Le Thai Hung, Tang Thi Thuy, Tran Lan Anh, Nguyen Tien Dung, Nguyen Phuong Anh, Nguyen Thi Quynh Giang

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Computerized Adaptive Testing (CAT) is a form of assessment test which requires fewer test questions to arrive at precise measurements of examinees' ability. One of the core technical components in building a CAT is mathematical algorithms which estimate examinees’ ability and select the most appropriate test questions for the estimation. Mathematical algorithms serve as a locomotive in operating the system of adaptive multiple-choice questions on computers.  This research aims to develop essential mathematical algorithms for a computerized system of adaptive multiple-choice tests. A question bank of 500 multiple-choice questions standardized by IRT theory with the difficulty level following the normal distribution satisfying Kolmogorov-Smirnov test, to measure the mathematical ability of 10th graders is also built. The experimenting of the question bank shows that it satisfies the requirements of a psychometric model and the constructed mathematical algorithms meet the criteria for applying in computerized adaptive testing.

Keywords: Computerized Adaptive Testing, ability measurement, mathematical ability, IRT.


[1] Rod Powers, Jennifer Lawler, ASVAB For Dummies, John Wiley @Sons Published house, 2007.
[2] M.D. Reckase, Item pool design for computerized adaptive tests, Paper presented at annual meeting of the National Council on Measurement in Education, Chicago, IL, 2003.
[3] D.J. Weiss, G.G. Kingsbury, Application of computerized adaptive testing to educational problems Journal of Educational Measurement 21 (1984) 361-375.
[4] A. Carol, Chapelle, Shannon Sauro, The Handbook of Technology and Second Language Teaching and Learning, John Wiley & Sons, 2017.
[5] Thompson, A. Nathan, Weiss, A. David, A Framework for the Development of Computerized Adaptive Tests. Practical Assessment, Research & Evaluation, 16 (1). Available online: http://pareonline.net/getvn.asp?v=16&n=1/, 2011.
[6] Lam Quang Thiep, Measurement and Evaluation in Education: Theory and Application, VNU Publishing house, 2011. (in Vietnamese).
[7] F.M. Lord, Maximum likelihood and Bayesian parameter estimation in item response theory, Journal of Educational Measurement 23 (1986) 157-162.
[8] Vu Huu Tiep, Basic Machine Learning, Scientific and Technical Publishing, 2018. (Vietnamese).
[9] ECD, PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy, OECD Publishing, 2013.
[10] Alper Şahin, David J. Weiss, Effects of Calibration Sample Size and Item Bank Size on Ability Estimation in Computerized Adaptive Testing, Educational Sciences: Theory & Practice, 2015.
Nguyen Thuy Giang, Le Thai Hung, Simulate an Computerized Adaptive Testing with R,
Vietnam Education Journal 11 (2018) 6-11. (in Vietnamese).