Capturing the interconnected development of whole number arithmetic operations using a network approach

We used network analysis to examine the structure and development of arithmetic fluency in Chinese students from Grades 3 to 6—a critical period during which fluency across the four operations becomes increasingly integrated. In two preregistered studies, students completed timed fluency tasks in addition, subtraction, multiplication, and division. In Study 1, we compared network structures in Grade 3 (N = 1,072; Mage = 9.1 years) and Grade 6 (N = 1,160; Mage = 12.1 years). We found that students in Grade 6 demonstrated more strongly interconnected and uniformly structured networks than those in Grade 3. In Study 2, students (N = 1,055; Mage = 9.8 years) were assessed in a longitudinal design at four time points from Grades 4 to 5. Addition and subtraction consistently emerged as central operations, forming the foundational core of the arithmetic network. Division reflected significant integration of knowledge from other operations whereas multiplication generally showed weak connections with the other operations. Overall, development was highly interdependent with improvements in one operation closely linked to gains in others. This research provides empirical evidence that arithmetic knowledge evolves from a differentiated structure into a unified and interconnected system, highlighting the value of viewing arithmetic development as a dynamic network of associations that consolidate over time.