An Experiment in Teaching Ratio and Proportion

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the corpus of ratio problems in a physical context. But in one class, here called “Partial-experiment”, the learning environment was exclusively a paper-pencil one and the teacher followed his usual method in designing and conducting teaching sequences. In the other class, here called “Full-experiment”, the teaching was based on a framework, emerging from our analysis of complexity of ratio problems, involving precise guidelines and a specific computer environment. Using a pre-test and a post-test, we observed clear progress in both classes compared to a sample of “standard” pupils. Our comparative pupil-oriented study indicates more complete improvement in the “full-experiment” class, i.e., a better acquisition of fractions and their use for solving usual proportionality problems. The average pupil’s progress is greater in the “full experiment”, with the pupils who were initially high- or low-level attainers benefiting the most from the “full-experiment”.