Syftet med vår studie var att ta reda på hur pedagoger tillvaratar barns informella kunskaper och hur de konkret arbetar för att utveckla barns begreppsuppfattning i matematik med hjälp av språket. Vi avsåg även att undersöka förutsättningarna för en sådan undervisning. Vi ville se till både individ-, grupp- och organisationsnivå. Ytterligare en specialpedagogisk frågeställning som vi avsåg att undersöka var hur barn i behov av särskilt stöd gynnas av detta arbetssätt. Vi genomförde tio kvalitativa forskningsintervjuer, som var delvis strukturerade, med pedagoger som arbetar med språket på ett medvetet sätt i sin matematikundervisning. Pedagogerna valdes ut efter ett riktat urval. Svaren sammanställdes och en analys av svaren gjordes. Resultatet visade att pedagogerna använde sig av laborativa övningar i stor utsträckning i sin undervisning och att samtalen kännetecknades av öppna frågor. För att möjliggöra en undervisning som har språket som verktyg behövs ett medvetet ställningstagande från pedagogens sida, utbildning i matematik, ledningens och kollegors stöd samt tid till planering och reflektion. Alla elever gynnas av en sådan undervisning eftersom den kan individualiseras så att den passar alla. / The aim of this paper was to study how educationalists use the children’s informal knowledge of mathematics, and how they work in order to develop the children’s understanding of concepts using the language as a means. We also intended to investigate the requirements for such teaching. We wanted to look into education regarding individual, group and organizational level. An additional issue, that we wanted to study, was weather children in need of special education benefited from such teaching. We carried out ten qualitative interviews, which were partly structured, with educationalists who used language in order to achieve understanding of mathematical concepts. The educationalists were chosen by a directed selection. The answers were put together and analysed. The result showed that the educationalists used concrete material to a wide extent in their work and that the questions they used were open-ended. To enable a teaching where the language is used as a means for learning, the educationalist needs to make a deliberate decision how to work. Education in mathematics, the support of the management and other colleagues and the time to prepare and reflect are also needed. All children benefit from such education since this way of teaching enables the educationalist to individualize.

The present study shows how students, eleven years old, solve problems in mathematics when they work together in groups. The main question raised is about the difficulties students experience in finding the relationship between mathematics and everyday discourse and vice versa. Two empirical studies about students' problemsolving in mathematics divided into three different articles are presented in this study. One is about how students discuss, while they are trying to solve what the area of the triangle is. The other study is about how different solutions in problemsolving have various meanings. The main finding ofthis work concems communication. Depending on the social contexts, different kinds oflanguages are developed in. When children are in their everyday contexts, they use one kind oflanguage, that is they use everyday concepts. In school, children have to leam the language ofmathematics. Leaming mathematics is about getting students to use the language of mathematics to mediate events and phenomens in the world around. One can describe learning as assimilating communicative and technical tools. Which are used as mediating tools in social practices. Another main finding of this study is to show how a teacher can get students attentive to how to change between different types of discourse and how to use special conc~pts for a special context. The most important aspect is that a teacher has pedagogical conversations with students on how to move between different communicative contexts. Often, students have difficulties in understanding in which communicative context they are involved.

Arbetet handlar om utomhuspedagogik inom matematik för elever i årskurs F-3. Syftet med studien är att undersöka hur utomhuspedagogik påverkar elevers användning av matematiska begrepp inom subtraktion, längdenheter och geometriska figurer. Studien jämför hur elever använder matematiska begrepp utomhus och inomhus. Studien jämför en klass i årskurs 1 och en klass i årskurs 3 för att undersöka skillnader och likheter i användningen av matematiska begrepp. Utomhuslektionen inom subtraktion och längdenheter för årskurs 1 fokuserade på "minus"-spel och mingel med sifferkort. Eleverna använde huvudsakligen första ordningens språk. Inomhuslektion för årskurs 1 hade fokus på repetition av subtraktion, där eleverna använde mestadels första men även andra ordningens språk. För årskurs 3 observerades en utomhuslektion inom geometriska former och längdenheter samt uppskattning, där eleverna använde till större del andra ordningens språk med vissa inslag av första ordningens språk. Inomhuslektionen i årskurs 3 inkluderade problemlösning inom olika områden, där eleverna använde främst första ordningens språk. Studien visar att utomhuspedagogik kan främja utvecklingen av andra ordningens språk inom matematik genom att koppla matematiska begrepp till verkliga situationer. Elevernas användning av olika språkliga uttryck inom matematiken ökade genom utforskning av matematik utomhus.

Undervisning och lärande är grundbultar i ett modernt demokratiskt samhälle. Dessa aktiviteter sker i stor utsträckning av lärare vilka bär ansvaret för att utbilda framtidens generationer. Inom utbildningsväsendet existerar en rad olika läromedel såsom böcker och datorer vilka ofta tenderar att vara statiska i sitt förhållande till eleven. Enligt internationella kunskapsmätningar har svenska elevers matematiska kunskap stagnerat de senaste två decennierna, även om en vändning har skett de senaste åren. En möjlig förklaring till detta kan vara att ett för stort fokus hos bl.a. lärare och matematikböcker ägnats åt procedurella färdigheter snarare än begreppslig förståelse. Detta i kombination med lärares upplevda svårigheter kring att tillämpa ett formativt arbetssätt kan innebära hinder för elevers matematiska kunskapsutveckling. Flera digitala verktyg har utvecklats för att stötta lärare och elever i deras lärandeprocess. Ett sådant digitalt verktyg är Mentimeter som utvecklats för att öka interaktionen mellan en presentatör (t.ex. en lärare) och dess publik. Mentimeterär inte avsett specifikt för en lärandekontext och det finns idag ingen etablerad utgivning av läromedel som använder Mentimeter för skolans värld. Det här examensarbetet har med bakgrund av detta haft som mål att designa och konstruera ett matematiskt läromedel med hjälp av Mentimeter, ämnat för att utveckla elevers förståelse för ett matematiskt begrepp (funktioner). Detta har gjorts med en designbaserad forskningsmetodik vilket är en metod som lämpar sig väl för att utveckla tekniska artefakter inom en skolkontext samt undersöka hur den utvecklade artefakten fungerar i en specifik kontext. Syftet med studien har varit att undersöka lärares upplevelse av att använda det utvecklade läromedlet och med den kunskapen, genom en iterativ process utveckla och samtidigt öka förståelse för hur ett digitalt utbildningsverktyg kan möjliggöra ett formativt arbetssätt. Ett grundantagande inom ramen för detta examensarbete är att ett formativt arbetssätt kan bidra till ett ökat lärande och därmed ökad förståelse för funktionsbegreppet, men att det behövs mer kunskap för att förstå sambandet mellan didaktisk teori och hur den kan användas inom en skolkontext. Detta examensarbete utgår både från en konstruktivistisk och en sociokulturell syn på lärande. Motiveringen av denna breda syn på lärande är att det möjliggör en mer induktiv ansats i förhållande till tolkningen av studiens resultat. Studiens resultat är en“Mentimeter-modul” som designats för att möjliggöra ökad förståelse för matematiska begrepp, samt en teoretisk förståelse för hur modulen upplevts av lärare i en skolkontext. Vidare visar studiens resultat på vikten av att lärare använder Mentimeter-modulen som ett komplement till den ordinarie undervisningen istället för att låta verktyget agera som en egen aktör. Slutsatsen är att den utvecklade Mentimeter-modulen upplevs möjliggöra ett formativt arbetssätt om syftet med modulen tydliggörs och lärarna ser på modulen som ett komplement till sin ordinarie undervisning. / Teaching and learning could be considered as cornerstones of a modern democratic society. These activities are largely being practiced by teachers who are in part responsible for educating future generations. In the education system, there are a number of different teaching materials such as books and computers, which often tend to be static with no or little interaction with the student. According to international surveys the mathematical knowledge among Swedish student’s has stagnated over the past two decades, although a turnaround has taken place in recent years. A possible explanation for this may be that too much focus has been devoted to procedural skills rather than conceptual understanding. This, combined with teachers' perceived difficulties in applying a formative approach, can slow down the development of students' mathematical knowledge. Several digital educational tools have been developed to support teachers and students in their learning process. One such tool is Mentimeter, which was developed to increase the interaction between a presenter (e.g. a teacher) and its audience (e.g. a student). Mentimeter is not intended specifically for a learning context and there is currently no mathematical educational materials developed with the software and that is accessible for everyone with a Menitemeter account. This master thesis has aimed to design and construct a mathematical teaching aid with the help of Mentimeter, intended to develop students' understanding of a mathematical concept (functions). This has been done with a design-based research methodology which is suited for exploring learning environments and gaining deeper theoretical understanding by introducing a designed technical artifact in the context that is being observed. The purpose of this Master Thesis has been to investigate teachers' experience of using the developed teaching aid and with that knowledge, through an iterative process develop understanding on how a digital educational tool can enable a formative approach. A basic assumption made by the authors of this study is that a formative approach can contribute to increased learning andthus increased understanding of the concept of a function. But more knowledge is needed to understand the connection between the didactic theory and how it can be applied in a school context. This study is based partly on a constructivist view of learning but also on a socio-cultural perspective. The motivation for this broad view of learning enables a more inductive approach in relation to the interpretation of the study results. The results of this thesis are a “Mentimeter module” designed to enable an increased understanding of mathematical concepts, as well as a theoretical understanding of how the module is experienced by teachers in a school context. Furthermore, the study shows the importance of teachers using the Mentimeter module as a complement to their regular teaching activities instead of letting the digital education tool act on its own. The conclusion is that the developed Mentimeter module is perceived to enable a formative approach if the purpose of the module is clarified and the teachers see the module as a complement to their established experience andprevious knowledge.

Made available in DSpace on 2016-07-27T13:45:07Z (GMT). No. of bitstreams: 1 MARCIO LEITE DE BESSA.pdf: 4565646 bytes, checksum: 71be3818ddbcc36d4bb1c64586513203 (MD5) Previous issue date: 2015-08-20 / The pivotal issue that we sought to clarify was how the organization of the geometry academic curriculum, founded on Davydovs Theory of Developmental Education, could help graduate students of Education formulate the concepts of area and perimeter. Research began with a diagnostic assessment, which revealed a lack ofdomain in students who are beginning the pedagogical program graduation centered on the basic operations of mathematics, specifically focusing on geometry. Beginning with the students shortcomings in the formulation of mathematical concepts, we sought to clarify the following questions: With the teaching of instrumental mathematics based on the theory of Developmental Education,what are the possible effects in the students quality of learning? Could thisteaching foster an environmentof intellectual development in students through learning the basic concepts of geometry, such as perimeter and area? What contradictions involve the practical realization of Developmental Education, in the context of a graduate degree in Pedagogy? What kind of interpretation and evaluation did students use from their learning about perimeter and area, on this alternative for organizing the teaching of mathematics? Therefore, the study aimed to: analyze the contributions of the Davydovs theory of Developmental Education to the organization of geometry and its practical application, in view of the learning of the perimeter and area concepts for students in the first semester of the Pedagogy program. The field study involved a thirty-six-student class in the pedagogy course and a teacher, with whom we developed a formative educational experiment. The investigation consisted of bibliographic and field research. The literature review spanned the periods from 2005 to 2014, focusing on the learning and training of these concepts. Data collection involved questionnaires, reports of the subjects, interviews, and audio and video recordings. The teaching experiment was conducted in eight (8) h(a) for ninety (90) minutes each between February and June 2014. The didactic experiment followed the basic premises of Davydov. In the data analysis, Bogdan & Biklen (1994) guidelines to the categorization and systematization of data were adopted. The data analysis revealed that this studys main contribution was to provide an alternative way of organizing mathematics teaching, considering that the experiment exhibitedthat on average, 85% (eighty five percent) of students demonstrated qualitative changes in the way thinking about the concept of perimeter and 72% (seventy two percent) about the concept of area. / O problema central que se buscou esclarecer foi o de que a organização do conteúdo escolar de Geometria, fundamentada na Teoria do Ensino Desenvolvimental de Davydov, pode ajudar os estudantes do curso de Pedagogia a formar os conceitos de Perímetro e Área. A pesquisa foi iniciada com uma avaliação diagnóstica a qual revelou a falta de domínio de estudantes que ingressam no curso de Pedagogia das operações elementares da Matemática, especificamente dos conteúdos de Geometria. Partindo-se das dificuldades dos estudantes na formação de conceitos matemáticos, buscamos esclarecer as questões: Que repercussões teriam, na qualidade da aprendizagem dos estudantes em Pedagogia, o ensino de Matemática Instrumental fundamentado na Teoria do Ensino Desenvolvimental? Esse ensino pode propiciar condições para o desenvolvimento intelectual dos estudantes por meio da aprendizagem dos conceitos básicos da geometria como Perímetro e Área? Que contradições envolvem a realização prática do Ensino Desenvolvimental no contexto de um curso de graduação em Pedagogia? Que leitura e avaliação os estudantes fazem de sua aprendizagem dos conteúdos de Perímetro e Área sobre essa alternativa para organização do ensino de Matemática? Desse modo, a pesquisa teve como objetivo analisar as contribuições da teoria do Ensino Desenvolvimental de Davydov para a organização dos conteúdos de Geometria e sua aplicação prática, tendo em vista a aprendizagem dos conceitos de Perímetro e Área, por estudantes do primeiro período do curso de Pedagogia. A pesquisa de campo envolveu uma turma do curso de Pedagogia com 36 (trinta e seis) estudantes e 1 (um) professor com os quais foi desenvolvido um experimento didático formativo. A investigação constou de pesquisa bibliográfica e pesquisa de campo. A pesquisa bibliográfica abrangeu o período de 2005 a 2014, com foco na aprendizagem e na formação desses conceitos. A coleta de dados envolveu aplicação de questionários, relatos dos sujeitos, entrevistas e gravações em áudio e vídeo. O experimento didático foi realizado em 8 (oito) h(a) de 90 (noventa) minutos cada, no período de fevereiro a junho de 2014 e seguiu as premissas básicas de Davydov (1988). Na análise dos dados, foram adotadas as orientações de Bogdan & Biklen (1994) para a categorização e sistematização dos dados. A análise dos dados revelou que a principal contribuição desta pesquisa consistiu em mostrar um caminho alternativo de organização do ensino de Matemática, haja vista que o experimento permitiu verificar que, em média, 85,0% (oitenta e cinco por cento) dos estudantes demonstraram mudanças qualitativas no modo de pensar Matemática o conceito de Perímetro e 72,0% (setenta e dois por cento), o conceito de Área.

Submitted by admin tede (tede@pucgoias.edu.br) on 2018-11-05T16:55:20Z No. of bitstreams: 1 ALINE MOTA DE MESQUITA ASSIS.pdf: 6688952 bytes, checksum: 94c9e4c183a133d7dbafd52f7e741501 (MD5) / Made available in DSpace on 2018-11-05T16:55:20Z (GMT). No. of bitstreams: 1 ALINE MOTA DE MESQUITA ASSIS.pdf: 6688952 bytes, checksum: 94c9e4c183a133d7dbafd52f7e741501 (MD5) Previous issue date: 2018-08-30 / This work falls into the category of research into Theories of Education and Pedagogical Processes, and has as its main investigative focus, the teaching-learning process according to the algebraic concept of linear transformation, based on V.V. Davydov´s theory of developmental teaching. The question it seeks to clarify is : what are the repercussions for teaching the concept of linear transformation, based on the historical-cultural theory, in specific, Davydov's developmental theory, in the process of concept formation by students? Specifically, it aims to analyze the history of the logical development of the concept of linear transformation in order to grasp the relations present in it and the forms of mental movement displayed, towards identifying the mental actions to be contemplated in the planning and conduct of the activity of study; to carry out the study activity through the development of a didactic formation experiment to understand, in the course of the teaching-learning process of the concept of linear transformation, elements that indicate qualitative and quantitative changes in the development of student thinking. To this end research was carried out that consisted of a teaching experiment in a class of Linear Algebra at the Federal Institute of Education, Science and Technology of Goiás - Câmpus Goiânia, based on the assumptions of Davydov. This was completed with fourteen students of the Bachelor in Electrical Engineering graduate course and done so according to the structure of the study activity proposed by Davydov. The procedures for collecting the data were as follows: a written record of semistructured interviews with the teacher, socio-cultural questionnaires completed by the students, a diagnostic instrument for evaluation, an experimental teaching plan and the notes from non-participant direct observers. Data analysis focuses on the process of concept formation and the elements involved in this process from the following categories: transformation of task data into the identification of the general principle of the concept of linear transformation; from modeling to transformation of a model to the concept of linear transformation and the use of the concept of linear transformation as a mental tool. The results showed: the motivation of students during the experimental teaching; an understanding of algebraic concepts after logical-historical analysis by the majority of the research subjects; indicators of the zone of proximal development of the students in relation to the concepts of matrix, function and vector space - considered here as the prerequisites for the formation of the concept of linear transformation, developing the ability to think Mathematically according to the logic of this science; evidence of qualitative changes in the development of theoretical thinking of the research subjects, again, regarding the concept of linear transformation. The main contribution of this research was to show an alternative way of organizing the teaching of the concept of linear transformation, and consequently Linear Algebra. It is believed that even with the contradictions present in the curricular structure of the courses in the areas of the exact and world sciences and in engineering, as well as in the students' school formation, it is possible to carry out teaching based on the theory of developmental teaching and contribute to the theoretical thought formation in the majority of students. / Este trabalho, inscrito na linha de pesquisa Teorias da Educação e Processos Pedagógicos, tem como principal foco investigativo o processo de ensino-aprendizagem do conceito algébrico de transformação linear, fundamentando-se na teoria do ensino desenvolvimental de V. V. Davydov. A questão que se buscou esclarecer foi: que repercussões teriam, no processo de formação de conceitos pelos alunos, o ensino do conceito de transformação linear fundamentado na teoria histórico-cultural, em específico, na teoria do ensino desenvolvimental de Davydov? Especificamente, objetiva-se: analisar a história do desenvolvimento lógico do conceito de transformação linear a fim de apreender as relações nele presentes e o tipo de movimento mental que ele contém para identificar as ações mentais a serem contempladas no planejamento e na condução da atividade de estudo; proceder à realização da atividade de estudo mediante o desenvolvimento de um experimento didático formativo; apreender, no decorrer processo de ensino-aprendizagem do conceito de transformação linear, elementos que indicam mudanças qualitativas e quantitativas no desenvolvimento do pensamento do aluno. Para tanto, realizou-se uma pesquisa que consistiu em um experimento de ensino, baseado nos pressupostos de Davydov, em uma turma de Álgebra Linear do Instituto Federal de Educação, Ciência e Tecnologia de Goiás – Câmpus Goiânia, desenvolvido com quatorze alunos do curso de Bacharelado em Engenharia Elétrica e seguindo a estrutura da atividade de estudo proposta por Davydov. Os procedimentos para a coleta dos dados foram: roteiro de entrevista semiestruturada com o professor, questionário sociocultural dos alunos, instrumento de avaliação diagnóstica, plano de ensino experimental e roteiro de observação direta não participante. A análise dos dados enfoca o processo de formação de conceitos e os elementos intervenientes nesse processo a partir das seguintes categorias: transformação dos dados da tarefa na condução da identificação do princípio geral do conceito de transformação linear; da modelação à transformação de um modelo para o conceito de transformação linear e o uso do conceito de transformação linear como ferramenta mental. Os resultados obtidos revelaram: motivação dos alunos durante o ensino experimental; compreensão dos conceitos algébricos, após a análise lógico-histórica, pela maioria dos sujeitos da pesquisa; indícios de progresso da zona de desenvolvimento proximal dos alunos no que tange aos conceitos de matriz, função e espaço vetorial, considerados aqui como os pré-requisitos para a formação do conceito de transformação linear, desenvolvendo a capacidade de pensar a Matemática de acordo com a forma de pensar desta ciência; indícios de mudanças qualitativas no desenvolvimento do pensamento teórico dos sujeitos da pesquisa quanto ao conceito de transformação linear. A principal contribuição desta pesquisa consistiu em mostrar um caminho alternativo de organização do ensino do conceito de transformação linear, consequentemente, da Álgebra Linear. Acredita-se que, mesmo com as contradições presentes na estrutura curricular dos cursos das áreas de Ciências Exatas e da Terra e Engenharias, bem como na formação escolar dos alunos, é possível realizar um ensino embasado na teoria do ensino desenvolvimental e contribuir para a formação do pensamento teórico da maioria dos alunos

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Detta examensarbete genomfördes i samarbete med K-ULF. De teoretiska ramverk som detta examensarbete vilar på är designbaserad forskning, framplockningsstrategin och aktivitetsbaserad inlärning. Det ena syftet i examensarbetet var att utforma flashcards inom matematikområdet procent. Detta för att undersöka hur matematiklärare i årskurs 9 använder dem i undervisningen för att stärka elevers begreppsförståelse och förmåga att lösa textuppgifter. Det andra syftet i detta examensarbete är att undersöka effekten av att använda flashcards på elevernas lärande. Målet med examensarbetet är att utforma en lärarhandledning utifrån lärarnas lärande av att tillämpa aktiviteterna i matematikundervisningen. Flashcards har utformats utifrån två matematiklärares behov och gäller endast inom matematikområdet procent. Utformningen av flashcards genomfördes genom en förstudie och matematiklärarna utvecklade aktiviteter med flashcards under en workshop. Effekten av att använda flashcards på elevernas lärande mättes genom att studiegruppen, som bestod av fyra klasser, delades in i två grupper. Två klasser användes som en experimentgrupp och de resterande två klasserna blev kontrollgruppen. Innan interventionen skrev både experimentgruppen och kontrollgruppen ett pre-test. Därefter genomfördes interventionen i experimentgruppen. Efter cirka 4 veckor av att använda flashcards i undervisningen skrev både experimentgruppen och kontrollgruppen ett post-test. Resultatet från pre-test och post-test sammanställdes manuellt i ett Exceldokument som senare analyserades med SPSS. I detta examensarbete genomfördes ett independent sample t-test. Eftersom p-värdet i studien var större än 0.05 så visade resultatet att det inte finns en statistisk signifikant skillnad mellan experimentgruppens och kontrollgruppens prestationer i pre-testet och post-testet. Resultatet visade även att det inte finns en signifikant skillnad mellan flickors och pojkars prestationer inom experimentgruppen i pre-testet och post-testet. Vidare visar resultatet att flashcards bör utformas sådant att sidan där begreppet är skriven bör skiljas från sidan där definitionen är skriven för att göra korten tydligare för eleverna. Båda matematiklärarna tror även på att det skulle vara mer gynnsamt för eleverna att själva skriva definitionerna än att få korten klara. Utifrån lärarnas lärande av att implementera flashcardaktiviteter så visar resultatet att antalet begrepp som eleverna arbetar med under aktiviteterna bör begränsas. Det är även viktigt att förklaringarna på korten är elevnära. / This thesis was conducted in collaboration with K-ULF. The theoretical frameworks that underpin this thesis are the design-based research, retrieval practice strategy and activity-based learning. One aim of this thesis was to design flashcards within the mathematics domain of percentages. The purpose was to investigate how mathematics teachers in grade 9 use them in their teaching to enhance students' conceptual understanding and ability to solve text problems. The second aim of this thesis is to examine the effect of using flashcards on students' learning. The objective of the thesis is to create a teacher's guide based on the teachers' learning from implementing the activities in mathematics instruction. The flashcards have been designed based on the needs of two mathematics teachers and are only valid in the area of mathematics percentages. The design of flashcards was carried out through a pre-study and the mathematics teachers developed activities with flashcards during a workshop. The effect of using flashcards on student learning was measured by dividing the study group, which consisted of four classes, into two groups. Two classes were used as an experimental group and the remaining two classes became the control group. Before the intervention, both the experimental group and the control group wrote a pre-test. The intervention was then carried out in the experimental group. After approximately 4 weeks of using flashcards in teaching, both the experimental group and the control group wrote a post-test. The results from the pre-test and post-test were compiled manually in an Excel document which was later analyzed with SPSS. In this thesis, an independent sample t-test was carried out. Since the p-value in the study was greater than 0.05, the result showed that there is no statistically significant difference between the experimental group and the control group's performance in the pre-test and post-test. The result also showed that there is no statistically significant difference between the performance of girls and boys within the experimental group in the pre-test and post-test. Furthermore, the result shows that flashcards should be designed in such a way that the side where the concept is written should be different from the side where the definition is written to make the cards clearer for the students. Both mathematics teachers also believe that it would be more beneficial for the students to write the definitions themselves than to provide ready-made cards. Based on the teachers' learning from implementing flashcard activities, the result shows that the number of concepts that the students work with during the activities should be limited. It is also important that the explanations on the cards are student-friendly.

I vår studie intar vi en hermeneutisk ansats och genomför en textanalys. I vår studie tolkar, analyserar och kategoriserar vi innehållet i åtgärdsprogrammets behov och åtgärd. Utifrån diskurser konstruerar vi en ram som hjälper oss att tolka formuleringar i åtgärdsprogram. Syftet med denna studie är att undersöka hur identitet, makt och matematiska begrepp synliggörs i åtgärdsprogram. I studien undersöker vi i vilken omfattning begreppen ovan förekommer i behov och åtgärder för årskurs 6 och 7. Vi utgår från ett diskursivt perspektiv mot makt och identitet. Vår studie visar att koppling mellan behov och åtgärd saknas i vissa åtgärdsprogram. Tillskriva identitet har den största andelen för åtgärder. Matematiska begrepp har störst andel för upptagna behov. Makt (makt genom kunskap och titel) har lägst förekomst i upprättade åtgärder. Det är varje skolas diskurs och dess skolpersonal som avgör på vilket sätt och i vilket forum som arbetet kring elevens behov fungerar. På samma sätt är den skillnad som existerar mellan olika upprättade åtgärdsprogram ett uttryck för den kultur eller diskurs som råder just nu, lokalt på skolan. Detta är avgörande om åtgärdsprogrammet används som ett fungerande verktyg. / In our study we take a hermeneutical approach and interpret text. In our study we interpret, analyse, and categorize the content of the IEP´s needs and arrangements. Based on discourses we construct a framework that helps us interpret phrasings in IEPs. The purpose of this study is to investigate how identity, power and mathematical concepts are made visible in the text of IEPs. In this study, we investigate to what extent the concepts above occur in the needs and arrangements for grades 6 and 7. We start from a discursive perspective on power and identity. Our study shows that the connection between needs and arrangements is missing in some IEPs. Attributing identity has the largest share of arrangements. Mathematical concepts have the greatest proportion of occupied needs. Power (power through knowledge and title) has the lowest occurrence of written arrangements. It is the discourse of every school and its school personal that decides in what direction and in what context the work toward the needs of the student. In the same way is the difference that exist between different IEPs an expressian in the culture that is dominant at schools. This is crusial if the IEPs is working as a functioning tool.

The following study aims to examine the special mathematical knowledge needed in order to teach mathematics. Furthermore, the study attempts to explore how teachers’ views on the knowledge needed in order to teach mathematics affects their student’s opportunities to develop their conceptual understanding. Qualitative and quantitative empirical data was attained by observations and complementary interviews. A total of three teachers, all working at the same school, was observed and interviewed. The study used Ball, Thames & Phelps (2008) practice-based theory of mathematical knowledge for teaching, MKT, as its theoretical framework when analyzing the empirical data. The result of the observations displays that math teachers tend to use common content knowledge far more than specialized content knowledge during their lessons. The outcome of this also study reveals that there is a tendency among teachers to interfuse mathematical concepts with terminology. Conceptual understanding is equated with the use of correct terminology. The students are not exposed to the underlying ideas of the mathematical concepts. The study also concludes that there seems to be a sectioning between the mathematical content taught in grade 4-6 from the rest of the content being taught in elementary school, with a low number of connections being made between mathematical topics and concepts included in the curriculum.