Negative Integer Understanding: Characterizing First Graders' Mental Models

This article presents results of a research study with a pretest, instruction, and posttest design that aimed to identify students' mental models of integers and investigate how these models change based on instruction on the unary and/or binary meanings of the minus sign. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students over-relied on various combinations of whole number principles as they tried to understand negative integers. However, a significant number of students developed formal mental models based on their instruction.