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.

This paper presents the results of a study of dyscalculia. It is a retrospective archival study implemented with a deductive approach. On the basis of established research and theory 18 analytical categories were formulated, before a deductive thematic analysis of empirical material, consisting of journal data of 17 students investigated for dyscalculia, 14 girls (82.4%) and 3 boys (17.6%). The purpose of this study was to investigate the relationship between the concepts formulated in research on dyscalculia and actual mathematical difficulties as those found in practice of students at school. All pupils had early and long-term difficulties with mathematics, while not showing any difficulties in other subjects. Most have had an unsatisfactory learning environment. All had normal intelligence but difficulty with certain cognitive, self-regulatory and linguistic features. Difficulties persisted despite numerous and protracted relief efforts at school. The study highlights that some difficulties are more prominent than others in connection with dyscalculia. This applies particularly to working memory, automation, activity control, spatial functions, certain linguistic abilities, concentration, and executive functions. Pedagogical action adaptation had been completed for most of the students but did not show to have any noticible effect. One question that requires further research would be “ why adaptation does not give the desired effect.” / I denna uppsats redovisas resultatet av en studie av dyskalkyli. Det är en retrospektiv arkivstudie med en deduktiv ansats som genomförts. Med utgångspunkt i etablerad forskning och teoribildning formulerades 18 analytiska kategorier, före en deduktiv tematisk analys, på ett empiriskt material bestående av journaldata för 17 elever utredda med avseende på dyskalkylidiagnos, 14 flickor (82,4 %) och 3 pojkar (17,6 %). Syftet med studien var att undersöka förhållandet mellan de begrepp forskningen formulerat om dyskalkyli och faktiska matematiksvårigheter så som sådana visar sig i praktiken hos elever i skolan. Samtliga elever hade tidiga och långvariga svårigheter i matematik, men vanligen inte i andra ämnen. De flesta hade haft en otillfredsställande inlärningsmiljö. Alla hade normal intelligens men svårigheter med vissa kognitiva, självreglerande och språkliga funktioner. Svårigheterna kvarstod trots många och långvariga hjälpinsatser i skolan. Studien lyfter fram att vissa svårigheter är mer framträdande än andra i samband med dyskalkyli. Det gäller framförallt arbetsminne, automatisering, aktivitetsreglering, spatiala funktioner, vissa språkliga förmågor, koncentration och exekutiva funktioner. Pedagogisk åtgärdsanpassning hade genomförts för de flesta av eleverna men verkade inte ha haft någon större effekt. Varför åtgärdsanpassning inte ger avsedd effekt är ett problem som behöver undersökas vidare.

The purpose of the present thesis was to test and contrast hypotheses about the cognitive conditions that support the development of mathematical learning disability (MLD). Following hypotheses were tested in the thesis: a) domain general deficit, the deficit is primarily located in the domain general systems such as the working memory, b) number sense deficit, the deficit is located in the innate approximate number system (ANS), c) numerosity coding deficit, the deficit is located to a exact number representation system, d) access deficit, the deficit is in the mapping between symbols and the innate number representational system (e.g., ANS), e) multiple deficit hypothesis states that MLD could be related to more than one deficit. Three studies examined the connection between cognitive abilities and arithmetic. Study one and three compared different groups of children with or without MLD (or risk of MLD). Study two investigated the connection between early number knowledge, verbal working memory and the development of arithmetic ability. The results favoring the multiple deficit hypothesis, more specifically the result indicate that number sense deficit together with working memory functions constitutes risk-factors to the development of MLD in children. A simple developmental model that is based on von Asters and Shalev´s (2007) model and the present results is suggested, in order to understand the development of MLD in children. / Avhandlingens syfte var att testa och kontrastera hypoteser om vilka kognitiva förutsättningar som är centrala för utvecklandet av matematiska inlärningssvårigheter (MLD) hos barn. De hypoteser som prövas i avhandlingen är följande: a) den domängenerella hypotesen, detta innebär att den förmodade störningen/nedsättningen finns primärt i barnets generella förmågor, främst då i arbetsminnes funktioner. b) en nedsättning i den medfödda approximativa antalsuppfattningen. c) nedsättning i den exakta antalskodningen. d) nedsättning gällande kopplingen mellan den kulturellt betingande symboliska nivå (räkneord och siffror) samt den medfödda antalsuppfattningen (eller antalskodningen). e) slutligen prövas även hypotesen att MLD kan härröras från flera nedsättningar i dessa förmågor. I tre studier undersöktes kopplingen mellan kognitiva förmågor och aritmetik. i studie1 och 3 jämfördes grupper av barn med MLD (eller risk för MLD) med grupper av barn som inte hade MLD i studie 2 undersöktes kopplingen mellan förmågorna verbalt arbetsminne och tidig sifferkunskap samt tidig aritmetiskförmåga. Sammantaget indikerar resultaten från denna avhandling att det kan vara både multipla och enstaka kognitiva förmågor, primärt i den approximativa antalsuppfattningen samt i arbetsminnesfunktioner, som kan fungera som riskförutsättningar för utvecklande av MLD hos barn. Dock måste dessa förmågor samspela med andra faktorer som kan fungera kompensatoriskt eller riskhöjande för utvecklandet av MLD. En förenklad utvecklingsmodell med utgångspunkten i resultaten från studierna samt von Asters och Shalevs (2007) modell föreslås. Syftet med modellen är att den ska kunna användas som teoretiskt ramverk för att förstå utvecklingen av MLD hos barn.

Os fatores genéticos e hereditários têm ganhado um foco especial como causa da dislexia, entretanto, há muito a ser estudado na busca de sua etiologia. Há vasta literatura associando o processamento fonológico ao aprendizado da leitura e escrita, porém pouco é investigado sobre a participação do processamento visual nas habilidades de leitura. Atualmente, a relação entre processamento fonológico e matemática tem sido apontada nas publicações científicas, sendo ainda pouco estudada, havendo necessidade de melhor compreensão entre a relação dessas habilidades, bem como as comorbidades entre dislexia e problemas na matemática. Este estudo teve como objetivo geral descrever o perfil endofenótipo dos sujeitos com dislexia referente à hereditariedade e influência do processamento fonológico e memória sequencial visual nas dificuldades da linguagem escrita e na matemática, no intuito de identificar semelhanças e diferenças no processamento da informação escrita entre indivíduos com dislexia e bons leitores. Participaram 35 indivíduos com o diagnóstico de dislexia e 46 bons leitores, de 8 a 13 anos e ambos os sexos. Nos dois grupos foram avaliadas as habilidades do processamento fonológico (consciência fonológica, acesso ao léxico e memória de trabalho fonológica), leitura de palavras, pseudopalavras, compreensão de texto, escrita e habilidades matemáticas. As habilidades do processamento fonológico e memória visual foram correlacionadas com a leitura, escrita e matemática nos dois grupos. Foi utilizado o Teste de Correlação de Pearson para correlacionar tais habilidades, e o Teste Qui-Quadrado e Teste U de Mann-Whitney para comparar o desempenho entre os grupos, adotando-se nível de significância de 5%. Encontrou-se que o histórico familial de problemas de aprendizagem esteve presente em mais da metade do grupo com dislexia, demonstrando que este é um importante fator de risco. Os indivíduos com dislexia apresentam pior desempenho no processamento fonológico, porém houve um pequeno número de disléxicos que não apresentou alterações na consciência fonológica e no acesso ao léxico. Em relação à memória de trabalho fonológica, os indivíduos com dislexia apresentaram pior desempenho, no entanto, quase metade dos bons leitores também apresentaram esta habilidade alterada. A maioria dos disléxicos apresentou o perfil de alteração nas três habilidades do processamento fonológico e um pequeno grupo apresentou a consciência fonológica e o acesso ao léxico preservado. Não houve diferenças significantes entre os grupos quanto à memória visual. Grande parte dos disléxicos apresentou dificuldades em habilidades matemáticas, o que foi encontrado em um pequeno grupo de bons leitores. Este estudo encontrou comorbidade entre dislexia e dificuldades matemáticas em 83% dos casos, sendo esta uma prevalência acima do que é descrito na literatura. As trocas ortográficas do tipo substituição de letras que representam fonemas surdos e sonoros e inversões parece ser um perfil da ortografia dos disléxicos. As habilidades de consciência fonológica, acesso ao léxico e memória de trabalho fonológica mostraram maior correlação na leitura e na escrita no grupo com dislexia, sugerindo que o processamento fonológico passa a ter menor participação na leitura e na escrita na medida em que os indivíduos se tornam leitores fluentes. A memória visual correlaciona-se com a matemática nos dois grupos. / Genetic and hereditarity factors have gained a special focus as the cause of dyslexia, however, there is much to be studied in the search for its etiology. There is extensive literature linking phonological processing to reading and writing learning, but the participation of visual processing in reading skills is little investigated. Currently, the relationship between phonological processing and mathematics has been identified in scientific publications, but still scarcely studied, there is need for better understanding the relationship between these skills as well as the comorbidities between dyslexia and problems in mathematics. This study aimed to describe the endophenotype profile of the subjects with dyslexia related to hereditarity and influence of phonological processing and visual sequential memory difficulties in written language and mathematics, in order to identify similarities and differences in written information processing between individuals with dyslexia and good readers. Participated in the study 35 diagnosed with dyslexia and 46 good readers, from 8 to 13 years old, both genders. Both groups were assessed the phonological processing skills (phonological awareness, lexical access and phonological working memory), words and pseudo words reading, reading comprehension, writing and math skills. The skills of phonological processing and visual memory were correlated with reading, writing and math in both groups. It was used the Pearson\'s Correlation Test to correlate these skills, and the Chi-square Test and Mann-Whitney Test to compare the performance between the groups, adopting a significance level of 5%. Family history of learning problems was present in more than half of the group with dyslexia, demonstrating that this is an important risk factor. Individuals with dyslexia performed worse in the phonological processing, but there was a small number of dyslexics that showed no alterations in phonological awareness and lexicon access. Regarding phonological working memory, individuals with dyslexia presented worse performance, however, nearly half of good readers also had this ability altered. Most dyslexics presented the profile of alterations in the three phonological processing skills and a small group presented phonological awareness and lexicon access preserved. There were no significant differences between groups as regards the visual memory. Much of dyslexics had difficulties in math skills, which were found in a small group of good readers. This study found comorbidity between dyslexia and mathematical difficulties in 83% of cases, which is a prevalence higher than what is described in the literature. Spelling exchanges like replacing letters that represent voiced and unvoiced phonemes and inversions appears to be a profile of the spelling of dyslexic. The phonological awareness skills, lexical access and phonological working memory showed higher correlation in reading and writing in the group with dyslexia, suggesting that phonological processing is replaced by lower participation in reading and writing insofar as individuals become fluent readers. The visual memory correlates with mathematics in both groups.

Inom forskningen råder stor oenighet angående vad som orsakar dyskalkyli och det används olika benämningar på liknande företeelser. Studiens övergripande syfte är därför att utifrån aktuell forskning om dyskalkyli undersöka vilka resultat som kan urskiljas samt undersöka i vilken grad man kan använda dessa i den dagliga verksamheten. Studien utgår ifrån två forskningsfrågor, ur vilka olika perspektiv beskrivs dyskalkyli i aktuell forskning, internationell såväl som svensk, samt vilka lämpliga och gynnsamma undervisningsmodeller rörande dyskalkyli rekommenderas av forskarna? För att besvara studiens frågeställningar har en litteraturstudie av nyare vetenskaplig forskning om dyskalkyli genomförts med blicken på vad som ligger bakom fenomenet, svårigheter vid kartläggning, samt att urskilja gynnsamma undervisningssätt för elever med dyskalkyli. Forskningsöversikten bygger på de forskare som varit mest aktiva och tongivande sedan decennieskiftet, detta för att ge en bild av dyskalkyli utgående från den senaste forskningen. Även vissa äldre arbeten nämns, då de hänvisas till i nyare arbeten. Studiens resultat tolkades och analyserades genom att använda systemteori samt Piagets utvecklingspsykologiska teori. Resultat visar att forskning om dyskalkyli genomförs i huvudsak från tre perspektiv, medicinskt, psykologiskt och pedagogiskt. Resultaten pekar på att det finns stor oenighet vad gäller forskningsinriktningar och intressen. Studien visar på några principer för undervisning av elever med dyskalkyli, vilka kan bli en vägledning för lärare. Fler konkreta pedagogiska exempel vilka bygger på vetenskapliga metoder, samt har prövats i verkligheten, behövs i framtiden. Resultaten visar att det finns ett behov av tvärvetenskaplig forskning för att kunna reda ut hur låga prestationer i matematik fastställs och förebyggs, samt vilken hjälp eleverna får i undervisningssituationen. Vidare kan man se att forskare är både positiva och negativa till begreppet dyskalkyli. Den övervägande delen av den forskningslitteraturen - såväl från det medicinska, psykologiska och pedagogiska området – nämner svårigheter i taluppfattning.

Dyskalkyli är en matematisk svårighet som innebär att individen har problem med aritmetik och att uppfatta siffror. Svårigheter i matematik uppträder olika hos individer och därav kan det vara svårt för läraren att upptäcka en elev i svårigheter. Forskningen är inte enig om begrepp och definitioner gällande matematiksvårigheter och dyskalkyli. Det är svårt att finna elever i matematiksvårigheter då det inte finns några tydliga kriterier för att diagnostisera dessa elever. Syftet med denna litteraturstudie att ta reda på vad forskningen säger om dyskalkyli och matematiksvårigheter. Därav kommer det undersökas varför elever drabbas av matematiksvårigheter samt hur dyskalkyli och matematiksvårigheter kan utmärka sig hos elever. I slutet av studien redovisas det resultat som framkommit i vår litteraturöversikt. Resultatet visar att svårigheter kan se ut på många olika sätt, därav är det svårt att finna elever i svårigheter. Svårigheterna kan bero på både inre och yttre faktorer, såsom stress eller ett bullrigt klassrum. Elever i svårigheter utmärker sig ofta tidigt och enligt forskning går det redan i förskoleåldern få syn på elever i matematiksvårigheter. Däremot anser forskare att begreppen matematiksvårigheter och dyskalkyli ska användas med försiktighet då det råder skilda åsikter kring hur svårigheterna ska definieras.

The purpose of this empirical study is to investigate special needs education teachers’ perception and knowledge before the concepts of mathematics difficulties and dyscalculia. We chose to emanate from three main questions. What meaning do the concepts of math difficulties and dyscalculia have for special needs education teachers? What do special needs education teachers think about the actuality regarding dyscalculia? What are the different approaches implemented by special needs education teachers towards mathematics difficulties and dyscalculia? Qualitative interviews were chosen as method because we believe that a survey would be too shallow and statistical. Responses may be too monotonous and short. By selecting interview as an information retrieval method gives us the opportunity to go more in depth with the help of supplementary questions, personal interaction and observation of the interviewee. The special needs education teachers we interviewed mostly agree with one another, however sometimes their perceptions differed which has led to an interesting and nuanced result. The result has given us many different approaches and beliefs facing difficulties in mathematics and dyscalculia, these makes us better equipped for our future students with difficulties in math. A definite conclusion from this study is that all our respondents jointly agreed that use of exploratory practical material and group works were suitable towards students with dyscalculia or math difficulties.

Diagnosen dyskalkyli är en av flera orsaker till varför en elev kan hamna i svårigheter inom matematik. Dyskalkyli påverkar förmågan att lära sig samt utföra specifika aritmetiska operationer. Trots att det kan finnas så många som en elev per klass som är diagnostiserade med dyskalkyli, är lärares kunskaper bristfälliga och forskningen är begränsad, vilket leder till en komplex undervisningssituation. Syftet med denna litteraturstudie är att sammanställa vad tidigare forskning säger om hur lärare kan stötta elever med diagnosen dyskalkyli. Studien är baserad på en systematisk litteraturstudie och materialet samlades in via databasen ERIC (EBSCO). Resultatet visar att det ger positiva effekter när undervisningen struktureras på ett varierat sätt för att stötta elever med diagnosen dyskalkyli. Digitala verktyg och instruerande strategier för lärande hade störst inverkan på utvecklingen av elevernas matematiska förmågor. Detta kan även ses utifrån ett individanpassat perspektiv där vikten ligger i att den enskilde eleven gynnas utifrån sina specifika behov. Lärarens roll är dessutom att göra matematiken attraktiv och intressant för att stärka självkänslan hos elever i svårigheter och bibehålla deras lust att lära. / Diagnosen dyskalkyli är en av flera bidragande faktorer som kan leda till att en elev stöter på svårigheter inom matematikområdet. Dyskalkyli påverkar förmågan att lära sig och utföra specifika aritmetiska operationer. Trots den potentiella närvaron av så många som en elev per klass som diagnostiserats med dyskalkyli, är lärarnas kunskaper bristfälliga och forskningen är begränsad, vilket resulterar i ett komplext utbildningsscenario. Denna litteraturstudie syftar till att sammanställa befintlig forskning om hur lärare kan stödja elever med diagnosen dyskalkyli. Studien bygger på en systematisk litteraturstudie och materialet har samlats in via databasen ERIC (EBSCO). Resultaten visar att en mångsidigt strukturerad undervisning för att stödja elever med diagnosen dyskalkyli har positiva effekter. Digitala verktyg och pedagogiska inlärningsstrategier hade störst inverkan på utvecklingen av elevernas matematiska förmågor. Detta kan också ses ur ett individualiserat perspektiv där tonvikten ligger på att tillgodose varje elevs specifika behov. Dessutom är lärarens roll att göra matematik tilltalande och engagerande för att stärka självkänslan hos elever som står inför utmaningar och för att upprätthålla deras entusiasm för lärande.

Approximately 5 to 14% of school age children are affected by mathematics learning disabilities. With the implementation of inclusion, many of these children are now being educated in the regular education class- room setting and may require additional support to be successful in algebra. Therefore, teachers need to know what interventions are available to them to facilitate the algebraic learning of students with mathemat- ics learning disabilities. This systematic literature review aims to identify, and critically analyze, interventions that could be used when teaching algebra to these students. The five included articles focused on interven- tions that can be used in algebra, specifically when solving equations. In the analysis of the five studies two types of interventions emerged: the concrete-representational-abstract model and graphic organizers. The concrete-representational-abstract model seems to show it can be used successfully in a variety of scenarios involving solving equations. The use of graphic organizers also seems to be helpful when teaching higher- level algebra content that may be difficult to represent concretely. This review discovered many practical implications for teachers. Namely, that the concrete-representational-abstract model of intervention is easy to implement, effective over short periods of time and appears to positively influence the achievement of all students in an inclusive classroom setting. The graphic organizer showed similar results in that it is easy to implement and appears to improve all students’ learning. This review provided a good starting point for teachers to identify interventions that could be useful in algebra; however, more research still needs to be done. Future research is suggested in inclusive classroom settings where the general education teacher is the instructor and also on higher-level algebra concepts.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-08-23T18:49:32Z No. of bitstreams: 1 2016 - M?nica Aparecida da Silva.pdf: 2434712 bytes, checksum: bf43f2692ace47e74176a777c1fa9ce7 (MD5) / Made available in DSpace on 2017-08-23T18:49:32Z (GMT). No. of bitstreams: 1 2016 - M?nica Aparecida da Silva.pdf: 2434712 bytes, checksum: bf43f2692ace47e74176a777c1fa9ce7 (MD5) Previous issue date: 2016-08-31 / CAPES / One of the challenges of today's education is to seek alternatives to quality education. Historically in Mathematics these results are not very good. In the search for causes, there are, among many others, the difficulties of learning, which reach a considerable number of students. Among these, it is possible to emphasize the Discalculia that is a specific difficulty of the area of Mathematics. Researching the subject, it is observed that such difficulty is little known by the teachers and, therefore, it is important to know it in order to help the learning of these students. Due to this scenario, the Discalculia theme was chosen as activity research, through which one can interact with the discalculic student. In order to investigate further the subject, a case study was conducted with a 3rd year elementary school student diagnosed with Dyscalculia, Dysshy and ADHD (Attention Deficit Hyperactivity Disorder) belonging to the Municipal Education Network of the city of Barra do Pira? in the state of Rio de Janeiro and a literature review analyzing some theories about learning, conceptualizing some learning difficulties and, more precisely, the Discalculia. Thus the research is applied and descriptive, having a qualitative approach, since it aims to detect the difficulties presented by a student diagnosed with Discalculia, analyzing possible advances in learning after analyzing the resolutions of the proposed activities. The activities carried out in this research were initiated through a diagnostic evaluation, to verify the prerequisites presented by the student. Games, play activities were carried out, some with concrete materials, tests, problem solving, which were researched and elaborated from researches on published works on the subject. In addition to the daily records, a final evaluation will be carried out to analyze the student's development. Interviews were carried out with people close to the student, such as his mother, a teacher of the 1st year in which he was retained, with the teacher of the Resource Room and the teacher of the years 2015 and 2016. The student in question had already Repeated twice in the first year and once in the second year, and since 2015 and at the moment, is interested in carrying out activities inside and outside the classroom, which is much facilitating its development, Which began with the approval in the 2nd year and performed satisfactorily in the 3rd year that is. / Um dos desafios da educa??o atual ? buscar alternativas para uma educa??o de qualidade. Historicamente em Matem?tica esses resultados n?o s?o muito bons. Na busca por causas, encontram-se, entre muitas outras, as dificuldades de aprendizagem, as quais atingem um n?mero consider?vel de estudantes. Dentre estas, pode-se destacar a Discalculia que ? uma dificuldade espec?fica da ?rea de Matem?tica. Pesquisando sobre o assunto, observa-se que tal dificuldade ? pouco conhecida pelos professores e, portanto, ? importante conhec?-la para poder auxiliar a aprendizagem destes alunos. Devido a este cen?rio, o tema Discalculia foi escolhido como pesquisa de atividades, atrav?s das quais pode-se interagir com o aluno discalc?lico. Para buscar um aprofundamento do assunto, foi realizado um estudo de caso com um aluno do 3? ano do Ensino Fundamental diagnosticado com Discalculia, Disgrafia e TDAH (Transtorno de D?ficit de Aten??o e Hiperatividade) pertencente ? Rede Municipal de Educa??o da cidade de Barra do Pira? no estado do Rio de Janeiro e um levantamento bibliogr?fico analisando algumas teorias sobre aprendizagem, conceituando algumas dificuldades de aprendizagem e, mais precisamente, a Discalculia. Assim a pesquisa ? aplicada e descritiva, tendo uma abordagem qualitativa, pois tem como objetivo detectar as dificuldades apresentadas por um aluno diagnosticado com Discalculia, analisando poss?veis avan?os na aprendizagem ap?s an?lise das resolu??es das atividades propostas. As atividades realizadas nesta pesquisa foram iniciadas atrav?s de uma avalia??o diagn?stica, para verificar os pr?-requisitos apresentados pelo aluno. Foram realizados jogos, atividades l?dicas, alguns com materiais concretos, testes, resolu??o de quest?es, os quais foram pesquisados e elaborados a partir de pesquisas em trabalhos publicados sobre o assunto. Al?m dos registros di?rios, ser? realizada uma avalia??o final para an?lise do desenvolvimento do aluno pesquisado. Foram realizadas entrevistas com as pessoas pr?ximas ao aluno, tais como sua m?e, uma professora do 1? ano, no qual foi retido, com a professora da Sala de Recursos e a professora dos anos de 2015 e 2016. O aluno em quest?o j? havia repetido por duas vezes o 1? ano e uma vez o 2? ano, e desde o ano de 2015 e no momento, encontra-se interessado na realiza??o de atividades dentro e fora de sala de aula, o que muito est? facilitando seu desenvolvimento, que se iniciou com a aprova??o no 2? ano e realiza??o de modo satisfat?rio no 3? ano que se encontra.