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Taluppfattning : En undersökning av elevers förståelse av decimaltal / Number sense : A study of students' understanding of decimal numbersAndersson, Carina January 2006 (has links)
<p>I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.</p>
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Taluppfattning : En undersökning av elevers förståelse av decimaltal / Number sense : A study of students' understanding of decimal numbersAndersson, Carina January 2006 (has links)
I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.
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Elevers olika uppfattningar av tal i decimalform i en svensk kontext. : - En studie som bygger på kategorisering av elevers uppfattningar framtagen av tidigare forskning inom det matematikdidaktiska forskningsfältet. / Students’ different perceptions of decimal numbers in a Swedish context. : – A study that focus on the categorization of students’ perceptions of decimal numbers based on earlier research in the mathematical field.Sandin, Sara January 2021 (has links)
I denna studie har tidigare internationell forskning inom området tal i decimalform undersökts i en svensk kontext. I den matematikdidaktiska forskningen har ett teoretiskt ramverk för elevers olika uppfattningar av tal i decimalform tagits fram. Tidigare studier har gjort flera försök till att kategorisera elevers olika förståelse av tal i decimalform (Moloney & Stacey, 1997; Resnik et al., 1989; Sackur-Grisvard & Léonard, 1985; Stacey & Steinle, 1998). Sackur-Grisvard och Léonards (1985) kategorisering utgår ifrån elevernas förkunskaper inom andra matematiska områden. Deras teoretiska ramverk består av elevers användning utav tre olika regler; heltalsregeln, bråkregeln och nollregeln. Sackur-Grisvard och Léonards (1985) teoretiska ramverk har inte använts i någon högre utsträckning i det svenska forskningsfältet. Ramverket har i denna studie använts för att ta reda på om det kan användas som ett verktyg för att kategorisera elevers olika förståelse av tal i decimalform i årskurserna 4-6. I studien har metoden triangulering använts med både ett skriftligt test och semistrukturerade intervjuer. Alla elever har genomfört ett skriftligt test där de fått lösa uppgifter genom att jämföra och storleksordna olika tal i decimalform. Elevernas resultat användes sedan där några få elever ifrån årskurserna 4 och 5 valdes ut till semistrukturerade intervjuer genom ett målstyrt urval. Resultatet visade att det teoretiska ramverket hade vissa begränsningar och att flera elever inte kunde kategoriseras till enbart en kategori utan flertalet använde sig av flera regler på det skriftliga testet. Elevernas resultat visade även en progression inom ämnesområdet där elever i årskurs 6 presterade bäst efterföljt av årskurs 5 och elever i årskurs 4 presterade sämst. / In this study earlier international research has been used from a Swedish perspective to investigate the field of decimal numbers. A theoretical framework for students’ various perceptions of decimal number has developed from the mathematical didactic research field. Earlier studies have done different attempts to categories students’ various perceptions of decimal numbers (Moloney & Stacey, 1997; Resnik et al., 1989; Sackur-Grisvard & Léonard, 1985; Stacey & Steinle, 1998). Sackur-Grisvard and Léonard (1985) categorization focus on students’ earlier knowledge in the mathematical field. Their theoretical framework involves the use of three different rules; the whole number rule, the fraction rule and the zero rule. Sackur-Grisvard and Léonard’s (1985) theoretical framework has not been used much in the Swedish research field. In this study the framework has been used to investigate if it can be used as a tool to categorise students in grade 4 and grade 5 various perception of decimal numbers. In this study the method triangulation has been used which involves a written test and semi-structure interviews. In the written test all students got tasks where they would compare and order different decimal numbers. The students result from the test were used to choose a few students from grade 4 and grade 5 to do the semi-structured interviews through a target-driven selection. The result showed that the theoretical framework did have some limits and several students´ did not belong to only one category, several students did use more than one of the three rules in the written test. The students result showed a progression where students from grade 6 performed best on the test followed by students from grade 5, students in grade 4 performed worst.
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Transformação de frações em números: uma experiência no Ensino Fundamental / The transformation of fractions into numbers: an experience in Basic EducationAnanias, Izabela Cesario Correa 27 February 2019 (has links)
Este estudo se insere na problemática do ensino e aprendizagem de frações no Ensino Fundamental e, mais particularmente, no que se refere à apreensão das frações como números pelos alunos. Essa concepção da fração como número é descrita na literatura da área de Educação Matemática como problemática para os alunos, pois, em geral, concebem a representação a/b (com a e b naturais e b não nulo) apenas como um duplo processo de contagem no modelo parte-todo. Decidiu-se, portanto, investigar o impacto de algumas abordagens que ampliassem a referida concepção de fração como parte de inteiro. Para tanto, tomou-se como base algumas pesquisas que destacam diferentes ideias e situações para conceituar frações, bem como a Teoria dos Registros de Representação Semiótica de Raymond Duval, devido à importância de se abordar as frações em seus vários significados, por meio de diferentes representações. Realizou-se um estudo experimental de caráter qualitativo, inspirado na metodologia de Design Experiment, envolvendo 24 alunos do 6º ano do Ensino Fundamental de uma escola em Goiânia. A elaboração das atividades fundamentou-se nos constructos teóricos do levantamento bibliográfico, bem como em um questionário inicial que permitiu identificar as principais dificuldades do grupo de alunos. As hipóteses consideradas no design foram: ênfase em atividades de conversão de representações entre os registros numérico ou figural e o gráfico (reta numérica), em ambos os sentidos; e foco na ideia da fração como representação do resultado de uma divisão de dois números naturais. Foram realizadas quatro atividades, com diversas tarefas em cada uma delas, ao longo de nove encontros no âmbito das aulas regulares de Matemática. As propostas transitaram entre trabalhos em grupo e individuais, envolvendo recursos tradicionais e materiais concretos, sendo que a coleta de dados deu-se essencialmente a partir das observações da pesquisadora e dos registros orais e escritos das produções dos alunos. Na atividade principal, foi introduzido um recurso para realizar a divisão de segmentos em partes congruentes, visando dar condição para os alunos representarem frações não decimais em retas numéricas, sem realizar a conversão para a representação decimal e/ou efetuar aproximações imprecisas. As análises mostraram que houve, em geral, um amadurecimento dos estudantes em relação às ideias apresentadas, aproximando-os da concepção de fração como número uma vez que explicitaram compreensão de aspectos de equivalência e ordem ao posicionar frações em retas numéricas e perceberam que tais frações correspondiam a resultados de divisões entre dois números naturais, isto é, a quocientes vistos como quantidades. / This study concerns the issue of teaching and learning fractions in Basic Education and, more particularly, regards the students apprehension of fractions as numbers. The notion of fractions as numbers is described in Mathematics Education literature as problematic for students, since, generally, they understand the representation a/b (where a and b are natural numbers and b is different than zero) only as a double counting process in the part-whole model. Therefore, we decided to investigate the impact of some approaches that broadened the notion of fraction as part of a whole. In order to achieve that, we used as a basis research that highlights different ideas and situations to conceptualize fractions, as well as Raymond Duvals Theory of Registers of Semiotic Representation, due to the importance of approaching fractions in their diverse meanings, through different representations. We carried out an experimental study of qualitative character, inspired by the Design Experiment methodology, with 24 students in the 6th grade from a school in Goiânia. The activities were written based on the theoretical constructs analyzed in the bibliographic search, as well as based on an initial questionnaire that allowed us to identify the main difficulties that the student group had. The hypotheses considered in the design were: emphasis on activities concerning representation conversion between numerical or figural registers and graphical (number line) in both directions; and focus on the idea of fraction as the representation of a division of two natural numbers. Four activities were carried out, with several tasks in each one, along nine meetings in the context of regular Math classes. The activities varied between group and individual tasks, involving traditional resources and concrete materials, with the data collection taking place essentially through the researchers observations and oral and written records of the students productions. In the main activity, we introduced a resource to facilitate the division of segments into congruent parts, aiming to help the students depict non-decimal fractions in number lines without converting them into the decimal register and/or using inaccurate approximations. The analysis shows that, generally, there was an improvement in the students concerning the ideas presented in the activities, bringing them closer to the concept of fractions as numbers, as they demonstrated understanding aspects of equivalence and order by placing fractions in number lines and realized that these fractions corresponded to the results of divisions of two natural numbers, that is, quotients perceived as quantities.
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Is it all in their heads? : A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary schoolBjörkström, Angela January 2008 (has links)
<p>Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today. Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible. Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system. Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled. Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident. These are highlighted since they are important aspects teachers should be aware of. The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results. Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals. Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies. Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable. </p>
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Is it all in their heads? : A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary schoolBjörkström, Angela January 2008 (has links)
Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today. Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible. Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system. Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled. Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident. These are highlighted since they are important aspects teachers should be aware of. The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results. Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals. Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies. Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable.
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Changes with age in students’ misconceptions of decimal numbersSteinle, Vicki Unknown Date (has links) (PDF)
This thesis reports on a longitudinal study of students’ understanding of decimal notation. Over 3000 students, from a volunteer sample of 12 schools in Victoria, Australia, completed nearly 10000 tests over a 4-year period. The number of tests completed by individual students varied from 1 to 7 and the average inter-test time was 8 months. The diagnostic test used in this study, (Decimal Comparison Test), was created by extending and refining tests in the literature to identify students with one of 12 misconceptions about decimal notation. (For complete abstract open document)
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Platsvärde, storleksordning och tallinje i läromedel : En läromedelsanalys som behandlar missuppfattningar gällande begrepp inom tal i decimalform och på vilka sätt de kan motverkas / Place value, order of magnitude and number line in learning materials : A learning material analysis of misconceptions regarding three concepts within decimal numbers and in which ways counteraction can be madePetersson, Vilma, Öberg, Adina January 2024 (has links)
Studien behandlar missuppfattningar gällande tre begreppen platsvärde, tallinje och storleksordning inom ämnesområdet tal i decimalform. Syftet för studien är att genom en läromedelsanalys undersöka vilka aspekter av missuppfattningar som motverkas i fyra olika läromedel för den svenska årskursen 5. Ett konceptuellt ramverk används i studien där begrepp sammanlänkas för att förstå ett fenomen, som i denna studie avser missuppfattningar. Metoden som har använts är läromedelsanalys där det genomförts både kvantitativa och kvalitativa analyser av läromedel. De läromedel som har analyserats i studien är: Mitt i Prick Matematik 5A, Koll på Matematik 5A, Matte Direkt-Borgen 5B och Pixel Matematik 5A. Resultatet visar en variation av erbjudanden där samtliga läromedel motverkar missuppfattningar gällande tal i decimalform i olika utsträckning. En slutsats utifrån studien är att läromedel kan vara en möjlig resurs för arbete med tal i decimalform men förutsätter ämnesdidaktiskt medvetna lärare i undervisningen. / The study deals with misconceptions connected to the three concepts place value, order of magnitude and number line in the mathematical field of decimal numbers. The purpose of the study is to investigate, through a learning material analysis, which aspects of misconceptions that are counteracted. The learning material analysis is based on four different learning materials for the Swedish grade 5. A conceptual framework is used in the study where concepts are linked together to understand a phenomenon, in this study misconceptions. The method that has been used is learning material analysis where both quantitative and qualitative analysis of learning materials have been done. The learning materials that have been analysed are: Mitt i Prick Matematik 5A, Koll på Matematik 5A, Matte Direkt-Borgen 5B and Pixel Matematik 5A. The result shows that all teaching materials contributes to counteractions of misconceptions in different ways. A conclusion based on the study shows that teaching materials are a possible resource for the education of decimal numbers in combination with didactical knowledge.
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Representações dos números racionais e a medição de segmentos: possibilidades com tecnologias informáticasLima, Claudio Woerle [UNESP] 01 April 2010 (has links) (PDF)
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lima_cw_me_rcla.pdf: 3093037 bytes, checksum: 82ceff562d5a32cc23b45ec23e51ab60 (MD5) / See-Sp / Essa pesquisa investiga as contribuições que a exploração dos números racionais como medidas de segmentos, em um programa de geometria dinâmica, podem trazer ao entendimento de frações, decimais e da reta numérica entre outras representações dos racionais. A pesquisa se fundamenta em evidências históricas e resultados de pesquisas que mostram a importância do significado de medida para o entendimento dos números. Através das tecnologias informáticas viu-se uma alternativa para a exploração da medida de segmentos. Essa pesquisa é baseada no processo de medição de segmentos, em teorias sobre visualização, experimentação e representações múltiplas. Também se inspira em preceitos construcionistas. Essa investigação qualitativa se baseou na metodologia de experimentos de ensino, em que foram formados dois grupos com alunos de 6ª série / 7º ano do ensino fundamental de uma escola pública estadual do interior de São Paulo. Esses grupos participaram de encontros em que foram desenvolvidas atividades que envolviam: divisão de segmentos; frações como medidas de segmentos; operações de adição e subtração de frações utilizando os segmentos; processo de medição para criação dos números decimais; relações entre decimais e frações; adição e subtração dos números decimais; adição e subtração de frações e decimais. As atividades realizadas se basearam nos recursos de visualização e experimentação proporcionadas pelo software de geometria dinâmica Régua e Compasso. O trabalho evidenciou a importância da aprendizagem das representações múltiplas dos números racionais e como as tecnologias informáticas (computadores, software de geometria e calculadoras) podem atuar nessa aprendizagem. A pesquisa também evidência que a utilização de recursos tecnológicos pode modificar a matemática da sala de aula, proporcionando aos estudantes... / This research investigates the contributions that the exploration of rational numbers as measure of segments, using geometry dynamic software, can introduce into the understanding of fractions, decimal numbers and the number line, amongst other rational number representations. The research is motivated by both historical evidence and evidence from the research literature showing the importance of the measure meaning to the understanding of rational numbers. Digital technologies offer an alternative method for the exploration of segments measure, as yet underexplored in the field of mathematics education. This research is based on an approach to numbers as measurements of segments, which draws from theories emphasizing the role of visualization, experimentation and multiple representations in mathematics learning. It is also inspired by a constructionist perspective. The qualitative investigation made use of the teaching experiment methodology, in that two groups were formed with students of 6th grade / 7th year within an elementary school of a public school in the state of São Paulo. These groups took part in research sessions where they developed activities that involve: division of segments; fractions as measure of segments; operations of addition and subtraction of fraction using segments; measurement for decimal numbers creation; relations between decimal numbers and fractions; addition and subtraction of decimal numbers; addition and subtraction of fractions and decimal numbers. The activities exploited the resources visualization and experimentation proportioned by the dynamic geometry software “Compass and Rule”. Analyses of the data collected pointed to the importance of the understanding of multiple representations for rational numbers and to the role that digital technologies (computers, geometry software and calculators) can play in this learning. This research, also, ... (Complete abstract click electronic access below)
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Representações dos números racionais e a medição de segmentos : possibilidades com tecnologias informáticas /Lima, Claudio Woerle. January 2010 (has links)
Orientador: Marcus Vinicius Maltempi / Banca: Marcelo de Carvalho Borba / Banca: Siobhan Victoria Healy / Resumo: Essa pesquisa investiga as contribuições que a exploração dos números racionais como medidas de segmentos, em um programa de geometria dinâmica, podem trazer ao entendimento de frações, decimais e da reta numérica entre outras representações dos racionais. A pesquisa se fundamenta em evidências históricas e resultados de pesquisas que mostram a importância do significado de medida para o entendimento dos números. Através das tecnologias informáticas viu-se uma alternativa para a exploração da medida de segmentos. Essa pesquisa é baseada no processo de medição de segmentos, em teorias sobre visualização, experimentação e representações múltiplas. Também se inspira em preceitos construcionistas. Essa investigação qualitativa se baseou na metodologia de experimentos de ensino, em que foram formados dois grupos com alunos de 6ª série / 7º ano do ensino fundamental de uma escola pública estadual do interior de São Paulo. Esses grupos participaram de encontros em que foram desenvolvidas atividades que envolviam: divisão de segmentos; frações como medidas de segmentos; operações de adição e subtração de frações utilizando os segmentos; processo de medição para criação dos números decimais; relações entre decimais e frações; adição e subtração dos números decimais; adição e subtração de frações e decimais. As atividades realizadas se basearam nos recursos de visualização e experimentação proporcionadas pelo software de geometria dinâmica "Régua e Compasso". O trabalho evidenciou a importância da aprendizagem das representações múltiplas dos números racionais e como as tecnologias informáticas (computadores, software de geometria e calculadoras) podem atuar nessa aprendizagem. A pesquisa também evidência que a utilização de recursos tecnológicos pode modificar a matemática da sala de aula, proporcionando aos estudantes ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research investigates the contributions that the exploration of rational numbers as measure of segments, using geometry dynamic software, can introduce into the understanding of fractions, decimal numbers and the number line, amongst other rational number representations. The research is motivated by both historical evidence and evidence from the research literature showing the importance of the measure meaning to the understanding of rational numbers. Digital technologies offer an alternative method for the exploration of segments measure, as yet underexplored in the field of mathematics education. This research is based on an approach to numbers as measurements of segments, which draws from theories emphasizing the role of visualization, experimentation and multiple representations in mathematics learning. It is also inspired by a constructionist perspective. The qualitative investigation made use of the teaching experiment methodology, in that two groups were formed with students of 6th grade / 7th year within an elementary school of a public school in the state of São Paulo. These groups took part in research sessions where they developed activities that involve: division of segments; fractions as measure of segments; operations of addition and subtraction of fraction using segments; measurement for decimal numbers creation; relations between decimal numbers and fractions; addition and subtraction of decimal numbers; addition and subtraction of fractions and decimal numbers. The activities exploited the resources visualization and experimentation proportioned by the dynamic geometry software "Compass and Rule". Analyses of the data collected pointed to the importance of the understanding of multiple representations for rational numbers and to the role that digital technologies (computers, geometry software and calculators) can play in this learning. This research, also, ... (Complete abstract click electronic access below) / Mestre
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