<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.

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No. of bitstreams: 1 andrade_js_me_bauru.pdf: 1028797 bytes, checksum: 9840b3755f6b3d30624e3479858775f0 (MD5) Previous issue date: 2016-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A implantação do Sistema de Avaliação do Rendimento Escolar do Estado de São Paulo – SARESP, desde 1996, deveria cumprir a função de produzir diagnósticos da situação da escolaridade básica paulista, visando orientar os gestores do ensino no monitoramento das políticas voltadas para a melhoria da qualidade educacional. Porém, a literatura salienta restrições nos impactos dos resultados dos sistemas de avaliação em larga escala, na atuação profissional do professor. Admite-se que a efetivação de funções diagnósticas do SARESP depende de investigações que ampliem a compreensão dos docentes da Educação Básica acerca de dimensões adotadas por esta política pública de avaliação externa, sendo tal compreensão componente essencial do repertório profissional de tais docentes. A presente pesquisa investigou fatores que poderiam influenciar nas correspondências que os professores devem estabelecer entre, de um lado, possíveis aprendizagens dos seus alunos em interação com as condições didáticas dispostas pelo próprio professor e, de outro lado, as aprendizagens preconizadas em documentos oficiais do SARESP sob a designação de habilidades ou descritores. Participaram da pesquisa uma professora do 7º e outra do 9º anos do Ensino Fundamental, responsáveis pelo componente curricular de Matemática, de uma escola da rede pública do Estado de São Paulo localizada no interior do estado. O procedimento consistiu em sete fases. Na Fase 1, ocorreu a caracterização dos planejamentos adotados pelas professoras para o ano letivo em curso quanto às Situações de Aprendizagem (SA) previstas. Na Fase 2, as participantes realizaram a descrição de uma SA já ministrada, priorizando o relato das aprendizagens previstas, as práticas e estratégias de ensino e de avaliação adotadas e as medidas de aprendizagem obtidas. Diante disso as professoras realizaram o cotejamento de tais aprendizagens com descritores previstos em documentos oficiais. Diante da transcrição dos relatos de suas ações, as professoras selecionaram uma aprendizagem e realizaram uma atividade de decomposição e de análises de lacunas assinaladas nos dados expressos na descrição da SA que foi desenvolvida. Na Fase 3 foram replicados os procedimentos da Fase 2, considerando uma SA não ministrada. Na Fase 4, o conjunto de aulas planejados na Fase 3 foram filmados e editados pela pesquisadora em episódios que priorizaram situações de interação de cada professora com os respectivos alunos. Na Fase 5, diante de cada episódio, cada professora deveria identificar: (a) se ocorreram as aprendizagens previstas; (b) quais seriam as evidências (medidas) de tais aprendizagens; e (c) quais foram os aspectos (pontos) críticos para a ocorrência das mesmas. Diante da transcrição dos relatos da professora e da descrição dos episódios, elaborada pela pesquisadora, relacionando ações do professor que antecederam respostas dos alunos, as respostas emitidas pelos alunos e ações subsequentes do professor a tais respostas, a professora estimou a correspondência entre as aprendizagens previstas nos documentos oficiais e as aprendizagens evidenciadas. Após isso as participantes indicaram outra SA ainda não ministrada para ser objeto de descrição do planejamento previstos na Fase 3. As Fases 6 e 7 consistiram na replicação das Fases 4 e 6 respectivamente para a nova SA. Considera-se que as condições metodológicas de interação adotadas nesta pesquisa possam ter favorecido o desenvolvimento de repertórios profissionais da docência definidos pela análise do alcance das práticas de ensino e de avaliação de aprendizagens adotadas cotidianamente pelas professoras participantes no trabalho. Contudo foi constatada a manutenção de expressivas diferenças entre a terminologia adotada nos documentos oficiais e a terminologia adotada nos relatos das professoras para a designação de habilidades e de medidas de aprendizagem, bem como restrições nos relatos das condições expressas no planejamento e nas descrições das ações dos alunos diante das condições de ensino oferecidas. / With the implementation of the SARESP system since 1996 carry out the function of producing a diagnosis of the state of São Paulo basic education in order to guide education managers in monitoring policies directed at improving educational quality. However, the literature reveals restrictions on the impacts of the results by the evaluation systems in large-scale,in the professional teacher action. Therefore, the present study investigated correspondences that teachers should be established between, on the one hand, possible learning of their students in interaction with the teaching conditions given by the teacher himself and, on the other hand, the proposed learning in official documents of SARESP system. The participants were two teachers of 5th and 6th grade of elementary school of a school from São Paulo. The procedure consisted of seven phases. In phase 1, the researcher contacted the planning of teachers for Learning Situations (SA) planned for the school year. In phase 2 the participants performed a description of an SA already given, prioritizing the account of planned learning the practices and teaching and assessment strategies adopted and obtained learning measures before that the teachers made the comparisons of learning with official documents. Given the transcription of reports of their actions, the teachers selected a learning and performed activities of a decompositions and gap analyzes indicated the data expressed in the description of SA that was developed. In phase 3 the procedures of Phase 2 been replicated, considering a SA not given. In the phase 4 the set of classes considered in Phase 3 were filmed and edited by the researcher that in phase 5, from the record of the classes, on episodes of teacher-student interaction, the teacher should identify: (a) There were evidenced learning by students, (b) What evidence of the measures of such learning and (c) What was the turning point for the occurrence of the learning. With the transcription of the teacher reports and description of the episodes, prepared by the researcher, relating teacher's actions leading up student responses, the answers given by students and subsequent actions teacher to such responses, the teacher estimated correspondence between planned learning in official documents and the learning evidenced by the students. After that the participants indicated another SA not given for description object of the planning set out in Phase 3. Phase 6 and 7 were characterized by the repetition of the phases 4 and 6 respectively. It is estimated that the methodological interaction conditions adopted in this research may have favored the development of professional teaching repertoires defined by analysis of the scope of teaching practices and evaluation of learning adopted by the participating teachers daily work. However the maintenance of significant differences between the terminology used in official documents and the terminology used in the reports of the teachers to describe skills and learning measures was found, as well as restrictions in the accounts of the conditions expressed in the planning and in the descriptions of the actions of students on the offered teaching conditions.