O uso da modelação matemática na construção do conceito de função - Pires, Rogério Fernando (2009)
This study aimed to achieve an interventional study to investigate the real possibilities of introducing the concept of affine function in the 7th year of elementary school, contrary to what is traditionally offered in the official documents of the Brazilian education. In fact, function is usually introduced only in the 9th year of elementary school, or at 1st year of high school, whilst our goal is to shorten this release for at least two school years. The research question of the study is: What are the real possibility of introducing the concept of affine function in the 7th year of elementary school by means of solving problems? In order to answer such question it was developed a quasi-experimental research which was conducted with 53 students from a public school sited in the Salto de Pirapora City, in São Paulo State. These students were divided into two groups: the experimental group (GE) formed by 29 students who took part in a teaching intervention planned to introduce the basic concepts of affine function - and control group (CG), composed by 24 students who did not have any type of teaching on the issue. All students had never being formally studied function before. All participants were given a pre and a post-test. The study was based on mathematical modeling, inspired mainly in Bassanezi´s ideas (2007), as well as Biembengut and Hein (2007). The results in the pre and in the post-test, in the two groups, were analysed according to the number of correct responses and according to the types of errors students made. It confirmed that no significant differences were found between groups in the pre-test. However, in contrast to GC, GE performed significantly better in the post-test than in the pre-test. Moreover, when groups are compared, the superior performance of GE over GC in post-test was statistically significant. Finally, the results pointed out that introducing affine function to 7th grade school, through problem solving and taking into account modeling mathematical, seems to be a suitable didactical strategy, since by the end of this study GE students were able to analyse the behavior of affine function graph, such as increasing and decreasing ,as well as to build the own function graph