The Dual Pathways of Proportional Reasoning on Mathematics Achievement: The Mediating Role of Whole Number Arithmetic and Latent Profile Analysis

Research Hypothesis: We hypothesized that proportional reasoning (PR) directly supports general math achievement (GMA) and indirectly through whole-number arithmetic (WNA). We also expected to find distinct student subgroups with different performance profiles.

Data & Methodology: Data was gathered from 123 second-graders (age ~7.9) in China. Participants completed three tasks:

A computer-based proportional reasoning task (choosing equivalent ratios).

A paper-and-pencil whole-number arithmetic test.

A comprehensive general math achievement test.
We used path analysis to test the mediation model and latent profile analysis (LPA) to identify subgroups.

Notable Findings:

Dual Pathways: Path analysis confirmed our model. PR had a significant direct effect on GMA (β = 0.328, p<.001) and a significant indirect effect via WNA (β = 0.143, p=.005). The model explained 47% of the variance in math achievement.

Two Subgroups: LPA identified two distinct profiles:

High-Performers (95%): Strong, balanced skills across all areas.

Low-Performers (5%): Showed significant difficulties in PR, WNA, and GMA.

Interpretation & Use: Proportional reasoning is a foundational skill that boosts math achievement directly and by enhancing arithmetic. The small but distinct low-performing group highlights the need for early identification and intervention to address broad mathematical difficulties, potentially linked to a "whole number bias." Educators should integrate proportional concepts early into instruction using visual and contextualized examples.