<p>För att bli en demokratisk medborgare behövs kunnande i matematik, då samhällsinformation ska förstås och kritiskt kunna granskas för att ha möjlighet att fatta välgrundade vardagsbeslut. Denna kunskap behövs även för fortsatta studier samt för att få ett fungerande yrkesliv. Fenomenet matematik¬undervisning kan av olika lärare beskrivas, upplevas och uppfattas på kvalitativt skilda sätt. Studiens syfte var att undersöka och beskriva nyexaminerade lärares uppfattningar av fenomenet matematikundervisning samt att nå en ökad förståelse för och kunskap om nyexaminerade lärares första tid som lärare i matematik. Studiens fenomenografiska ansats var kvalitativt analytisk och beskrivande. Ett strategiskt urval har gjorts, där sex lärare har intervjuats. Den kvalitativa forskningsintervjun transkriberades och analyserades, vilket ledde till studiens resultat i form av beskrivnings¬kategorier. Den överordnade beskrivningskategorin var legitimitet, vilket i sin tur beskrevs på tre kvalitativt skilda sätt, som att legitimitet formellt tillskrivs, att legitimitet förvärvas samt att legitimitet tilldelas. Dessa beskrivningskategorier motsvarade studiens kvalitativa variation. Slutsatsen blev att legitimitet påverkade den nyexaminerade lärarens matematikundervisning samt relationen med övriga matematiklärare.</p>

<p><em>The purpose</em> of this thesis is to examine whether the teacher's background affect students' approach to mathematics teaching. Characteristically, in Sweden today is that mathematics is perceived as difficult subject and that the number of foreign teachers has increased. <em>The study examines a phenomenon</em> which the relationship between the teacher's language accent and substance difficulties.</p><p><em>The method</em> used for data collection is questionnaires, in order to investigate the phenomenon as the relationship between the teacher's accent and substance difficulties.</p><p>The investigation has been carried out based on the students' point of view, both secondary and primary school pupils. What difficulties have arisen in teaching?  What is the biggest obstacle to achieve the goals of mathematics, to understand the teacher's language accent first in order to understand the subject, or that mathematics is difficult in itself to be understood as a substance.</p><p><em>The result</em> clearly shows that the teacher's accent does not affect teaching and students' view of mathematics as a subject. The students think that mathematics is a difficult subject in itself and the difficulty arises in the abstract data that is not reality linked, and that they rely too much on independent work with individual support as the teacher does not have time to. Students' learning is influenced by other factors like the socio-coherent, which Vygotskji mean. Communication is an important prerequisite in the socio-cultural interaction. It affected in turn by various factors, like cultural affinities, and how to speak and the tone used.</p>

The purpose of this thesis is to examine whether the teacher's background affect students' approach to mathematics teaching. Characteristically, in Sweden today is that mathematics is perceived as difficult subject and that the number of foreign teachers has increased. The study examines a phenomenon which the relationship between the teacher's language accent and substance difficulties. The method used for data collection is questionnaires, in order to investigate the phenomenon as the relationship between the teacher's accent and substance difficulties. The investigation has been carried out based on the students' point of view, both secondary and primary school pupils. What difficulties have arisen in teaching?  What is the biggest obstacle to achieve the goals of mathematics, to understand the teacher's language accent first in order to understand the subject, or that mathematics is difficult in itself to be understood as a substance. The result clearly shows that the teacher's accent does not affect teaching and students' view of mathematics as a subject. The students think that mathematics is a difficult subject in itself and the difficulty arises in the abstract data that is not reality linked, and that they rely too much on independent work with individual support as the teacher does not have time to. Students' learning is influenced by other factors like the socio-coherent, which Vygotskji mean. Communication is an important prerequisite in the socio-cultural interaction. It affected in turn by various factors, like cultural affinities, and how to speak and the tone used.

För att bli en demokratisk medborgare behövs kunnande i matematik, då samhällsinformation ska förstås och kritiskt kunna granskas för att ha möjlighet att fatta välgrundade vardagsbeslut. Denna kunskap behövs även för fortsatta studier samt för att få ett fungerande yrkesliv. Fenomenet matematik¬undervisning kan av olika lärare beskrivas, upplevas och uppfattas på kvalitativt skilda sätt. Studiens syfte var att undersöka och beskriva nyexaminerade lärares uppfattningar av fenomenet matematikundervisning samt att nå en ökad förståelse för och kunskap om nyexaminerade lärares första tid som lärare i matematik. Studiens fenomenografiska ansats var kvalitativt analytisk och beskrivande. Ett strategiskt urval har gjorts, där sex lärare har intervjuats. Den kvalitativa forskningsintervjun transkriberades och analyserades, vilket ledde till studiens resultat i form av beskrivnings¬kategorier. Den överordnade beskrivningskategorin var legitimitet, vilket i sin tur beskrevs på tre kvalitativt skilda sätt, som att legitimitet formellt tillskrivs, att legitimitet förvärvas samt att legitimitet tilldelas. Dessa beskrivningskategorier motsvarade studiens kvalitativa variation. Slutsatsen blev att legitimitet påverkade den nyexaminerade lärarens matematikundervisning samt relationen med övriga matematiklärare.

Studien syftar till att beskriva hur lärare i matematik upplever att de praktiskt hanterar elevers olika förutsättningar i sin matematikundervisning. Undersökningen genomfördes som en fallstudie av två lärare i matematik i grundskolans senare år. Det empiriska materialet består av fyra klassrumsobservationer, som analyserades för att identifiera olika typer av individualisering, samt fyra intervjuer, för att belysa lärarnas upplevelser av och tankar kring individualisering. Det framkom att det förekommer flera olika typer av individualisering. En del individualisering var ett resultat av lärarens medvetna val, men det förekom även individualisering som lärarna delvis var omedvetna om. / The study aims to describe how teachers of mathematics feel that they practically handle student differences in their mathematics teaching. The survey was conducted as a case study of two teachers of mathematics in secondary school. The empirical material consists of four classroom observations, which were analyzed to identify types of individualization, and four interviews, to highlight the teachers' experiences of and thoughts about individualization. It was found that there are several different types of individualization. Some individualization was the result of the teacher's conscious choice, but there were also individualization as teachers in part, were unaware of.

På hösten 2011 beslutade regeringen att göra en satsning på matematik i skolan på grund av elevers sjunkande resultat. Detta sett i ett internationellt perspektiv. Satsningen gick bland annat ut på fler undervisningstimmar samt kompetensutveckling till lärare. Med bakgrund av denna matematiksatsning valde vi i denna studie att ta elevernas perspektiv på frågan varför elevernas resultat blivit sämre. Anser de till exempel att undervisningen i matematik är meningsfull? Syftet med studien är att undersöka vilket förhållningssätt eleven i årskurs 4 har till matematikundervisningen samt dess betydelse för elevens vardag och jämföra det med det uppdrag som läroplanen uttrycker avseende matematikämnet och matematikundervisningen. Då en ny läroplan införts, har vi också valt att jämföra syftet för matematikundervisningen med elevernas svar. Datainsamlingen har skett genom gruppintervjuer och analysen har gjorts med hjälp av kvalitativ innehållsanalys. Som stöd i vårt analysarbete har vi använt begreppen; uppfattningar, erfarenhet och meningsfullhet. Resultatet visar att eleverna uppfattar matematiken som något väldigt positivt. De kan också se en meningsfullhet i att kunna matematik, men framförallt som en kunskap som ska användas i framtiden. Eleverna får framförallt erfarenheter i matematik genom eget arbete i matematikboken, eller genom pararbete. Resultatet visar också att elevernas uppfattningar i hög grad stämmer överens med syftet i för matematikundervisningen i läroplanen. Slutligen diskuterar vi resultatet med våra teoretiska utgångspunkter som stöd. Bland annat diskuterar vi varför elevernas positiva syn på matematik förändras under tiden de går i skolan. Vi diskuterar också hur eleverna kommit fram till att matematik är viktig i framtiden. / In the autumn of 2011 the Swedish Government decided to make an investment in mathematics in schools, due to declining student performance, as seen from an international perspective. The investment focused on, for example, more hours of instruction in class, and competence development for teachers. With this investment in mind, we have chosen to study the question of why pupil performance becomes worse, from the pupils' perspective. For example, do they find the teaching of mathematics meaningful? The study aims to explore the attitudes of pupils in fourth grade towards mathematics teaching and its relevance in their daily lives. Furthermore, the study aims to compare these attitudes with the mission expressed regarding the subject of mathematics and mathematics teaching in the curriculum. Because of the new curriculum, we have chosen to compare the aim of mathematics teaching with the pupils’ responses. The data collection was done through group interviews and the analysis was done using qualitative content analysis. To support our analysis we have used three concepts: perceptions, experience and meaningfulness. The result shows that pupils perceive mathematics as something very positive. They can also see meaningfulness in mathematics, but mostly as a knowledge that will be used in the future. The pupils get experience in mathematics through their own work in a book, or through work in pairs. The result also shows that pupils' perceptions highly correspond with the aims of the mathematics teaching in the curriculum. Finally, we discuss the result supported by our theoretical concepts. For example, we discuss why the pupils' positive view of mathematics changes during the time they go to school. We also discuss how students come to the conclusion that mathematics is important in the future.

The purpose of this study is to examine in what extent primary school teachers, teaching children in the age of 6 to 9, choose to use digital tools in their teaching of mathematics. I also want to examine what these teachers think, in terms of advantages and disadvantages, about using digital tools on their mathematics lessons. Finally I want to examine what skills they possess about digital tools. I am using a quantitative method to collect my data. The quantitative survey consisted of a questionnaire survey of ten questions that 38 primary school teachers have answered. The results of my study show that the teachers to some extent use digital tools when they teach mathematics and that the availability of various digital tools are generally good. But it turns out that the availability of tools is not a guarantee that they are used in teaching of mathematics. There is a great desire among the teachers in my study to use digital tools with greater frequency than in the current situation because it increases students' learning and motivation. To achieve this, the teachers need more resources such as skills, time and student computers / tablet computers.

In this investigation, two schools - a control school and an experimental school – were compared in terms of learner performance in two traditional grade 11 mathematics tests, namely the pre-intervention test and the post-intervention test. Both schools completed the two tests simultaneously. Educators saw both tests before intervention. In the experimental school, four grade 11 mathematics classes were studied. The four classes were given worksheets that complied with an open-ended approach (OEA) to mathematics teaching and learning for learners to work independently on, with the teacher only facilitating. The learner-centredness expressed in the OEA complied with learner-centredness as envisaged by the National Curriculum Statement (NCS), and was predominantly constructivist in character. Throughout the five-month intervention, the author observed proceedings in two of the four classes in the experimental school, ensuring that questions the teacher asked complied with the OEA. The two classes would be referred to as monitored classes. The other two classes at the experimental school worked on the worksheet, with the teacher having been briefed about what was expected of the learners using the worksheet -basically that the learners would have to take own initiatives in solving the mathematics problems with minimal teacher intervention. The two grade 11 mathematics classes were monitored, but not as frequently as the monitored classes. The classes will be referred to as unmonitored classes. At the control school the educators followed their usual (traditional) teaching approach. Both the experimental and control schools followed the same grade 11 mathematics work schedule. The educators in the control school taught without any interference from the author, but the classes at the control school were occasionally observed by the author. In addition to the intervention comparison, the author also gathered qualitative information about participating educators' and learners' experiences and opinions about the OEA at the experimental school by using interviews. The results of the pre-intervention test showed no statistical difference between the experimental and control school performance, meaning that the learners from both schools were of comparable pre-requisite knowledge. In the post-intervention test, learners from the two monitored classes meaningfully outperformed those from the two unmonitored experimental classes and those from the control school. However, there was no significant difference in performance between learners from the two unmonitored classes and those from control school, The study concludes that the appropriate OEA intervention was responsible for the good results of the monitored classes., and then uses the gathered qualitative information to design a model for the successful implementation of' OEA in mathematics classes. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2010.

In this investigation, two schools - a control school and an experimental school – were compared in terms of learner performance in two traditional grade 11 mathematics tests, namely the pre-intervention test and the post-intervention test. Both schools completed the two tests simultaneously. Educators saw both tests before intervention. In the experimental school, four grade 11 mathematics classes were studied. The four classes were given worksheets that complied with an open-ended approach (OEA) to mathematics teaching and learning for learners to work independently on, with the teacher only facilitating. The learner-centredness expressed in the OEA complied with learner-centredness as envisaged by the National Curriculum Statement (NCS), and was predominantly constructivist in character. Throughout the five-month intervention, the author observed proceedings in two of the four classes in the experimental school, ensuring that questions the teacher asked complied with the OEA. The two classes would be referred to as monitored classes. The other two classes at the experimental school worked on the worksheet, with the teacher having been briefed about what was expected of the learners using the worksheet -basically that the learners would have to take own initiatives in solving the mathematics problems with minimal teacher intervention. The two grade 11 mathematics classes were monitored, but not as frequently as the monitored classes. The classes will be referred to as unmonitored classes. At the control school the educators followed their usual (traditional) teaching approach. Both the experimental and control schools followed the same grade 11 mathematics work schedule. The educators in the control school taught without any interference from the author, but the classes at the control school were occasionally observed by the author. In addition to the intervention comparison, the author also gathered qualitative information about participating educators' and learners' experiences and opinions about the OEA at the experimental school by using interviews. The results of the pre-intervention test showed no statistical difference between the experimental and control school performance, meaning that the learners from both schools were of comparable pre-requisite knowledge. In the post-intervention test, learners from the two monitored classes meaningfully outperformed those from the two unmonitored experimental classes and those from the control school. However, there was no significant difference in performance between learners from the two unmonitored classes and those from control school, The study concludes that the appropriate OEA intervention was responsible for the good results of the monitored classes., and then uses the gathered qualitative information to design a model for the successful implementation of' OEA in mathematics classes. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2010.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A presente dissertação tem o objetivo de propor a reinclusão de elementos de Cálculo no ensino médio, pois no passado o Cálculo fazia parte do currículo e foi abolido após uma reforma no ensino da matemática. O trabalho apresenta os resultados de um levantamento estatístico sobre os índices de reprovação na disciplina Cálculo Diferencial e Integral I nos períodos mais recentes da Universidade do Estado do Rio de Janeiro (UERJ) e, também, uma pesquisa quantitativa com quarenta professores de matemática com o objetivo de analisar a viabilidade do projeto e os problemas a serem enfrentados. Por fim, a dissertação conta com uma série de atividades comentadas sobre o tema de limites, que é o foco do trabalho. Tais atividades podem ser incluídas já no 1 ano do ensino médio, paralelamente ao conteúdo de funções, e visam proporcionar aos estudantes o contato com elementos de Cálculo em uma linguagem acessível, e orientar o professor nesta tarefa / This dissertation has the objective of proposing the reinclusion of Calculus elements in high school, because in the past Calculus was part of the curriculum and it was abolished after a reform in mathematics teaching. This paper presents the results of a statistical return about the rates of fails in the subject Differential and integral Calculus I in recent terms at Universidade do Estado do Rio de Janeiro (UERJ) and also a quantitative research with forty mathematics teachers, which has the objective of analyzing the viability of the project and the problems to be faced. Finally, the dissertation has a series of discussed activities about the theme of limits, which is the focus of this paper. These activities can be included in the first year of high school, at the same time as functions content. They aim to offer students a contact with Calculus elements in an accessible language and also to orientate the teacher in this task.