Esse trabalho é um estudo sobre circuitos resistivos que apresentam a característica da autossimilaridade em sua configuração. A construção desses circuitos é feita de uma maneira recursiva, de forma análoga a um fractal autossimilar. Os circuitos são analisados pelas suas resistências equivalentes, sendo obtida uma condição para convergência desse valor. Os conceitos auxiliares necessários ao tema desta dissertação abordam a representação de um circuito resistivo como um grafo, além de conceitos envolvendo fractais autossimilares. São propostas ao final de cada capítulo atividades interdisciplinares acessíveis a alunos de ensino médio, com conteúdos envolvendo resistência equivalente, sequências, conjuntos, e noções de área e perímetro. / This work is a study of resistive circuits which present a characteristic of self similarity in their configuration. The construction of these circuits is made in a self recursive way, analogously to a self similar fractal. The circuits are analyzed by their equivalent resistance, and a condition for convergence of this quantity is obtained. Auxiliary concepts that are necessary to this dissertation theme treat the resistive circuit as a graph, and concepts involving self similar fractals. It is proposed at the end of each chapter interdisciplinary activities that are accessible to high school students, with topics involving equivalent resistence, sequences, sets, and notions of area and perimeter.

Esse trabalho é um estudo sobre circuitos resistivos que apresentam a característica da autossimilaridade em sua configuração. A construção desses circuitos é feita de uma maneira recursiva, de forma análoga a um fractal autossimilar. Os circuitos são analisados pelas suas resistências equivalentes, sendo obtida uma condição para convergência desse valor. Os conceitos auxiliares necessários ao tema desta dissertação abordam a representação de um circuito resistivo como um grafo, além de conceitos envolvendo fractais autossimilares. São propostas ao final de cada capítulo atividades interdisciplinares acessíveis a alunos de ensino médio, com conteúdos envolvendo resistência equivalente, sequências, conjuntos, e noções de área e perímetro. / This work is a study of resistive circuits which present a characteristic of self similarity in their configuration. The construction of these circuits is made in a self recursive way, analogously to a self similar fractal. The circuits are analyzed by their equivalent resistance, and a condition for convergence of this quantity is obtained. Auxiliary concepts that are necessary to this dissertation theme treat the resistive circuit as a graph, and concepts involving self similar fractals. It is proposed at the end of each chapter interdisciplinary activities that are accessible to high school students, with topics involving equivalent resistence, sequences, sets, and notions of area and perimeter.

The aim of this study is to ascertain what misconceptions N2 students have about DC resistive circuits and how screencasts could effect on the rectification of these misconceptions. This study was conducted at the Kathu Campus of the Northern Cape Rural Further Education and Training College in the town Kathu in the arid Northern Cape. The empirical part of this study was conducted during the first six months of 2013. A design-based research (DBR) method consisting of four phases was used. DBR function is to design and develop interventions such as a procedure, new teachinglearning strategies, and in the case of this study a technology-enhanced learning (TEL) tool (screencast) with the purpose of solving a versatile didactic problem and to acquire information about the interventions of the TEL tool (screencast) on the learning of a student. In the first and second phase of DBR quantitative data for this research were gathered with the Determining and Interpreting Resistive Electric circuits Concepts Test (DIRECT) in order to determine the four most common misconceptions. The DIRECT test was conducted in the first trimester to find the misconceptions; the test was conducted in the second trimester also to confirm the misconceptions. Further quantitative data were collected from a demographic questionnaire. The qualitative data were collected by individual interviews in the fourth phase of the research project. Phase three of this study was the development of screencasts in the four most prominent misconceptions in DC resistive circuits of the students. The respondents of this study were non-randomly chosen and comprised of two groups, one in the first trimester of the year and one in the second trimester of the year, which enrolled for the N2 Electrical or Millwright courses. The respondents were predominant male and representing the three main cultural groups in the Northern Cape namely: Black, Coloured and White. The four misconceptions on DC resistive circuits that were identified were: (i) understanding of concepts, (ii) understanding of short circuit, (iii) battery as a constant current source, and (iv) rule application error. Screencasts clarifying the four misconceptions were developed and distributed to the respondents. On the foundation of the results of this research, it can be concluded that the students have several misconceptions around direct current resistive direct current circuits and that the use of TEL like screencasts can be used to solve some of these misconceptions. Screencasts could supplement education when they were incorporated into the tutoring and learning for supporting student understanding. The results of this research could lead to the further development and refinement of screencasts on DC resistive circuits and also useable guidelines in creating innovative screencasts on DC resistive circuits. / MEd (Curriculum Development), North-West University, Potchefstroom Campus, 2014

The aim of this study is to ascertain what misconceptions N2 students have about DC resistive circuits and how screencasts could effect on the rectification of these misconceptions. This study was conducted at the Kathu Campus of the Northern Cape Rural Further Education and Training College in the town Kathu in the arid Northern Cape. The empirical part of this study was conducted during the first six months of 2013. A design-based research (DBR) method consisting of four phases was used. DBR function is to design and develop interventions such as a procedure, new teachinglearning strategies, and in the case of this study a technology-enhanced learning (TEL) tool (screencast) with the purpose of solving a versatile didactic problem and to acquire information about the interventions of the TEL tool (screencast) on the learning of a student. In the first and second phase of DBR quantitative data for this research were gathered with the Determining and Interpreting Resistive Electric circuits Concepts Test (DIRECT) in order to determine the four most common misconceptions. The DIRECT test was conducted in the first trimester to find the misconceptions; the test was conducted in the second trimester also to confirm the misconceptions. Further quantitative data were collected from a demographic questionnaire. The qualitative data were collected by individual interviews in the fourth phase of the research project. Phase three of this study was the development of screencasts in the four most prominent misconceptions in DC resistive circuits of the students. The respondents of this study were non-randomly chosen and comprised of two groups, one in the first trimester of the year and one in the second trimester of the year, which enrolled for the N2 Electrical or Millwright courses. The respondents were predominant male and representing the three main cultural groups in the Northern Cape namely: Black, Coloured and White. The four misconceptions on DC resistive circuits that were identified were: (i) understanding of concepts, (ii) understanding of short circuit, (iii) battery as a constant current source, and (iv) rule application error. Screencasts clarifying the four misconceptions were developed and distributed to the respondents. On the foundation of the results of this research, it can be concluded that the students have several misconceptions around direct current resistive direct current circuits and that the use of TEL like screencasts can be used to solve some of these misconceptions. Screencasts could supplement education when they were incorporated into the tutoring and learning for supporting student understanding. The results of this research could lead to the further development and refinement of screencasts on DC resistive circuits and also useable guidelines in creating innovative screencasts on DC resistive circuits. / MEd (Curriculum Development), North-West University, Potchefstroom Campus, 2014