Arithmetic and Algebra through Mathematical Structure: Performance and Solution Strategies of 6th- and 7th-Grade Students

Abstract

This study examined the performance and solution strategies of 6th- and 7th-grade students on structurally matched arithmetic and algebraic tasks within the framework of generalized arithmetic. An explanatory sequential mixed-methods design was employed with 150 students, including 90 sixth graders and 60 seventh graders, followed by task-based interviews with six students. Written responses were classified as correct, incorrect, or blank, while solution strategies were categorized as procedural/computational or relational/structural. The findings showed that correct-response rates were higher for arithmetic than for corresponding algebraic tasks at both grade levels and were generally higher among seventh-grade students. Procedural/computational strategies predominated, particularly in arithmetic tasks, whereas relational/structural strategies were observed more frequently in seventh-grade algebraic tasks. However, the use of a relational/structural strategy did not always result in a correct solution. Interview findings further illustrated that students’ strategy use varied across tasks and mathematical structures. Overall, the findings indicate that performance and strategy use constitute related but distinct dimensions and that understanding the relationship between arithmetic and algebra requires attention not only to accuracy but also to how students recognize and use mathematical structure across different representations.