A scoring framework that does not reflect true performance of an examinee would ultimately result in an abnormal score. This study assessed invariance person estimates of 2017 Nigerian National Examinations Council Basic Education Certificate Examination Mathematics Multiple Choice using classical test theory (CTT) and item response theory (IRT) scoring frameworks. The study adopted survey design method. Simple random sampling technique was adopted to select 978 subjects (425 males, 553 females, M=12 years) for the study. One research instrument was used. Data were analyzed using descriptive and paired sample t-tests. There was significance difference (t = 2.635, df = 977, p = 0.01) in the overall mean score of CTT (mean=50.70, SD=10.30) and IRT (mean=47.78, SD=8.49). Also, IRT method of scoring produced different test scores for examinees who had the same raw scores under the CTT method. National Examinations Council should be encouraged to shift their paradigm of scoring from CTT to IRT method.