The purpose of this study was to compare selected sixth, seventh and eighth grades mathematics textbooks from Turkey, Singapore and the United States of America and explore their implications for presenting same opportunity to learn to the students at the same grade level. In this study, the selected books were analyzed in terms of whether they included perimeter, area and volume topics, how they presented the topics on the basis of the selected features and the complexity of to-be-solved mathematical problems related to the topics. Some similarities and differences were observed among the textbooks. It was found that the Turkish textbooks are inclusive in terms of subtopics related to perimeter, area and volume. However, the number of pages dedicated to present the topics is the highest in the Singaporean textbooks. That is, in comparison to the Turkish textbooks, the Singaporean textbooks include fewer number of subtopics related to perimeter, area and volume, but the subtopics are presented in a more detail manner. These books are also rich in terms of mathematically relevant illustrations that make the topics more understandable for students. While the U.S textbooks benefit heavily from technology to present the topics, especially by using three-dimensional shapes / the Turkish and Singaporean textbooks do not make use of technology. The textbooks do not show a difference in terms of complexity of to-be-solved problems. Since all of them mostly include the problems with moderate complexity. Despite there is not any difference among the textbooks in terms of the complexity of to-be-solved problems, there is a difference in terms of the number of to-be-solved problems in the textbooks. The Singaporean textbooks encompass more to-be-solved problems compared to others. The study was concluded by providing some useful suggestions to cover the perimeter, area and volume topics in a way that makes students&rsquo / learning easier and to present same opportunity to learn to the students.

La présente étude s’intéresse particulièrement au concept mathématique de fraction et à son enseignement-apprentissage au cycle 3 de l’école primaire en France. Ce concept étant souvent difficile à comprendre par les élèves, il est introduit formellement dès la classe de CM1 du cycle 3 de l’école primaire.L’objectif de cette recherche a été, dans un premier temps, l’étude de l’enseignement des fractions. Pour ce faire, sont analysées les situations d’apprentissage qui proposent des activités portant sur les fractions dans cinq manuels scolaires de mathématiques de CM1 et cinq manuels de CM2, de même collection ; le but est de connaître les différentes significations de la fraction présentes dans ces manuels.Dans un deuxième temps, l’objectif de cette recherche fut de savoir ce qu’il reste chez les élèves après qu’ils ont étudié les fractions. Pour cela, un échantillon de 275 sujets, 160 de CM1 et 115 de CM2 de l’école primaire, ont répondu à un questionnaire écrit portant sur les fractions. Le but est d’étudier les conceptions et les représentations chez ces élèves à l’égard de la notion de fraction, en particulier à l’égard des différentes significations de la fraction données par ces élèves.Dans un troisième temps, nous voulions connaître les conceptions de quelques enseignants sur la manière avec laquelle ils abordent les fractions avec leurs élèves. Pour ce faire, 8 enseignants parmi les 12 enseignants des classes concernées ont participé à l’étude.L’analyse effectuée sur les manuels scolaires a été faite à l’aide d’une grille d’analyse, les résultats de cette analyse relèvent que les activités ou les situations d’apprentissage proposées dans les manuels scolaires choisis ne sont pas réparties à égalité entre les diverses significations de la fraction. De plus, les significations de la fraction les plus présentes dans les manuels scolaires de CM1 à travers les activités analysées sont respectivement les suivantes : Partie-tout (quantité continue), Mesure, Nombre ; dans les manuels scolaires de CM2, les significations les plus présentes sont respectivement les suivantes : Nombre, Partie-tout (quantité continue) et Mesure. En revanche, les activités relatives aux autres significations sont généralement présentes, mais avec des fréquences réduites.Pour traiter de l’apprentissage des fractions chez les élèves, l’analyse s’est effectuée autour des connaissances et des représentations des élèves de CM1 et de CM2 par rapport aux différentes significations de la fraction. Cette analyse, effectuée sur les réponses des élèves sur le questionnaire, montre que la signification de la fraction la plus utilisée, par les élèves de CM1 et de CM2, est celle de Partie d’un tout (quantité continue). Les significations Nombre, Mesure, Partie d’un tout (quantité discrète) et Nombre sur une droite graduée sont présentes dans les réponses des élèves. En revanche, les autres significations sont celles qui sont les moins utilisées par les élèves. De plus, en ce qui concerne les significations manifestées de la fraction, les élèves de ces deux niveaux scolaires ne diffèrent pas beaucoup. Enfin, notre étude permet de constater que les élèves utilisent les significations de la fraction les plus fréquemment présentes dans les manuels scolaires, cela nous donne un éclairage sur l’objet de l’influence de l’enseignement des fractions sur l’apprentissage des élèves.Afin de connaître les conceptions pédagogiques et épistémologiques des enseignants sur leur manière d’aborder l’enseignement de la fraction, nous avons construit les données au moyen d’une enquête par questionnaire auprès de 8 enseignants. Les réponses à ce questionnaire ont été analysées suivant deux perspectives, pédagogique et mathématique..... / This study concerns the fraction mathematical concept, mainly in its teaching-learning in the cycle 3 of French primary school. This concept is often difficult to be understood by pupils; it is formally introduced in the CM1 class of the cycle 3 in primary school.The object of this research was, firstly, the study of fractions’ teaching. To do that, we analyzed learning situations that offer activities bearing on fractions in five math textbooks of CM1 and five math textbooks of CM2, all from the same collection ; the goal is to know the different meanings of the fraction present in these books.In a second time, the object of this research was to find out what pupils remain after they studied fractions. For that, a sample of 275 subjects, 160 from CM1 and 115 from CM2, answered to a written questionnaire bearing on fractions. The goal is to study conceptions and representations that pupils have in respect of the concept of fraction, particularly in respect of different meanings of fraction given by these pupils.In a third time, we wanted to know the opinions of a few teachers about the way in which they approach fractions at school. To do that, 8 teachers among the 12 teachers of the classes concerned participated in the study.The analysis conducted on the books was made with the help of an analysis grid; the results of this analysis point out that the activities or learning situations offered in selected books are not equally distributed between the various meanings of fraction.Moreover, the most present meanings of fraction in CM1 books through the activities analyzed are respectively the following: Part of a whole, Measurement and Number; in CM2 books, the most present meanings are respectively the following: Number, Part of a whole and Measurement. However, the activities related to the other meanings are generally present, but with a reduced frequency.To treat fractions’ learning by pupils, the analysis was made around of the knowledge and the representations of the pupils of CM1 and CM2 relative to different meanings of fraction. This analysis, performed on the pupils' answers on the questionnaire, shows that the meaning of fraction the most used by the students of CM1 and CM2, is that of Part of a whole (continuous quantity). The meanings Number, Measure, Part of a whole (discrete quantity) and Number on a number line are present in pupils' answers. However, the other meanings are those who are the less used by the pupils. Moreover, in regards to the manifested meanings of fraction, pupils of both school levels do not differ much. Finally, our study shows that pupils use the most fraction’s meanings found in books. It gives us a light on the subject of the influence of fractions’ teaching in pupils’ training.To know the epistemological and pedagogical conceptions of teachers in their approach to fraction’s teaching, we built the data by a sample survey with 8 teachers. The answers were analyzed using two perspectives, pedagogic and mathematic. For the pedagogical character analysis, a grid was built around the privileged modes of representation by the teachers and around the respective roles reserved to teacher and pupils. In parallel, we verified the mathematical value of the answers provided by the teachers. To introduce the concept of fraction, the teachers say that they give a large place to concrete or graphical representations. Also, the teachers have an important role throughout teaching and learning approaches.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2018-10-16T18:31:56Z No. of bitstreams: 1 2013 - Diuliano Azeredo Gouv?a.pdf: 3074684 bytes, checksum: 1637a9c9273f537aed4b0b6fadefe6f8 (MD5) / Made available in DSpace on 2018-10-16T18:31:56Z (GMT). No. of bitstreams: 1 2013 - Diuliano Azeredo Gouv?a.pdf: 3074684 bytes, checksum: 1637a9c9273f537aed4b0b6fadefe6f8 (MD5) Previous issue date: 2013-07-17 / CAPES / This study aims to present the importance of the history of mathematics for teaching and learning, seeking to provide opportunities for readers to approach the topic with a historical bias, in order to understand what potential that is replaced when under a historical perspective; it would have with respect to the learning process. To achieve this goal, we conducted an analysis of four (4) textbooks, chosen by PNLD in order to see how these books had the logarithms, it was the presence of the History of Mathematics and presenting this approach as this, suggestions for authors to improve their work. Then we conducted a field study where we applied two questionnaires, one designed for teachers and another for students. In order to get the opinion of these two groups on the approach of logarithms from a bias in the history of mathematics and also to check the view that these two groups have the relationship of mathematics with its own history in loco history of logarithms, as well as open avenues for the emergence of new research. Conducted surveys present our methodology for the analysis of the same. We also made a brief analysis of dissertations related in order to make a reading that was measured and developed by colleagues who studied the same order subject. For analyze the results, we gave our suggestions to create a conclusion about the topic / Este estudo tem como objetivo chamar a aten??o para a import?ncia da Hist?ria da Matem?tica no ensino-aprendizado dos logaritmos, buscando apresentar possibilidades de abordagem do tema com um vi?s hist?rico. Para atingir esse objetivo, realizamos uma an?lise de 4 (quatro) livros did?ticos, escolhidos pelo PNLD, a fim de verificar como esses livros apresentavam os logaritmos, se havia a presen?a da Hist?ria da Matem?tica nesta abordagem no que acreditamos possa ser mais atrativas e adequadas ao ensino deste importante t?pico. Ap?s uma an?lise n?o exaustiva, apresentando, com isso, sugest?es para que os autores possam melhorar suas obras. Realizamos uma pesquisa de campo, onde aplicamos dois question?rios, um destinado para os professores e outro destinado aos alunos. Com o objetivo de obter a opini?o desses dois grupos sobre a abordagem dos logaritmos a partir de um vi?s da hist?ria da Matem?tica e tamb?m de verificar a vis?o que esses dois grupos tem da rela??o da matem?tica com sua pr?pria hist?ria in loco a hist?ria dos logaritmos, assim como abrir caminhos para o surgimento de novas pesquisas. Fizemos tamb?m uma breve an?lise de disserta??es correlatas com objetivo de fazer uma leitura do que foi aferido e desenvolvido por colegas que estudaram o mesmo assunto. Por fim analisamos os resultados, demos nossas sugest?es a fim de criar uma conclus?o sobre o tema abordado.

The purpose of this study was to investigate teachers&rsquo / ways of using mathematics textbooks while planning the lesson and during the lesson, to document teachers&rsquo / views about elementary students&rsquo / usage of mathematics textbook during the classroom time and for their homework and teachers&rsquo / views about mathematics textbooks&rsquo / characteristics. A case study was conducted in a private elementary school with more class hours for mathematics and six mathematics teachers teaching 4th, 5th, 6th, and 7th grade mathematics in this school participated. Data were collected in the spring semester of 2010-2011 academic year through an interview protocol with 16 main questions addressing teachers&rsquo / mathematics textbook usage and students&rsquo / mathematics textbook usage developed for this study by the researcher through the findings and discussions in the literature. Data analysis was conducted through qualitative methods. The findings of this study showed that participant teachers expressed both positive and negative views about characteristics of textbook and usage of textbook. All of them stated that the textbook was their main tool for lesson preparations and teaching. They followed the curriculum from textbook and decided what to do, how to do, and when to do. Participants underlined that textbook was an effective helper but it needed improvement in many aspects. The findings also showed that teachers viewed that students did not use their textbook efficiently. All of the teachers expressed that students did not prefer to study from textbook if there were not any assignment or homework. Teachers specified that students could improve studying habits from textbook if teachers could direct them efficiently. The findings of this study might be useful to prepare more effective lessons for teachers, to give ideas to teachers for guiding their students for effective textbook usage, and to increase the quality of textbooks.

Este trabalho tem por objetivo analisar de que forma os Objetos Educacionais Digitais (OED) recursos recentemente integrados a algumas coleções de livros didáticos adquiridas pelo Ministério da Educação podem contribuir para a construção do conhecimento em Matemática. Para tanto, foi estabelecido um referencial teórico constituído por autores que conceberam teorias e desenvolveram pesquisas visando a construção do conhecimento em Matemática. Esses autores se entrelaçam, se relacionam e se complementam. Com base em tal referencial, foram estabelecidos os critérios para a análise. O primeiro diz respeito à relação aluno OED tarefa, e está relacionado ao modo como o OED contribui para que as capacidades cognitivas dos alunos sejam mobilizadas e eles construam o conhecimento. O segundo, baseado na Teoria dos Registros de Representação Semiótica, está associado ao modo como os OED trabalham as diferentes representações de um mesmo objeto matemático. Por fim, o terceiro critério foca em como o contexto utilizado no OED possibilita ao aluno estabelecer relações entre diferentes conceitos da Matemática ou mesmo de outras áreas do conhecimento. Os resultados mostraram, dentre outras coisas, que os OED lidam com dois ou mais registros de representação diferentes, porém sem levar os alunos a coordená-los e que, na maioria deles, estão presentes situações que permitem aos alunos atribuir significados aos conteúdos matemáticos. / This study aims to examine how the Digital Educational Objects (OED) newly integrated features to some collections of textbooks acquired by the Ministry of Education can contribute to the construction of knowledge in mathematics. Therefore, it was established a theoretical framework consisted of authors who conceived theories and research developed to aim the construction of knowledge in mathematics. These authors intertwine, are closely relate and complement each other. Based on this framework, the criteria for analysis were established. The first, concerns the relationship student - OED - task, and is related to how the OED contributes to the cognitive abilities of students are mobilized and they build knowledge. The second, based on the Theory of Semiotics Representation Registers, is associated with how the OED work the different representations of the same mathematical object. Finally, the third criteria, focuses on how the context used in the OED enables students to establish relationships between different concepts of mathematics or even other areas of knowledge. The results showed, among other things, that the OED deal with two or more registers of different representations, but without having students to coordinate them, and in most of them, there are situations that allow students to assign meanings to the mathematical contents.

Este trabalho tem por objetivo analisar de que forma os Objetos Educacionais Digitais (OED) recursos recentemente integrados a algumas coleções de livros didáticos adquiridas pelo Ministério da Educação podem contribuir para a construção do conhecimento em Matemática. Para tanto, foi estabelecido um referencial teórico constituído por autores que conceberam teorias e desenvolveram pesquisas visando a construção do conhecimento em Matemática. Esses autores se entrelaçam, se relacionam e se complementam. Com base em tal referencial, foram estabelecidos os critérios para a análise. O primeiro diz respeito à relação aluno OED tarefa, e está relacionado ao modo como o OED contribui para que as capacidades cognitivas dos alunos sejam mobilizadas e eles construam o conhecimento. O segundo, baseado na Teoria dos Registros de Representação Semiótica, está associado ao modo como os OED trabalham as diferentes representações de um mesmo objeto matemático. Por fim, o terceiro critério foca em como o contexto utilizado no OED possibilita ao aluno estabelecer relações entre diferentes conceitos da Matemática ou mesmo de outras áreas do conhecimento. Os resultados mostraram, dentre outras coisas, que os OED lidam com dois ou mais registros de representação diferentes, porém sem levar os alunos a coordená-los e que, na maioria deles, estão presentes situações que permitem aos alunos atribuir significados aos conteúdos matemáticos. / This study aims to examine how the Digital Educational Objects (OED) newly integrated features to some collections of textbooks acquired by the Ministry of Education can contribute to the construction of knowledge in mathematics. Therefore, it was established a theoretical framework consisted of authors who conceived theories and research developed to aim the construction of knowledge in mathematics. These authors intertwine, are closely relate and complement each other. Based on this framework, the criteria for analysis were established. The first, concerns the relationship student - OED - task, and is related to how the OED contributes to the cognitive abilities of students are mobilized and they build knowledge. The second, based on the Theory of Semiotics Representation Registers, is associated with how the OED work the different representations of the same mathematical object. Finally, the third criteria, focuses on how the context used in the OED enables students to establish relationships between different concepts of mathematics or even other areas of knowledge. The results showed, among other things, that the OED deal with two or more registers of different representations, but without having students to coordinate them, and in most of them, there are situations that allow students to assign meanings to the mathematical contents.