<p>During my practice as a teacher trainee at an upper secondary school it became clear to me that many pupils had difficulties with mathematics. I was surprised to find that many pupils seemed to get stuck on the level of attainment for the senior level of the nine-year compulsory school. As I have not studied anything about difficulties in Mathematics during my training to become a qualified teacher, I would like to get to know more about this.</p><p>After studying research done on this subject I made the following approach to the problem:</p><p>• What fields regarding Mathematics do the pupils themselves find most difficult?</p><p>• What factors have been contributory causes to these problems?</p><p>• What are the factors that have helped pupils with difficulties in Mathematics to reach the goals for the syllabuses in Mathematics?</p><p>The answers to my questionnaire and interviews resulted in the following conclusions:</p><p>• Pupils find theory of equation and conversion of units as most difficult at senior level of the nine-year compulsory school.</p><p>• Teaching should be done in special instruction groups to give the pupil the opportunity to develop his/her skills on an individual level.</p><p>• Pupils find it hard to deal with all moments in Mathematics during the time given for each course.</p><p>• The pace for teaching Mathematics is too high according to the pupils.</p><p>• Pupils wish for instructions on a lower level.</p><p>• There is often a lack of contact between teacher and pupil.</p><p>• The teacher should use more time to help the pupil receive good self-confidence and increase the motivation for instructions in Mathematics.</p> / <p>Sammanfattning</p><p>Under mina praktikperioder på gymnasiet som lärarstudent kom jag i kontakt med många elever som hade det svårt med matematiken. Jag förundrades över att många elever verkade ha fastnat på högstadiets kunskapsnivå. Då jag inte har fått någon undervisning om elever med matematiksvårigheter i min lärarutbildning, vill jag lära mig mer om detta.</p><p>Efter litteraturstudier kom jag fram till följande problemformuleringar:</p><p>• Vilka områden inom matematiken tycker eleverna själva att de har problem med?</p><p>• Vilka faktorer har bidragit till dessa problem?</p><p>• Vilka är de faktorer som har hjälpt elever med matematiksvårigheter att nå kunskapsmålen i matematik?</p><p>Som svar på mina enkät- och intervjufrågor kom jag fram till följande:</p><p>• Eleverna upplever ekvationslösning och enhetsomvandlingar som svårast på</p><p>högstadiet.</p><p>• Undervisning bör ske i särskild undervisningsgrupp, för att ge eleven möjlighet att utvecklas på sin egen nivå.</p><p>• Eleverna upplever att de inte har nog med tid för att hinna klart momenten i matematikundervisningen.</p><p>• Eleverna menar att tempot i undervisningen är för högt.</p><p>• Eleverna vill ha undervisning på en lägre nivå.</p><p>• Relationen mellan lärare och elev är ofta bristfällig.</p><p>• Läraren ska lägga mer tid på att stötta elevens självkänsla och försöka öka dennes motivation till matematikundervisningen.</p>

During my practice as a teacher trainee at an upper secondary school it became clear to me that many pupils had difficulties with mathematics. I was surprised to find that many pupils seemed to get stuck on the level of attainment for the senior level of the nine-year compulsory school. As I have not studied anything about difficulties in Mathematics during my training to become a qualified teacher, I would like to get to know more about this. After studying research done on this subject I made the following approach to the problem: • What fields regarding Mathematics do the pupils themselves find most difficult? • What factors have been contributory causes to these problems? • What are the factors that have helped pupils with difficulties in Mathematics to reach the goals for the syllabuses in Mathematics? The answers to my questionnaire and interviews resulted in the following conclusions: • Pupils find theory of equation and conversion of units as most difficult at senior level of the nine-year compulsory school. • Teaching should be done in special instruction groups to give the pupil the opportunity to develop his/her skills on an individual level. • Pupils find it hard to deal with all moments in Mathematics during the time given for each course. • The pace for teaching Mathematics is too high according to the pupils. • Pupils wish for instructions on a lower level. • There is often a lack of contact between teacher and pupil. • The teacher should use more time to help the pupil receive good self-confidence and increase the motivation for instructions in Mathematics. / Sammanfattning Under mina praktikperioder på gymnasiet som lärarstudent kom jag i kontakt med många elever som hade det svårt med matematiken. Jag förundrades över att många elever verkade ha fastnat på högstadiets kunskapsnivå. Då jag inte har fått någon undervisning om elever med matematiksvårigheter i min lärarutbildning, vill jag lära mig mer om detta. Efter litteraturstudier kom jag fram till följande problemformuleringar: • Vilka områden inom matematiken tycker eleverna själva att de har problem med? • Vilka faktorer har bidragit till dessa problem? • Vilka är de faktorer som har hjälpt elever med matematiksvårigheter att nå kunskapsmålen i matematik? Som svar på mina enkät- och intervjufrågor kom jag fram till följande: • Eleverna upplever ekvationslösning och enhetsomvandlingar som svårast på högstadiet. • Undervisning bör ske i särskild undervisningsgrupp, för att ge eleven möjlighet att utvecklas på sin egen nivå. • Eleverna upplever att de inte har nog med tid för att hinna klart momenten i matematikundervisningen. • Eleverna menar att tempot i undervisningen är för högt. • Eleverna vill ha undervisning på en lägre nivå. • Relationen mellan lärare och elev är ofta bristfällig. • Läraren ska lägga mer tid på att stötta elevens självkänsla och försöka öka dennes motivation till matematikundervisningen.

The aim of this study is to explore the adult immigrant students’ experience of maths in Sweden. I will present an understanding rather than an explanation on how second language adult students learn maths. It can be argued that people who study maths as adults in a new homeland and in a foreign language face particular challenges. At the same time research reports that people sometimes approach the subject in a more fruitful way as adults compared to their childhood experiences. I want to contribute to the general knowledge of the subject and furthermore provide improved understanding of how mathematics teachers can guide their students towards their goals.I have performed semi-structured qualitative research interviews. My informants are my own maths students on the basic level with incomplete grades in maths from secondary school, or they have failed in their maths studies in upper secondary school due to a low level of know-ledge. They are over 20 years of age and they are all immigrants and have arrived in Sweden as adults. I have used my students statements, written as narratives as the material which is to be interpreted and understood. Because of my use of my own students in the interview, I will not take into account their statements about the teacher’s role in my conclusion.I find that:1. The difficult experience of being forced to leave the home country, together with a wish to take revenge on the failures from their youth, can lead to a kind of struggle for decom-pensation that can be reflected in the participants' positive evaluation of their maths studies.2. Having a family is a great motivational help for studying regardless of the time it takes to take care of the same.3. The memories of previous failures with the incomprehensible, abstract mathematics characterise the students’ inception of the subject.4. It seems possible that adult students can understand themselves in a new way and redefine their relationship with maths and their own ability to study the subject.

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No. of bitstreams: 1 josemarceloguimaraesvillar.pdf: 3124465 bytes, checksum: 287e4a96ec7d01d437b06c31b1b8bf42 (MD5) Previous issue date: 2017-06-28 / O presente trabalho, intitulado Discalculia na sala de aula de Matemática: um estudo de caso com dois estudantes, apresenta-se como um estudo preliminar dos aspectos neurológicos relacionados à dificuldade de aprendizagem na matemática, particularmente o distúrbio Discalculia. Primeiramente, elabora-se um questionário com docentes buscando investigar se os possíveis problemas na aprendizagem matemática se dão por fatores neurológicos. Após, é realizado outro questionário com profissionais da saúde procurando obter informações do processo de identificação, formas de tratamento, propostas de habilitação, orientações e propostas para o professor de matemática com o aluno discalcúlico. Por fim, dois alunos realizam um conjunto de exercícios problema, com intuito de identificar e reconhecer traços característicos da Discalculia, e atividades investigativas com perfil lúdico, utilizadas como ferramentas de intervenção pedagógica para reabilitar alunos com Discalculia e aqueles que apresentam problemas de aprendizagem na matemática. A análise buscou identificar as características ou sintomas por situação problema dentro do contexto de ensino. O estudo está fundamentado em leituras de vários teóricos, como Bastos (2008, 2016), Farrell (2008), Díaz (2011), Shalev et al. (2004, 2005, 2007), entre outros. A partir do questionário com os docentes, foi possível contatar que os mesmos, como não distinguem e nem reconhecem os termos dificuldades de aprendizagem, transtornos e distúrbios de aprendizagem, não foram capazes de identificar que as causas do déficit de aprendizagem na matemática também podem estar atribuídas às disfunções neurológicas, como é o caso do distúrbio de aprendizagem, a Discalculia. Já as especialistas reconheceram esse distúrbio, mas apontaram que esse tema ainda está em processo de pesquisa e que os problemas associados às dificuldades de aprendizagem, às vezes, são semelhantes e se sobrepõem, acarretando dificuldades na avaliação e identificação. A partir dos resultados obtidos das análises dos exercícios problemas, constatou-se que um dos alunos diagnosticado como discalcúlico apresentou fortes características de Discalculia. O outro, que não apresentava laudo, também apresentou traços significativos, surpreendendo. Importante salientar que esse resultado é inicial, havendo a necessidade de uma investigação com especialistas. Os resultados permitem afirmar também que os déficits apresentados nos sujeitos não foram necessariamente idênticos, mas qualitativamente diversificados. O estudo ressalta também a importância dos professores conhecerem as dificuldades dos alunos para que se tenha um planejamento e uma condução de ensino que corresponda aos mesmos. / This study, entitled Dyscalculia in the Mathematics classroom: a case study with two students, is presented as a preliminary study of the neurological aspects related to the difficulty of learning in mathematics, particularly the Dyscalculia disorder. Firstly, we made a questionnaire to teachers to investigate that it is possible problems in mathematical learning are due to neurological factors. After that, we made another questionnaire with health professionals, to get information on the identification process, treatment forms, habilitation proposals, guidelines and proposals for the math teacher with the dyscalculia student. Finally, two students perform a set of problem exercises in order to identify and recognize characteristic features of Dyscalculia, and research activities with a playful profile, used as pedagogical intervention tools to rehabilitate students with Dyscalculia and those with learning problems in mathematics. The analysis sought to identify the characteristics or symptoms by problem situation within the teaching context. The study is based on readings by several theorists, such as Bastos (2008, 2016), Farrell (2008), Díaz (2011), Shalev et al. (2004, 2005, 2007), Campos (2014), among others. From the questionnaire with the teachers, it was possible to contact them, as they do not distinguish and do not recognize the terms learning difficulties, disorders and learning disorders. Then, they were not able to identify that the causes of the learning deficit in mathematics can also be attributed to neurological dysfunctions, such as the learning disorder, Dyscalculia. Experts have acknowledged this disorder, but pointed out that this theme has still been in the process of researched and that problems associated with learning difficulties are sometimes similar and overlapping, leading to difficulties in evaluation and identification. From the results, that was obtained from the analyzes of the problem exercises, it was verified that one of the students diagnosed as dyscalculia presented strong characteristics of Dyscalculia. The other, which did not present an award, has also presented significant features, surprising. It is important to point out that this result is initial, and there is a need for an investigation with specialists. The results have also allowed us to affirm that the deficits presented in the subjects were not necessarily identical, but qualitatively diversified. The study has also highlighted the importance of teachers to know the difficulties of the students so that they have a planning and a teaching direction that corresponds to them.

Syftet med studien är att utveckla ett analytiskt ramverk som fungerar för analysering av 11 appar och kategorisera dem utifrån deras användbarhet i undervisningen av elever i matematiksvårigheter. Vilka undervisningsaspekter som valdes ut grundades på en anpassning för elever i svårigheter i matematik. Alla appar används av elever i förskoleklass eller grundskolan år 1-6. Det urval som gjorts för studien var appar som redan granskats av tidigare forskare. Aspekterna som valdes ut för studien var explicit undervisning, visuella representationer, belöningssystem och färdighetsträning. Apparnas möjlighet till explicit undervisning skapar förutsättningar för att eleverna ska bli självständiga och känna sig trygga. Visuella repesentationer presenterar om appen ger eleven ett bildligt verktyg för att kunna utveckla sitt lärande. Området belöningssystem i apparna erbjuder återkoppling och skapar förutsättningar till engagemang hos eleven. Om eleven får utöva färdighetsträning kommer arbetsminnet att stärkas och den matematiska förmågan att utvecklas. Det är viktigt att lösa många uppgifter för att nå djupare kunskaper i matematikämnet.  Studien resulterade i att det analytiska ramverket kan användas av lärare för att analysera vilka aspekter som ger ett fungerande stöd för elever i matematiksvårigheter, när de arbetar i den utvalda appen. / The purpose of the study is to develop and use an analytical framework that works for the analysis of 11 apps and categorize them based on their applicability in teaching students with mathdifficulties. Which teaching aspects were selected was based on an adaptation for students with difficulties years 1-6. The selection made for the study was apps that are already being reviewed by previous researchers. The aspects selected for the study were explicit teaching, visual representations, reward systems and skilling training. The apps opportunity for explicit teaching creates the condition for students to become independent and confident. Visual representations present whether the app gives the students a pictorial tool to be able to develop their learning. The area of rewards systems in the apps offers feedback and creates conditions for the students commitment. If the student is allowed to practice skills training, the working memory will be strengthened, and the mathematical ability will be developed. It is important to solve many tasks to reach deeper knowledge in the subject of mathematics. The study resulted in an analytical framework that provides a tool for teachers. The tool can be used when scrutinizing apps aiming for a functional support for students with mathematical difficulties.

Matematik har ett unikt ämnesspråk som elever behöver behärska både skriftligt som muntligt. Brister i den muntliga matematiska kommunikationsförmågan bidrar till att elever med matematiksvårigheter inte får godkänt betyg i matematik för årskurs 9. Dessa elever behöver hjälp och stöd från sin omgivning för att inte riskera att bli underkända. Denna studie har genomförts med syftet att skildra och analysera matematiklärares syn på stödjande faktorer för elever med matematiksvårigheter med fokus på den muntliga matematiska kommunikationsförmågan. Som metod har en innehållsanalytisk forskningsansats med induktiv tematiseringsmetodik använts och studien baseras på fem semistrukturerade intervjuer. Matematiklärares synsätt har bedömts vara möjliga att skildras och analyseras genom följande sex teman: 1. Balansen mellan muntlig och skriftlig kommunikation 2. Den muntliga kommunikationsförmågans beståndsdelar 3. Aktiviteter baserade på elevernas behov 4. Stödjande lärandemiljö för eleven 5. Elevens deltagande i matematiska diskussioner 6. Samarbete med föräldrar De intervjuade lärarna är eniga om att elever med matematiksvårigheter behöver anpassningar av innehåll och kunskapsmål för den muntliga matematiska förmågan. Det råder dock ingen enighet i lärares syn på adekvata mål och innehåll, utan detta anses vara ett resultat av en mängd faktorer såsom elevernas förkunskaper, lärares tolkning av läroplanen, den skriftliga tyngdpunkten i matematik, få bedömningsmoment för den muntliga förmågan, stress och tidsbrist samt den mindre bra tillgången på specialpedagoger. Elever med matematik‐svårigheter behöver även få stöd i det sammanhang som de befinner sig i. Detta anser lärare kan hanteras genom att antingen blanda sammanhanget med olikheter i kunskap hos elever eller se till att elever med matematiksvårigheter får samarbeta med elever de känner sig trygga med. Lärare försöker även stödja eleverna med styrning, kontroll och ordning, vilket kan förklaras av att dessa elever upplevs gå igenom tonåren. Läraren gör en subjektiv bedömning av elevernas behov av styrning och detta slår då igenom på elevernas möjligheter att få vara med och påverka i olika grad. Lärare har vidare olika förväntningar på elevernas prestationer i ett deltagande, där vissa lärare anser att eleverna ska prestera varmed vissa nöjer sig med ett deltagande. Lärare har således olika fokus för dessa elever – antingen kunskapsmål eller värdemål. Det sista temat berör lärares syn på samarbetet med föräldrarna. Vissa lärare upplevs tro att denna kontakt bidrar positivt varmed andra inte har tolkats riktigt ha samma övertygelse. / Mathematics has a unique subject language that students need to master in writing as well as verbally. Shortcomings in the oral mathematical communication capacity contribute to the fact that students with mathematical difficulties do not receive an approved grade in mathematics for grade 9. These students need help and support from their environment in order not to risk being disapproved. This study has been conducted with the purpose of portraying and analyzing mathematics teachers' views on supportive factors for students with mathematical difficulties focusing on oral mathematical communication skills. As a method, a content analytical research approach with inductive thematic methodology has been used and the study is based on five semi structured interviews. Mathematics teachers' views have been judged to be possible to be depicted and analyzed by the following six themes: 1. The balance between oral and written communication 2. The oral mathematical communications skills components 3. Activities based on the students' needs 4. Supporting learning environment for the student 5. The student's participation in mathematical discussions 6. Cooperation with the parents Teachers agree that students with mathematical difficulties need adaptations of content and knowledge objectives for oral mathematical ability. However, there is no unanimity in the teacher's view of adequate goals and content, but this is considered being the result of a variety of factors such as the student's knowledge, teacher's interpretation of the curriculum, the written focus in mathematics, the lack of adequate situations to assess oral capacity, stress and time shortages and the less good availability of special educators. Students with mathematical difficulties also need support in the context they are in. This believes teachers can be managed by either blending the context of differences in student knowledge or ensuring that students with mathematical difficulties interact with friends who they feel safe interacting with. Teachers also try to support the students with control, control and order, which can be explained by the fact that these students experience through their teens. The teacher makes a subjective assessment of the students' need for governance, and this then paves the way for the students to participate and influence in different ways. Teachers also have different expectations of student performance in a participation, where some teachers believe that the students are performing, with which some people are content with a participation. Teachers thus have different focus on these students ‐ either knowledge or value goals. The last theme concerns teachers' views on cooperation with the parents. Some teachers are interpreted believing that this contact contributes positively whereas others have not been interpreted having the same beliefs.