The Sound of Fractions: teaching inherently abstract representations from an aural and embodied approach

Learning fractions is the focus for much of elementary school mathematics instruction because it is important and can be difficult. Fractions constitute a system of thinking about numbers and representations that differs in important ways from counting numbers. To understand fractions requires, for example, perceiving that a symbol such as 6 is not automatically associated with a larger quantity than 5 if they are denominators. In the system that constitutes fractions, 1/5 is bigger than 1/6. When students fail to master the system of fractions by a certain age, the inherent difficulty of the concepts can become confounded with discouragement, boredom, and humiliation. Music, especially percussion, not only provides an engaging context for many students but musical patterning can also provide deep analogic experiences to fractions at embodied and representational levels. Reasonable questions about musical patterns can both motivate and guide students towards understanding the properties of systems of fractions and their representations. We utilize this possibility in a new tool and associated curriculum called Sound of Fractions (SoF). SoF incorporates three main ideas to leverage musical interest and skill to provide an alternative approach to teaching fractions:

Experiencing the whole and the part at the same time is crucial to learning fractions;

Drumming is a compelling, embodied, culturally-relevant activity that allows students to experience the wholes, the parts, and the relationships between them at the same time;

A new computer-based representational infrastructure utilizing aural, visual, physical, and temporal components that scaffolds classroom-based activities that bridge the relationship between percussion-related and mathematics activities in such a way as to gradually bring the student towards more standard mathematical representations and usages.

We conducted preliminary testing of this approach in two series of after school programs with 5th-8th grade children who were significantly behind in learning fractions. Preliminary indications are that the approach is promising and ready to be tried in more formal contexts. This work illustrates that instruction rich in representational infrastructure and domains continues to be an important component of how technology can have positive impact.