Representational variation among elementary school students. A study within a functional approach to early algebra

Overview & Synopsis

This paper describes the differences in the types of representations used by eight third-grade (8 to 9-years-old) and eight fifth-grade (10 to 11-years-old) students when working with problems that involve different linear functions. We present an analysis of students’ written and oral answers during a Classroom Teaching Experiment (CTE) and semi-structured interviews from a functional approach to early algebra. The study examines how students’ representations varied when working with different types of linear functions (y=x+a; y=ax; y=ax+b), when solving for specific values, and when generalizing. The findings show that students in both grades primarily used the representation present in the problem. The type of linear function involved appears to have had no effect on either group’s use of one representation or another.