PSYCHOMETRIC VALIDATION OF MTH 112 KNOWLEDGEASSESSMENT TOOL FOR NIGERIAN FEDERAL POLYTECHNICS

Abstract

Standardized, psychometrically sound assessment instruments are essential for measuring students' mastery of foundational mathematics courses such as MTH 112 (Algebra and Elementary Trigonometry) in Nigerian Federal Polytechnics, yet classroom tests in this sub-sector are rarely subjected to formal validation. This study evaluated the content validity, reliability, item difficulty, and item discrimination of a multiple-choice MTH 112 Knowledge Assessment Tool developed for National Diploma I Engineering students, using both Classical Test Theory (CTT) and a two-parameter logistic (2PL) Item Response Theory (IRT) model. The instrument, originally comprising 77 items, was reviewed by ten subject-matter experts; 74 items met the minimum Content Validity Ratio criterion and were retained (Scale-Content Validity Index = 0.88). The refined instrument was administered to 81 candidates, of whom 58 supplied usable responses and were retained for psychometric analysis after 23 blank scripts were excluded and five isolated data-entry anomalies were corrected. Internal consistency, estimated with the Kuder-Richardson Formula 20, was 0.94, with a Standard Error of Measurement of 3.53 marks. The mean CTT difficulty index was 0.63 (moderate-to-easy), and the mean point-biserial discrimination index was 0.40, with 43 of 74 items classified as excellent discriminators. The 2PL IRT calibration corroborated the CTT findings, showing a mean discrimination parameter of 1.41 and difficulty parameters concentrated in the low-to-moderate range. Eight items displayed weak or negative discrimination and were flagged for expert review rather than automatic deletion. The instrument is judged to be a substantially valid and reliable measure of MTH 112 achievement, and recommendations are offered for item banking, periodic re-validation, and Polytechnic-wide adoption.