IJSER Home >> Journal >> IJSER
International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 8    
Website: http://www.ijser.org
scirp IJSER >> Volume 3,Issue 8,August 2012
Modelling Students' Mathematical Ability and Items' Difficulty Parameters: Application of the Rasch Measurement Model
Full Text(PDF, )  PP.123-127  
Ahmad Zamri bin Khairani, Nordin bin Abd. Razak, Hasni binti Shamsuddin
— mathematical ability, item difficulty, students’ ability, Rasch Measurement Model
Measurement of students' ability is one of the most important purposes of educational measurement. Nevertheless, the purpose is considered difficult and inadequate based on the inappropriateness of the analyses used, especially when the students' ability measurement is always dependent of the test chosen for the studies. The purpose of this study is to explore the adequacy of the Rasch Measurement Model to provide so-called 'test-free' estimation of students' ability parameter based on their response in a set of items. A total of 411 Form 2 students were employed as sample for this study while a 40 multiple-choice Mathematics items provide a set of data for the modeling purpose. A Rasch Measurement Model software, the WINSTEPS 3.63 is employed for the purpose. Result showed that there is enough evidence of consistency between what been expected by the model and what been observed by the data. In short, results show that the Rasch Model analysis is able to provide richer interpretation towards better understanding of students' mathematical ability based on difficulty of the items. Implications of the results towards educational measurement are also reported.
[1] A. J. Nitko, Educational assessment of students (2nd ed.), Merrill, Englewood Cliffs, NJ (1996)

[2] T. G. Bond, and C. M. Fox, Applying the Rasch model: Fundamental measurement in the human sciences, Lawrence Erlbaum, Mahwah, NJ (2001)

[3] B. D. Wright, and M. H. Stone, Best Test Design, MESA Press, Chicago, IL (1979)

[4] [4] B. D. Wright and G. N. Masters, Rating scale analysis, MESA Press, Chicago, IL (1982)

[5] S. E. Embretson and S. P. Reise, Item response theory for psychologists, Mahwah, NJ: Lawrence Erlbaum (2000)

[6] T. Forkmann, M. Boecker, N. Wirtz, M. Eberle, P. Westhofen, K. Schauerte, K. Mischke, and C. Norra., Development and Validation of the Rasch-based Depression Screening (DESC) using Rasch Analysis and Structural Equation Modeling, 3,40 (2009)

[7] K. Y. Chang, M. Y. Tsou, K. H. Chan, S. H. Chang, J. J. Tai and H. H. Chen, Item Analysis for the Written Test of Taiwanese Board Certification Examination in Anesthesiology using the Rasch Model, British Journal of Anesthesia, 6, 104 (2010)


[9] P. Baghaei, A comparison of three polychotomous Rasch models for superitem analysis, Psychological Test and Assessment Modeling, 3, 52 (2010)


[11] K. R. Muis, P. H. Winne, and O. V. Edwards, Modern Psychometrics for Assessing Achievement Goal Orientation: A Rasch analysis. British Journal of Educational Psychology, 3, 79 (2009)

[12] K. Ahmad Zamri, Application of the Bookmark Method in Setting Performance Standards for Form 2 Students in Mathematics, unpublished doctoral thesis (2010)

[13] Curriculum Development Centre, Ministry of Education, Curriculum specifications for Mathematics Form 2 (2002)

[14] J. Kilpatrick, J. Swafford, and B. Findell, Adding it Up: Helping How Children Learn Mathematics, Washington DC: National Academy Press (2001)

[15] J. M. Linacre, A user‘s guide to Winsteps (2005)

[16] T. G. Bond, and C. M. Fox, Applying the Rasch Model: Fundamental Measurement in Human Sciences, Lawrence Erlbaum: Mahwah, NJ (2001)

[17] R. K. Green and C. G. Frantom, Survey development and validation with Rasch Model. http://www.ipsm.umd.ed/qdet/final_papers/green.pdf, retrieved April 23 (2012)

Untitled Page