using the Rasch model. Instrumentation research design was employed. The scales used to

measure achievement test in Nigeria rely on classical test theory (CTT) approach. As a result,

they have limitations like poor precision, sample dependency and undue focus on aggregate

scores that deny test developers the opportunity of determining how the examinees performed on

a test item. Multistage sampling procedure was used to sample 266 students from the population

of 2150 students.

The instrument was a self-developed 20 multiple choice questions. The

instrument was face validated by three experts from Mathematics Education and two from

measurement and Evaluation while the content and parametric properties were ascertained using

the table of specification and Rasch model. Internal consistency reliability value of the instrument

using KR20 was 0.85 while the inter-rater reliability was 0.74. The result showed that items

difficulty ranged from -0.02 to 1.00 while the difficulty level indices were 1.2 to 2.5. The infit and

outfit ranged from 0.6 to 1.2. Findings also showed that gender difference in upper basic II

students’ conceptual understanding was not statistically significant. It was therefore concluded

that two-tier mathematics diagnostics test (TTMDT) developed is reliable and valid to be used

for both summative and formative assessments in schools and by examination bodies. It was

recommended among others that seminars should be organized for mathematics teachers on how

to structure and use two-Tier diagnostic mathematics test in the classroom.