Raciocínio matemático em conjuntos numéricos: Uma investigação no 3.º ciclo

Abstract

This article aims to analyze grade 7 and grade 9 students` mathematical reasoning while working on tasks involving properties of number sets Z and R. The conceptual framework emphasises generalization and justification as key aspects of mathematical reasoning, and also con- siders representations and sense making. The methodology is qualitative and data collection includes interviews and observation of classes (both video-recorded) and analysis of written tasks of four grade 7 students and three grade 9 students. Making generalization, most students follow an inductive approach, generalizing the relations observed in particular cases to a larger class of objects. There are also instances of abductive reasoning. Grade 9 students generalize in a more effective way and sometimes these generalizations have a deductive nature. Justifying is not done spontaneously, but, in response to teacher’s questioning, students show to be able to make justifications based on previous knowledge of properties or mathematical concepts and based on counterexamples that refute a statement.