What Conceptions have US Grade 4-6 Students' Generalized for Formal and Informal Common Representations of Unknown Addends?

Abstract

This article reports findings from a study of grade 4-6 students' conception(s) for various representations of unknown addends [variables] commonly found in US elementary mathematics textbooks. Specifically, thirty-six US grade 4-6 students participated in two semi-structured task based interviews designed to explore their conception(s) of formal and informal representations of unknown addends as revealed by the types of numbers substituted across core mathematical tasks and task types.