Categories of children’s understandings of function tables and graphs

Early algebra involves engaging students in the algebraic thinking practices of generalizing, justifying, representing, and reasoning about mathematical structure and relationships. Building on research on young learners’ functional thinking, we focused on young learners’ representations of functional relationships and how they reason with these relationships in the context of two representations. Using classroom teaching experiments, we studied how Kindergarten and Grades 1 and 2 students reason about function tables and graphs. The classroom teaching experiments entailed a sequence of 16 lessons with kindergarten students and 14 lessons with Grades 1 and 2 students, with individual interviews with a subset of students before, during, and after the lessons. Through qualitative analysis, we developed analytic categories that describe students’ understandings of function tables and graphs. We present these categories and suggest ways future research might build on them and how they might inform the development of resources that support early algebra learning.