Padrões na aprendizagem matemática : uma possibilidade a partir do uso de software de computação gráfica
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Data
2016-02-29
Autores
Santos, Leandra Gonçalves dos
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Universidade Federal do Espírito Santo
Resumo
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.
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Palavras-chave
Mathematics education , Mathematical patterns , Graphical computation , Fundamental schooling , Junior Scientific Initiation Project , Educação Matemática , Projeto de Iniciação Científica Júnior , Padrões Matemáticos , Percepção de padrões