Aprendiendo funciones complejas con GeoGebra

In this paper we describe a teaching experiment targeting with students of Complex Analysis attending an undergraduate course of a Portuguese university. Our main goal is the understanding of the GeoGebra role with respect to visualization and as a technological mediator, according to Vygotsky theory, in the teaching and learning process of complex functions. The first step of our study was the conception of a sequence of didactical tasks and the development of GeoGebra tools related to the target didactical objectives. Here we will describe the procedure related to the tasks implementation in a classroom environment and the achieved results based on the collected data composed by written assignments produced by students, video recording the student performance during the experiment, and the student constructions with GeoGebra. All the collected data were analysed from a qualitative and interpretative paradigm.publishe

A projeção estereográfica no GeoGebra

O GeoGebra permite a manipulação de objetos no plano, no espaço e a representação de funções vetoriais reais uni ou bidimensionais de duas variáveis reais. A criação da ferramenta Projeção Estereográfica de um ponto do plano na esfera de Riemman, estendido com as propriedades das cores dinâmicas que permitiram representar os domínios coloridos, possibilitou o desenvolvimento de aplicações que podem ser usadas no ensino e da aprendizagem de tópicos de análise complexas entre outros. Neste artigo apresentamos o essencial da ferramenta e algumas das suas aplicações para o ensino.GeoGebra allows the manipulation of objects in the plane, in space and the representation of real or two-dimensional vector functions of two real variables. The creation of the Stereographic Projection tool of a point of the plane in the Riemann sphere, extended with the properties of the dynamic colours allowing the representation of coloured domains, allowed the development of applications that can be used, among others, in the teaching and learning of complex analysis topics. In this paper we present the essential tools and some of their applications in the teaching process

Complex function with GeoGebra

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from to through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software

Promoting geometric reasoning in students with Autism Spectrum Disorder through a digital environment

O raciocínio e a construção do sentido espacial são capacidades essenciais em todos os processos de aprendizagem e compreensão matemática de crianças com desenvolvimento típico. Em crianças com Perturbação do Espectro do Autismo (PEA), estas capacidades se tornam ainda muito mais significativas, considerando o papel relevante que desempenham para uma vida independente bem-sucedida. O uso da tecnologia é referido como uma forma eficaz de trabalhar o conteúdo acadêmico com crianças com PEA, possibilitando a criação de ambientes criativos e construtivos onde se podem desenvolver atividades diferenciadas, significativas e de qualidade. No entanto, o desenvolvimento de aplicações tecnológicas para crianças e jovens com PEA continua a merecer pouca atenção, nomeadamente as que dizem respeito ao desenvolvimento do pensamento geométrico. O objetivo deste artigo é relatar os principais resultados obtidos com crianças com PEA utilizando o ambiente digital Learning Environment on Mathematics for Autistic Children desenvolvido, particularmente, no que se refere à promoção das suas capacidades matemáticas fundamentais em geometria. O “PISA 2015 Mathematics Framework” foi a base teórica utilizada para a recolha dos dados, cuja análise, para além de situar o pensamento geométrico dos alunos participantes entre parcialmente estruturado e estruturado, apontou, também, para o redesenho de algumas das atividades implementadas no ambiente digital, tendo em vista a promoção do pensamento geométrico.Reasoning and sense-making are essential capabilities in all mathematical learning and understanding processes, in children with typical development. In children with Autism Spectrum Disorder (ASD), these capabilities become much more significant, considering their importance for a successful independent living. The use of technology is considered an effective way to work academic content with children with ASD enabling the creation of creative and constructive environments where we can be develop differentiated, meaningful, and qualitative activities. However, the development of technological applications for children and youth with ASD continues to attract little attention, namely the ones regarding the development of geometric thinking. The purpose of this paper is to report the main results obtained with children with ASD using the digital Learning Environment on Mathematics for Autistic Children developed, particularly regarding the promotion of their fundamental mathematical capabilities in geometry. The “PISA 2015 Mathematics Framework” was the theoretical basis for the data collection. Its analysis allowed to place the geometric thought of the participating students between partially-structured and structured and has also pointed to the redesign of some of the activities implemented in the digital environment, in view of the promotion of geometric thinking.publishe