Differential Item Functioning of Performance-Based Assessment in Mathematics for Senior High Schools


Abraham Gyamfi


The purpose of the study was to validate performance-based assessment in mathematics (Quantitative Reasoning) for Senior High Schools for Differential Item Functioning (DIF). The study sought to found out if the five-items on a newly developed performance-based assessment in mathematics (quantitative reasoning items) has DIF. The study employed descriptive research design embedded in Graded Response Model (GRM).  Stratified, census, simple random sampling and purposive samplings procedures were employed to select 750 SHS Three students in the Western Region from three categories of SHS. The Performance-based assessment test was used as the main data collection instruments. Data were analyzed with winGEN and independent t test using SPSS. It was also found that with the exception of the linear equation item that showed DIF for category A and C schools, there was no presence of DIF in the items for both gender and category of school. Based on the findings, it was recommended that performance-based assessment should be an integral part in the methods of assessment lessons and courses at both the colleges of education and universities and that major method of assessment strategy in teaching and learning of mathematics.


How to Cite
Gyamfi, A. (2023). Differential Item Functioning of Performance-Based Assessment in Mathematics for Senior High Schools . Jurnal Evaluasi Dan Pembelajaran, 5(1), 20–34. Retrieved from https://jepjurnal.stkipalitb.ac.id/index.php/hepi/article/view/80


    Adegoke, B. A. (2013). Comparison of item statistics of physics achievement test using classical test and item response theory frameworks. Journal of Education and Practice, 4(22), 87 – 96
    Adjei, E., & Tagoe, M. (2009). Research methods in information studies. Accra: IAE (UG)
    Ainsworth, L., & Viegut, D. (2006). Common formative assessments, how to connect standards-based instruction and assessment. Thousand Oaks, CA, Corwin
    Ani, E. N. (2014). Application of item response theory in the development and validation of multiple-choice test in economics. University of Nigeria, Nsukka: masters’ Thesis.
    Annan-Brew, R (2020). Differential item functioning of West African senior secondary certificate examination in core subjects in southern Ghana. UCC, Ghana: PhD thesis
    Arhin, A. K. (2015). The effect of performance assessment-driven instruction on the attitude and achievement of senior high school students in mathematics in Cape Coast Metropolis , Ghana. Journal of Education and Practice, 6(2), 112–114.
    Baker, F. B. (2001). The basis of item response theory. USA: ERIC Clearinghouse on Assessment and Evaluation.
    Bichi, A. A., Hafiz, H. & Bello, S. A. (2016). Evaluation of Northwest University, Kano Post-UTME Test Items Using Item Response Theory. International Journal of Evaluation and Research in Education (IJERE), 5(4), 261~270
    Bichi, A. A; Embong, R; Mamat, M. & Maiwada, D. A. (2015). Comparison of classical test theory and item response theory: A review of empirical studies. Austrian Journal of Basic & Applied Science 9(7): 549-556.
    Brennan, R. L. (Ed). (2006). Educational measurement (4th ed). USA: American Council on Education, Praeger Series on Education.
    Bruckner, S., Forster, M., Zlatkin-Troitschanskaia, O., Happ, R., Walstad, W. B., Yamaoka, M., & Asano, T. (2015). Gender Effects in Assessment of Economic Knowledge and Understanding: Differences Among Undergraduate Business and Economics Students in Germany, Japan, and the United States. Peabody Journal of Education, 90 (4): 503-18. doi: http://dx.doi.org/10.1080/0161956X.
    Burkhardt, H., & Swan, M. (2008). Designing assessment of performance in mathematics. Educational Measurement: Issues and Practice, 9(4), 1–24.
    Carvalho, L. F., Primi, R. & Baptista, M. N. (2015). IRT application to verify psychometric properties of the Beck Depression Inventory (BDI) University Psychological. Bogotá, Colombia, 14 (1), 91-102
    Chalmers, P. R. (2012). Mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of statistical software, 48(6), 231-246
    Cohen, L., Manion, L. & Marrison, K. (2000). Research methods in education. London: Routedge Falmer.
    de Ayala, R. J. (2009). The theory and practice of item response theory. New York: The Guilford Press.
    Downing, S. M. (2003). Item response theory: applications of modern test theory in medical education. Medical Education; 37, 739–745
    Egberink, I. J. L; Meijer, R. & Veldkamp, B. P. (2010) Conscientiousness in the workplace: Applying mixture IRT to investigate scalability and predictive validity. Journal of Research in Personality 44(2):232-244. DOI:10.1016/j.jrp.2010.01.007
    Ellis, D. P (2011). Item-analysis methods and their implications for the ILTA guidelines for practice: A comparison of the effects of classical test theory and item response theory models on the outcome of a high-stakes entrance. instruction. Topics in Language Disorders, 1, 71-88.
    Etsey, Y. K. A. & Abu, A. (2013). Colleges of Education tutors' capacity in classroom assessment in northern Ghana. Journal of Educational Assessment in Africa, 8 , 101-109.
    Gao, M. (2012) Classroom Assessments in Mathematics: High School Students’ Perceptions International Journal of Business and Social Science,.3( 2), 63-74
    Karaali, G. E., Hernandez, H. V., & Taylor, J. A. (2016). What’s in a Name? A Critical Review of Definitions of Quantitative Literacy, Numeracy and Quantitative Reasoning. Numeracy 9 (1), 14-26. doi: http://dx.doi.org/10.5038/1936-4660.9.1.2.
    Le, D. (2013). Applying item response theory modeling in educational research. Iowa State University: Masters’ Dissertation.
    Min, S. & He, L. (2014). Applying unidimensional and multidimensional item response theory models in testlet-based reading assessment. Language Testing, 31(4) 453–477
    Neuman, W. L. (2003). Social research methods: Qualitative and quantitative approaches. Boston: Allyn and Bacon.
    Nitko, A. J. (2004). Educational Tests and Measurements (3rded.). USA: Prentice-Hall, Inc
    Park, J. (2012). Developing and Validating an Instrument to Measure College Students’ Inferential Reasoning in Statistics: An Argument-Based Approach to Validation. University of Minnesota: PhD dissertation
    Pegg J., (2003). Assessment in mathematics: A developmental approach. In J. Royer (Ed.), Mathematical Cognition (pp. 227–259). Greenwich, CT: Information Age Publishing.
    Royal, K. D & Gonzalez, L. M. (2016). An evaluation of the psychometric properties of an advising survey for medical and professional program students. Journal of Educational and Developmental Psychology, 6(1), 195 – 203
    Shavelson, R. J. (2008). Reflections on Quantitative Reasoning: An Assessment Perspective. In Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education, edited by Bernard L. Madison and Lynn Arthur Steen, 27-44. Washington: Mathematical Association of America.
    Zanon, C., Hutz, C. S., Yoo, H. & Hambleton, R. K. (2016). An application of item response theory to psychological test development. Psicologia: Reflexão e Crítica, 29 (18), 345-367
    Zubairi, A. M. and Kassim,N. L. A. (2006).Classical and Rasch analysis of dichotomously scored reading comprehension test items. Malaysian Journal of ELT Research, 2, pp.1-20.