The balance model: Hindrance or support for the solving of linear equations with one unknown

The use of concrete models for teaching students how to solve equations is often debated in scientific literature. This article aims to examine the balance model and to identify the issues that divide scientists. We based our reflections on the results of an empirical study and analysis of the various arguments put forward by supporters and opponents of the model. We describe learning situations that were the subject of the empirical study, which involved forty students in two 8th-grade classes. The aim was to teach the formal solving method, which involved performing the same operations on both sides of the equation using, notably, the balance model. Analysis of students' reasoning showed that the presence of negative numbers gave rise to many errors. The difficulties presented by negative numbers were reviewed, eight months later, during an interview with five students, chosen from those who took part in the experiment. Within that context, we discuss the relevance of the balance model and analyse the arguments put forward by researchers who either defend or reject its use.This revised version was published online in September 2005 with corrections to the Cover Date.