How different groups solve conditional and non-conditional combinatorial problems

Abstract

This study was developed collectively with elementary pre-service teachers and sought to investigate the performance presented by eight distinct groups with regard to resolution of conditional and non-conditional combinatorial problems. The test used is composed of eight problems, two of each type of combinatorial problems – cartesian product, arrangement, permutation and combination – one conditional and one non-conditional problem. The existence of the conditions was perceived and taken into account by the majority of participants. The Cartesian product problems presented larger number of correct answers in the different groups investigated, while in the combination ones were obtained the lowest percentage of correct answers. Within all the groups performance was better in the conditional problems. This result is attributed to the existence of a greater number of possibilities in non-conditional problems and the extensive use of informal strategies, such as listings, which hindered the exhaustion of possibilities.