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Math Proficiency Assessment Based Upon Item Response Theory

By Muhammad Azeem and Muhammad Bashir Gondal.

Published by The International Journal of Interdisciplinary Social Sciences

Curriculum, instruction, and assessment are now viewed as an interconnected entity in standards-based education. Performance standards are called competency standards, proficiencies, and benchmarks. Mathematical proficiency is broadened from the ability to perform the computations necessary to solve math problem, to the ability to understand mathematical concepts, to apply mathematics to novel problems, and to reason mathematically. Mathematical proficiency is to capture what we believe is necessary for anyone to learn mathematics successfully. Measurements of proficiency demands a better tool than a simply the solutions to problems. A 60-item math proficiency test was constructed. This math proficiency was aligned to the newly developed standards, benchmarks, and indicators and national math curriculum 2000. In this study fit statistics along with items difficulty and discrimination power were used for selection of items for final math proficiency test. The math proficiency test was administered to the 2680 students of 143 schools. Sample was selected using sample design tables and IRT based analysis requirements. Data was received from 2617 students. Data was analyzed by using SPSS, Conquest, and Multilog software. Data was well fitted with Rasch Model. The reliability of test was above 0.90. The Item Response Theory-based person-item map showed that test items covered ±3 range of abilities. Test characteristics and item characteristics curves also support the reliably and validity of the test. Different reliability estimations also support to reliability and validity of test items. Out of eight null hypotheses only one null hypothesis is rejected. It seemed that math proficiency test is appropriately constructed.

International Journal of Interdisciplinary Social Sciences, Volume 6, Issue 1, pp.105-122. Article: Print (Spiral Bound). Article: Electronic (PDF File; 868.727KB).

Muhammad Azeem

Assessment and Research Specialist, Assessment and Research Section, Punjab Education Assessment System (PEAS), Lahore, Pakistan

Muhammad Bashir Gondal

Senior Research Fellow, Punjab Education Commission (PEC), Govt. of the Punjab, Lahore, Pakistan