Cristiane Azevêdo dos Santos Pessoa

ESTUDO DE CASO: COMO DUAS CRIANÇAS PASSAM A COMPREENDER A COMBINATÓRIA A PARTIR DE INTERVENÇÕES?

In this case study we analyzed the performance of two students in the 5th year of elementary school by working with combinatorial problems. A pre-test, two intervention sessions and a post-test with the whole class were performed, but for the present analysis only the performances of Lucas and Marcos were taken into consideration, trying to analyze in detail how these two children have come to understand the four types of combinatorial problems (Cartesian Product, Arrangement, Permutation and Combination). We observed the contributions of the interventions, which were based on the list of possibilities as a strategy and on three pillars that are important for understanding the combinatorics: the emphasis on the invariants of combinatorial problems, the systematization and generalization of the possibilities. The listing strategy was seen as important for teaching, after it had been detected in previous studies as a way of probing used by students in different grade levels. Although the other pillars (invariants, systematization and generalization) appear less frequently in probing studies, they are known as facilitators of the combinatorics comprehension, so they were highlighted during procedures. The two investigated students showed a better performance on quantitative and qualitative terms, with a higher level of correct answers and better understanding of problems after the interventions. They started using the pillars worked in the interventions, which shows that the path chosen to work with the combinatorics was significant for learning.

Discutindo combinatória em um processo de formação continuada com professores dos anos iniciais

The study aims to analyze the effect of continuing education based on situations, invariants and symbolic representations of combinatorial problems. This research is composed of initial individual interviews, four formation meetings and a final interview, also individual, with the participant teachers. In this article, we analyze the development of a teacher taking part in the process. The results indicate a difficulty in the recognition and in the approach of combinatorics during the initial interview; however, after the interventions, there is a more detailed recognition of different situations and their invariants, as well as of representations. It is clear; therefore, that continuing education in combinatorics may constitute an important action because it stimulates teachers to reflect about this content, which can be used from initial grades on.