No description available.

The official school mathematics curriculum - textbooks, teacher's handbooks, and syllabus - has a powerful influence on classroom practice in a developing country like Ghana, where many teachers with low teaching qualifications hardly ever have access to other sources of information and activity for their teaching. The official mathematics curriculum for Ghanaian primary schools was originally written with the small intellectual elite, who will proceed to secondary and further education, in mind. Concerns have been raised internationally for countries still using such curricula to adjust them, but the Ghanaian official school mathematics curriculum has remained in use in the nation's schools since their introduction in 1975 with no significant revision. The study, on the one hand, involved an investigation of the extent to which primary teachers in Ghana translate the contents of the official mathematics curriculum into classroom reality. On the other hand, it addressed issues related to the nature, and appropriateness, of the current official primary mathematics curriculum, which was an adaptation of the products of the `new-math' project spearheaded by the West African Regional Mathematics Programme in the 1970s. The study used a range of methods for data collection. These include an extensive content and curriculum analysis of the official primary mathematics curriculum materials, and a questionnaire survey of teachers' coverage of the content and teaching methods prescribed by the official curriculum. The questionnaire survey of teachers' coverage of teaching methods involved the observation of teachers in classroom settings. Tape recordings of lessons and instructions from teacher's handbooks were transcribed to provide both qualitative and quantitative data on classroom practice. The analysis of the curriculum revealed several inefficiencies in the Ghanaian primary mathematics curriculum. Though there was rhetoric in the introduction of the curriculum materials on the use of teaching skills that suggest discovery methods, the analysis indicated that learning/teaching activities that would encourage the use of such teaching skills in the materials were not included. It emerged from the findings that neither what the teachers really taught, nor what the official mathematics curriculum prescribed, was found to be adequate enough to meet the full mathematical needs of pupils. It was found that a very substantial part of the content of the curriculum was taught by the teachers, and both the official curriculum and the teachers, who implement it, emphasised expository teaching methods. It was argued in this light that the low pupils' attainment observed in the subject could not be seen simply as a reflection of the teachers' poor coverage of the curriculum, but as a reflection of inefficiencies within it. The findings of this study corroborate what is known about curriculum adaptation in school mathematics. It showed that coverage of textbooks does influence the emphasis on topics presented by teachers in their instruction, and also that topics in arithmetic are the most emphasised by both official mathematics curriculum materials and in teachers' actual classroom practice.

The presented work is intended to serve as a teaching material in particular for pupils of the first year of secondary school, focusing on the basic knowledge of mathematics. The first part of the thesis is devoted to an analysis of existing web page, which corresponds to the theme of the diploma thesis. The evaluation takes into account the expertise as well as the scope of use of interactive elements. In the next part, the created teaching material in a form of web page is presented. It deals with the subject matter of powers, roots, polynomials and rational expressions. In accordance with current trend, the emphasis is put on both visualisation of curriculum (charts, use of graphics) and interactivity. All exercises to practise involve solution, therefore users are allowed to gain immediate feedback and thus to study individually. Web page is free available.

Este trabalho, realizado no âmbito do Curso de Mestrado Profissional em Ensino de Ciências e Matemática, do Programa de Pós-Graduação em Ensino de Ciências e Matemática da Faculdade de Ciências Integradas do Pontal da Universidade Federal de Uberlândia, visa apresentar uma sequência didática para favorecer o desenvolvimento do raciocínio proporcional tendo como suporte teórico a Teoria dos Campos Conceituais (TCC) de Gerard Vergnaud. São objetivos específicos: (a) analisar uma sequência didática, organizada na forma de situações-problema visando favorecer o estabelecimento das relações de covariação e de invariância de grandezas, necessárias para conceituar razão e proporção e (b) analisar o desempenho e as estratégias utilizadas pelos alunos para resolver situações- problema envolvendo o raciocínio proporcional, ao longo da aplicação da proposta didática. O trabalho tem apoio metodológico na Engenharia Didática e foi desenvolvido junto a aproximadamente 26 alunos do 6º ano do Ensino Fundamental de uma escola da cidade de Ituiutaba/MG, no período regular de aulas. A sequência teve seis etapas, na primeira foi aplicada uma avaliação tipo lápis e papel e as etapas seguintes foram constituídas por situações-problema aplicadas com mediação da professora e também por avaliações, sendo que estes instrumentos foram elaborados com base na literatura existente sobre o tema raciocínio proporcional. Os dados foram analisados quantitativamente por meio da estatística descritiva e qualitativamente quando foram organizadas categorias de análise. Na primeira etapa, houve mais dificuldade nos problemas de comparação que nos de valor omisso e as estratégias multiplicativas utilizadas pelos alunos indicaram alguma inferência e predição na compreensão de que as grandezas envolvidas nos problemas variavam em conjunto. Ao longo da aplicação da sequência, verificou-se que os alunos passaram a identificar as grandezas proporcionais envolvidas nas situações e a maioria deles conseguiu justificar as repostas por meio da relação de covariação, valendo-se da simbologia adequada. Considera-se que a opção metodológica de oferecer situações diversificadas antes da apresentação formal desse conteúdo (que acontece a partir do sétimo ano do Ensino Fundamental) contribui para desenvolver o raciocínio proporcional dos alunos. Espera-se que as análises e discussões teóricas realizadas nesse trabalho possam contribuir para a prática do professor de matemática. / This work, carried out during the Masters Course for teaching Science and Mathematics, within the postgraduate program in teaching Science and Mathematics at the Pontal College of Integrated Sciences of the Federal University of Uberlândia. It a aims to introduce a didactic sequence to encourage the development of proportional reasoning with the theoretical support the Theory of Conceptual Fields (TCC) by Gerard Vergnaud. The specific objectives are: (a) to analyze a didactic sequence, arranged in the form of problem situations in order to promote the establishment of relations of covariance and invariance of quantities, required to conceptualize reason and proportion and (b) examine the performance and the strategies used by the students to solve problem situations involving proportional reasoning, through the application of didactic proposal. The work has methodological support in Teaching Engineering and was developed together with approximately 26 students of the sixth grade of an elementary school in the city of Ituiutaba, Minas Gerais, during regular class periods. The sequence had six stages, the first was a pencil and paper type evaluation and review the following stages were composed of problem situations applied with mediation of a teacher as well as evaluations, being that these instruments have been drawn up on the basis of the existing literature on the subject of proportional reasoning. Data was analyzed through quantitative and qualitative descriptive statistics when the categories of analysis were set up. In the first step, there was more difficulty with the problems of comparison than those of omissive value and the multiplicative strategies used by the students indicated some inference and prediction on the understanding that the values involved in the problems varied together. Throughout the implementation of the result, it was found that the students have come to identify the proportional quantities involved in situations and most of them managed to justify the answers through the relationship of covariance, using the appropriate symbol. The methodological option of offering diverse situations before the formal presentation of this content (which happens from the seventh grade of primary school) helps to develop proportional reasoning of students. It is expected that the analysis and theoretical discussions undertaken in this work could contribute to the work of a Maths teacher. / Dissertação (Mestrado)