(anglicky) Fractions are one of the critical areas of mathematics at the primary school. The aim of this diploma thesis is to describe didactic practices used when teaching fractions (focusing in particular on additive operations with fractions) and find out what strategies are used by pupils at selected tasks focusing on fractions, what difficulties are an obstacle in their successful solutions and what images of fractions the pupils have. The theoretical part contains considerations about the teaching and learning of mathematics, the overview of the historical development of the concept of fraction and operations with fractions and also selected research related to fractions. The practical part begins with the analysis of the textbooks where their semantic and structural models used for fractions are identified as well as ways of teaching operations with fractions. My own research consists of semi-structured interviews with five experienced teachers (one of whom is not qualified) on the topic of teaching fractions, the difficulties of pupils with fractions and of clinical interviews with three pupils from different primary schools. Interviews with the pupils were focused on the solution of the diagnostic tasks in the field of fractions. Transcripts of both interviews were analyzed by techniques...

1 Abstract The goal of the diploma thesis was to identify and describe didactic practices of selected experienced mathematics teachers, used in the teaching of indirect proportion, to make an analysis of the most used textbooks from the point of view of teaching indirect proportion, to select suitable problems which diagnose pupils' knowledge of indirect proportion and to identify pupils' strategies and their mistakes in solving them. Indirect proportion is first described from the point of view of curricular documents and of Czech pupils' results in this area in both national and international surveys. The pupil's knowledge gaining process is characterised from the point of view of didactic constructivism. Next, ways and conceptions of teaching indirect proportion as provided by selected primary textbooks are given. The content analysis of textbooks was made and compared to results of similar studies. Next, the thesis deals with some results of international research on proportional thinking and solving strategies for problems on proportion which are then used as a starting point of my own research on pupils' strategies for problems on indirect proportion. The next part of research consists of semi-structured interviews with experienced teachers, observations of their lessons and analysis of their pupils'...

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Nossa pesquisa teve como objetivo explorar as implicações relativas à utilização de material didático de natureza virtual livre em contexto formal de ensino-aprendizagem de italiano LE/L2. As implicações foram tratadas em forma de Problemas de Ensino e o termo utilização foi desdobrado em dois aspectos: utilização em sala de aula presencial e produção. Orientou-nos a hipótese de que o uso de materiais didáticos de natureza virtual livre, em contexto formal de ensino-aprendizagem de língua italiana como LE/L2, deflagra uma série de implicações observáveis e específicas as quais podem ser definidas em termos de Problemas de Ensino (ORTALE, 2010) , dada a sua natureza peculiar, ou seja, livre. A fim de alcançar nossos objetivos, lançamos mão de uma metodologia qualitativa de viés construtivista e interpretativista. Os Problemas de Ensino foram identificados por meio da análise de Relatos de Problemas de Ensino (ORTALE, 2010). Balizaram nossas análises a metodologia de formação de professores, alicerçada na ideia de Aprendizagem Baseada em Problemas (ABP), explicitada em Ortale (2010), e as técnicas e procedimentos de desenvolvimento de teoria fundamentada, conforme Strauss e Corbin (2008). Os Problemas de Ensino relativos à utilização foram investigados em duas disciplinas de língua italiana ofertadas em nível de graduação junto à Faculdade de Letras de uma universidade pública do estado de São Paulo. Os Problemas de Ensino relativos à produção foram pesquisados nos contextos de duas edições de um curso de formação de professores de língua italiana em serviço e em pré-serviço que ministramos no âmbito de duas universidades públicas brasileiras - uma no estado de Santa Catarina e outra no estado de São Paulo. Encontramos um total de 11 (onze) Problemas de Ensino - 7 (sete) relacionados ao aspecto da produção de Material Didático Virtual Livre e 4 (quatro) relacionados ao aspecto da utilização. Notamos, por meio de nossa análise, a proeminência de dois fatores associados aos Problemas de Ensino encontrados: as crenças a respeito de materiais didáticos de natureza virtual livre e a demanda pelo desenvolvimento de competências relativas aos aspectos virtual e livre desse tipo de material didático. Concluímos que os Problemas de Ensino identificados não são específicos, mas, sim, característicos dos materiais didáticos de natureza virtual livre / The aim of our research was to explore the implications related to the use of Free Virtual Educational Materials in the context of formal teaching and learning Italian as FL/SL. The implications were dealt as Problems of Teaching (ORTALE, 2010) and the term use was considered according to two aspects: use in presential classrooms and production. The hypothesis was that the use of Free Virtual Educational Materials, in the context of formal teaching and learning Italian as FL/SL, triggers a series of observable and specific implications, which can be defined in terms of Problems of Teaching due to its peculiar nature, that is, being a free educational material. The methodology adopted here was qualitative, both constructivist and interpretativist. The Problems of Teaching were identified through the analysis of the Reports of Problems of Teaching (ORTALE, 2010). The analyses were based on the methodology of teacher education, supported by the idea of Problem-Based Learning (PBL), explained in Ortale (2010), and the techniques and procedures of the Grounded Theory, according to Strauss e Corbin (2008). The Problems of Teaching related to the use were investigated in two undergraduate subjects of Italian Language offered by the College of Arts in a public university in São Paulo state. The Problems of Teaching related to the production were researched in the context of two editions of the training course for teachers of Italian Language in-service and pre-service, taught at two Brazilian public universities one in Santa Catarina state and the other in São Paulo state. We have found the total of 11 (eleven) Problems of Teaching 7 (seven) related to the aspect of production of Free Virtual Educational Materials and 4 (four) related to the aspect of its use. We have noticed through our analysis, the prominence of two factors associated to the Problems of Teaching which were found in the research: the beliefs regarding Free Virtual Educational Materials and the demand to develop the competences related to the free and virtual aspects of this sort of material. We concluded that the Problems of Teaching identified here are not specific but are typical of educational materials that are virtual and free

Nossa pesquisa teve como objetivo explorar as implicações relativas à utilização de material didático de natureza virtual livre em contexto formal de ensino-aprendizagem de italiano LE/L2. As implicações foram tratadas em forma de Problemas de Ensino e o termo utilização foi desdobrado em dois aspectos: utilização em sala de aula presencial e produção. Orientou-nos a hipótese de que o uso de materiais didáticos de natureza virtual livre, em contexto formal de ensino-aprendizagem de língua italiana como LE/L2, deflagra uma série de implicações observáveis e específicas as quais podem ser definidas em termos de Problemas de Ensino (ORTALE, 2010) , dada a sua natureza peculiar, ou seja, livre. A fim de alcançar nossos objetivos, lançamos mão de uma metodologia qualitativa de viés construtivista e interpretativista. Os Problemas de Ensino foram identificados por meio da análise de Relatos de Problemas de Ensino (ORTALE, 2010). Balizaram nossas análises a metodologia de formação de professores, alicerçada na ideia de Aprendizagem Baseada em Problemas (ABP), explicitada em Ortale (2010), e as técnicas e procedimentos de desenvolvimento de teoria fundamentada, conforme Strauss e Corbin (2008). Os Problemas de Ensino relativos à utilização foram investigados em duas disciplinas de língua italiana ofertadas em nível de graduação junto à Faculdade de Letras de uma universidade pública do estado de São Paulo. Os Problemas de Ensino relativos à produção foram pesquisados nos contextos de duas edições de um curso de formação de professores de língua italiana em serviço e em pré-serviço que ministramos no âmbito de duas universidades públicas brasileiras - uma no estado de Santa Catarina e outra no estado de São Paulo. Encontramos um total de 11 (onze) Problemas de Ensino - 7 (sete) relacionados ao aspecto da produção de Material Didático Virtual Livre e 4 (quatro) relacionados ao aspecto da utilização. Notamos, por meio de nossa análise, a proeminência de dois fatores associados aos Problemas de Ensino encontrados: as crenças a respeito de materiais didáticos de natureza virtual livre e a demanda pelo desenvolvimento de competências relativas aos aspectos virtual e livre desse tipo de material didático. Concluímos que os Problemas de Ensino identificados não são específicos, mas, sim, característicos dos materiais didáticos de natureza virtual livre / The aim of our research was to explore the implications related to the use of Free Virtual Educational Materials in the context of formal teaching and learning Italian as FL/SL. The implications were dealt as Problems of Teaching (ORTALE, 2010) and the term use was considered according to two aspects: use in presential classrooms and production. The hypothesis was that the use of Free Virtual Educational Materials, in the context of formal teaching and learning Italian as FL/SL, triggers a series of observable and specific implications, which can be defined in terms of Problems of Teaching due to its peculiar nature, that is, being a free educational material. The methodology adopted here was qualitative, both constructivist and interpretativist. The Problems of Teaching were identified through the analysis of the Reports of Problems of Teaching (ORTALE, 2010). The analyses were based on the methodology of teacher education, supported by the idea of Problem-Based Learning (PBL), explained in Ortale (2010), and the techniques and procedures of the Grounded Theory, according to Strauss e Corbin (2008). The Problems of Teaching related to the use were investigated in two undergraduate subjects of Italian Language offered by the College of Arts in a public university in São Paulo state. The Problems of Teaching related to the production were researched in the context of two editions of the training course for teachers of Italian Language in-service and pre-service, taught at two Brazilian public universities one in Santa Catarina state and the other in São Paulo state. We have found the total of 11 (eleven) Problems of Teaching 7 (seven) related to the aspect of production of Free Virtual Educational Materials and 4 (four) related to the aspect of its use. We have noticed through our analysis, the prominence of two factors associated to the Problems of Teaching which were found in the research: the beliefs regarding Free Virtual Educational Materials and the demand to develop the competences related to the free and virtual aspects of this sort of material. We concluded that the Problems of Teaching identified here are not specific but are typical of educational materials that are virtual and free

The diploma thesis deals with the topic of the mathematical environment Bus realized through mathematical tasks in textbooks Hejný et al. The issue is aimed at pupils of the fourth grade of primary school. The main point of the theoretical part is study of gradual gradation of tasks in environment Bus from 1st to 5th grade of primary school. It was found that the frequency of the tasks in the textbook for the fourth grade is impaired and on the basis has been prepared experiment that complement the tasks so that the frequency has been unimpaired. The practical part includes the preparation of an experiment in which custom- designed tasks were formulated. They were linked with fourth-year primary school curriculum. By performing two experiments was obtained 262 pupil's solutions of tasks, in which were recorded and analyzed pupil's mistakes. This enabled to formulate phenomenons that could be caused by impaired frequency of tasks in environment Bus in textbooks Hejný et al. KEYWORDS graduaded problems, experiment, Hejný's teaching method, mathematical environment Bus, word problems, work with table

This diploma thesis deals with the teaching specificity of the history of the 20th century in upper primary schools and with methodical drafts of selected thematic units of the same period. The thesis puts emphasis on problems related to teaching on the 20th century. The work summarizes theoretical knowledge of teaching on the history of the 20th century and follows up the classification of this historical period into the General educational program for basic education. Methods and strategies suitable for teaching the history of the 20th century and the approach how to give lessons about controversial and delicate topics in history are also included in the present thesis. The methodical drafts of selected thematic units from the history of the 20th century are one part of the thesis. These drafts were worked out in respect of using various teaching styles and educational strategies. The thesis also pays attention to the utilization of didactic media in the teaching of history.