Representing equality: a tangible balance beam for early algebra education

In this paper we describe the design and implementation of a tangible balance beam that we created for early algebra education. We also present data from an exploratory study with seven children (ages 9--10 years) in a local elementary summer school classroom. Our results provide insight into how students solve algebra problems using our tangible interface, how they coordinate multiple representations (both digital and physical) in the problem solving process, and how they understand the concept of algebraic equality in this context. The data suggests that our interface helps students think about equations in a relational context, which has been shown to be an important skill for understanding more advanced concepts in algebra. Whether or not the combination of physical and digital representations provided by our interface helps students apply this relational understanding to equations written using standard algebraic notation is an open question that we hope to investigate in future work.