Mathematical Reasoning Gaps and Problem-Solving Confidence among Grade 6 Learners

Abstract

This study traced how mathematical reasoning gaps were associated with problem-solving confidence among Grade 6 learners in a public elementary school in the City of Ilagan, Isabela. A cross-sectional diagnostic relational design was used. Data were collected through the Mathematical Reasoning Gap Assessment and the Problem-Solving Confidence Inventory, both of which underwent expert validation, pilot testing, and reliability analysis. Partial credit Rasch modeling was applied to identify reasoning difficulties, while a Rasch rating scale model measured confidence. Robust regression, Spearman correlation, and a reasoning-confidence calibration index were also employed. Results showed an overall moderate mathematical reasoning gap, with the greatest weaknesses found in logical justification and answer verification, followed by mathematical representation and strategy selection. Problem-solving confidence was at a developing level, with the lowest confidence observed in explaining solutions and persisting after an unsuccessful attempt. Confidence significantly predicted mathematical reasoning ability, although it explained only a modest portion of the variance. Calibration findings further revealed that several learners either overestimated or underestimated their actual reasoning performance. The findings indicated that mathematical difficulty was not confined to computation but also involved interpretation, strategy use, explanation, verification, and self-judgment. Mathematics instruction should therefore include diagnostic reasoning tasks, structured justification, multiple representations, explicit verification strategies, opportunities for solution revision, and feedback that helps learners align confidence with demonstrated competence.