Structural relationships among number sense performance, fraction and decimal understanding, and mathematics achievement: Evidence from sixth-grade students in Türkiye

This study investigates the structural relationships among sixth-grade students’ number sense, understanding of fractions and decimals, and mathematics achievement through Structural Equation Modeling (SEM). The sample consisted of 272 sixth-grade students (aged 11–12) from public schools in western Türkiye. Number Sense Test (NST), Fraction Conceptual Understanding Test (FCUT), and Decimal Conceptual Understanding Test (DCUT) were used. Data were analyzed using SPSS and SEM path analysis. Results showed that students’ overall number sense performance was low and differed across components. Students performed better in numerical meaning and magnitude but struggled with interpreting operations and judging result reasonableness. SEM results showed NST significantly predicted FCUT and DCUT, which in turn predicted GPA. NST had indirect effects on GPA through FCUT and DCUT and a direct effect in the partial mediation model, explaining 46% of GPA variance. Overall, number sense influences achievement directly and indirectly through rational number understanding.