Made available in DSpace on 2016-06-02T20:02:56Z (GMT). No. of bitstreams: 1 6348.pdf: 5950256 bytes, checksum: 045f3c058bbb3f83ec90b1bd1f959acd (MD5) Previous issue date: 2014-08-14 / Financiadora de Estudos e Projetos / The objective of this research is to analyze the production of feelings and meanings that high-school students experience when enrolled in activities related to the concept of the Prisma Volume. The activities were organized by the teacher and considered the contents of composition and decomposition of figures. During the development of the manipulatives activities, for example, the golden material was used. Acrylic prisms were also used so that students could manipulate and calculate their volumes. The research is qualitative and can be characterized as a Case Study. The question guiding this study is: what are the feelings and the meanings that can be produced by high-school students when they experience educational activities while studying the concept of Materials Volume? The survey was conducted in a private school in São Carlos-SP, where classes were filmed and, after the development of activities, an analysis of their speeches and writings was held based on the interactions within the classroom with the teacher s mediation. Students performed three activities in thirteen classes, which were divided didactically, to be analyzed in the form of teaching episodes. Thus, information that enabled the understanding of what is interpreted to be the production of feelings and meanings made by students were pooled. Results suggest that the production of feelings and meanings explicited by the students are related to the skill of spatial visualization of the prism and its constituent elements, such as: measurement, size, composition area and perimeter. / O objetivo desta investigação é analisar a produção de sentidos e de significados produzidos por estudantes do Ensino Médio quando vivenciam atividades de ensino sobre o conceito de Volume de Prisma. As atividades foram organizadas pelo professor e consideram os conteúdos de composição e decomposição de figuras. Durante o desenvolvimento das atividades foram utilizados materiais manipuláveis, como, por exemplo, o material dourado. Além disso, prismas de acrílicos também foram utilizados para que os estudantes pudessem manipular e calcular os respectivos volumes. A pesquisa é qualitativa e pode ser caracterizada como Estudo de Caso. A questão que norteia o estudo é: quais são os sentidos e os significados que podem ser produzidos por estudantes do Ensino Médio ao vivenciarem atividades de ensino enquanto estudam o conceito de Volume de Primas? A pesquisa foi realizada numa escola particular de São Carlos-SP, onde as aulas foram filmadas e, após o desenvolvimento das atividades, a narrativa e a escrita dos estudantes foram analisadas com base nas interações que ocorreram na sala de aula e na mediação do professor. Os estudantes realizaram três atividades em treze horas-aula, as quais foram divididas, didaticamente, para serem analisadas, na forma de episódios de ensino. As informações obtidas possibilitaram o entendimento do que se interpretou como a produção de sentidos e de significados feitas pelos estudantes. Os resultados sugerem que a produção de sentidos e de significados explicitadas pelos estudantes estão relacionadas à habilidade da visualização espacial do prisma e de seus elementos constitutivos, tais como: medida, dimensão, composição e decomposição, área e perímetro.

Title: Understanding Area and Volume Formulae of Geometric Figures in the History of Mathematics and by Pupils Author: Bc. Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, DSc. The aim of this thesis is to describe the nature and possible causes of problematic areas in pupils' understanding of area and volume of geometric shapes and solids and treat this issue from the point of view of its ontogeny and phylogeny. Modern theories of gradual formation of the concepts of area and volume in pupils' minds will be characterized, together with the historical development of these concepts (from ancient Egypt and Greece to modern day). Complex analysis of the current Mathematics course books for primary and lower-secondary level is offered in the second part of the thesis. The analysis is based on the criteria following from the study of academic literature and on the historic research in this area. The aim of the analysis is to describe the way in which the course books treat geometric formulae and to what extent they respect their gradual development. In the final discussion, general aspects leading from the analysis will be summarized and offered as possible inspiration for pupils, teachers and future teachers of Mathematics. Key Words: formula, area, volume, algebraic language, hypothetical...