Elementary Students’ Inquiry into the Order of Operations with Addition and Subtraction, Addition and Multiplication

This study examines students’ inquiry into the order of operations with addition and subtraction and the order of operations with addition and multiplication in a fifth-grade classroom. At the beginning, students passively accepted the rules for the order of operations based on external authority, with little interest in possibility of alternative calculations or the reasons for the rules. However, as their inquiry progressed, students faced various issues related to the order of operations and made a significant development in their understanding of the rules through class discussion. Based on the results, this paper discusses two key educational implications: First, the order of operations can be a good material for students to develop the ability to handle numerical expressions flexibly. Second, the order of operations offers a meaningful context for students to fulfill their subjectivity and develop into autonomous and responsible learners.