Analysis of the characteristic of mathematical literacy test items on algebraic elements using IRT
DOI:
https://doi.org/10.29407/jmen.v12i1.26949Keywords:
algebra, mathematical literacy, item response theoryAbstract
Accurate measurement tools are needed to assess mathematical literacy in algebra. This study purposes to describe the test items characteristics in a mathematical literacy test using IRT. This study conducted by modifying the test development steps according to Downing & Haladyna. Subjects in this study were 179 7th students at a junior high school in Yogyakarta. The data collection instruments included a validation sheet and a test instrument. Data analysis techniques included content validity, construct validity, construct reliability, item and person characteristics using the PCM model. The results of the study indicate that there are eight items of mathematical literacy in algebra for seventh grade. All items are content-valid with a value of V >0.80, construct-valid (SLF > 0.45), and construct-reliable (CR>0.70). The difficulty level of items is in the good category with a b value in the range -2<b<2. The ICC curve shows that there are 2 items with ideal ICC and 6 items with non-ideal ICC. The information function and SEM indicate that the test instrument provides the best information when administered to students with abilities slightly below average. There were 6 questions that met the item fit criteria and 112 students who met the person fit criteria.
References
Apriatni, S., Yuhana, Y., & Sukirwan. (2022). Pengembangan Instrumen Literasi Numerasi Materi Trigonometri Kelas X SMA. EDU-MAT: Jurnal Pendidikan Matematika, 2759(2), 185–198. https://doi.org/10.20527/edumat.v10i2.13720
Ardiansari, L. (2018). Pra-aljabar: Langkah Baru Mengajar Aljabar Awal (Penerapan Didactical Design Research. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 1(1), 32–44. https://doi.org/https://e-journal.my.id/proximal/article/view/182
Azzahra, N. T., Ali, S. N. L., & Bakar, M. Y. A. (2025). Teori Konstruktivisme dalam Dunia Pembelajaran. Jurnal Ilmiah Research Student, 2(2), 64–75. https://doi.org/10.61722/jirs.v2i2.4762
Bahar, R., & Retnawati, H. (2022). Analisis Karakteristik Soal Kemampuan Koneksi Matematika Penskoran Politomus. Jurnal Tarbiyah, 29(2), 195–211. https://doi.org/10.30829/tar.v29i2.1650
Cendana, V., Syamsuri, & Pujiastuti, H. (2024). Pengembangan Instrumen Literasi Matematis Model PISA dengan Konteks Batik Krakatoa Cilegon untuk Siswa SMP. Himpunan: Jurnal Ilmiah Mahasiswa Pendidikan Matematika, 4(1), 29–40. https://doi.org/https://jim.unindra.ac.id/index.php/himpunan/article/view/11188
Dewanti, S. S., Ayriza, Y., & Setiawati, F. A. (2020). The Application of Item Response Theory for Development of a Students' Attitude Scale Toward Mathematics. New Educational Review, 60, 108–123. https://doi.org/10.15804/tner.2020.60.2.09
Dewanti, S. S., Hadi, S., Nu'man, M., & Ibrahim. (2021). The Application of Item Response Theory in Analysis of Characteristics of Mathematical Literacy Test Items. Ilkogretim Online - Elementary Education, 20(1), 1226–1237. https://doi.org/10.17051/ilkonline.2021.01.119
Dewanti, S. S., Izzah, J. N., Kiranasari, S. P., & Sholihin, K. F. (2024). Utilizing Item Response Theory for the Analysis of Self-regulated Learning Scale in Mathematics. Jurnal Elemen, 10(June), 614–629. https://doi.org/10.29408/jel.v10i3.26618
Downing, S. M., & Haladyna, T. M. (2006). Handbook of Test Development. Lawrence Erlbaum Associates.
Evendi, E. (2020). Evaluasi Pembelajaran Matematika.
Farida, R. N., Qohar, A., & Rahardjo, S. (2021). Analisis Kemampuan Literasi Matematis Siswa SMA Kelas X dalam Menyelesaikan Soal Tipe PISA Konten Change and Relationship. Jurnal Cendekia : Jurnal Pendidikan Matematika, 05(03), 2802–2815. https://doi.org/https://j-cup.org/index.php/cendekia/article/view/972
Fitraynsyah, M. A., Hilmiyati, F., & Habudin. (2024). Peran Tingkat Kesukaran dan Daya Pembeda dalam Analisis Butir Tes : Kajian Literatur untuk Pendidikan Menengah. JREP: Jurnal Riset Dan Evaluasi Pendidikan, 1(4), 252–262. https://doi.org/10.51574/jrep.v1i4.2250
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (Eighth. Cengage Learning EMEA.
Hambleton, R. K., & Swaminathan, H. (1985). Item Response Theory. Kluwer Inc.
Hambleton, R. K., Swaminathan, H., & Rogers, D. J. (1991). Fundamentals of Item Response Theory. Sage Publications.
Hidayatulloh, D. A., Agustin, D. R., & Malik, F. A. (2025). Menumbuhkan Literasi Matematis Siswa dalam Pembelajaran Melalui Lensa Konstruktivistime. Wacana Akademika: Majalah Ilmiah Kependidikan Volume, 9(1), 99–105. https://doi.org/10.30738/wacanaakademika.v9i1.19786
Linacre, J. M. (2002). What Do Infit and Outfit, Mean-square and Standardized Mean? Rasch Measurement Transactions, 16(2), 878.
Mardapi, D. (2017). Pengukuran, Penilaian, dan Evaluasi Pendidikan (2nd ed.). Parama Publishing.
Mardianto, R. ., Susanti, V. D., & Sulastri, Y. E. . (2025). Enhancing mathematical literacy through the integration of PBL and CRT: A Case study of grade X. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 11(1), 107-117. https://doi.org/10.29407/jmen.v11i1.23370
Meijer, R. R. (2009). Person-Fit Research : An Introduction. Applied Measurement in Education, 9(1), 37–41. https://doi.org/10.1207/s15324818ame0901
Mulyani, S., Efendi, R., & Ramalis, T. R. (2017). Karakterisasi Tes Keterampilan Pemecahan Masalah Fisika berdasarkan Teori Respons Butir.
Nanda, E. M. ., Kismiantini , K. ., & Arliani , E. . (2025). Item analysis of mathematical literacy test and self efficacy of learners. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 11(2), 307-318. https://doi.org/10.29407/jmen.v11i2.27281
Nursakiah, N., Arriah, F., & Dharma, S. (2022). Developing Mathematical Literacy Test with Context of Bugis-Makassar Local Wisdom for Junior High School Students. Jurnal Elemen, 8(1), 16–28. https://doi.org/10.29408/jel.v8i1.4049
O.e.c.d. (2023a). PISA 2022 Assessment and Analytical Framework. In OECD (Organisation for Economic Co-operation and Development) Publishing. OECD Publishing. https://www.oecd-ilibrary.org/education/pisa-2022-assessment-and-analytical-framework_dfe0bf9c-en
O.e.c.d. (2023b). Pisa 2022 Results (Volume I): The State of Learning and Equity in Education. In OECD Publishing (Vol. I). OECD Publishing. https://doi.org/10.1787/53f23881-en
Ojose, B. (2011). Mathematics Literacy: Are We Able To Put The Mathematics We Learm Into Everyday Use. Journal Of Mathematics Education, 4(1), 89–100. https://educationforatoz.com/images/Bobby_Ojose.pdf
Reise, S. P. (1990). A Comparison of Item- and Person-Fit Methods of Assessing Model-Data Fit in IRT. Applied Psychological Measurement, 14(2), 127–137.
Retnawati, H. (2014). Teori Respon Butir dan Penerapannya. Nuha Medika.
Samritin. (2022). Identifikasi Muatan Differential Item Functioning Pada Data Ujian Nasional Matematika. Journal on Education, 04(04), 1675–1684. https://doi.org/10.31004/joe.v4i4.2508
Santoso, A. (2018). Karakteristik Butir Tes Pengantar Statistika Sosial berdasarkan Teori Respon Butir. Jurnal Pendidikan Matematika dan Sains, VI(2), 1–11. https://doi.org/10.21831/jpms.v4i1.10111
Sarea, M. S., & Ruslan, R. (2019). Karakteristik Butir Soal: Classical Test Theory vs Item Response Theory? Didaktika. Jurnal Pendidikan, 13(1), 1–16. https://doi.org/10.30863/didaktika.v13i1.296
Selan, M., Daniel, F., & Babys, U. (2020). Analisis Kemampuan Literasi Matematis Siswa dalam Menyelesaikan Soal PISA Konten Change and Relationship. AKSIOMA: Jurnal Matematika Dan Pendidikan Matematika, 11(2), 335–345. https://doi.org/10.26877/aks.v11i2.6256
Siregar, N. H., Remiswal, & Khadijah. (2024). Analisis Butir Soal Ujian Tengah Semester pada Mata Pelajaran Pendidikan Agama Islam. Urwatul Wutsqo: Jurnal Studi Kependidikan Dan Keislaman, 13(2), 179–189. https://doi.org/10.54437/juw
Sudaryono. (2012). Dasar-Dasar Evaluasi Pembelajaran. Graha Ilmu.
Sumaryanta. (2021). Teori Tes Klasik & Teori Respon Butir (Konsep & Contoh Penerapannya. CV Confident.
Wibowo, A. A., Rif'at, M., & Yani, A. (2020). Pengembangan Instrumen Tes Untuk Mengukur Kemampuan Literasi Matematis Siswa SMP. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 9(7). https://doi.org/10.26418/jppk.v9i7.41316
Wu, M., & Adams, R. (2007). Applying the Rasch model to psycho-social measurement: A practical approach. In Educational Measurement Solutions.
Zahrah, M. (2024). Penelitian Literasi Matematis di Sekolah: Pengertian dan Kesulitan-Kesulitan Siswa. Jurnal Riset Pendidikan Matematika Jakarta, 6(1), 27–36. https://doi.org/10.21009/jrpmj.v6i1.29024
Zubairi, A. M., & Kassim, N. L. A. (2006). Classical and Rasch Analyses of Dichotomously Scored Reading Comprehension Test Items. Malaysian Journal of ELT Research, 2(March), 1–20. https://doi.org/https://meltajournals.com/index.php/majer/article/view/663
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