Rational numbers and intensive quantities: Challenges and insights to pupils' Implicit knowledge

This paper analyzes the difficulties that pupils have in learning to use rational numbers to refer to quantities as well as those involved in understanding equivalence and order in rational numbers. It is shown that pupils' performance in all these tasks is not a matter of an all-or-nothing knowledge. Rational numbers are used in different situations, which can help or hinder pupils' insights into the logic of rational numbers. The concluding section suggests that there is less awareness of the logic of rational numbers because culture often is organised to facilitate our functioning even if we don't understand rational numbers well. We argue that it is important to develop this understanding in school so that young people are not at a loss when this knowledge is required. © 2008: Servicio de Publicaciones de la Universidad de Murcia