COMPARISON OF SECONDARY SCHOOL STUDENTS’ ABILITY IN MATHEMATICS CONSTRUCTED-RESPONSE ITEMS UNDER CLASSICAL TEST AND ITEM RESPONSE MEASUREMENT THEORIES IN THE IBADAN METROPOLIS, NIGERIA

Abstract

Test items of public examinations are expected to be valid and reliable when good frameworks are used. Besides, the scoring of the items must be guided by an objective theoretical framework. Studies have shown that Mathematics Constructed-Response Test Items (MCRTI) of the West African Examinations Council (WAEC) and National Examinations Council (NECO) are scored using Classical Test Theories (CTT) framework which have been adjudged subjective. This study was, therefore, designed to score and compare students’ ability in WAEC and NECO MCRTI under CTT and Item Response Theory (IRT). The dimensionality, equivalence of scores and differential item functioning (between males and females) of WAEC and NECO MCRTI under CTT and IRT were also examined. The study was anchored to the Classical Test and Item Response Measurement Theories, while descriptive survey design was adopted. Counterbalance procedure was employed in the tests administration. One educational zone out of the two in Ibadan was sampled. All the five Local Government Areas (LGAs) in the educational zone were used. Twenty-four co educational public Senior Secondary Schools (SSS) were randomly selected from the LGAs using proportionate to size sampling technique. Two intact classes of Senior Secondary School 3 (SSS3) in each school were used. In all, 1151 (565 males, 586 females) SSS3 students were sampled. The WAEC and NECO MCRTI (2013-2015) were used for data collection. The reliability coefficient established were WAEC MCRTI (r = 0.72) and NECO MCRTI (r = 0.71). Data were subjected to Exploratory Factor Analysis, Parallel Analysis (CTT models), IRT-Generalized Partial Credit Model (GPCM) and Graded Response Model (GRM), and correlated samples t-test at 0.05 significance level. The two MCRTI were multi-dimensional. Under CTT, WAEC MCRTI had four dimensions, while NECO MCRTI had three dimensions. Under IRT, WAEC MCRTI and NECO MCRTI had three dimensions each. The WAEC MCRTI (GPCM=0.24, GRM=-3.16) were easier than NECO MCRTI (GPCM=2.10, GRM=4.95). Students’ mean score in WAEC MCRTI under CTT was lower ( ̅=35.88, SD=10.02) than under IRT (GPCM) ( ̅=41.70, SD=7.0). The mean score in NECO MCRTI under CTT was lower ( ̅=33.49, SD= 12.39) than under IRT (GPCM) ( ̅=41.67, SD=6.98). The mean differences were significant t (1150) = 34.83 (WAEC) and t(1150) = 33.32 (NECO). Students’ mean score in WAEC MCRTI under CTT was lower ( ̅= 35.88, SD = 10.02) than under IRT (GRM) ( ̅=41.70, SD=7.04). The mean score in NECO MCRTI under CTT was lower ( ̅=33.49, SD=12.39) than under IRT (GRM) ( ̅=41.67, SD=7.01). The mean differences were significant t(1150) = 34.86 (WAEC) and t(1150) = 35.04 (NECO). The adjusted scores under CTT and IRT models were equal. Three items out of 15 WAEC MCRTI exhibited DIF under CTT, while 14 exhibited DIF under IRT in favour of males. None of the NECO MCRTI items exhibited DIF under CTT, while nine exhibited DIF under IRT in favour of males. Item Response Theory models were more effective than Classical Test Theory in scoring constructed-response tests, equating and detecting differential item functioning. Public examining bodies should score constructed-response test items using Item Response Theory models.