Padrões na aprendizagem matemática : uma possibilidade a partir do uso de software de computação gráfica - Santos, Leandra Gonçalves dos (2016)
The doctoral research was a study in mathematics education that investigates the potentialities of learning of a group of tem students from 8th and 9th grades from fundamental schooling, participating in a Junior Scientific Initiation Project [PIBIC Jr] from a municipal school of Vitoria, in the state of Espírito Santo. This study took place from July 2013 until February 2014. It aimed to explore mathematical tasks that helped students to find out patterns and regularities and helped them to come up with generalizations of mathematical ideas. It still aimed to identify students’ strategies to solve pattern tasks and represent them with graphical computing software. The methodological procedures had their background on qualitative research in the field of mathematics education. The inquiry observed the representations that students showed in the process of learning to formalize and generalize mathematical and computational patterns. It has used, for this matter, during the Junior Scientific Initiation Project, two graphical computational software, the Sweet Home® and the Auto Cad®. The theoretical-methodological foundations from the studies of patterns come from the work from Vale and Pimentel. Tall, Skemp, Vygotsky, among others, that contributed to the comprehension of the mathematical representations done by the pupils when solving a mathematical task. For the studies of computational images, Azevedo and Conci, as well as Tall, contributed in the comprehension of the mathematical patterns’ identification in such images. Our results indicate that the students learn in an instrumental way and show difficulties to represent a generalization and to find the general term. In the computational tasks, even though the students identified the mathematical concepts and patterns necessary to solve the tasks they still felt difficulties in explicating verbally and in representing the concepts and images involved. However, they made the images requested with the help of the computational software and they arrived by trial and error in the representations of the images. Nonetheless, when they received an image of a computational task already done, they were not able to represent this computational image by means of a mathematical concept or a general formula. With this, our study calls attention to the relevance of working on a routine basis with mathematical patterns tasks as well as to link those ideas involved with their mathematical and computational representations. Therefore, our thesis is that the pupils participating at PIBIC Jr felt themselves motivated to learn mathematical concepts and to solve computational tasks and also developed cognitive and emotional competences of junior researchers. In addition to that, they tried to find out strategies to solve the mathematical patterns tasks, but exhibited difficulties to identify the general term. In this way, they were able to perceive the mathematical elements from graphical computation, but they had trouble to represent images and to associate them to mathematical patterns related with this computational task.