, what type of math instruction will most effectively raise student achievement for students with disabilities (SWD) remains a matter of debate. Problem-based learning (PBL) is a promising methodology for engaging and motivating students’ learning while increasing their math skills. Enhanced Anchored Instruction (EAI) is a form of problem-based learning, rooted in a constructivist framework, which guides students through complex problems through video anchors and context rich environments that has been shown to significantly improve math performance of SWD. Assessing student performance during PBL units is often difficult. Formative assessments supplement curriculum by allowing teachers to gather information and assess student learning during the course of instruction. However, despite the rise in formative assessment use, the effects of formative assessment in PBL curricula are rarely addressed. This study examined the effect of embedding formative assessments in the EAI curriculum on academic outcomes in middle school math classrooms. Results showed that problem solving performance did not improve with the addition of formative assessment and gains on computation performance were mixed.

Esta dissertação discute a inserção do vídeo nas aulas de matemática. O planejamento e a realização de um conjunto de cinco oficinas sobre vídeos e matemática, com participação de alunos do oitavo ano do Ensino Fundamental de um colégio de Porto Alegre, RS, e a análise desse planejamento e do que ocorreu nessas oficinas constituíram o material empírico da pesquisa. Durante o planejamento, o professor definiu que os alunos iriam assistir vídeos de matemática pré-selecionados, que posteriormente seriam testados em algum formato de questionário. No entanto, antes que as oficinas ocorressem, o professor mudou seu planejamento e, a partir dessa modificação, os alunos passaram a ser os responsáveis por escolher os vídeos e agrupá-los em um conjunto, por assunto, com temas pré-estabelecidos pelo docente. Presumindo que esta mudança tenha sido um dos fatores para que o experimento ultrapassasse os limites cronológicos das oficinas, o professor sentiu-se instigado a buscar por ressonâncias da noção deleuziana de ideia no âmbito da Educação Matemática. Esta busca gerou uma questão potencial a respeito dessa modificação de rumo: seria a mudança feita no planejamento uma ideia em Educação Matemática? / This thesis discusses the insertion of video in elementary school math classes. The empiric material of the study comprises the plans and execution of a set of five workshops concerning video and mathematics, with the participation of eighth grade students of an Elementary School located in Porto Alegre, RS, as well as the analysis of the plans and what took place in these workshops. The teacher‘s initial plan was for students to watch pre-selected videos, which would later be tested in some form of questionnaire. However, before the workshops began, the teacher changed his plan, giving the students the responsibility of choosing the videos and grouping them in a set determined by topic, with an overarching theme pre-established by the teacher. Presuming that such a change was one of the factors for the experiment to surpass the chronological limits of the workshops, the teacher felt urged to search for resonances of Deleuze‘s notion of idea in Math Education. This search generated a potential question regarding that change of plans: could the change made in planning be considered as an idea in Math Education?

A presente Dissertação de Mestrado pretende discutir e analisar dois imperativos enunciados nas Engenharias Didáticas de alunos- professores – que frequentaram o Curso de Especialização para professores de Matemática (UAB/IMAT-UFRGS), na modalidade a Distância – e que produziram efeitos nos seus modos de dizer e ver Educação (e) Matemática. O material empírico que tomei para análise faz parte do jogo avaliativo instituído por esse Curso de Especialização. Neste jogo destaca-se a produção de “práticas inovadoras” no ensino de matemática pelos alunos-professores que realizaram o desenvolvimento de suas atividades no Polo de Rosário do Sul/RS. Este estudo apresenta um exercício teórico, dos principais conceitos presentes nas obras do pensador Michel Foucault e de autores afins – Deleuze, Larrosa, Bujes, Bello, entre outros – que nos permitem refletir como o sujeito professor se constitui. Conclui-se, a partir dos enunciáveis recorrentes que foram capturados nas produções escritas dos sujeitos-docentes, o funcionamento de dispositivos disciplinadores que operam a proliferação discursiva de dois imperativos, quais sejam: (i) a incorporação de saberes matemáticos não institucionalizados às práticas escolares; (ii) a indicação da utilização de ferramentas tecnológicas como potencializadoras do processo de ensino e aprendizagem de matemática. / This master’s degree thesis wants to discuss and analyze these recurring statements in Engineering Teaching, which constitute the discursive practices of students-teachers - who attended the Specialization Course for Teachers of Mathematics (UAB / IMAT-UFRGS), in distance module - and that produce of effects in their ways of saying and see the education and the mathematics. The empirical analysis that was made the evaluative part of the game established by the Post Graduate Course. In this game there is the production of "innovative practices" in teaching of mathematics student, teachers who completed the development of this activities at the Polo of Rosario do Sul / RS. This examination has proposed a theoretical exercise, the main of conceptions in the works of the philosopher Michel Foucault and authors alike – Deleuze, Larrosa, Eizirik, Bujes, Bello, and others – that allow us to reflect how the individual teacher’s made. It follows from the recurrent enunciable who were captured in the written production of subject-teachers, disciplining the functioning of devices that operate the proliferation of two imperative discursives, namely: (i) the incorporation of mathematical knowledge to non-institutionalized school practices (ii) an indication of the use of technological tools such as potentiating the process of teaching and learning of mathematics.

Submitted by FERNANDA PIZZIGATTI MARQUES JASINEVICIUS null (ferpizzi@uol.com.br) on 2016-01-25T17:35:06Z No. of bitstreams: 1 DEFESA DE DISSERTACAO Fernanda Pizzigatti final.pdf: 7736036 bytes, checksum: 2fc26bfeb49858ae296a605eac26e2dc (MD5) / Approved for entry into archive by Sandra Manzano de Almeida (smanzano@marilia.unesp.br) on 2016-01-25T18:16:47Z (GMT) No. of bitstreams: 1 jasinevicius_fpm_me_bauru.pdf: 7736036 bytes, checksum: 2fc26bfeb49858ae296a605eac26e2dc (MD5) / Made available in DSpace on 2016-01-25T18:16:47Z (GMT). No. of bitstreams: 1 jasinevicius_fpm_me_bauru.pdf: 7736036 bytes, checksum: 2fc26bfeb49858ae296a605eac26e2dc (MD5) Previous issue date: 2015-12-18 / Outra / Esta pesquisa tem como objetivo geral analisar e avaliar a competência leitora e suas relações com o processo de ensino e aprendizagem da Matemática de uma turma de 38 estudantes do 9º ano dos anos finais do ensino fundamental de uma escola do interior de São Paulo. Foi realizado o estudo de pressupostos teóricos pertinentes ao tema, abordados por pesquisadores como Polya (1994), Mayer (1992), Sternberg (1992), Solé (1998), Bakhtin (1993), Schneuwly e Dolz (2004) e o levantamento bibliográfico de trabalhos publicados em eventos que abordam a questão da leitura e da escrita no ensino da Matemática. A pesquisa teve como ponto de partida a análise dos resultados obtidos pelos estudantes nas Avaliações de Aprendizagem em Processo (A.A.P) nas disciplinas de Matemática e Língua Portuguesa do 6º ao 9º ano e a análise de dois questionários semiestruturados que foram elaborados com o intuito de investigar as dificuldades dos estudantes quanto à Matemática e à Leitura. Após o tratamento qualitativo dos dados, realizaram-se intervenções por meio da metodologia de pesquisa-ação junto aos estudantes, trabalhando situações e sequências didáticas relacionadas ao conteúdo proposto no Currículo Oficial do Estado de São Paulo. Como conclusão, a análise qualitativa das avaliações durante toda a trajetória escolar dos estudantes constatou a falta de proficiência na leitura e escrita em suas diversas formas, e a dificuldade no tratamento das informações nos problemas matemáticos. Entretanto, após serem realizadas as intervenções consideradas necessárias, os estudantes, em sua totalidade, tiveram um avanço, uma melhora, em suas dificuldades mediante os resultados apresentados na Avaliação de Aprendizagem em Processo aplicada no 2º Semestre do ano letivo quando comparados à 1ª A.A.P. As intervenções durante as aulas mostraram ser perfeitamente praticável e pertinente a união entre o ensino da Matemática e o aprimoramento da linguagem. O gerenciamento das aulas, o objetivo que se pretende alcançar, as perguntas determinantes realizadas aos estudantes pela professora, a cautela com a interpretação textual dos enunciados e com o levantamento das informações implícitas e explícitas contidas nos problemas matemáticos acabaram resultando em maior motivação por parte dos estudantes em realizar as atividades, contribuindo imensamente para seu desenvolvimento e das aulas. Além disso, baseando-se nos resultados e nas experiências vivenciadas, e em conformidade com o que determina a Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), foi elaborado o produto educacional, denominado Proposta de Sequências didáticas aos professores de Educação Básica, apontando os referenciais teóricos que as embasam e sugestões metodológicas em prol do desenvolvimento da competência leitora dos estudantes. / This research has as a general goal to analyze and evaluate the reading competence and its relations to the process of teaching and learning of mathematics of 38 students from 9th year of the last years of fundamental grade of an inner school in São Paulo. A study has been performed of theoretical assumptions about the theme and studied by the researchers Polya (1994), Mayer (1992), Stenberg (1992), Solé(1998), Bakhtin (1993), Schneuwly e Dolz (2004), the survey bibliographic of the published tasks in events that talk about the reading and the writing in math learning. The survey has its beggining, the analysis of the obtained results by the students in the evaluations of the learning process (A.A.P) in Math and Portuguese subjects from the sixth to the ninth year and the analysis of the two questionnaires that have been semi structured that have been elaborated in order to investigate the difficulties of the students about math and reading. After the qualitative treatment of the data, interventions have been performed using the action-research methodology along with the students and the teaching sequences related to the pre established content in the official curriculum of São Paulo state. As the parcial conclusion the qualitative analysis of the evaluations during all the schooling time of the students have shown the lack of proficiency in the reading and writing an in their different ways and the difficulty in treating the information about the mathematical problems. Although, after being made the interventions considered needed the students in the whole had an upgrade, a considerable change in their difficulties by the presented results in the evaluation of learning in process apllied in the second semester when compared to the first A.A.P. The interruptions during the classes showed to be perfectly practicable and relevant the union between the math teaching and the improvement of the language. The management of the classes, the aim in which we intend to reach, the relevant questions asked to the students by the teacher, the caution about the textual interpretation of the statements and the survey of the implicit and explicit information in the mathematical problems ended up resulting in a bigger motivation for the students to accomplish the activities, contributing hugely to their development and to their classes. Besides it is based on the results and on the experience they have lived and to what in accordance to the personal improvement coordination of the higher level (CAPES), it was made the educational product, named The Proposal of the didatics sequence of the basic education teachers, pointing out the theorical referencials that base and methodology suggestions to the development of the reading competence of the students.

Esta dissertação discute a inserção do vídeo nas aulas de matemática. O planejamento e a realização de um conjunto de cinco oficinas sobre vídeos e matemática, com participação de alunos do oitavo ano do Ensino Fundamental de um colégio de Porto Alegre, RS, e a análise desse planejamento e do que ocorreu nessas oficinas constituíram o material empírico da pesquisa. Durante o planejamento, o professor definiu que os alunos iriam assistir vídeos de matemática pré-selecionados, que posteriormente seriam testados em algum formato de questionário. No entanto, antes que as oficinas ocorressem, o professor mudou seu planejamento e, a partir dessa modificação, os alunos passaram a ser os responsáveis por escolher os vídeos e agrupá-los em um conjunto, por assunto, com temas pré-estabelecidos pelo docente. Presumindo que esta mudança tenha sido um dos fatores para que o experimento ultrapassasse os limites cronológicos das oficinas, o professor sentiu-se instigado a buscar por ressonâncias da noção deleuziana de ideia no âmbito da Educação Matemática. Esta busca gerou uma questão potencial a respeito dessa modificação de rumo: seria a mudança feita no planejamento uma ideia em Educação Matemática? / This thesis discusses the insertion of video in elementary school math classes. The empiric material of the study comprises the plans and execution of a set of five workshops concerning video and mathematics, with the participation of eighth grade students of an Elementary School located in Porto Alegre, RS, as well as the analysis of the plans and what took place in these workshops. The teacher‘s initial plan was for students to watch pre-selected videos, which would later be tested in some form of questionnaire. However, before the workshops began, the teacher changed his plan, giving the students the responsibility of choosing the videos and grouping them in a set determined by topic, with an overarching theme pre-established by the teacher. Presuming that such a change was one of the factors for the experiment to surpass the chronological limits of the workshops, the teacher felt urged to search for resonances of Deleuze‘s notion of idea in Math Education. This search generated a potential question regarding that change of plans: could the change made in planning be considered as an idea in Math Education?

A presente Dissertação de Mestrado pretende discutir e analisar dois imperativos enunciados nas Engenharias Didáticas de alunos- professores – que frequentaram o Curso de Especialização para professores de Matemática (UAB/IMAT-UFRGS), na modalidade a Distância – e que produziram efeitos nos seus modos de dizer e ver Educação (e) Matemática. O material empírico que tomei para análise faz parte do jogo avaliativo instituído por esse Curso de Especialização. Neste jogo destaca-se a produção de “práticas inovadoras” no ensino de matemática pelos alunos-professores que realizaram o desenvolvimento de suas atividades no Polo de Rosário do Sul/RS. Este estudo apresenta um exercício teórico, dos principais conceitos presentes nas obras do pensador Michel Foucault e de autores afins – Deleuze, Larrosa, Bujes, Bello, entre outros – que nos permitem refletir como o sujeito professor se constitui. Conclui-se, a partir dos enunciáveis recorrentes que foram capturados nas produções escritas dos sujeitos-docentes, o funcionamento de dispositivos disciplinadores que operam a proliferação discursiva de dois imperativos, quais sejam: (i) a incorporação de saberes matemáticos não institucionalizados às práticas escolares; (ii) a indicação da utilização de ferramentas tecnológicas como potencializadoras do processo de ensino e aprendizagem de matemática. / This master’s degree thesis wants to discuss and analyze these recurring statements in Engineering Teaching, which constitute the discursive practices of students-teachers - who attended the Specialization Course for Teachers of Mathematics (UAB / IMAT-UFRGS), in distance module - and that produce of effects in their ways of saying and see the education and the mathematics. The empirical analysis that was made the evaluative part of the game established by the Post Graduate Course. In this game there is the production of "innovative practices" in teaching of mathematics student, teachers who completed the development of this activities at the Polo of Rosario do Sul / RS. This examination has proposed a theoretical exercise, the main of conceptions in the works of the philosopher Michel Foucault and authors alike – Deleuze, Larrosa, Eizirik, Bujes, Bello, and others – that allow us to reflect how the individual teacher’s made. It follows from the recurrent enunciable who were captured in the written production of subject-teachers, disciplining the functioning of devices that operate the proliferation of two imperative discursives, namely: (i) the incorporation of mathematical knowledge to non-institutionalized school practices (ii) an indication of the use of technological tools such as potentiating the process of teaching and learning of mathematics.

A presente Dissertação de Mestrado pretende discutir e analisar dois imperativos enunciados nas Engenharias Didáticas de alunos- professores – que frequentaram o Curso de Especialização para professores de Matemática (UAB/IMAT-UFRGS), na modalidade a Distância – e que produziram efeitos nos seus modos de dizer e ver Educação (e) Matemática. O material empírico que tomei para análise faz parte do jogo avaliativo instituído por esse Curso de Especialização. Neste jogo destaca-se a produção de “práticas inovadoras” no ensino de matemática pelos alunos-professores que realizaram o desenvolvimento de suas atividades no Polo de Rosário do Sul/RS. Este estudo apresenta um exercício teórico, dos principais conceitos presentes nas obras do pensador Michel Foucault e de autores afins – Deleuze, Larrosa, Bujes, Bello, entre outros – que nos permitem refletir como o sujeito professor se constitui. Conclui-se, a partir dos enunciáveis recorrentes que foram capturados nas produções escritas dos sujeitos-docentes, o funcionamento de dispositivos disciplinadores que operam a proliferação discursiva de dois imperativos, quais sejam: (i) a incorporação de saberes matemáticos não institucionalizados às práticas escolares; (ii) a indicação da utilização de ferramentas tecnológicas como potencializadoras do processo de ensino e aprendizagem de matemática. / This master’s degree thesis wants to discuss and analyze these recurring statements in Engineering Teaching, which constitute the discursive practices of students-teachers - who attended the Specialization Course for Teachers of Mathematics (UAB / IMAT-UFRGS), in distance module - and that produce of effects in their ways of saying and see the education and the mathematics. The empirical analysis that was made the evaluative part of the game established by the Post Graduate Course. In this game there is the production of "innovative practices" in teaching of mathematics student, teachers who completed the development of this activities at the Polo of Rosario do Sul / RS. This examination has proposed a theoretical exercise, the main of conceptions in the works of the philosopher Michel Foucault and authors alike – Deleuze, Larrosa, Eizirik, Bujes, Bello, and others – that allow us to reflect how the individual teacher’s made. It follows from the recurrent enunciable who were captured in the written production of subject-teachers, disciplining the functioning of devices that operate the proliferation of two imperative discursives, namely: (i) the incorporation of mathematical knowledge to non-institutionalized school practices (ii) an indication of the use of technological tools such as potentiating the process of teaching and learning of mathematics.

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization there is little research into what types of figures students are exposed to through their textbooks. This study examines 14 high school geometry textbooks in total, comprised of eight physical textbooks from the top three major textbook publishers in the United States and six FlexBooks created by a non-profit organization developing free and customizable textbooks online. In each textbook the printed images from four topics were classified: Parallel Lines and Transversals, Classifying Triangles, Parallelograms, and Trapezoids. The ‘typical’ images in each of the four topics were defined and the percentages of images that were typical for each textbook in both the lesson and exercise portions were calculated. Results indicate that lesson portions of sections generally contain more typical images than exercise portions and that the total percentage of typical images in an average section varies from 51.9% typical images in the Parallel Lines and Transversals section to 75.2% typical images in the Trapezoid section. Based on these results we list possible avenues for further research in this area.