Weaknesses in Basic Math Skills Non-Numerate Learners in Key Stage 2 Using Cognitive Diagnostic Modeling

Abstract

This study applied Cognitive Diagnostic Modeling (CDM) to identify the specific basic mathematics attributes underlying non-numeracy among purposively selected Grades 4 to 6 learners in public elementary schools of the Paniqui West District. A quantitative, non-experimental diagnostic design was used. Learners identified as performing in the lowest quartile of a curriculum-based numeracy assessment completed a researcher-developed Diagnostic Numeracy Assessment linked to an expert-validated Q-matrix. Item-level responses were analyzed through the G-DINA model, mastery/non-mastery classification, Latent Class Analysis, hierarchical dependency testing, and concordance analysis using Cohen's Kappa. The highest non-mastery rates occurred in Subtraction with Regrouping (78.5%) and Addition with Regrouping (71.2%), while Place Value was not mastered by 62.1% of the learners. Latent Class Analysis identified a Basic Facts Master profile as the largest group (39.5%), followed by a Global Deficit profile (28.1%) and a Regrouping Barrier profile (18.9%). Hierarchical testing confirmed that Place Value was a significant prerequisite for Addition with Regrouping (Chi-square = 15.90, p < .001) and that Single-Digit Subtraction was a prerequisite for Subtraction with Regrouping (Chi-square = 25.43, p < .001). Agreement between CDM and traditional total-score classifications was only moderate (Kappa = 0.45), with a combined misclassification rate of 28.8%. The findings show that conventional total scores conceal distinct cognitive deficits and that remediation should follow the demonstrated skill hierarchy, beginning with place value and basic subtraction before advancing to regrouping. CDM provides a more precise basis for differentiated and evidence-based numeracy intervention.