A longitudinal investigation of the co-development and bidirectional relations among whole number arithmetic and conceptual and procedural fraction knowledge

How do conceptual and procedural fraction knowledge influence the development of each other over time? Is their pattern of development a reflection of instruction? In the present study we conducted a four-wave longitudinal investigation of the co- and bidirectional development of whole number arithmetic, and conceptual and procedural fraction knowledge during a critical phase of fraction learning. Chinese students (N = 1,055, Mage = 9.8, SD = 0.7) educated through a linear curriculum completed whole number arithmetic, and conceptual and procedural fraction assessments during the first and second terms in Grade 4 and Grade 5. Cross-lagged panel analysis, controlling for students’ non-verbal reasoning skills, revealed that conceptual and procedural fraction knowledge did not influence the development of one another prior to Grade 5. However, starting in Grade 5, a unidirectional pattern emerged, where conceptual fraction knowledge supported the development of procedural fraction knowledge. This unilateral conceptual-to-procedural pattern of development contrasts with findings from studies with students in the U.S., suggesting that educational experiences may shape the co-development of these two types of fraction knowledge. Furthermore, proficiency in whole number arithmetic predicted the development in both conceptual and procedural fraction knowledge, highlighting its important role alongside conceptual knowledge in supporting the acquisition of fraction procedures. Our findings emphasize the need to consider educational experiences and foster meaningful connections between concepts and procedures during fraction instruction while promoting mastery of whole number arithmetic to promote students’ development of fraction knowledge.