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’ nonverbal 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 United States, suggesting that educational experiences may shape the codevelopment 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.