Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-11T14:56:10Z No. of bitstreams: 1 emersontomazdacosta.pdf: 8177799 bytes, checksum: 632d980c765ede7360c28b736b9599e5 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T03:36:55Z (GMT) No. of bitstreams: 1 emersontomazdacosta.pdf: 8177799 bytes, checksum: 632d980c765ede7360c28b736b9599e5 (MD5) / Made available in DSpace on 2016-04-24T03:36:55Z (GMT). No. of bitstreams: 1 emersontomazdacosta.pdf: 8177799 bytes, checksum: 632d980c765ede7360c28b736b9599e5 (MD5) Previous issue date: 2013-08-30 / Esta pesquisa, de caráter qualitativo, tem como objetivo investigar, identificar e analisar o uso de Tecnologias da Informação e Comunicação (TICs) no ensino do Teorema Fundamental da Álgebra (TFA) no Ensino Médio (EM). Especificamente, o objetivo é organizar e delinear atividades investigativas em que se utilizem as TICs no estudo dos Polinômios, no que concerne à apreciação de pontos, círculos e curvas de R2 em R2 . As atividades foram desenvolvidas com alunos do 3º ano do Ensino Médio, de uma escola militar, identificando as contribuições que ocorreram no processo de ensino e aprendizagem do TFA com o uso do Software TFA. A fundamentação da Metodologia de Pesquisa quanto ao uso das TICs na Educação Matemática pautou-se nas ideias de Miskulin (1999), Borba e Penteado (2010) e outros. O resultado da pesquisa revela uma expressiva necessidade de atividades inovadoras com o uso pelas TICs no estudo dos Polinômios, em que aluno e professor possam interagir de forma que, a aprendizagem do objeto matemático e a prática pedagógica, se torne evidente nesse processo. Dessa forma, como Produto Educacional, resultado da presente Dissertação, são apresentadas atividades investigativas que podem ser desenvolvidas no Ensino Médio, no estudo dos Polinômios. / This search with qualitative character has as an aims to investigate, identify and analyze the use of information and Communication Technologies (ICTs) in teaching the Fundamental Theorem of algebra (TFA) in high school (in). Specifically, the goal is to organize and outline investigative activities in wich ICTs are used in the study of polynomials, concerning the assessment of points, circles and curve of R2 at R2. The activities were developed with students of the third of high year school, a military school, by identifying the contributions that have occurred in the process of teaching an learning software rising the TFA. The basis of the research methodology for the use of ICT in mathematics education was based on the ideas of Miskulin (1999), Borba, Penteado (2010) and others. The result of the research reveals a significant need for innovative activities using ICT in the study of polynomials, where students and teachers can interact so that, learning the objective mathematical and pedagogical practice, this process becomes evident. Thus, educational product as a result of this dissertation are presented research that can be developed in high school, in the study if polynomials.

The thesis is concerned with the introduction of complex num- bers. This topic is often perceived by pupils and students as very mysterious. This is often due to excessive formality, to which more time is devoted than to the illustrative geometrical concept of complex numbers. As a result, the important theorems achieved by complex numbers in the field of mathema- tics are consequently skipped. This thesis focuses on an illustrative geometric view on the field of complex numbers that will facilitate the understanding of related undergraduate curriculum. The text is written for readers at the upper grades of high school and first years of college. Examples are also included to create a coherent text useful for teaching and self-study. 1

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)

In this thesis I present new insights into aspects of Peter Guthrie Tait's life and work, derived principally from largely-unexplored primary source material: Tait's scrapbook, the Tait–Maxwell school-book and Tait's pocket notebook. By way of associated historical insights, I also come to discuss the innovative and far-reaching mathematics of the elusive Frenchman, C.-V. Mourey. P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen's College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin. Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait's life in connection with The Unseen Universe (1875) which Tait co-authored with Balfour Stewart (1828–1887). I also reveal Tait's surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a re-evaluation of C.-V. Mourey's 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.