<p>The purpose of my study is to investigate teachers’ opinions about learning difficulties in mathematics.</p><p>I have read relevant literature on this subject. I have conducted interviews with seven class teachers, one special-needs teacher, a psychologist and one special-needs teachers who specifically worked with investigations concerning pupils with difficulties in mathematics.</p><p>The result of my study shows that learning difficulties in mathematics can/might be prevented if children in pre-school are introduced to mathematics as early as possible. This should be done in a delightful way in their daily activities and while there are playing. I didn’t find any complete method to help children with mathematics difficulties in compulsory school. But a good teaching method is to vary the teaching, strengthen pupil’s self-confidence and “talk mathematics”. It is important to make mathematics more understandable.</p><p>One of my conclusions is that there is a lack of research about learning difficulties in mathematics. Another conclusion from the literature is that it is hard to distinguish between different kinds of difficulties in mathematics.</p> / <p>Syftet med min studie är att undersöka pedagogers syn på elevers matematiksvårigheter.</p><p>För att få svar på mina frågor har jag läst relevant litteratur i ämnet samt intervjuat sju lärare, en speciallärare samt utredningspersonal.</p><p>Resultatet av undersökningen visar att man redan i förskolan genom leken och i det vardagliga arbetet med barnen bör arbeta med matematik för att förebygga matematiksvårigheter. Jag fann ingen färdig metod att använda i grundskolan för att avhjälpa matematiksvårigheter. Det man kan göra är att variera undervisningen, stärka självförtroendet och samtala om matematik för att matematiken ska bli mer begriplig för elever med svårigheter.</p><p>En av mina slutsatser är att det saknas forskning om matematiksvårigheter. En annan slutsats är att det finns litteratur i ämnet men det är ändå svårt att skilja de olika matematiksvårigheterna åt.</p>

The purpose of my study is to investigate teachers’ opinions about learning difficulties in mathematics. I have read relevant literature on this subject. I have conducted interviews with seven class teachers, one special-needs teacher, a psychologist and one special-needs teachers who specifically worked with investigations concerning pupils with difficulties in mathematics. The result of my study shows that learning difficulties in mathematics can/might be prevented if children in pre-school are introduced to mathematics as early as possible. This should be done in a delightful way in their daily activities and while there are playing. I didn’t find any complete method to help children with mathematics difficulties in compulsory school. But a good teaching method is to vary the teaching, strengthen pupil’s self-confidence and “talk mathematics”. It is important to make mathematics more understandable. One of my conclusions is that there is a lack of research about learning difficulties in mathematics. Another conclusion from the literature is that it is hard to distinguish between different kinds of difficulties in mathematics. / Syftet med min studie är att undersöka pedagogers syn på elevers matematiksvårigheter. För att få svar på mina frågor har jag läst relevant litteratur i ämnet samt intervjuat sju lärare, en speciallärare samt utredningspersonal. Resultatet av undersökningen visar att man redan i förskolan genom leken och i det vardagliga arbetet med barnen bör arbeta med matematik för att förebygga matematiksvårigheter. Jag fann ingen färdig metod att använda i grundskolan för att avhjälpa matematiksvårigheter. Det man kan göra är att variera undervisningen, stärka självförtroendet och samtala om matematik för att matematiken ska bli mer begriplig för elever med svårigheter. En av mina slutsatser är att det saknas forskning om matematiksvårigheter. En annan slutsats är att det finns litteratur i ämnet men det är ändå svårt att skilja de olika matematiksvårigheterna åt.

<p>An increasing number of students leave the Swedish compulsory school without having a satisfactory grade in mathematics. Causes why students risk ending up with difficulties in the subject of mathematics are debated but one explanation might be that more and more students are diagnosed with dyscalculia. The purpose of this study is to investigate how educationalists identify and organize their teaching in order to help students with difficulties in mathematics to reach the schools requirement and long-term goals that are defined in advance. It is vital to detect learning difficulties at an early stage. Accordingly, it can be avoided that the student starts to develop a negative self-image due to repeated failures and in the same time provide relevant help. Educationalists working actively with teaching possess valuable knowledge that is presently well managed. However, there are many indications that the schools steadily reducing amount of resources will limit their efforts. My contribution is an attempt to elucidate this complex of problems that are part of the daily rounds of an educationalist and that have been debated profoundly during the last years. The studie is based in qualitative iterviews with teachers in compulsory shool and one special educationalist and the interwiews are, after compilation, compared with earlier research of difficulties in mathematics.</p>

<p>My purpose with this examination paper has been to inquire and make a contribution with knowledge about how teachers and remedial teachers work with children who has difficulties in mathematics.</p><p> </p><p>My specified question of issue was: How do teachers work with children who have difficulties in mathematics?</p><p> </p><p>My methods have been to read literature and to accomplish an examination by qualitative interviews with teachers and remedial teachers. My choice of methods has been contributing of me getting a good materiel about how teachers can work with children who has difficulties in mathematics. </p><p>The examination paper begins with the schools curriculum ”Lpo94” and definitions of difficulties in mathematics. Further the examination paper withholds charters of knowledge and capacity within mathematics, the learning process and different causes to difficulties in mathematics. Afterwards comes the primary part of the examination paper that withholds the teachers work, the educational contents, materiel and individualisation. Then comes the chapter of methods and the result of the inquire with the interview questions and answers. Afterwards comes an analyse of the inquires result and earlier research. The examination paper is completed with a discussion and a proposal to continued research.</p><p>My definitive conclusion is that teachers different work options like with elaborative materiel, solution of problems and words within mathematics, gives a better learning process and development for pupils with difficulties in mathematics. The teacher shall also adjust the educational contents too the pupils qualifications and needs.</p> / <p>Mitt syfte med examensarbetet har varit att undersöka och bidra med kunskap om hur lärare och speciallärare/specialpedagoger arbetar med barn som har matematiksvårigheter.</p><p> </p><p>Min preciserade frågeställning var: Hur arbetar lärare med barn som har matematiksvårigheter?</p><p> </p><p>Mina metoder har varit att läsa litteratur och att genomföra en undersökning som gjordes genom kvalitativa intervjuer med lärare och speciallärare. Mina metodval har bidragit till att jag fått ett bra material om hur lärare kan arbeta med barn som har matematiksvårigheter.</p><p>Examensarbetet inleds med skolan läroplan Lpo94 och definitioner av matematiksvårigheter. Vidare innehåller examensarbetet avsnitt om kunskap och förmåga inom matematik, inlärningsprocessen och olika orsaker till matematiksvårigheter. Sedan kommer examensarbetets huvudavsnitt som innehåller lärarens arbete, undervisningens innehåll, material och individualisering. Efter detta kommer metodkapitlet och resultatet av undersökningen med intervjufrågor och svar. Sedan kommer en analys av undersökningens resultat och tidigare forskning. Examensarbetet avslutas med en diskussion och förslag till fortsatt forskning.      </p><p> </p><p>Min slutsats är att lärarens olika arbetssätt som t.ex. med laborativa material, problemlösning och begrepp inom matematiken bidrar till en bättre inlärningsprocess och utveckling hos elever som har matematiksvårigheter. Läraren ska även anpassa undervisningens innehåll till elevens förutsättningar och behov.</p>

My purpose with this examination paper has been to inquire and make a contribution with knowledge about how teachers and remedial teachers work with children who has difficulties in mathematics.   My specified question of issue was: How do teachers work with children who have difficulties in mathematics?   My methods have been to read literature and to accomplish an examination by qualitative interviews with teachers and remedial teachers. My choice of methods has been contributing of me getting a good materiel about how teachers can work with children who has difficulties in mathematics.  The examination paper begins with the schools curriculum ”Lpo94” and definitions of difficulties in mathematics. Further the examination paper withholds charters of knowledge and capacity within mathematics, the learning process and different causes to difficulties in mathematics. Afterwards comes the primary part of the examination paper that withholds the teachers work, the educational contents, materiel and individualisation. Then comes the chapter of methods and the result of the inquire with the interview questions and answers. Afterwards comes an analyse of the inquires result and earlier research. The examination paper is completed with a discussion and a proposal to continued research. My definitive conclusion is that teachers different work options like with elaborative materiel, solution of problems and words within mathematics, gives a better learning process and development for pupils with difficulties in mathematics. The teacher shall also adjust the educational contents too the pupils qualifications and needs. / Mitt syfte med examensarbetet har varit att undersöka och bidra med kunskap om hur lärare och speciallärare/specialpedagoger arbetar med barn som har matematiksvårigheter.   Min preciserade frågeställning var: Hur arbetar lärare med barn som har matematiksvårigheter?   Mina metoder har varit att läsa litteratur och att genomföra en undersökning som gjordes genom kvalitativa intervjuer med lärare och speciallärare. Mina metodval har bidragit till att jag fått ett bra material om hur lärare kan arbeta med barn som har matematiksvårigheter. Examensarbetet inleds med skolan läroplan Lpo94 och definitioner av matematiksvårigheter. Vidare innehåller examensarbetet avsnitt om kunskap och förmåga inom matematik, inlärningsprocessen och olika orsaker till matematiksvårigheter. Sedan kommer examensarbetets huvudavsnitt som innehåller lärarens arbete, undervisningens innehåll, material och individualisering. Efter detta kommer metodkapitlet och resultatet av undersökningen med intervjufrågor och svar. Sedan kommer en analys av undersökningens resultat och tidigare forskning. Examensarbetet avslutas med en diskussion och förslag till fortsatt forskning.         Min slutsats är att lärarens olika arbetssätt som t.ex. med laborativa material, problemlösning och begrepp inom matematiken bidrar till en bättre inlärningsprocess och utveckling hos elever som har matematiksvårigheter. Läraren ska även anpassa undervisningens innehåll till elevens förutsättningar och behov.

An increasing number of students leave the Swedish compulsory school without having a satisfactory grade in mathematics. Causes why students risk ending up with difficulties in the subject of mathematics are debated but one explanation might be that more and more students are diagnosed with dyscalculia. The purpose of this study is to investigate how educationalists identify and organize their teaching in order to help students with difficulties in mathematics to reach the schools requirement and long-term goals that are defined in advance. It is vital to detect learning difficulties at an early stage. Accordingly, it can be avoided that the student starts to develop a negative self-image due to repeated failures and in the same time provide relevant help. Educationalists working actively with teaching possess valuable knowledge that is presently well managed. However, there are many indications that the schools steadily reducing amount of resources will limit their efforts. My contribution is an attempt to elucidate this complex of problems that are part of the daily rounds of an educationalist and that have been debated profoundly during the last years. The studie is based in qualitative iterviews with teachers in compulsory shool and one special educationalist and the interwiews are, after compilation, compared with earlier research of difficulties in mathematics.

The purpose of my examination work was to show the need for support for students with another mother-tongue than Swedish, so that these students would be able to get through mathematics tuition better. To achieve this purpose, I chose to start from the perspective that presented itself at interviews with two class teachers and two mother-tongue supervisors. I also chose to use the qualitative research interview as study method, as I tried to understand those informing me in a thorough and in-depth way. In my study I have had a sociocultural perspective as starting point where the conceptions teaching, language and communication, support and individualizing are central for the development of knowledge.  The questions for my study during this process were as follows:  What difficulties, according to the teachers interviewed can occur for second language students in mathematics?  What ways and methods of working do the teachers chosen give priority to, so that   the second language students` results in mathematics will improve?  The results from my interviews show that the difficulties with mathematics for second anguage students can be perceived as being dependent on a combination of reasons, where amongst other things language plays a central part. Difficulties can even arise when the students have other mathematical abilities from their own home environment. Another result shows that even the class teachers are of the opinion that there are difficulties to individualize the teaching in schools with large classes. This can possibly be interpreted that those large classes in the schools can be seen as the reason for the inadequate study results in mathematics, where the students are unable to understand sufficiently suited lessons. These difficulties do not arise for the mother tongue teachers as they sit with each student individually. From these results we see that even the class teachers and mother tongue tutors have different ways and methods of working with mathematic tuition to be able to improve the results in mathematics for second language students. The result of the study shows that all teachers are of the opinion that language is a tool, thus enabling the student to succeed in mathematics. However, there is disagreement between the class teachers and mother tongue tutors, as to whether it is the student’s knowledge of Swedish or their mother tongue that could best help them in their understanding of mathematics. The study also shows that the class teachers believe that it is important that the students are allowed to sit in groups with other students and interact. However, the mother tongue tutors believe that the communication between student and tutor is the most important as they sit with each student individually and believe that the students will develop better in this way. The result of the study also shows that all teachers believe that support and motivation is required for the students to develop. The class teachers also believe that even laboratory material is excellent support for students with difficulties and should be used in teaching. However, the mother tongue tutors believe that laboratory material is good support but say that it is better to work abstractly with mathematics. From the results I am able to see, that the class teachers and mother tongue tutors give priority to different ways and methods of working with mathematics to strengthen second language students.

O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.

O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.

O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.