Ensino e aprendizagem de problemas de produto cartesiano: inter-relações entre diferentes representações
AUTOR(ES)
Vera Lucia da Silva
DATA DE PUBLICAÇÃO
2006
RESUMO
This research is about a teaching project aiming at mastering abilities and concepts related to the solution of problems of Cartesian product. The selected population were students of 4th Grade from a State School in the eastern region of the city of São Paulo. Our reference is the G. Vergnaud Conceptual Fields Theory and we took in consideration theoretical elements from researchers interested in studying the multiplicative reasoning. Data were collected from continuous observation and evaluation of the students performance, from the analyses of the materials produced by them and from interviews. The activities were designed with the intent of establishing connections between adding and multiplying processes and the processes involved in the determination of all the pairs of the Cartesian product. These connections become evident when represented by means of spatial relations promoting the evolution of non-conventional representations, produced by the students, to conventional representations, in Cartesian graphics and tree diagrams. The major contributions of this research for understanding the cognitive operations involved in solving Cartesian product problems are the repertory of non-conventional processes, employed by the selected group of participants, and their justification, and the analyses of the phenomena that occur in the passage from one to the other of the different representations of the Cartesian product. This research also offers contribution for the training of elementary education teachers
ASSUNTO(S)
combinações procedimentos aditivos e multiplicativos educacao matematica word problems produto cartesiano matematica representações espaciais cartesian product adding and multiplying processes spatial representations
