The purpose of this study was to investigate the views of elementary school teachers about their implementation of assessment techniques recommended in the new mathematics curriculum. The study was conducted with 306 elementary school teachers from 29 public schools in Kirikkale, Malatya and Ankara in the 2006-2007 academic year. &lsquo / Opinions about Assessment Questionnaire&rsquo / was used as the instrument for assessing the opinions of the teachers about assessment techniques offered in new mathematics curriculum. The results showed that, teachers did not have negative views towards the implementation of the new assessment techniques in mathematics lessons. However, they needed support from curriculum experts about more suitable implementation of the assessment process. To assess the effects of teaching experience, class size and grade level they teach on the views of the teachers about their implementation of assessment techniques recommended in new mathematics curriculum, the Univariate Analysis of Variance was used. The results revealed that the opinions of the teachers about their implementation of assessment techniques offered in new mathematics curriculum did not show any significant difference according to the experience of the teachers, class size and grade level teachers teach.

This qualitative study examines the connections between teachers’ views of large-scale assessment and their classroom practice, based on a case study of Ontario teachers and the Ontario Education Quality and Accountability Office [EQAO] Grade 9 Applied Assessment of Mathematics. Large-scale assessments are a prominent aspect of the Ontario education system; given that they are also mandatory, it is imperative that their impact on teaching be documented. This study enriches the existing literature on the topic of the Grade 9 EQAO Assessment of Mathematics, and provides a more-recent portrayal of the teachers’ views of this assessment and the potential impact of these views on classroom teaching by highlighting teacher attitudes, concerns, and classroom practices.

The purpose of this study was to evaluate the effectiveness of cooperative learning in a liberal arts mathematics course and to examine any gender-related differences in the effects of cooperative learning in terms of achievement, composition of the cooperative groups, mathematics anxiety, attitudes toward mathematics, attendance, and retention. The quasi-experimental design compared a control section using individualized learning methods with three treatment sections using cooperative learning methods based on the Learning Together model of Johnson and Johnson (1991). The compositions of the three treatment groups varied: heterogeneous ability/heterogeneous gender, heterogeneous ability/homogeneous gender, and self-selected. The Academic Skills Assessment Program (ASAP) was used as a pre-test to show that the groups were equal. The Revised Math Attitude Scale and the Mathematics Anxiety Rating Scale (MARS) were used as pre- and post-tests to measure changes in attitudes and anxiety. Achievement was measured by individual and group course grades. Group grades were determined by taking 67% of a student's individual exam score plus 33% of the group's average on the exam. Cooperative learning and composition of groups had no significant effect on achievement. The differences between individual and group grades were insignificant, and the group grading method benefited the grades of only five students. Attendance had a large effect on achievement, and the ASAP score and the Math Attitude Post-test were significant predictors of achievement. / The MARS post-test was negatively correlated with individual course grade. While no significant gender-related differences surfaced, some trends appeared. The ASAP, MARS, and Math Attitude pre-test scores were equal, however, females achieved slightly higher course grades than males. In each of the four research groups the individual course grades were higher for females than for males. Also, females had a larger decrease in mathematics anxiety with a drop of 22 points compared to the males' drop of 10 points. Males and females each improved their attitudes toward mathematics by only one point, however, in three of the four research groups, females had smaller attitude changes than males, and two of the cooperative learning groups had decreases in their attitude scores.

Made available in DSpace on 2015-09-25T12:18:45Z (GMT). No. of bitstreams: 1 NELSON ROBERTO CARDOSO DE OLIVEIRA.pdf: 1875376 bytes, checksum: f02f554126b827ac3c9ebe95764f6ce3 (MD5) Previous issue date: 2012-07-02 / The objective of this research is to investigate concepts and evaluation practices of teachers of elementary school mathematics II of four schools in the city of Campina Grande, Paraíba, comprising public and private schools. Data collection in the form of questionnaires and interviews carried out in two moments, and the research environment of the schools surveyed. The survey data were analyzed taking into account the theoretical and methodological assumptions of content analysis of Bardin and Franco through the categories and subcategories. They are: The school education in the training of teachers of mathematics, Mathematics learning in practice teacher; Design assessment professor of mathematics; evaluative tools and their meanings; Assessment as a tool of teaching practice and the Relationship between conceptions of assessment and Learning mathematics. The school environment was conducive to our noticing the daily school life with its multiple and diverse realities. As a result, the survey revealed that the conceptions of assessment of school mathematics teachers vary both from a technical and conceptual realm independent of private or public, regardless of the teachers also belong to a single teaching unit or not. It was evident that the qualitative aspects of evaluation are not as effective for the final diagnosis of both the personal view of the teacher and the school for administrative matters. The data also showed that there can be a standard evaluation because the reality of each class varies in age, behavior, discipline and preparation of the previous series. Today, the issue of failure depend, to some part of the teacher, for system requirements. The survey also pointed to the lack of relevance of the assessment as a teaching resource for learning and methodological mathematics. Teachers' conceptions tend towards a more cognitive and sociocultural. These changes occurred in assessment practices should be obedience, rules, regulations and decisions of the administration and not by the spirit of engagement. / O objetivo desta pesquisa consiste em investigar as concepções e práticas avaliativas dos professores de Matemática do Ensino Fundamental II de quatro escolas da cidade de Campina Grande, Paraíba, contemplando escolas públicas e particulares. A coleta de dados na forma de questionários e entrevista se deu em dois momentos, sendo o ambiente da pesquisa as próprias escolas dos entrevistados. Os dados da pesquisa foram analisados levando em consideração os pressupostos teórico-metodológicos da Análise de Conteúdo de Bardin e Franco por meio das categorias e subcategorias. Sendo elas: A Educação Escolar na Formação dos Professores de Matemática; A aprendizagem matemática segundo a prática do professor; Concepção de avaliação do professor de matemática; Instrumentos avaliativos e seus significados; A avaliação como ferramenta da prática pedagógica e a Relação entre concepções de avaliação e Aprendizagem matemática. O ambiente escolar foi propício para que percebêssemos o cotidiano escolar com suas múltiplas e diversificadas realidades. Como resultados, a pesquisa revelou que as concepções de avaliação escolar dos professores de Matemática variam tanto do ponto de vista técnico quanto conceitual independente da esfera particular ou pública, independente também dos professores pertencerem a uma mesma unidade de ensino ou não. Ficou evidente que os aspectos qualitativos da avaliação não são considerados eficientes para o diagnóstico final tanto do ponto de vista pessoal do professor quanto para questões administrativas da escola. Os dados também evidenciaram que não é possível haver um modelo padrão de avaliação porque a realidade de cada turma varia de faixa etária, comportamento disciplinar e preparação das séries anteriores. Hoje, a questão da reprovação independe, em certa parte, do professor, por exigências do sistema. A pesquisa também apontou a falta de relevância da avaliação como recurso didático-metodológico para a aprendizagem matemática. As concepções dos professores tendem para uma abordagem mais cognitivista e sociocultural. Tais mudanças que ocorreram nas práticas avaliativas se devem a obediência, regimentos, normas e determinações da administração e não pelo espírito do engajamento.

Made available in DSpace on 2016-04-27T16:57:35Z (GMT). No. of bitstreams: 1 Andre Ricardo Cola.pdf: 838534 bytes, checksum: 8b14e9e3b0edb6aae2caf2406846bf8f (MD5) Previous issue date: 2015-03-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The main idea of this research was to investigate teachers comprehension who teach mathematics in basic education about external and large-scale assessments. The theoretical assumptions that supported the reflections and analyses were based on the learning evaluation, assessment in mathematics education and external and large-scale assessments. The main papers used as a reference in each of the areas are respectively: Almeida and Franco (2011), Arredondo and Diago (2009), Fernandes (2009), Buriasco and Soares (2012), Cury (2009), Sameshima (2008) , Moraes and Moura (2009), Amaro (2013), Bonamino and Sousa (2012), Dantas (2009), Horta Neto (2010a, b), Rosistolato and Viana (2014). The methodology adopted for the development of the research was the qualitative approach, with data collection procedure performed through semi-structured interviews. The results showed that the interviewers understanding about the evaluation processes that permeate the school environment is very superficial and misunderstandings identified in various concepts that circumscribe the external and large-scale assessments can result in damage to the pedagogical action. In mathematics education, the survey revealed that the external and large-scale assessments incorporate elements of a traditional evaluation practice, which does not favor the error perspective as an opportunity to improve knowledge that was not well acquired / A ideia central dessa pesquisa foi investigar o entendimento de professores, que ensinam matemática na educação básica, acerca das avaliações externas e em larga escala. Os pressupostos teóricos que embasaram as reflexões e análises pautaram-se na avaliação da aprendizagem, avaliação em educação matemática e avaliações externas e em larga escala. Os principais trabalhos utilizados como referência em cada uma das áreas são, respectivamente: Almeida e Franco (2011), Arredondo e Diago (2009), Fernandes (2009), Buriasco e Soares (2012), Cury (2009), Sameshima (2008), Moraes e Moura (2009), Amaro (2013), Bonamino e Sousa (2012), Dantas (2009), Horta Neto (2010a,b), Rosistolato e Viana (2014). A metodologia adotada para o desenvolvimento da investigação foi a pesquisa de abordagem qualitativa, com procedimento de coleta dos dados realizado por meio de entrevistas semiestruturadas. Os resultados obtidos mostraram que o entendimento, por parte dos entrevistados, acerca dos processos avaliativos que permeiam o ambiente escolar é bastante superficial e os equívocos identificados em diversos conceitos que circunscrevem as avaliações externas e de larga escala pode acarretar em prejuízos à ação pedagógica. No âmbito da educação matemática, a pesquisa revelou que as avaliações externas e em larga escala acabam incorporando elementos de uma prática avaliativa tradicional, que não privilegia a perspectiva do erro como oportunidade para superação de saberes não dominados

Orientador: Lourdes de la Rosa Onuchic / Banca: Rosana Giaretta Sguerra Miskulin / Banca: Raquel Normandia Moreira Brumatti / Resumo: Esta pesquisa tem como objetivo trabalhar a Análise Combinatória, fazendo uso da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas. Abordamos, em nossa fundamentação teórica, a Análise Combinatória contida na Matemática Discreta, iniciando a pesquisa com uma introdução histórica da Análise Combinatória, seguida por uma análise de livros didáticos e pela busca de trabalhos de outros autores que se referiam ao ensino e à aprendizagem desse conteúdo. Criamos três projetos para trabalhar com a metodologia de ensino adotada por nós, em três cenários diferentes, onde a pesquisadora assumiu três posturas diferentes frente ao problema da pesquisa: como uma professora-pesquisadora, com seus próprios alunos, em sua sala de aula; como uma pesquisadora, ministrando uma oficina de trabalho, em um encontro de Educação Matemática, tendo como participantes, professores, educadores matemáticos e até alunos da Licenciatura em Matemática; e, como uma pesquisadora, em Encontros em Educação Matemática, divulgando sua pesquisa. Através da análise dos dados, obtidos nas aplicações dos três projetos, pudemos mostrar como os participantes desses projetos se envolveram ao fazer uso da metodologia de ensino adotada e relatamos as contribuições que trouxeram para nossa pesquisa. Verificamos que houve envolvimento ativo dos participantes na construção de novos conceitos e conteúdos, através da resolução dos problemas propostos, por meio de um trabalho investigativo, que proporcionou uma aprendizagem com compreensão e significado, com resultados importantes para a prática docente. Esta pesquisa foi desenvolvida seguindo a Metodologia de Pesquisa apresentada por Thomas A. Romberg. / Abstract: This paper has the objective to study the Combinatory Analysis using Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving. In our theoretical fundamentation we address the Combinatory Analysis contained in the Discrete Mathematics, starting the research with a historical introduction of the Combinatory Analysis followed by a review of textbooks and the search for other author's articles concerning this content's teaching and learning. We have developed three projects to apply the teaching methodology we adopted in three different settings, where the researcher played three distinct roles facing the research's problem: a) as a teacher-researcher, with her own students in her own classroom; b) as a researcher, conducting a workshop in a Mathematical Education conference, with teachers, mathematics educators and graduate students; c) as a researcher, in Mathematics Education Conferences divulgating her research. By analyzing all the data obtained in the application of the three projects we could show how the participants were engaged in using the adopted teaching methodology and we also reported the contributions they have brought to our research. We could verify that there was significant involvement from all the participants in the construction of new concepts and contents by solving the proposed problems in an investigative way, providing a different learning, full of understanding and meaning, with very significant results in terms of teaching practice. This research was developed following the Research Methodology presented by Thomas A. Romberg. / Mestre

Adapting useful knowledge to the individual and unique mathematical needs of each student in the midst of an entire classroom, and evaluating the outcome of this endeavor are the scope of the web philosophy - the didactic-mathematic strategy explored in this work. This dissertation aims to construct a didactic learning culture of mathematics, of a constructivist nature, that articulates in a personalized way learning and evaluation, which can be experienced in classroom and online educational practice, with and without digital technologies, much Although it is only with these tools that the elements of this evaluative style are fully utilized. Based on the assumptions that the model of the web is a new conception of didactic strategy in which the learning and evaluation of the student generated by psychological theories are articulated, which both compose it and gain new meanings during such interlacing; And that the pedagogical proposal embedded in this style of evaluation gives the mathematical educator flexibility and updating in the teaching-learning-evaluation process; And also that the web can favor the interest in learning Mathematics, it offers in this research a brief history of the evaluation of human learning, the articulation of the psychological and statistical elements of this evaluative philosophy and, through action research, the working hypotheses were validated. In addition to four scientific articles published in qualified journals, this dissertation resulted in the assimilation of intelligences: (in the teaching dimension) in the establishment of which to evaluate with adaptability is synonymous with intelligence in the group view, and (in the student dimension) the intelligence of the understanding of That can have its cognitive peculiarities assisted in the process teaching-learning-evaluation in Mathematics. The resulting educational product is the Web Manual, where the Math teacher finds the step-by-step to build his own web and use it daily with his students. / Adaptar conhecimento útil às necessidades matemáticas individuais e peculiares de cada estudante em meio à coletividade de uma sala de aula inteira, e avaliar o resultado desse empreendimento são o escopo da filosofia da teia – a estratégia didático-matética explorada neste trabalho. Nesta dissertação objetivou-se construir uma cultura didática de aprendizagem da matemática, de natureza construtivista, que articula de modo personalizado aprendizagem e avaliação, a qual pode ser vivenciada na prática educativa em sala de aula e online, com e sem as tecnologias digitais, muito embora somente com estas ferramentas se usufrua plenamente o conjunto de elementos desse estilo avaliativo. Com base nas premissas de que o modelo da teia é uma nova concepção de estratégia didática na qual se articulam a aprendizagem e a avaliação do educando gerada a partir de teorias psicológicas, as quais tanto a compõem quanto ganham novos significados durante tal entrelaçamento; e que a proposta pedagógica embutida nesse estilo de avaliação oportuniza ao educador matemático flexibilidade e atualização no processo ensino-aprendizagem-avaliação; e também que a teia pode favorecer o interesse por aprender Matemática, se oferece nesta pesquisa um breve histórico da avaliação da aprendizagem humana, a articulação dos elementos psicológicos e estatístico dessa filosofia avaliativa e, através da pesquisa-ação se validou as hipóteses de trabalho. Além de quatro artigos científicos publicados em revistas qualificadas, esta dissertação resultou na assimilação de inteligências: (na dimensão docente) no estabelecimento de que avaliar com adaptabilidade seja sinônimo de inteligência na visão de grupo, e (na dimensão discente) a inteligência do entendimento de que se pode ter suas peculiaridades cognitivas assistidas no processo ensino-aprendizagem-avaliação em Matemática. O produto educacional resultante é o Manual da Teia, onde o professor de Matemática encontra o passo a passo para construir sua própria teia e usá-la cotidianamente com seus estudantes.

Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-24Bitstream added on 2014-06-13T20:52:44Z : No. of bitstreams: 1 souza_acp_me_rcla.pdf: 6507132 bytes, checksum: a4ba6e1c2a6b5b1061118d1485c4e613 (MD5) / See-Sp / Esta pesquisa tem como objetivo trabalhar a Análise Combinatória, fazendo uso da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas. Abordamos, em nossa fundamentação teórica, a Análise Combinatória contida na Matemática Discreta, iniciando a pesquisa com uma introdução histórica da Análise Combinatória, seguida por uma análise de livros didáticos e pela busca de trabalhos de outros autores que se referiam ao ensino e à aprendizagem desse conteúdo. Criamos três projetos para trabalhar com a metodologia de ensino adotada por nós, em três cenários diferentes, onde a pesquisadora assumiu três posturas diferentes frente ao problema da pesquisa: como uma professora-pesquisadora, com seus próprios alunos, em sua sala de aula; como uma pesquisadora, ministrando uma oficina de trabalho, em um encontro de Educação Matemática, tendo como participantes, professores, educadores matemáticos e até alunos da Licenciatura em Matemática; e, como uma pesquisadora, em Encontros em Educação Matemática, divulgando sua pesquisa. Através da análise dos dados, obtidos nas aplicações dos três projetos, pudemos mostrar como os participantes desses projetos se envolveram ao fazer uso da metodologia de ensino adotada e relatamos as contribuições que trouxeram para nossa pesquisa. Verificamos que houve envolvimento ativo dos participantes na construção de novos conceitos e conteúdos, através da resolução dos problemas propostos, por meio de um trabalho investigativo, que proporcionou uma aprendizagem com compreensão e significado, com resultados importantes para a prática docente. Esta pesquisa foi desenvolvida seguindo a Metodologia de Pesquisa apresentada por Thomas A. Romberg. / This paper has the objective to study the Combinatory Analysis using Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving. In our theoretical fundamentation we address the Combinatory Analysis contained in the Discrete Mathematics, starting the research with a historical introduction of the Combinatory Analysis followed by a review of textbooks and the search for other author’s articles concerning this content’s teaching and learning. We have developed three projects to apply the teaching methodology we adopted in three different settings, where the researcher played three distinct roles facing the research’s problem: a) as a teacher-researcher, with her own students in her own classroom; b) as a researcher, conducting a workshop in a Mathematical Education conference, with teachers, mathematics educators and graduate students; c) as a researcher, in Mathematics Education Conferences divulgating her research. By analyzing all the data obtained in the application of the three projects we could show how the participants were engaged in using the adopted teaching methodology and we also reported the contributions they have brought to our research. We could verify that there was significant involvement from all the participants in the construction of new concepts and contents by solving the proposed problems in an investigative way, providing a different learning, full of understanding and meaning, with very significant results in terms of teaching practice. This research was developed following the Research Methodology presented by Thomas A. Romberg.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-17T14:20:07Z No. of bitstreams: 1 dionebaptistaribeiro.pdf: 9609173 bytes, checksum: e8c30c7bee1de88851147085c5b8dfdf (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-28T14:35:19Z (GMT) No. of bitstreams: 1 dionebaptistaribeiro.pdf: 9609173 bytes, checksum: e8c30c7bee1de88851147085c5b8dfdf (MD5) / Made available in DSpace on 2016-06-28T14:35:19Z (GMT). No. of bitstreams: 1 dionebaptistaribeiro.pdf: 9609173 bytes, checksum: e8c30c7bee1de88851147085c5b8dfdf (MD5) Previous issue date: 2012-10-05 / A presente pesquisa tem como objetivo investigar as características de uma avaliação em Matemática para que ela esteja a serviço da aprendizagem dos estudantes. Para tal empreendimento tomamos como ponto de partida os documentos oficiais e os estudos desenvolvidos sobre o tema. O projeto foi elaborado considerando a avaliação no Ensino Fundamental no qual os sujeitos de pesquisa foram os estudantes do 7º ano de uma escola pública e caracterizou-se pelo desenvolvimento de uma abordagem qualitativa de investigação. O Produto Educacional decorrente da dissertação será um texto dirigido a professores do Ensino Fundamental com nossas considerações sobre avaliação. / This research aims to investigate the characteristics of an assessment in mathematics so that is in the service of student learning. For this development, we took as starting point the official documents and studies that have been done on the topic. The project was designed considering the assessment in elementary school, so the research subjects were students in 7th grade at a public school and it was characterized by the development of a qualitative research approach. The Educational Product arising from a text dissertation is aimed at elementary school teachers with our assessment considerations.

Made available in DSpace on 2016-04-04T18:33:12Z (GMT). No. of bitstreams: 1 Lauro Araujo Mota.pdf: 3184997 bytes, checksum: db8e3fa3195313d7638a86c3efe44e2b (MD5) Previous issue date: 2013-12-09 / The Program Read and Write currently installed in the whole education system of the State and the city of Sao Paulo was organized and structured with the objective of reversing the low indicators of school learning related to reading and writing, and the high rates of dropout and repetition present in the paulista system teaching up to the mid years of 2000s.As the focus of the Program Read and Write are the skills of reading and writing, we proposed to investigate the teaching and evaluation in the area of mathematics in a 5th grade group.The guiding question of the research was: What is the relationship between the practices employed to assess the issues of mathematics by a teacher of 5th grade who uses the Program Read and Write and the surveys proposed by the referred Program?The methodology used in this r search is of a qualitative nature through a field study of an exploratory and descriptive analysis of official documents of the program.We used as a technique of data collection the semi-structured interviews conducted with the teacher of 5th grade and with the pedagogical coordinator, as well as the observations of lessons of mathematics and of evaluations that have occurred during the second half of 2012.The analysis of the documents focused on the Learner Guide, Planning Guide and Didactic Orientations of the professor, Curriculum Guidelines for the teaching of mathematics of the education system of Sao Paulo, guidelines of evaluative surveys (dictation of numbers, field additive and multiplicative) and self evaluations.The results indicate little familiarity of the teacher with respect to the theoretical basis needed for the interpretation of opinion polls mathematics and for the understanding of how this tool can foster the redirection of the students' learning.Theself evaluations showed an awareness that the students present on their evaluation process and its relationship with the teaching of mathematics, identifying progress and difficulties.The observations of lessons point to the use of some assessment instruments in addition to the opinion polls: written test, homework, correction of activities, oral exercises. / O Programa Ler e Escrever, implantado atualmente em toda rede de ensino do Estado de S?o Paulo, foi organizado e estruturado com o objetivo de reverter os baixos indicadores de aprendizagem escolar relacionados com a leitura e a escrita e os altos ?ndices de evas?o e repet?ncia presentes na rede de ensino paulista at? meados da d?cada de 2000. Como o foco do Programa Ler e Escrever s?o as habilidades de leitura e escrita, nos propusemos a investigar o ensino e a avalia??o na ?rea de matem?tica em uma turma do 5? ano do Ensino Fundamental. A quest?o norteadora da investiga??o assim se configurou: qual a rela??o entre as pr?ticas empregadas para avaliar as quest?es matem?ticas por uma professora de 5? ano que utiliza o Programa Ler e Escrever e as sondagens propostas pelo referido Programa? A metodologia utilizada nessa investiga??o ? de natureza qualitativa, realizada a partir de um estudo de campo de car?ter explorat?rio descritivo e da an?lise dos documentos oficiais do programa. Utilizamos como t?cnicas de coleta de dados as entrevistas semiestruturadas realizadas com a professora do 5? ano e com a coordenadora pedag?gica, bem como as observa??es de aulas de matem?tica e das avalia??es ocorridas durante o segundo semestre de 2012. A an?lise dos documentos incidiu sobre o Guia do Aluno, Guia de Planejamento e Orienta??es Did?ticas do professor, Orienta??es Curriculares para o ensino de matem?tica da rede de ensino do Estado de S?o Paulo, pautas das sondagens avaliativas (ditado de n?meros, campo aditivo e campo multiplicativo) e as autoavalia??es dos alunos. Nas observa??es das aulas, verificamos o uso de alguns instrumentos avaliativos al?m das sondagens: prova escrita, tarefa de casa, corre??o das atividades, exerc?cios orais. Os resultados indicam a pouca familiaridade da professora com rela??o ? fundamenta??o te?rica necess?ria para a interpreta??o das sondagens matem?ticas e para o entendimento de como esse instrumento pode favorecer o redirecionamento da aprendizagem dos alunos. As autoavalia??es dos alunos evidenciaram a consci?ncia que os mesmos apresentavam sobre o seu processo avaliativo e sua rela??o com o ensino de matem?tica, seus avan?os e dificuldades.