A Cross-Sectional Investigation of Students’ Reasoning About Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. The authors applied their previously developed framework for 5 Ways of Reasoning (WoRs) to their data set to describe patterns within and across participant groups. The authors provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory of learning about integers.