Related Experiment Video
Updated: Oct 4, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
Published on: August 28, 2021
Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese
Chang Xu1, Hongxia Li2, Sabrina Di Lonardo Burr3
1Department of Psychology, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
Abstract:
How do whole number arithmetic skills support students' understanding of fraction magnitude during the emerging stages of fraction learning? Chinese students in Grade 4 (N = 1038; Mage = 9.9 years; 55.6% boys) completed assessments of whole number arithmetic skills (i.e., addition, subtraction, multiplication, and division), fraction mapping (i.e., connecting visual fraction representations to fraction notations), and fraction comparison (i.e., comparing magnitudes of fraction symbols). We found that division skills uniquely differentiated students who had a basic understanding of fraction notation (mappers) from students with no understanding of fraction notation (non-mappers). Furthermore, we found that division mediated the relations between all three other arithmetic operations (i.e., addition, subtraction, and multiplication) and fraction mapping performance for the mappers. For fraction comparison, there was evidence of the whole number bias for the majority of students. The current results highlight the importance of the mastery of division skills and its dominance in predicting individual differences in fraction mapping for Chinese students in Grade 4.
Related Concept Videos
Propagation of Uncertainty from Random Error
Piaget's Stage 3 of Cognitive Development
Conservation and Constancy of Quantity
A significant cognitive milestone in the...
Significant Figures in Calculations
Dimensional Analysis
Conversion Factors and Dimensional Analysis
The unit...
Numerical Calculations
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
SFG Algebra
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...

