O objetivo central do presente trabalho é analisar e discutir a presença e relação entre análise e síntese, no contexto do ensino de matemática e os possíveis desdobramentos em relação à aprendizagem dos alunos. Como o par análise e síntese pode estar presente nas aulas de Matemática e como esses elementos se relacionam com os processos de ensino e de aprendizagem dessa disciplina? Uma revisão bibliográfica centrada em elementos da didática da Matemática, da história da educação brasileira e do desenvolvimento do conhecimento matemático, e da noção de competências, e um estudo de documentos curriculares oficiais foram necessários para fundamentar e desenvolver a análise e discussão de duas situações-problema ilustrativas do ensino de Matemática da Educação Básica. Para cada uma das situações propostas, são apresentadas e analisadas quatro resoluções possíveis, a partir das quais são feitas a discussão e sistematização de noções matemáticas mobilizadas, e uma reflexão sobre as dimensões e implicações do par análise e síntese nessas resoluções. / The main objective of this study is to analyze and discuss the relationship and presence between analysis and synthesis in the context of mathematics education and the possible consequences in relation to students learning. How the pair analysis and synthesis may be present in math class? How these elements relate to processes of teaching and learning that discipline? A literature review focused on didactics of mathematics elements and the Brazilian education history and the study of official curriculum documents were necessary to support and develop the analysis and discussion of two illustrative situations on teaching mathematics in basic education. For each of the proposed conditions are presented and analyzed four possible resolutions to discussion and systematization of mathematical notions mobilized are made and reflect on the dimensions and implications of the pair analysis and synthesis in the resolutions.

O objetivo central do presente trabalho é analisar e discutir a presença e relação entre análise e síntese, no contexto do ensino de matemática e os possíveis desdobramentos em relação à aprendizagem dos alunos. Como o par análise e síntese pode estar presente nas aulas de Matemática e como esses elementos se relacionam com os processos de ensino e de aprendizagem dessa disciplina? Uma revisão bibliográfica centrada em elementos da didática da Matemática, da história da educação brasileira e do desenvolvimento do conhecimento matemático, e da noção de competências, e um estudo de documentos curriculares oficiais foram necessários para fundamentar e desenvolver a análise e discussão de duas situações-problema ilustrativas do ensino de Matemática da Educação Básica. Para cada uma das situações propostas, são apresentadas e analisadas quatro resoluções possíveis, a partir das quais são feitas a discussão e sistematização de noções matemáticas mobilizadas, e uma reflexão sobre as dimensões e implicações do par análise e síntese nessas resoluções. / The main objective of this study is to analyze and discuss the relationship and presence between analysis and synthesis in the context of mathematics education and the possible consequences in relation to students learning. How the pair analysis and synthesis may be present in math class? How these elements relate to processes of teaching and learning that discipline? A literature review focused on didactics of mathematics elements and the Brazilian education history and the study of official curriculum documents were necessary to support and develop the analysis and discussion of two illustrative situations on teaching mathematics in basic education. For each of the proposed conditions are presented and analyzed four possible resolutions to discussion and systematization of mathematical notions mobilized are made and reflect on the dimensions and implications of the pair analysis and synthesis in the resolutions.

Cette thèse à l’objectif général de faire une analyse du Manuel Scolaire de mathématique, utilisé dans l'enseignement au collège et au lycée en France et au Brésil, comme vecteur de formation continue pour l'enseignant de mathématique que enseigne la statistique dans ces niveaux de enseignement. Cette étude a été développée avec l’aide du « Programme Alβan, Programme de bourses de haut niveau de l'Union Européenne pour Amérique Latine, bourse n º [E06D101218BR] ». Ce travail est structuré en deux parties. La première partie est dirigée au traitement des bases théoriques qui donnent de support à cette thèse. D’abord aborde l'insertion de Manuel Scolaire comme un outil qui possède sa place et son utilisation à l'intérieur de l'enseignement apprentissage. Ensuite il aborde les processus d'apprentissage professionnelle à travers de la Théorie des Champs Conceptuels et la Didactique Professionnelle. Après il aborde la fonction et la formation des enseignants en ayant pour but d’élucider sur la formation continue de l'enseignant. Pour finir la première partie de cette recherche été fait approche sur l'enseignement de la statistique. La deuxième partie de ce travail est dédie à la procédure de la recherche. Initialement aborde la reconstruction de la problématique de recherche à travers toute la procédure théorique qui a été vue précédemment, et la méthodologie en abordant les sujets, les places, les instruments, les analyses utilisées, les outils et les catégorisations d’analyse. Pour conclure il aborde toute la procédure d'analyse de la recherche avec les données collectées au Brésil et en France en trois paramètres: d’effectifs et de fréquence; relations et dépendances entre des variables (similarité et implication) et analyse de questions subjectives. / This thesis has as objective generality to analyze the Didactic Book of mathematic used on the basic education and high school in France and in Brazil as vector of formation continued for the mathematics teacher who makes the teaching of the statistics in these respective levels of education. This study was developed with supported by the “Programme Alβan, the European Union Program of High Level Scholarships for Latin America, scholarship [E06D101218BR]”. This work is structuralized in two parts. The first part has as objective to the treatment of the theoretical bases which give support to our thesis. The initially approach the insertion of the didactic book as a tool whose has its place and use of teaching learning. Then it approaches the processes of training professional through Theory of the Conceptual Fields and the Didactic Professional. After that it approaches the function and formation of teacher in search to clarify on the continued formation of teacher. To finish the first part of this research made approach on teaching of the statistics. The second part of this work east dedicates to the procedure of research. Initially the rebuilding of the problematic of research approaches through all the theoretical procedure which was seen previously, and methodology by tackling the subjects, the places, the instruments, the analyses used the tools and categorizations for analysis. To conclude it approaches all the procedure of research with the data collected in Brazil and in France in three parameters analyzes: manpower and of frequency; relations and dependences between variables (similarity and implication) and analysis of subjective questions. / Esta tese possui como objetivo geral fazer uma análise do Livro Didático de matemática do ensino fundamental «6° ao 9° ano» e médio ao Brasil e na França como vetor de formação continuada para o professor de matemática que leciona estatística nesses respectivos níveis de ensino. Este estudo foi desenvolvido com apoio do “Programa Alβan, Programa de bolsas de alto nível da União Européia para America Latina, bolsa n° [E06D101218BR]”. Este trabalho está estruturado em duas partes. A primeira parte é direcionada a tratar das bases teóricas que dão suporte a nossa tese. Inicialmente aborda a inserção do livro didático como ferramenta que possui seu lugar e uso dentro do ensino aprendizagem. Em seguida busca elucidar os processos de aprendizagem profissional através da Teoria dos Campos Conceituais e com a Didática Profissional. Após, trata da função e formação de professores em busca de elucidar sobre formação continuada de professor. Para concluir a primeira parte da pesquisa, o último capítulo se estrutura com a busca de uma análise sobre o ensino da estatística.A segunda parte deste trabalho está direcionada ao processo da pesquisa como um todo. Inicialmente aborda a reconstrução da problemática da pesquisa através de todo processo teórico visto anteriormente, e a metodologia abordando os sujeitos, os lugares, o instrumento, as análises utilizadas, as ferramentas e as categorias de analise. Por concluir aborda todo o processo de análise da pesquisa com os dados coletados no Brasil e na França e em três parâmetros: efetivos e freqüência; relações e dependências entre variáveis (similaridade e implicabilidade) e análise de questões subjetivas.

The network "Developing Quality in Mathematics Education II" is a continuation of the associated project "Developing Quality in Mathematics Education" (http://www.dqime.unidortmund. de). In this project participate universities, teacher education institutions and schools from 11 European countries. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils support developing quality in mathematics education, especially in the area of mathematical modelling. The quality and application of the developed learning materials is also guaranteed by using, comparing and modifying them in eleven different countries. This comparison leads to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus we want to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century. A special feature of this project is the strong connection between theory and practice and between the research and development of mathematics education. In this project our Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava manage testing of translated teaching materials at the high school „Gymnazium Sturovo“. We know that using ICT and didactical software in schools is almost present and wide spread. So we try to focus on several possibilities in solving real-life tasks using this technologies, regard to the fact technologies are hard upon the young generation of students.

The network "Developing Quality in Mathematics Education II" is a continuation of the associated project "Developing Quality in Mathematics Education" (http://www.dqime.unidortmund. de). In this project participate universities, teacher education institutions and schools from 11 European countries. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils support developing quality in mathematics education, especially in the area of mathematical modelling. The quality and application of the developed learning materials is also guaranteed by using, comparing and modifying them in eleven different countries. This comparison leads to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus we want to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century. A special feature of this project is the strong connection between theory and practice and between the research and development of mathematics education. In this project our Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava manage testing of translated teaching materials at the high school „Gymnazium Sturovo“. We know that using ICT and didactical software in schools is almost present and wide spread. So we try to focus on several possibilities in solving real-life tasks using this technologies, regard to the fact technologies are hard upon the young generation of students.