Mental computation: An opportunity to develop students’ strategies in rational number division

Mental computation provides a good environment to develop students’ strategies in division of rational numbers. In this paper, we seek to analyze mental computations strategies in rational number division used by grade 6 students, during a teaching experiment. The teaching experiment emphasizes collective discussions and was based on tasks involving number sentences and word problems with the four basic operations. The methodology was design-based research with two experimental cycles involving two teachers and 39 students. All lessons were audio and video recorded. The results show that students mostly use numerical relationships strategies supported by propositional representations in rational number division. Initially, students’ strategies are based on applying a procedure and evolve to strategies that relate division and multiplication.