>Magister Scientiae - MSc / The aim of the thesis is to research the difficulties that first year mainstream mathematics students at UWC experience when solving Related Rates problems in calculus. In chapter 2, an in-depth study was made of the nature of Related Rates problems by studying a number of examples. The findings of this study are summarized in section 2.12. The study adopted the same model of the solution of all types of Related Rates that was used by Martin (2000) for the solution of geometric Related Rates problems. In chapter 3 of this thesis, many examples were used to illustrate how the seven step solution procedure of the Standard Solution model is applied. In the literature review in chapter 4, the underlying concepts which underpin Related Rates problems are identified and specific examples of research on each of these concepts are given. For example, the review of the literature on word problems is done comprehensively and covers extensively the range of issues involved in this topic. Drawing on the work in chapter 2 on the nature of Related Rates problems, it is explained in chapter 5 why this study is underpinned by Constructivism as a theoretical basis. Chapter 6 of the thesis is devoted to answering the 3 research questions posed in chapter 1. The thesis contains many worked examples of Related Rates problems which can be used by the lecturers assigned to the MAT105 course.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho tem como objetivo auxiliar professores de Educação Básica a abordar alguns conceitos básicos de Cálculo Diferencial e Integral no terceiro ano do ensino médio, utilizando os softwares wxMaxima e Geogebra. Nossa proposta visa resgatar o ensino do Cálculo no âmbito escolar, mas de uma maneira diferente da tradicional, utilizando a tecnologia em nosso favor, como uma ferramenta facilitadora no processo ensino-aprendizagem de conceitos de limites, derivadas e integrais. A ideia é que toda a parte algébrica e gráfica, que exige conhecimentos matemáticos específicos, seja feita pelos softwares e que os estudantes aprendam a interpretar as soluções que as ferramentas nos fornecem e a conhecerem um pouco mais sobre a matemática e suas aplicações. / The present work aims to help Basic Education teachers to approach some basic concepts of Differential and Integral Calculus in the third year of high school using the software wxMaxima and Geogebra. Our purpose is to recover the teaching of Calculus in the school context, but in a different way from the traditional one, using the technology in our favor, as a facilitating tool in the teaching-learning process of boundary, derivative and integral concepts. The idea is that all the algebraic and graphic part, which requires specific mathematical knowledge, is done by software and that students learn to interpret the solutions that the tools provide us and to know a little more about mathematics and its applications.