Rasch Model Analysis of Algebraic Numeracy Literacy Items Using Winsteps

Rifqi Hidayat; Turmudi Turmudi; Jarnawi Jarnawi; Elah Nurlaelah

doi:10.58421/gehu.v4i4.736

DOI:

https://doi.org/10.58421/gehu.v4i4.736

Authors

Rifqi Hidayat Universitas Pendidikan Indonesia https://orcid.org/0009-0005-6556-0177
Turmudi Turmudi Universitas Pendidikan Indonesia
Jarnawi Jarnawi Universitas Pendidikan Indonesia
Elah Nurlaelah Universitas Pendidikan Indonesia

Keywords:

Algebra, Numeracy Literacy, Rasch Model, Winsteps.

Abstract

The limited availability of valid and reliable numeracy literacy test instruments, particularly in the algebra domain, for junior high school students in preparation for the Minimum Competency Assessment exam makes this research important to conduct. This study aims to describe the quality of a numeracy literacy test instrument in the algebra domain for junior high school students. It is a quantitative study with a descriptive approach. This method is used to describe the quality of the numeracy literacy test instrument in the algebra domain, which was developed based on Rasch modeling. The research procedure comprises three main phases: item development, limited trial testing with 8th-grade students, and item quality analysis using the Rasch model analysis with the Winsteps software. The developed numeracy literacy test instrument consists of 12 essay questions. The instrument was then used to collect quantitative data from 34 8th-grade students selected as research respondents through purposive sampling. The results indicate that one item is categorized as invalid (requiring revision), while the remaining items are deemed valid. The reliability index is 0.80, which falls into the ideal category. The analysis of item difficulty levels reveals that one item is categorized as difficult, nine items as moderate, and two items as easy. Overall, the developed algebra numeracy literacy instrument meets the criteria of Rasch modelling, although one item requires revision. Teachers can use this instrument as an assessment tool to evaluate students' algebraic numeracy literacy skills in junior high school. This instrument can also serve as a model for developing numeracy literacy test instruments in other domains.

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References

Pusat Asesmen dan Pembelajaran, AKM dan implikasinya pada pembelajaran. Jakarta: Kemdikbud, 2020.

J. Cai and E. Knuth, Eds., Early Algebraization. in Advances in Mathematics Education. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. doi: 10.1007/978-3-642-17735-4.

C. Kieran, “Learning and teaching algebra at the middle school through college levels,” Second Handbook of Research on Mathematics Teaching and Learning, pp. 707–762, Jan. 2007.

A. C. Valenzeo and E. Sumiaty, “Learning Obstacles Siswa SMP dalam Menyelesaikan Operasi Bentuk Aljabar,” Jurnal Pendidikan Matematika (JUDIKA EDUCATION), vol. 7, no. 1, pp. 37–48, Jun. 2024, doi: 10.31539/judika.v7i1.8675.

N. Syamsuddin, S. S. Manik, and K. Safrina, “Pengembangan E-Modul Literasi Numerasi Aljabar Siswa Sekolah Menengah Pertama,” Jurnal Ilmiah Pendidikan Matematika Al Qalasadi, vol. 8, no. 1, pp. 39–52, Jun. 2024, doi: 10.32505/qalasadi.v8i1.8230.

R. Qolbiyah and C. K. Sari, “Analisis Literasi Matematis Siswa SMP Dalam Menyelesaikan Soal Aljabar Berorientasi AKM Numerasi Ditinjau Dari Gaya Kognitif,” JP2M (Jurnal Pendidikan dan Pembelajaran Matematika), vol. 10, no. 2, pp. 467–480, Sep. 2024, doi: 10.29100/jp2m.v10i2.6122.

F. H. Fitri and K. N. S. Effendi, “Numeration ability of junior high school students in solving numeration problems algebra material,” Union: Jurnal Ilmiah Pendidikan Matematika, vol. 11, no. 1, pp. 103–110, Mar. 2023, doi: 10.30738/union.v11i1.13395.

N. Aprilia, Y. Setiani, and C. A. Hadi FS, “Pengembangan Instrumen Tes Numerasi Pada Asesmen Kompetensi Minimum Yang Bernilai Budaya Lokal,” Jurnal Educatio FKIP UNMA, vol. 9, no. 2, pp. 850–857, Jun. 2023, doi: 10.31949/educatio.v9i2.4824.

B. Sumintono and W. Widhiarso, plikasi Pemodelan Rasch Pada Assesmen Pendidikan. Cimahi: Trim Komunikata, 2015.

C. Han, “William J. Boone, John R. Staver and Melissa S. Yale. Rasch Analysis in the Human Sciences,” Journal of Research Design and Statistics in Linguistics and Communication Science, vol. 5, no. 1–2, pp. 208–211, Dec. 2019, doi: 10.1558/jrds.37535.

J. W. Creswell, Research design: qualitative, quantitative, and mixed methods approaches, 4th ed., no. c. Los Angeles: SAGE, 2014.

R. T. Wardani, E. Nuraeni, and S. Diana, “Rasch model analysis of essay questions to measure literacy and numeracy skills in plant and animal bioprocess topics based on AKM,” REID (Research and Evaluation in Education), vol. 11, no. 1, pp. 29–44, Jul. 2025, doi: 10.21831/reid.v11i1.85614.

M. J. Peeters and J. M. Augustine, “Using Rasch measurement for instrument rating scale refinement,” Curr Pharm Teach Learn, vol. 15, no. 1, pp. 110–118, Jan. 2023, doi: 10.1016/j.cptl.2023.02.015.

F. Rasyid, E. Istiyono, and C. W. Gunawan, “Developing and analyzing items of a physics conceptual understanding test on wave topics for high school students using the Rasch Model,” REID (Research and Evaluation in Education), vol. 11, no. 1, pp. 1–16, Jun. 2025, doi: 10.21831/reid.v11i1.75575.

J. Haruta, R. Nakajima, and T. Monkawa, “Development of a validated assessment tool for medical students using simulated patients: an 8-year panel survey,” BMC Med Educ, vol. 24, no. 1, p. 399, Apr. 2024, doi: 10.1186/s12909-024-05386-2.

G. Engelhard and J. Wang, Rasch Models for Solving Measurement Problems: Invariant Measurement in the Social Sciences. 2455 Teller Road, Thousand Oaks California 91320: Sage, 2021. doi: 10.4135/9781071878675.

F. Rasyid, E. Istiyono, and C. W. Gunawan, “Developing and analyzing items of a physics conceptual understanding test on wave topics for high school students using the Rasch Model,” REID (Research and Evaluation in Education), vol. 11, no. 1, pp. 1–16, Jun. 2025, doi: 10.21831/reid.v11i1.75575.

S. McCombes, “Descriptive Research | Definition, Types, Methods & Examples.” Accessed: Nov. 25, 2025. [Online]. Available: https://www.scribbr.com/methodology/descriptive-research/

J. Linacre, “Predicting responses from Rasch measures,” J Appl Meas, vol. 11, pp. 1–10, Jan. 2010.

Kemendikbud, Materi Pendukung Literasi Numerasi. Jakarta: Kementerian Pendidikan dan Kebudayaan, 2017.

S. Azwar, Reliabilitas dan Validitas. Pustaka Pelajar, 2012.

V. Viyanti, U. Rosidin, and R. E. Shintya, “Collaborative and Problem Solving Instruments in Project-Based Physics Learning,” Indonesian Journal of Science and Mathematics Education, vol. 5, no. 1, pp. 96–108, Mar. 2022, doi: 10.24042/ijsme.v5i1.11636.

P. E. Larasati, Supahar, and D. R. A. Yunanta, “Validity and reliability estimation of assessment ability instrument for data literacy on high school physics material,” J Phys Conf Ser, vol. 1440, no. 1, p. 012020, Jan. 2020, doi: 10.1088/1742-6596/1440/1/012020.

J. M. Linacre, A User’s Guide to WINSTEPS® Rasch-Model Computer Programs: Program Manual 4.4.6. Chicago: Mesa-Press, 2019.

B. Sumintono, “Rasch Model Measurements as Tools in Assesment for Learning,” in Proceedings of the 1st International Conference on Education Innovation (ICEI 2017), Paris, France: Atlantis Press, 2018. doi: 10.2991/icei-17.2018.11.

C. J. Perera, B. Sumintono, and N. Jiang, “The Psychometric Validation Of The Principal Practices Questionnaire Based On Item Response Theory,” International Online Journal of Educational Leadership, vol. 2, no. 1, pp. 21–38, Feb. 2018, doi: 10.22452/iojel.vol2no1.3.

S.-W. Chan, C.-K. Looi, and B. Sumintono, “Assessing computational thinking abilities among Singapore secondary students: a Rasch model measurement analysis,” Journal of Computers in Education, vol. 8, no. 2, pp. 213–236, Jun. 2021, doi: 10.1007/s40692-020-00177-2.

M. Maryati, Z. K. Prasetyo, I. Wilujeng, and B. Sumintono, “Measuring Teachers’ Pedagogical Content Knowledge Using Many-Facet Rasch Model,” Jurnal Cakrawala Pendidikan, pp. 452–464, Oct. 2019, doi: 10.21831/cp.v38i3.26598.

J. R. S. and M. S. Yale. William J. Boone, “Rasch Analysis in the Human Sciences,” Journal of Research Design and Statistics in Linguistics and Communication Science, vol. 5, no. 1–2, pp. 208–211, Dec. 2019, doi: 10.1558/jrds.37535.

P. W. Duncan, R. K. Bode, S. Min Lai, and S. Perera, “Rasch analysis of a new stroke-specific outcome scale: the stroke impact scale11No commercial party having a direct financial interest in the results of the research supporting this article has or will confer a benefit upon the author(s) or upon any organ,” Arch Phys Med Rehabil, vol. 84, no. 7, pp. 950–963, Jul. 2003, doi: 10.1016/S0003-9993(03)00035-2.

J. A. Oluwatayo, “Validity and Reliability Issues in Educational Research,” Journal of Educational and Social Research, vol. 2, no. 2 SE-Articles, p. 391, May 2012, [Online]. Available: https://www.richtmann.org/journal/index.php/jesr/article/view/11851

L. SÜRÜCÜ and A. MASLAKÇI, “Validity and Reliability in Quantitative Research,” Business & Management Studies: An International Journal, vol. 8, no. 3, pp. 2694–2726, Sep. 2020, doi: 10.15295/bmij.v8i3.1540.

M. M. Mohamad, N. L. Sulaiman, L. C. Sern, and K. M. Salleh, “Measuring the Validity and Reliability of Research Instruments,” Procedia Soc Behav Sci, vol. 204, pp. 164–171, Aug. 2015, doi: 10.1016/j.sbspro.2015.08.129.

B. Sumintono and W. Widhiarso, Aplikasi Pemodelan Rasch Pada Assesmen Pendidikan. Cimahi: Trim Komunikata, 2015.

D. Ambarwati and S. Maarif, “Rasch Model Analysis: Development of Students’ Numeracy Literacy Interest Instruments in Mathematics Learning,” JP2M (Jurnal Pendidikan dan Pembelajaran Matematika), vol. 11, no. 1, pp. 41–52, Mar. 2025, doi: 10.29100/jp2m.v11i1.7279.

H. K. Rusyid, D. Suryadi, T. Herman, M. Adnan, A. Lutfi, and A. Mukhibin, “Rasch modeling approach to measure the quality of algebraic thinking questions for junior high school students,” Beta: Jurnal Tadris Matematika, vol. 17, no. 1, pp. 55–71, May 2024, doi: 10.20414/betajtm.v17i1.652.

R. Sheptian, R. Arthur, and R. Wardhani, “Psychometric Analysis of Mathematics Readiness Assessment Tool for Elementary School Students: A Rasch Model Approach,” LEARNING : Jurnal Inovasi Penelitian Pendidikan dan Pembelajaran, vol. 4, no. 4, pp. 1213–1220, Dec. 2024, doi: 10.51878/learning.v4i4.3725.