Development of a Three-Tier Test Diagnosing Learners’ Misconceptions in Operations on Polynomials

Abstract

This assessment-development research design utilizing a carefully developed and initially validated Three-Tier Test aligned with MATATAG Curriculum was conducted to two participant groups taken from a private secondary school in Bislig City. With twenty Grade 8 learners for the preliminary open-ended diagnostic phase and forty separate Grade 8 learners for the pilot administration, the instrument assessed the interrelated areas: conceptual understanding (Tier 1), reasoning justification (Tier 2) and confidence level (Tier 3). Results elucidated that five (5) glaring misconception patterns: from notably conjoining errors in unlike monomials with 37.5%; then for factoring expansion confusion of 32.5% and for distributive property misapplication of 32.5%, all with high confidence, confirmed that confidence ratings accurately identified strong misconceptions from knowledge gaps. It was also found out that the instrument revealed satisfactorily content relevance with a mean expert agreement of 0.97, adequate construct discrimination with a mean Person Measure correlation of 0.47, good internal consistency (α = 0.848), properly ordered thresholds in 93.3% of items, and preliminary fairness evidence across sex groups with no statistically significant score differences detected. Hence, it could be noted that with the findings, the Three-Tier Test was a theoretically grounded diagnostic tool and defensible for formative classroom applications. It just had to be utilized for a large-scale validation with more diverse sample and with broader or higher-stakes deployment. With this, Mathematics teachers are highly encouraged to use the instrument to design targeted conceptual interventions that address persistent polynomial misconceptions.