Facilitating the development of proportional reasoning through teaching ratio

This study was part of a Master of Education project to design an assessment interview to identify the points of growth, or stages of development, in children’s thinking about ratio problems. Ratio is a sub-construct of rational number (Kieren, 1976) that requires proportional reasoning. The purpose of ‘growth points’ is to describe the developmental pathway children typically follow, and to inform teachers of where children have reached developmentally so that further learning can be targeted to their zone of proximal development. Two questions are explored in this paper: how do children typically develop ratio understandings, and can teachers use this knowledge in order to facilitate the development of proportional reasoning