Pupils' difficulties in solving selected word problems from TIMSS research. (Diploma Thesis.) Abstract The theoretical part of the diploma thesis describes international comparative surveys, namely PISA and TIMSS, and analyses results of Czech pupils. Some areas are distinguished in which our pupils were unsuccessful and from them, the area of word problems and their mathematisation was selected for further work. Next, a solving strategy is characterised and some relevant research from this area is given. The core of the work lies in the experimental part whose goal was to find out what strategies pupils use when solving selected problems from TIMSS research and why they fail in them, via the analysis of pupils' written solutions complemented by interviews with them. Causes of failure of our pupils in these problems in TIMSS 2007 are looked for in mistakes pupils make, while it is also followed in what phase of the solving process they appear. The participants of research were pupils of Grade 9 of a primary school who solved three selected word problems from TIMSS research. Their written solutions were complemented by interviews with the experimenter focused on their mistakes and lack of clarity of the solutions. Four pupils participated in a pilot study. The atomic analysis of their solutions confirmed...

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No. of bitstreams: 1 PDF - Tiêgo dos Santos Freitas.pdf: 4205398 bytes, checksum: 7984a99df7362d4303051b595948b58f (MD5) Previous issue date: 2015-04-24 / In this study we will try to explain the difficulties of the students before the set of mathematical problems, in particular the obstacles in understanding both their Mother Tongue and the Mathematical Language, and the influence of them in the mathematical problem solving process. For the foundation of this study, we conducted a literature review on national studies that have addressed this question in order to understand what they point out about the issue of reading and interpretation problems in Mathematics classes. The researches point out to a lack of an adequate job with the issue of reading and interpretation of texts in Mathematics classes, in a context where this work is only restricted to teachers of Portuguese Language, which, of course, is not enough, since the preoccupation concerning the issue of reading and interpretation should be given in all subjects, especially in Mathematics classes, given the specificities of this area of knowledge. So based on several researches about this subject, we could see the need in try to understand the difficulties that the students of the first year of high school have before the statements of mathematical problems regarding Mother Language and Mathematics Language, as well as the influence of these languages in the process of problem solving, since most of the surveyed research was located in Elementary Education I and II. The research was developed in three steps: application of a previous questionnaire, application of a list of problems, and didactic intervention. The intervention was developed in a regular class of the first year of high school, in a public school of Paraíba state network, where the work consists in 15 questions, within a period of 10 meetings. The research is qualitative (SAMPIERI, COLLADO AND LUCIO 2013; STAKE, 2011), in the pedagogical research mode (LANKSHEAR AND KNOBEL, 2008). In some of the obtained results it was possible to highlight the limited vocabulary used by the students, before the lack of several words, whether Mother Language or Mathematics Language, written with many spelling and grammatical errors, a weak argument, while they also have difficulties in various mathematical knowledge series earlier, mainly in fraction, algebra and in the understanding of different words that have a frequently use in the mathematical Language (perimeter, consecutive numbers, folded, progression ) as well as in their Mother Tongue. / No presente trabalho buscamos identificar e analisar as dificuldades dos alunos diante dos enunciados de problemas matemáticos, em especial os obstáculos no entendimento da Língua Materna, da Linguagem Matemática e a influência das mesmas no processo de resolução de problemas matemáticos. Para fundamentação de nosso estudo, realizamos uma revisão bibliográfica de pesquisas nacionais que abordaram essa temática, a fim de compreender o que elas apontam sobre a questão da leitura e interpretação de problemas nas aulas de matemática. As investigações consultadas apontam para a falta de um trabalho adequado com a questão da leitura e interpretação de textos nas aulas de matemática, ficando esse trabalho restrito, apenas, aos professores de Língua Portuguesa, o que, evidentemente, não é suficiente, pois, a preocupação com a questão da leitura e interpretação deve se dar em todas as disciplinas, principalmente nas aulas de matemática, diante das especificidades dessa área de conhecimento. Assim, embasando-se nos diversos estudos consultados sobre a temática, verificamos a necessidade de buscar compreender as dificuldades que os alunos do primeiro ano do Ensino Médio apresentam diante dos enunciados de problemas matemáticos com relação ao entendimento da Língua Materna e da Linguagem Matemática, bem como, a influência dessas linguagens no processo de resolução de problemas, já que a maior parte das pesquisas consultadas situava-se no Ensino Fundamental I e II. A investigação foi desenvolvida em três etapas: aplicação de um questionário prévio, aplicação de uma lista de problemas e a intervenção didática. A intervenção foi desenvolvida em uma turma regular de primeiro ano do Ensino Médio, em uma Escola Pública da Rede Estadual da Paraíba, consistindo no trabalho com 15 questões, durante 10 encontros. A pesquisa é de caráter qualitativo (SAMPIERI, COLLADO E LUCIO 2013; STAKE, 2011), na modalidade de pesquisa pedagógica (LANKSHEAR E KNOBEL, 2008). Entre os resultados obtidos destacamos o vocabulário limitado dos alunos diante do desconhecimento de diversas palavras, sejam elas da Língua Materna ou da Linguagem Matemática, escrita com diversos erros ortográficos e gramaticais, argumentação frágil, bem como dificuldades em diversos conhecimentos matemáticos de séries anteriores, principalmente fração e álgebra e entendimento de palavras recorrentes na Linguagem Matemática (perímetro, números consecutivos, dobrado, progressão) e na Língua Materna.

Made available in DSpace on 2016-04-28T19:33:54Z (GMT). No. of bitstreams: 1 Isabele Veronese.pdf: 48942048 bytes, checksum: 6f99b8572880482c160bf6d09af02e2a (MD5) Previous issue date: 2015-02-05 / Considering that is common toal location of students' difficulties in solving problems to the inability to read; there are studies that point to the relationship between reading and solve problems, and the formation of problems player requires specific strategies to approach these texts in the classroom, we aim in this research was to analyze the text plan and textual sequences of math problems to verify the predominant text marks in these texts that can contribute tothe development of reading strategies appropriate to these texts.Therefore, based on Adam's studies (2004, 2011), Marquesi (2004 ) and Travaglia (1991, 2007) on text plan, textual sequences and text types, we analyzed tenmath problems proposed for students from 5th grade of elementary school in Five text books of great national movement, namely: 1) A conquista da Matemática, da editora FTD; 2) Matemática Pode contar comigo, da editora FTD; 3) Saber Matemática, da editora FTD; 4) Projeto Buriti Matemática, da editora Moderna; 5) Asas para voar Matemática, da editora Ática. Based on these analyzes, we discuss the regular text marks and high light text plan and textual sequences present in the texts of math problems / Considerando-se que é comum a atribuição das dificuldades dos alunos em resolver problemas à inabilidade de leitura; que estudos apontam para as relações entre ler e resolver problemas, e que a formação do leitor de problemas requer estratégias específicas de abordagem desses textos na sala de aula, temos por objetivo, nesta pesquisa, analisar o plano de texto e as sequências textuais dos problemas de matemática, a fim de verificar as marcas textuais preponderantes nesses textos que podem contribuir para a elaboração de estratégias de leitura adequadas a esses textos. Para tanto, tomando por base os estudos de Adam (2004, 2011), Marquesi (2004) e Travaglia (1991, 2007) acerca de plano de texto, sequências textuais e tipologias textuais, analisamos dez problemas de matemática propostos para alunos de 5o ano do ensino fundamental, em cinco livros didáticos de grande circulação nacional, quais sejam:1) A conquista da Matemática, da editora FTD; 2) Matemática Pode contar comigo, da editora FTD; 3) Saber Matemática, da editora FTD; 4) Projeto Buriti Matemática, da editora Moderna; 5) Asas para voar Matemática, da editora Ática. A partir dessas análises, discutimos as marcas textuais regulares e destacamos o plano de texto e as sequências textuais presentes nos textos dos problemas de matemática

Vi som har skrivit arbetet har haft olika erfarenheter kring läsning av matematiska textuppgifter. Intresset växte, då vi blev intresserade kring varför det kan vara svårt att läsa en matematisk text. Syftet med studien är att undersöka hur elevers läsförståelse binds samman med läsning av matematiska textuppgifter samt se vilka inre och yttre faktorer som påverkar förståelsen. Kvalitativa intervjuer tillsammans med en kombination av fallstudier och observationer ligger till grund för metoden som använts i studien. I undersökningen deltog 63 elever och fyra lärare. Totalt gjordes studien i fyra klasser, varav två klasser i årskurs 2 och två i årskurs 3. Resultatet visar att många elever blev oroliga över att se textuppgifterna. En del av eleverna visade ett engagemang för att klara uppgifterna, men uppgifternas struktur och nivå var allt för krävande för dem. Pedagogerna i intervjun är övertygade om att för lite kunskap kring ämnet och stress är bidragande orsaker till att matematikförståelsen hämmas vid läsning av matematiska textuppgifter. Slutsatsen är att det är svårt med läsning av matematiska textuppgifter, och elever bör besitta en större kognitiv förmåga samt ha ett brett ordförråd för att kunna förstå matematiska texter. Textens struktur spelar roll vid förståelse, och det är pedagogens ansvar att hjälpa eleverna med matematiska textuppgifter.

Det råder en brist på en entydig definition av begreppet taluppfattning som är grunden för all matematik. Genom att veta vilka vanligt förekommande problem som finns inom ett ämne kan lärare förebygga problem och främja förståelse. Den här systematiska litteraturstudien syftar därmed till att sammanställa hur begreppet taluppfattning definieras inom forskning, samt undersöka vilka återkommande problem som enligt forskning finns inom taluppfattning i årskurs F-3. Genom en systematisk litteratursökning har relevant litteratur valts ut och granskats med hjälp av en innehållsanalys. Resultatet visar att det finns många skilda definitioner av taluppfattning som i denna studie sammanställs till 13 olika aspekter. Definitionerna skiljer sig beroende på vilket teoretiskt perspektiv utvald forskning använder sig av, samt vilken ålder utvalda forskare utgår ifrån i definition av begreppet. Resultatet visar även brist på forskning kring återkommande problem inom taluppfattning. Trots spekulationer är det inte möjligt att redogöra vilka vanliga problem som finns inom taluppfattning med anledning av brist på tidigare forskning.

Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa ett matematiskt problem. Vi genomförde en observation och nio individuella intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i yttre och inre representationer. Strategier som bilder, grafiska framställningar och matematiska symboler (siffror) hör till de yttre representationerna, då de består av konkreta bilder som eleverna måste se framför sig på papper när de löser matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är samtliga strategier som tillhör de inre representationsformerna. Med inre representationer menar vi det som sker i huvudet, det eleverna inte behöver se framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än väljer till sin problemlösning är det oundvikligt att använda sig av någon form av inre representationsform, för att tänka måste alla göra oberoende av vilken lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde individens behov. / The purpose of the study was to discern which strategies pupils employ when they solve a mathematical problem. We carried through one observation and nine individual interviews with pupils in school year 3. They were asked to solve a mathematical problem, which was observed. On the basis of the pupils’ solutions, we carried out interviews in order to determine which strategies they chose to employ. The outcome of the pupils’ solutions showed several problem solving strategies. These were divided into external and internal representations. Strategies such as pictures, graphs and mathematical symbols (numerals) are external representations, as they consist of concrete pictures that the pupils must see in front of them on a paper when solving mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all strategies that belong to internal modes of representation. With internal representations, we mean what happens inside our heads – what pupils need not see in front of them in order to solve a problem. We found that the pupils’ solutions contained combinations of several different strategies. Irrespective of which strategy or strategies the pupil choose in his or her problem solving, it is inevitable to use some variety of internal representations; everyone has to think, regardless of the strategy chosen and the problem solving skills of the pupil. When pupils are young, it may be difficult for them to present the flow of their problem solving processes in writing. Consequently, as teachers we must have time to familiarize ourselves with how the pupil thinks in order to develop our teaching on the basis of the needs of the individual pupil.

<p>Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa</p><p>ett matematiskt problem. Vi genomförde en observation och nio individuella</p><p>intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som</p><p>observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att</p><p>ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av</p><p>elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i</p><p>yttre och inre representationer. Strategier som bilder, grafiska framställningar och</p><p>matematiska symboler (siffror) hör till de yttre representationerna, då de består av</p><p>konkreta bilder som eleverna måste se framför sig på papper när de löser</p><p>matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är</p><p>samtliga strategier som tillhör de inre representationsformerna. Med inre</p><p>representationer menar vi det som sker i huvudet, det eleverna inte behöver se</p><p>framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll</p><p>kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än</p><p>väljer till sin problemlösning är det oundvikligt att använda sig av någon form av</p><p>inre representationsform, för att tänka måste alla göra oberoende av vilken</p><p>lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När</p><p>eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur</p><p>lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur</p><p>eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde</p><p>individens behov.</p> / <p>The purpose of the study was to discern which strategies pupils employ when they solve</p><p>a mathematical problem. We carried through one observation and nine individual</p><p>interviews with pupils in school year 3. They were asked to solve a mathematical</p><p>problem, which was observed. On the basis of the pupils’ solutions, we carried out</p><p>interviews in order to determine which strategies they chose to employ. The outcome of</p><p>the pupils’ solutions showed several problem solving strategies. These were divided</p><p>into external and internal representations. Strategies such as pictures, graphs and</p><p>mathematical symbols (numerals) are external representations, as they consist of</p><p>concrete pictures that the pupils must see in front of them on a paper when solving</p><p>mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all</p><p>strategies that belong to internal modes of representation. With internal representations,</p><p>we mean what happens inside our heads – what pupils need not see in front of them in</p><p>order to solve a problem. We found that the pupils’ solutions contained combinations of</p><p>several different strategies. Irrespective of which strategy or strategies the pupil choose</p><p>in his or her problem solving, it is inevitable to use some variety of internal</p><p>representations; everyone has to think, regardless of the strategy chosen and the</p><p>problem solving skills of the pupil. When pupils are young, it may be difficult for them</p><p>to present the flow of their problem solving processes in writing. Consequently, as</p><p>teachers we must have time to familiarize ourselves with how the pupil thinks in order</p><p>to develop our teaching on the basis of the needs of the individual pupil.</p>

Le Programme de formation de l’école québécoise situe l’élève au cœur de ses apprentissages. L’enseignant peut faciliter le développement des compétences en offrant une rétroaction permettant à l’élève de progresser dans ses apprentissages. Il est difficile pour les enseignants de faire des annotations pertinentes et efficaces en mathématique, car l’accent est mis sur le concept travaillé et non sur la démarche mathématique. C’est pourquoi, nous avons porté notre regard sur l’incidence que peut avoir l’enseignement explicite des stratégies ainsi que sur les annotations faites par l’enseignant sur les copies des élèves en ce qui a trait au développement de leurs compétences à résoudre des problèmes complexes en mathématique. Nous avons opté pour une recherche qualitative et collaborative pour vivre un échange avec l’enseignant et vivre une interinfluence entre le praticien et le chercheur. La qualité des sujets a été favorisée. La technique d’échantillonnage retenue pour le choix de l’enseignant a été celle de cas exemplaires, tandis que celle que nous avons choisie pour les élèves était l’échantillonnage intentionnel critérié. La recherche a duré du mois de novembre au mois de mai de l’année scolaire 2008-2009. Comme instruments de cueillette de données, nous avons opté pour des entrevues avec l’enseignant et des mini-entrevues avec les élèves à deux moments de la recherche. Nous avons consulté les travaux corrigés des élèves dans leur portfolio. Notre étude fait ressortir l’apport de l’enseignement stratégique de la démarche mathématique. Les résultats précisent que les annotations de type méthodologique ont été celles qui ont été les plus utilisées et ont permis une meilleure compréhension chez l’élève. De plus, elles favorisent le transfert d’une situation à l’autre et permettent à l’élève d’obtenir de meilleurs résultats. / The Programme de formation de l’école québécoise (PFEQ) places the student in the center of his learning. The teacher can facilitate the development of the student’s skills by offering a feedback that allows the student to progress in his learning. It is difficult for the teacher’s to make relevant and effective annotations in math, because the emphasis is placed on the concept that was worked on and not on the mathematical process. This is the reason why we decided to concentrate our research on the incidence the teacher’s annotations can have on the development of the student’s mathematical skills. We opted for a qualitative and collaborative research to experiment an exchange with the teacher and live an inter influence between the practitioner and the researcher. The quality of the subjects was favoured. The teacher was chosen according to the sampling of exemplary case techniques and the students were chosen according to the intentional criteria sampling technique. The research lasted from november till may of the school year 2008-2009. Interviews with the teacher and mini interviews with the students at two moments of the research were used to collect data. We also consulted the corrected work placed in the pupil’s portfolios. Our study highlights the contribution of strategic teaching of the mathematical approach. The results specify that methodological annotation was mostly used and aims at a better understanding of the student. Furthermore, this type allows the transfer from a situation to another and allows the student to obtain better results.

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