Measuring Learning Loss Due to Disruptions from COVID-19: Perspectives from the Concept of Fractions

Mulia Lestari, Rahmah Johar, Mailizar Mailizar, Ali Ridho


Ineffective learning during Covid-19 can be a major cause of learning loss. Through polytomous item response theory analysis, this study seeks to identify learning loss of fractions and investigate the reliability and validity of the DINA model diagnostic test. This study involved 177 Grade 8 students from six junior high schools in Banda Aceh, Indonesia, to obtain information about the validity and reliability of the diagnostic test and learning loss of fraction due to Covid-19. The research was conducted by designing diagnostic test, expert validation, and empirical testing. Multiple choice problems with polytomous options were developed. This study produced 20 valid problems based on the level of item discriminant, item difficulty, and slip and guess, with a reliability of 0.899. This study revealed that learning loss was experienced by 62 students from low-level junior high schools (100%), 51 students from middle-level junior high schools (98%), and 54 students from high-level junior high schools (85.7%). It can be said that low-level schools have the highest percentage of students with learning loss. It is recommended that future studies evaluate the effectiveness of diagnostic tests in identifying learning weaknesses in mathematics before semester exams using the items generated in this study.


diagnostic test, learning loss, fraction

Full Text:



Aiken, L. R. (1985). Three coefficients for analyzing the reliability and validity of ratings. Educational and psychological measurement, 45(1), 131-142.

Antara, A. A. P. (2020). Penyetaraan vertikal dengan pendekatan klasik dan item response theory (teori dan aplikasi). Sleman: Deepublish Publisher.

Australian Curriculum, Assessment and Reporting Authority (ACARA). (2015). Mathematics: Sequence of content. V8.1.

Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628-648.

Barnard-Brak, L., Lan, W. Y., & Yang, Z. (2018). Differences in mathematics achievement according to opportunity to learn: A 4pL item response theory examination. Studies in Educational Evaluation, 56, 1-7.

Burkholder, E., Wang, K., & Wieman, C. (2021). Validated diagnostic test for introductory physics course placement. Physical Review Physics Education Research, 17(1), 010127.

Candraningsih, Y., & Warmi, A. (2023). Kesalahan siswa SMA dalam menyelesaikan soal cerita matematika berdasarkan teori newman. JPMI (Jurnal Pembelajaran Matematika Inovatif), 6(1), 235-242.

Crocker, L. & Algina, J. (1986). Introduction to clasical and modern test theory. New York: Holt, Rinehart and Winston, Inc.

De La Torre, J. (2009). DINA model and parameter estimation: A didactic. Journal of educational and behavioral statistics, 34(1), 115-130.

De La Torre, J., & Karelitz, T. M. (2009). Impact of diagnosticity on the adequacy of models for cognitive diagnosis under a linear attribute structure: A simulation study. Journal of Educational Measurement, 46(4), 450-469.

De La Torre, J., Hong, Y., & Deng, W. (2010). Factors affecting the item parameter estimation and classification accuracy of the DINA model. Journal of Educational Measurement, 47(2), 227-249

De La Torre, J., & Lee, Y. S. (2010). A note on the invariance of the DINA model parameters. Journal of Educational Measurement, 47(1), 115-127.

De La Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.

Deringöl, Y. (2019). Misconceptions of primary school students about the subject of fraction. International Journal of Evaluation and Research in Education (IJERE). 8(1), 29-38.

Engzell, P., Frey, A., & Verhagen, M. D. (2021). Learning loss due to school closures during the covid-19 pandemic. Proceedings of the National Academy of Sciences, 118(17), e2022376118.

Fatkhudin, A., Surarso, B., & Subagio, A. (2014). Item response theory model empat parameter logistik pada computerized adaptive test. Jurnal Sistem Informasi Bisnis, 2, 121-129.

Ferlia, W., Putra, R. W. Y., Meyronita, F. MKS., & Fajar, R. (2023). Analisis loss learning di SMP insan mandiri pada masa pandemi covid-19. Jurnal Simki Pedagogia, 6(2), 386-397.

George, A. C., & Robitzsch, A. (2015). Cognitive diagnosis models in R: A didactic. The Quantitative Methods for Psychology, 11(3), 189-205.

Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505-515.

Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory (Vol. 2). London: Sage Publications.

Haser, Ç., Doğan, O., & Erhan, G. K. (2022). Tracing students’ mathematics learning loss during school closures in teachers’ self-reported practices. International Journal of Educational Development, 88, 102536.

Huang Y. M., Lin, Y. T. & Cheng S. C. (2009). An adaptive testing system for supporting verstile educational assessment. Journal of Computers & Education, 52(1), 53-67.

Ketterlin-Geller, L. R., & Yovanoff, P. (2009). Diagnostic assessments in mathematics to support instructional decision making. Practical Assessment. Research and Evaluation, 14(16), 1-11.

Kalkan, Ö. K., & Çuhadar, İ. (2020). An evaluation of 4PL IRT and DINA models for estimating pseudo-guessing and slipping parameters. Journal of Measurement and Evaluation in Education and Psychology, 11(2), 131-146. doi: 10.21031/epod.660273

Khan, M. J., & Ahmed, J. (2021). Child education in the time of pandemic: Learning loss and dropout. Children and Youth Services Review, 127, 106065.

Köhn, H. F., & Chiu, C. Y. (2016). A proof of the duality of the DINA model and the DINO model. Journal of Classification, 33, 171-184.

Kuhfeld, M., Soland, J., Tarasawa, B., Johnson, A., Ruzek, E., & Liu, J. (2020). Projecting the potential impact of covid-19 school closures on academic achievement. Educational Researcher, 49(8), 549-565.

Kusaeri. (2012). Menggunakan model DINA dalam pengembangan tes diagnostik untuk mendeteksi salah konsepsi. Jurnal Penelitian dan Evaluasi Pendidikan. 16(1), 281-305.

Lee, G., Kolen, M. J., Frisbie, D. A., & Ankenmann, R. D. (2001). Comparison of dichotomous and polytomous item response models in equating scores from tests composed of testlets. Applied Psychological Measurement, 25(4), 357-372.

Leighton, J., & Gierl, M. (Eds.). (2007). Cognitive diagnostic assessment for education: Theory and applications. Cambridge University Press.

Maldonado, J., & De Witte, K. (2020). The effect of school closures on standardised student test. British Educational Research Journal, 48(1), 49-94.

National AssEssment of Educational Progress (NAEP). (2022). Assassmen Mathematics. diakses melalui

Namkung, J., & Fuchs, L. (2019). Remediating difficulty with fractions for students with mathematics learning difficulties. Learning Disabilities: A Multidisciplinary Journal, 24(2), 36-48.

Paechter, M., Luttenberger, S., Macher, D., Berding, F., Papousek, I., Weiss, E. M., & Fink, A. (2015). The effects of nine-week summer vacation: Losses in mathematics and gains in reading. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1399-1413.

Pier, L., Hough, HJ, Chriatian, M, Bookman, N., Wilkenfeld, B., & Miller, R. (2021). Covid-19 impacts on student learning: Evidence from assessments in California. PACE: Policy Analysis for California Education.

Prasetyawan, D. G. (2016). Diagnosis kesulitan belajar matematika siswa kelas IV SD negeri congkrang 1 muntilan magelang. Basic Education, 5(26), 2-481.

Rauch, D., & Hartig, J. (2020). Interpretation von testwerten in der item-response-theorie (IRT). Testtheorie und Fragebogenkonstruktion, 411-424.

Rupp, A.A., Templin, J. & Henson, R. A. (2010). Diagnostic measrement: Theory, methods and applications. New York: The Guilford Press.

Şiap, İ., & Duru, A, (2004). The Ability to Use Geometrical Models in Fractions. Kastamonu Education Journal, 12(1), 89-96.

Sutiarso, S., Rosidin, U., & Sulistiawan, A. (2022). Developing assessment instrument polytomous response in mathematics. European Jurnal of Education Research, 11(3), 1441-1462.

Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia-Social and Behavioral Sciences, 8, 142-151.

Tatsuoka, K. K. (1990). Toward an integration of item response theory and cognitive analysis. In N. Frederisken, R. Glaser, A. Lesgold. Diagnostic Monitoring of Skill and Knowledge Acquisition. Hillsdale, NJ: Erlbaum.

Tatsuoka, K. K., Corter, J. E., & Tatsuoka, C. (2004). Patterns of diagnosed mathematical content and process skills in TIMSS-R across a sample of 20 countries. American educational research journal, 41(4), 901-926.

Liu, Y., Douglas, J. A., & Henson, R. A. (2009). Testing person fit in cognitive diagnosis. Applied psychological measurement, 33(8), 579-598.

Yuhasriati, Y., Johar, R., Khairunnisak, C., Rohaizati, U., Jupri, A., & Zubaidah, T. (2022). Students mathematical representation ability in learning algebraic expression using realistic mathematics education. Jurnal Didaktik Matematika, 9(1), 151-169.

Wijaya, A., Retnawati, H., Setyaningrum, W., & Aoyama, K. (2019). Diagnosing students' learning difficulties in the eyes of indonesian mathematics teachers. Journal on Mathematics Education, 10(3), 357-364.

Wong, A., & Sixl-Daniell, K. (2017). The importance of e-learning as a teaching and learning approach in emerging markets. iJAC, 10(1), 45-54.

Zhang, W. (2006). Detecting differential item functioning using the DINA model. Doctoral dissertation, unpublished. The University of North Carolina at Greensboro.


Article Metrics

Abstract view : 0 times
PDF - 0 times


  • There are currently no refbacks.

Copyright (c) 2023 Rahmah Johar, S.Pd, M.Pd, Mulia Lestari, Mailizar Mailizar

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Jurnal Didaktik Matematika

ISSN 2355–4185 (print) | 2548–8546 (online)

Published by:

Master Program of Mathematics Education incorporated with Himpunan Matematika Indonesia (Indonesian Mathematical Society/IndoMs)

Faculty of Teacher Training and Education

Universitas Syiah Kuala

Darussalam, Banda Aceh, Indonesia - 23111

Website : 
Email     : 

Creative Commons License

Jurnal Didaktik Matematika by Program Studi Magister Pendidikan Matematika FKIP Universitas Syiah Kuala is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at