Η παρούσα διπλωματική εργασία αφορά στη μελέτη της ανάπτυξης της πολλαπλασιαστικής σκέψης των μαθητών του Δημοτικού Σχολείου. Σκοπός της έρευνας ήταν η αξιολόγηση της επίδοσης των μαθητών των δύο τελευταίων τάξεων του Δημοτικού Σχολείου σε προβλήματα αναλογίας, ως χαρακτηριστικό παράδειγμα προβλημάτων πολλαπλασιαστικής σκέψης, όσο και η διερεύνηση των μαθηματικών στρατηγικών που χρησιμοποιούν για την επίλυση αυτών. Η πολλαπλασιαστική σκέψη αποτελεί μία ιδιαίτερα σημαντική ικανότητα που παρέχει τη δυνατότητα στους μαθητές να σχεδιάζουν εύστοχες στρατηγικές λύσης σε κατηγορίες προβλημάτων που έχουν αυξημένες δυσκολίες δομής και περιεχομένου. Τα δεδομένα που συλλέχθηκαν συγκρίθηκαν μεταξύ των μαθητών των δύο τάξεων και διαπιστώθηκαν οι διαφορές μεταξύ αυτών. Με τον τρόπο αυτό, ερμηνεύθηκε ο ρόλος της ηλικίας των μαθητών, ως παράγοντας που συνδέεται με την ανάπτυξη της πολλαπλασιαστικής σκέψης. Η έρευνα έδειξε ότι οι μαθητές και των δύο τάξεων παρουσιάζουν ιδιαίτερα σημαντικές δυσκολίες στην επίλυση προβλημάτων αναλογίας. Ταυτόχρονα, φαίνεται ότι οι μεγαλύτεροι σε ηλικία μαθητές έχουν μεγαλύτερη ικανότητα στη λύση των προβλημάτων. Τέλος, η έρευνα δείχνει ότι η δομή και το περιεχόμενο των προβλημάτων αυτών αποτελούν παράγοντες που επηρεάζουν τους μαθητές στη διαδικασία επίλυσης που επιλέγουν να εφαρμόσουν. / This thesis concerns the study of the development of multiplicative thinking of primary school students. The purpose of this study was to evaluate the performance of grade 5 and grade 6 students on proportional problems, as an example of multiplicative thinking problems, and exploring mathematical strategies used to solve them. The multiplicative thinking is a very important skill that enables students to design targeted strategies in different categories of proportional problems which have increased difficulties in structure and content. The collected data were compared between students of the two grades and found the differences between them. In this way interpreted the role of students’ age, as a factor associated with the development of multiplicative thinking. The survey shows that the students of both grades have substantial difficulties in solving proportional problems. At the same time, the survey appears that the older students have greater ability in problem solving. Finally, research shows that the structure and the content of these problems are factors that affect students in the process of resolving which they choose to apply.

Made available in DSpace on 2016-04-27T16:58:56Z (GMT). No. of bitstreams: 1 Marcia Regiane Miranda.pdf: 8663809 bytes, checksum: db65a0e8bef94d2cc5fa9a3b0bfd9e23 (MD5) Previous issue date: 2009-10-14 / Secretaria da Educação do Estado de São Paulo / The goal of this work is to make a synthesis of investigations focused on the mathematical expressions generated (or reflected) from manifestation and development of the proportional thinking. Our study object are activities set out in thesis produced in the State of São Paulo aimed at improving the teaching and learning proportional thinking aspects. Our research methodology is characterized as a documentary denominated qualitative metanalysis study which seeks to make a systematic review of a set of surveys that produce new results or synthesis. In order to transcend the results obtained by investigations, we used in analysis, elements which we believe are essentials of theoretical, historical and curricular references. We conduct our studies based on procedures of content analysis of Bardin (2008), in a qualitative approach, leading our research according to the following phases: 1) The preparation of the documentary corpus and register selection models. 2) The first analysis of documents. 3) Second analysis. 4) The final synthesis. As a result, we verified that the activities proposed in two dissertations of the State of São Paulo have fostered expression and the development of our students proportional thinking, and privileged aspects were those that had intended to represent proportional situations through charts, tables, symbols, drawings or diagrams; using central ideas associated with directions from rational numbers, or relations and operations between them, besides their representations, to solve problems involving functions or ideas associated with the functions and their representations and using multiplication and division to solve problems involving ratio or proportional ideas / O objetivo deste trabalho é fazer uma síntese de investigações, que focalizam as expressões matemáticas, geradas na (ou reflexos da) manifestação e desenvolvimento do pensamento proporcional. Nosso objeto de estudo são as atividades realizadas e explicitadas em dissertações de mestrado produzidas no Estado de São Paulo que visam melhorar o ensino e aprendizagem de aspectos do pensamento proporcional. Metodologicamente nossa pesquisa se caracteriza como um estudo documental denominado metanálise qualitativa na qual se procura fazer uma revisão sistemática de um conjunto de pesquisas, visando à produção de novos resultados, ou sínteses. Na intenção de transcender os resultados obtidos pelas investigações estudadas, utilizamos nas análises elementos que julgamos essenciais dos referenciais teórico, histórico e curricular. Baseamo-nos em procedimentos de análise de conteúdo de Bardin (2008), em uma abordagem qualitativa, conduzindo a nossa pesquisa conforme as seguintes fases: 1) Elaboração do corpus documental e seleção dos modelos de fichamento. 2) Primeira análise dos documentos. 3) Segunda análise. 4) Síntese final. Como resultado de nossa pesquisa, verificamos que a realização de atividades propostas em duas dissertações do Estado de São Paulo favoreceu a expressão e o desenvolvimento do pensamento proporcional em estudantes, e os aspectos privilegiados foram os que tiveram como objetivo representar situações proporcionais por meio de gráficos, tabelas, símbolos, desenhos ou diagramas; utilizar idéias centrais associadas aos sentidos do número racional, ou de relações e operações entre eles, além de suas representações, para resolver problemas envolvendo funções ou idéias associadas às funções e suas representações e utilizar multiplicação ou divisão para resolver problemas envolvendo idéias de razão ou proporção

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-17T14:04:52Z No. of bitstreams: 1 mariliariosdepaula.pdf: 694561 bytes, checksum: 3234a2405fae49608f1264c5a8f6c696 (MD5) / Rejected by Adriana Oliveira (adriana.oliveira@ufjf.edu.br), reason: Bom dia! Por gentileza corrija as palavras-chave, apenas a primeira palavra deve ser iniciada em caixa alta. Obrigada! on 2016-06-28T14:28:22Z (GMT) / Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-28T14:35:49Z No. of bitstreams: 1 mariliariosdepaula.pdf: 694561 bytes, checksum: 3234a2405fae49608f1264c5a8f6c696 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T15:49:09Z (GMT) No. of bitstreams: 1 mariliariosdepaula.pdf: 694561 bytes, checksum: 3234a2405fae49608f1264c5a8f6c696 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T15:49:21Z (GMT) No. of bitstreams: 1 mariliariosdepaula.pdf: 694561 bytes, checksum: 3234a2405fae49608f1264c5a8f6c696 (MD5) / Made available in DSpace on 2016-07-13T15:49:21Z (GMT). No. of bitstreams: 1 mariliariosdepaula.pdf: 694561 bytes, checksum: 3234a2405fae49608f1264c5a8f6c696 (MD5) Previous issue date: 2012-10-26 / A presente pesquisa discute o ensino de razão como taxa enquanto parte da formação matemática dos estudantes do ensino fundamental. Nossa investigação tem como base teórica o Modelo dos Campos Semânticos que nos permitiu, através de seus pressupostos, o desenvolvimento da pesquisa de campo e do produto educacional. O estudo teve como objetivo investigar o ensino do tema razão como taxa na sala de aula de matemática do 9º ano do Ensino Fundamental através da inserção de tarefas que estimulassem a produção de significados dos estudantes. O Produto Educacional, produzido a partir da pesquisa, resultou em um texto, voltado para o professor, sobre o tema Razão como taxa, indicando a importância do tema e sugerindo tarefas que podem ser utilizadas em salas de aula e em atividades de ensino. / This research discusses the teaching rate as tax as part of students ' mathematics education in elementary school. Our research is based on the theoretical Model of Semantic Fields which allowed us, through its assumptions, the development of field research and educational product. The study aimed to investigate the teaching of the subject rate as tax in the classroom of the 9th math grade by inserting tasks that stimulate the production of meanings of students. The Educational Product, produced from the survey, resulted in a text for the teacher, on the topic of Rate as Tax, indicating the importance of the subject and suggesting tasks that can be used in classrooms and in teaching activities.