The purpose of this study was to examine the use of manipulative materials in mathematics education with the main focus on grades 4 to 6. With the use of a phenomenological approach all the aspects of this phenomenon was examined. Qualitative interviews, participant observations and comparative content analysis of textbooks has been conducted to investigate the use of manipulative materials in mathematics education. The results indicates that the teachers that were interviewed possesses good knowledge of this teaching method. However these teachers struggled to find time to put this method into practice and there was not enough teachers to attend these classes. Because of this these teachers often let the subjects textbook determine how the planning of the lesson will turn out. These aspects are discussed as the cause of the reduced use of manipulative material in mathematics education in these grades.

The purpose of the present study is to investigate what research show about the use of manipulative materials in the mathematics education and what factors have an impact on this approach. A definition of the problem<img src="https://cdncache-a.akamaihd.net/items/it/img/arrow-10x10.png" /> was formed when considering the decrease of Swedish pupils mathematical abilities presented in PISA. The intention with the present study was to assemble further knowledge in whether or not the use of manipulative materials could be a teaching method that could help improve this. The method used in this study was a systematic review based on an analysis of 8 studies. The results of the studies were thoroughly examined and presented in a result chapter. When comparing the results categories were found. These categories structured the result chapter as following: the beliefs of pre- and in- service teachers, the situations in which manipulative materials are used / not used, the use of manipulative materials in relation to grades and duration and pupils’ beliefs and achievements. Results show a positive meaning to the use of manipulatives, however it is the question of how they are used that is discussed.

Med denna litteraturstudie var syftet att sammanställa forskning kring laborativt material och dess effekt på aritmetikundervisningen för elever i de lägre årskurserna. Forskningsunderlaget samlades in via databasen ERIC Ebsco.  Resultatet påvisar en övervägande positiv effekt på aritmetikinlärningen för elever och definierar aspekter för hur dessa positiva effekter kan nås. Resultatet indikerar även att lärare har blandad kunskap kring manipulering av laborativt ma-terial och kring materialets användning i undervisningen. För en god undervisning behöver lärare få tillgång till mer kunskap kring laborativt material. Detta ger elever en ökad möjlighet att nå avsikten med manipulering av laborativt material, nämligen att se de bakomliggande matematiska principerna. / The purpose of this literature review was to compile research on manipulative materials and its effect on arithmetic teaching for students in the lower grades. Research data was collected through the ERIC Ebsco database. The results show a predominantly positive effect on arith-metic learning for students and define aspects for how these positive effects can be achieved. The result also indicates that teachers have mixed knowledge about the manipulation of ma-nipulative materials and the use of the materials in teaching. For a good teaching situation, teachers need access to more knowledge about manipulative materials. This gives students an increased opportunity to reach the intention of manipulating manipulative materials, namely to see the underlying mathematical principles.

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Esta dissertação apresenta uma experiência de abordagem do conceito de ângulo a partir de sua mobilização em diversos contextos, com a utilização de diferentes materiais manipulativos. O estudo foi desenvolvido com alunos do sétimo ano do Ensino Fundamental de uma escola pública municipal de Canoas, no Rio Grande do Sul. Inspirada pelo desenvolvimento do conceito de ângulo por abstração progressiva proposta por Michael Mitchelmore e Paul White e embasada na teoria da abstração reflexionante de Jean Piaget, foram desenvolvidas e analisadas atividades exploratórias em diferentes contextos e utilizando materiais manipulativos diversos para a construção do conceito de ângulo, com base nesses referenciais teóricos. Os dados foram coletados através de gravação em áudio e vídeo, fotografias das produções dos alunos e anotações em um diário de bordo. A análise dos dados permitiu concluir que a mobilização da noção de ângulo em diferentes contextos e a utilização de materiais manipulativos contribuíram para a construção do pensamento geométrico e conceito de ângulo. / This work presents an experience in approaching the angle concept from its mobilization in different contexts and by the use of different manipulative materials. The study was developed with seventh grade students from a public school in the city of Canoas, Rio Grande do Sul. Inspired by the development of angle concepts by progressive abstraction proposed by Michael Mitchelmore and Paul White and based on the Jean Piaget's reflective abstraction theory, exploratory activities were developed and analyzed in different contexts and using several manipulative materials for the construction of the angle concept, based on these references. The data were collected through video and audio recording, students' productions photographs and logbook notes. The analysis allowed us to conclude that the mobilization of the angle concept in different contexts and the use of manipulative materials contributed to the construction of the geometrical thinking and concept of angle.

Esta dissertação apresenta uma experiência de abordagem do conceito de ângulo a partir de sua mobilização em diversos contextos, com a utilização de diferentes materiais manipulativos. O estudo foi desenvolvido com alunos do sétimo ano do Ensino Fundamental de uma escola pública municipal de Canoas, no Rio Grande do Sul. Inspirada pelo desenvolvimento do conceito de ângulo por abstração progressiva proposta por Michael Mitchelmore e Paul White e embasada na teoria da abstração reflexionante de Jean Piaget, foram desenvolvidas e analisadas atividades exploratórias em diferentes contextos e utilizando materiais manipulativos diversos para a construção do conceito de ângulo, com base nesses referenciais teóricos. Os dados foram coletados através de gravação em áudio e vídeo, fotografias das produções dos alunos e anotações em um diário de bordo. A análise dos dados permitiu concluir que a mobilização da noção de ângulo em diferentes contextos e a utilização de materiais manipulativos contribuíram para a construção do pensamento geométrico e conceito de ângulo. / This work presents an experience in approaching the angle concept from its mobilization in different contexts and by the use of different manipulative materials. The study was developed with seventh grade students from a public school in the city of Canoas, Rio Grande do Sul. Inspired by the development of angle concepts by progressive abstraction proposed by Michael Mitchelmore and Paul White and based on the Jean Piaget's reflective abstraction theory, exploratory activities were developed and analyzed in different contexts and using several manipulative materials for the construction of the angle concept, based on these references. The data were collected through video and audio recording, students' productions photographs and logbook notes. The analysis allowed us to conclude that the mobilization of the angle concept in different contexts and the use of manipulative materials contributed to the construction of the geometrical thinking and concept of angle.

Esta dissertação apresenta uma experiência de abordagem do conceito de ângulo a partir de sua mobilização em diversos contextos, com a utilização de diferentes materiais manipulativos. O estudo foi desenvolvido com alunos do sétimo ano do Ensino Fundamental de uma escola pública municipal de Canoas, no Rio Grande do Sul. Inspirada pelo desenvolvimento do conceito de ângulo por abstração progressiva proposta por Michael Mitchelmore e Paul White e embasada na teoria da abstração reflexionante de Jean Piaget, foram desenvolvidas e analisadas atividades exploratórias em diferentes contextos e utilizando materiais manipulativos diversos para a construção do conceito de ângulo, com base nesses referenciais teóricos. Os dados foram coletados através de gravação em áudio e vídeo, fotografias das produções dos alunos e anotações em um diário de bordo. A análise dos dados permitiu concluir que a mobilização da noção de ângulo em diferentes contextos e a utilização de materiais manipulativos contribuíram para a construção do pensamento geométrico e conceito de ângulo. / This work presents an experience in approaching the angle concept from its mobilization in different contexts and by the use of different manipulative materials. The study was developed with seventh grade students from a public school in the city of Canoas, Rio Grande do Sul. Inspired by the development of angle concepts by progressive abstraction proposed by Michael Mitchelmore and Paul White and based on the Jean Piaget's reflective abstraction theory, exploratory activities were developed and analyzed in different contexts and using several manipulative materials for the construction of the angle concept, based on these references. The data were collected through video and audio recording, students' productions photographs and logbook notes. The analysis allowed us to conclude that the mobilization of the angle concept in different contexts and the use of manipulative materials contributed to the construction of the geometrical thinking and concept of angle.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-14T13:00:21Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_AnaPaulaNoro.pdf: 1815913 bytes, checksum: 140ce8a40fb7aa9590310ac557d3e7cb (MD5) / Made available in DSpace on 2018-08-14T13:00:21Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_AnaPaulaNoro.pdf: 1815913 bytes, checksum: 140ce8a40fb7aa9590310ac557d3e7cb (MD5) Previous issue date: 2012-03-27 / The present work aims to analyze the possibilities that the proposition of a sequence based on the methodology of Curriculum Teaching Engineering brings to the learning and teaching Poliedros. O theoretical research involves the teaching of mathematics, in particular the teaching of geometry, the Teaching fundamentals of engineering and the use of manipulatives. The research was qualitative. The main instruments used were participatory observations during the whole process of developing the teaching sequence in which the researcher and participants interacted. Survey participants were students from the Third Year of High School, a public school in the State of São Martinho da Serra, RS. Through these instruments were recorded and analyzed the possibilities that the methodology of Didactic Engineering can offer to the study of polyhedra. It was found that the proposal of a didactic sequence, which had the support of manipulatives and media, collaborated effectively for teaching and learning of polyhedra. The didactic sequence designed and implemented is a product that can help both high school teachers and students of degree courses in Mathematics to overcome the difficulties in passing plane geometry for the space. / O presente trabalho tem como objetivo analisar as possibilidades que a proposição de uma Sequência Didática fundamentada na metodologia da Engenharia Didática traz para o ensino e aprendizagem dos Poliedros.O referencial teórico da investigação envolve o ensino de Matemática, em particular o ensino de Geometria, os fundamentos da Engenharia Didática e o uso de materiais manipuláveis. A pesquisa teve cunho qualitativo. Os principais instrumentos utilizados foram observações participativas durante todo o processo de desenvolvimento da sequência didática em que a pesquisadora e participantes interagiram. Os participantes da pesquisa foram alunos do Terceiro Ano do Ensino Médio, de uma escola da rede pública Estadual de São Martinho da Serra- RS. Através destes instrumentos foram registrados e analisados quais as possibilidades que a metodologia da Engenharia Didática pode oferecer ao estudo de poliedros. Foi verificado que a proposta de uma sequência didática, que teve apoio de materiais manipuláveis e de mídias, colaborou, de forma efetiva, para o ensino e aprendizagem de poliedros. A sequência didática elaborada e aplicada é um produto que pode auxiliar tanto professores do ensino médio quanto os estudantes dos cursos de licenciatura em Matemática a superarem as dificuldades na passagem da geometria plana para a espacial.

Målsättningen med studien är att belysa vilka laborativa material som används, hur de kan användas och varför laborativa material ska används i matematikundervisningen i förskoleklass. Detta mynnar ut i studiens syfte som är att med hjälp av intervjuer och observationer synliggöra lärares användning av laborativa material i matematikundervisningen i förskoleklass.   Kvalitativ metod används och inspiration hämtas från etnografin. Det insamlade datamaterialet som har analyserats består av kvalitativa intervjuer med två förskollärare samt deltagande observation under en heldag på två skolor. Teorin inspireras av didaktisk teori och didaktiska frågor som vad, hur och varför. Empirin består av transkriberingar och fältanteckningar som analyseras utifrån den didaktiska triangeln och Bishops matematiska aktiviteter.   I resultatet framkommer att laborativa material används vid alla Bishops sex aktiviteter och att olika typer av laborativa material används som vardagliga föremål, pedagogiska material och spel. Laborativt material används inte enbart vid matematiklektioner utan kan även användas vid temaarbete, på idrottslektioner och utomhus. Förskollärarna är positiva till användandet av laborativt material och ser dem som en självklar del av förskoleklasselevernas matematikundervisning. Förskollärarens syn på vad som är laborativa material påverkar hur laborativa material används. I resultatet framkommer att laborativt material kan vara en hjälp för elever att konkretisera matematiken och att valet av material beror på vilken elev som ska använda det och elevens förkunskaper.

Denna studie beskriver hur en kommunal grundskola i sydvästra Indien undervisar matematik.Vår frågeställning var: Hur fungerar en indisk statlig grundskola arbetar med matematik? Vilka är lärarnas uppfattningar om skolans sätt att undervisa? För att ha möjlighet att fördjupa oss i frågorna undersökte vi även Hur lärarnas föreställningar om matematik påverkar normerna i klassrummet utifrån ramen av Yack och Cobbs normteori. Det är en kvalitativ studie där vi utförde observationer av undervisningen och intervjuer med lärare och rektorn på skolan om deras syn på matematikundervisningen, under tre veckor. Vi samlade också information om och dokumenterade deras matematikverkstad.Utifrån våra intervjuer och observationer kunde vi dra slutsatsen att samtliga på skolan arbetade med en aktivitetsbaserad undervisning där matematik lärs med hjälp av manipulativt, laborativt material. De arbetade tillsammans i ett arbetslag med en strävan att uppfylla läroplanens mål och med en gemensam arbetsmetod. Vi fann också att lärarnas värderingar och föreställningar om hur matematik ska läras ut, påverkar de normer som verkar i klassrummet.Denna studie kan inte generaliserbar eftersom detta är en fallstudie på denna skola. Dock förespråkar den indiska läroplanen att undervisningen ska ske utifrån elevnära aktiviteter, men matematikverkstaden på denna skola var speciell och utvecklad på denna skola. / For our study, we visited a Government Lower Primary School in India to inquiry about how a school in another schooling context teaches mathematics. Our research questions were: How does an Indian Government Lower Primary School work with mathematics? What are the teachers' perceptions of the school’s teaching approach? In addition to these questions and to inquire deeper into this subject, we also investigated How do the teachers’ perceptions and method of teaching connect to Yackel and Cobb’s framework of the different kinds of norms operating in the classroom?We did a qualitative study, staying at the school for three weeks to interview teachers about their method of teaching mathematics as well as observing how they were teaching mathematics and the norms that operated in the classroom. We also gathered information about their mathematics laboratory. During our interviews and observations we came to the conclusion that the school worked with activity-based learning by using manipulative materials. All teachers as well as the principal cooperatively strived to meet the curricula objectives, with the same teaching approach. We also found that the teachers’ values and beliefs about how mathematics should be taught, affect the norms operating in the classroom.This study cannot be generalised for all schools in India or even in this area. This study is a minor study which only considered one particular school which used an interesting teaching method, activity-based learning with manipulatives.