Enhancing Decimal Learning Through Mathematics Grounding Activities — Preprint

Raw gain scores, computed as the arithmetic difference between posttest and pretest performance, represent one of the most widely used metrics for evaluating instructional effectiveness in pre–post designs. However, raw gains become systematically biased when posttest distributions approach the upper bound of the measurement scale, a condition known as the ceiling effect. This study examines how ceiling effects distort raw gain estimates and evaluates whether normalized gain provides a more stable alternative under such conditions. Data were drawn from a one-group pretest–posttest study in which 26 third-grade students received Mathematics Grounding Activities (MGA) instruction on two-decimal concepts in Taipei, Taiwan. Substantial improvements were observed following instruction (Cohen's d = 1.93; mean normalized gain g = 0.739), accompanied by a pronounced ceiling effect in posttest scores (skewness = −2.271; Shapiro–Wilk W = .744, p < .001). Under these conditions, pretest scores accounted for 51.1% of variance in raw gain (R² = .511, β = −.72, p < .001), whereas the same predictor explained virtually no variance in normalized gain (R² = .000, β = .018, p = .932). Group-level comparisons showed that normalized gain yielded comparable estimates of learning progress across ability groups, whereas raw gain systematically underestimated improvement among high-pretest students. These findings suggest that metric selection constitutes a substantive methodological decision in ceiling-constrained instructional contexts, and illustrate a diagnostic framework for evaluating learning gains in pre–post intervention studies.This manuscript has been submitted to F1000Research for peer review. This version is a pre-peer review author manuscript.Dataset available at:https://doi.org/10.5281/zenodo.19447551