Types of Students’ Reasoning and Difficulties in Solving Integer Addition and Subtraction Problems - Puspita Sari; Paul Maurice Edmund Shutler (Mathematics Education Journal, 2026)
Students' well-documented difficulties and errors with integer arithmetic often stem from a reliance on procedural rules over conceptual understanding. Although numerous studies have examined various types of students’ reasoning and difficulties involved in solving integer addition and subtraction problems, existing research remains fragmented, and there is a lack of a systematic synthesis that explicitly links types of students’ reasoning to the specific difficulties they experience across different contexts and grade levels. This systematic literature review (SLR) paper synthesizes findings from 45 studies to describe types of students’ reasoning and the associated difficulties in solving integer addition and subtraction problems. Data was derived from both exploratory and experimental studies that provide descriptions on how students in grade 1 to 8 reason when solving integer addition and subtraction problems.  Data collection method involved identifying peer-reviewed journal articles through database searches and reference tracing, guided by specific inclusion and exclusion criteria. Across three broad categories of students’ reasoning-magnitude-based, order-based, and symbolic-logical-this review offers a synthesized framework that characterizes students’ conceptions of negative integers, strategies in solving integer addition and subtraction problems, and difficulties students encounter in the reasoning process. The findings indicate that students’ difficulties stem from their conceptions of integers within specific reasoning types, which often conflict with their prior understanding of whole numbers. This literature review also found that students sometimes apply reasoning that does not align with the context of a given problem. Such misalignment reflects students’ misconceptions, which contribute to difficulties in solving problems accurately and meaningfully.