A GRADED RESPONSE MODEL APPROACH TO ASSESS MATHEMATICAL CRITICAL THINKING ON FRACTION PROBLEMS IN JUNIOR HIGH SCHOOL

Pebi Pitri Anasari; Nur Izzati; Metta Liana

doi:10.15408/ajme.v8i1.51066

Authors

Pebi Pitri Anasari Universitas Pendidikan Indonesia
Nur Izzati Universitas Maritim Raja Ali Haji https://orcid.org/0000-0001-7165-1298
Metta Liana Universitas Maritim Raja Ali Haji https://orcid.org/0000-0001-9921-4153

DOI:

https://doi.org/10.15408/ajme.v8i1.51066

Keywords:

mathematical critical thinking, graded response model, fraction, junior high school students

Abstract

Abstract

Mathematical critical thinking ability (MCTA) plays a crucial role in problem solving and reasoned decision-making, yet many students still struggle with fraction problems, particularly in providing justification, evaluating strategies, and drawing conclusions. This study aims to examine junior high school students' mathematical critical thinking ability in solving fraction problems using a mixed-methods approach. Unlike previous studies, this research integrates qualitative analysis with the Graded Response Model (GRM) to provide a more comprehensive profile of students' critical thinking ability. The participants were 27 seventh-grade students. Data were collected through a mathematical critical thinking test, questionnaires, and semi-structured interviews, and analyzed using the GRM and thematic analysis with methodological triangulation. The findings indicate that most students demonstrated moderate to high levels of mathematical critical thinking. Students with higher ability demonstrated stronger reasoning, justification, and reflection, whereas students across all ability levels struggled to evaluate solution strategies and draw conclusions. These findings highlight the importance of instructional practices that foster mathematical reasoning, evaluation, and justification.

Abstrak

Kemampuan berpikir kritis matematis (MCTA) berperan penting dalam pemecahan masalah dan pengambilan keputusan, tetapi siswa masih mengalami kesulitan pada materi pecahan, terutama dalam memberikan justifikasi, mengevaluasi strategi, dan menarik kesimpulan. Penelitian ini bertujuan mengkaji kemampuan berpikir kritis matematis siswa SMP dalam menyelesaikan masalah pecahan menggunakan pendekatan mixed methods. Berbeda dari penelitian sebelumnya, studi ini mengintegrasikan analisis kualitatif dengan Graded Response Model (GRM) untuk menghasilkan profil kemampuan yang lebih komprehensif. Partisipan terdiri atas 27 siswa kelas VII. Data diperoleh melalui tes, angket, dan wawancara semi-terstruktur, kemudian dianalisis menggunakan GRM dan analisis tematik dengan triangulasi metode. Hasil menunjukkan sebagian besar siswa berada pada kategori kemampuan tinggi dan sedang. Siswa berkemampuan tinggi menunjukkan penalaran, justifikasi, dan refleksi yang lebih baik, sedangkan seluruh siswa masih lemah dalam mengevaluasi strategi dan menarik kesimpulan. Temuan ini menegaskan pentingnya pembelajaran yang mendorong penalaran, evaluasi, dan justifikasi matematis.

Downloads

Download data is not yet available.

References

Alexandra, G., & Ratu, N. (2018). Profil kemampuan berpikir kritis matematis siswa smp dengan graded response models. Mosharafa: Jurnal Pendidikan Matematika, 7(1), 103–112. https://doi.org/10.31980/mosharafa.v7i1.346

Alfisyah, N. (2022). Analisis kemampuan berpikir kritis siswa kelas VIII di SMPN 4 Arut Selatan dengan menggunakan graded response models (GRM). UIN Antasari Banjarmasin.

Alpian, Y., Anggraeni, S. W., Wiharti, U., & Soleha, N. M. (2019). Pentingnya pendidikan bagi manusia. Jurnal Buana Pengabdian, 1(1), 66–72. https://doi.org/10.36805/jurnalbuanapengabdian.v1i1.581

Anasari, P. P., Izzati, N., & Liana, M. (2023). Analisis Kemampuan Berpikir Kritis Matematis Peserta Didik Pasca Pandemi Covid-19 dengan Graded Response Models (GRM) dalam Menyelesaikan Soal Pecahan Kelas VII SMP [Universitas Maritim Raja Ali Haji]. https://lib.umrah.ac.id/

Christodoulakis, A., Kritsotakis, G., Linardakis, M., Sourtzi, P., & Tsiligianni, I. (2024). Evaluating critical thinking disposition, emotional intelligence, and learning environment of nursing students: A longitudinal study. Western Journal of Nursing Research, 46(5), 381–388. https://doi.org/10.1177/01939459241238687

Ennis, R. (2011). Critical Thinking. Inquiry: Critical Thinking Across the Disciplines, 26(2), 5–19. https://doi.org/10.5840/inquiryctnews201126215

Facione, P. A. (2020). Critical thinking: What it is and why it counts. Insight Assessment.

Fatimah, A. E. (2021). Analisis kemampuan berpikir kritis matematis ditinjau dari resiliensi matematis mahasiswa pendidikan teknik informatika dan komputer. Journal of Didactic Mathematics, 2(2), 94–100. https://doi.org/10.34007/jdm.v2i2.871

Gabriel, F., Van Hoof, J., Gómez, D. M., & Van Dooren, W. (2023). Obstacles in the development of the understanding of fractions. In Mathematical Cognition and Understanding: Perspectives on Mathematical Minds in the Elementary and Middle School Years (pp. 209–225). https://doi.org/10.1007/978-3-031-29195-1_11

Hendriana, H., Sumarmo, U., & Rohaeti, E. E. (2013). Kemampuan komunikasi matematik serta kemampuan dan disposisi berpikir kritis matematis. Jurnal Matematika Dan Pendidikan Matematika, 2(1), 35–45. https://doi.org/10.33387/dpi.v2i1.97

Hwang, J., & Riccomini, P. J. (2021). A descriptive analysis of the error patterns observed in the fraction-computation solution pathways of students with and without learning disabilities. Assessment for Effective Intervention, 46(2), 132–142. https://doi.org/10.1177/1534508419872256

Ibrahim. (2020). Analisis Miskonsepsi Siswa Pada Materi Persamaan Dan Pertidaksamaan Nilai Mutlak Linear Satu Variabel Dengan Menggunakan Three Tier Test Di Sma N 1 Toapaya. Universitas Maritim Raja Ali Haji.

Kunaedi, J., Sinaga, P., Samsudin, A., & Hasanah, L. (2022). Evaluating student higher order thinking on geometrical optics in the distance learning during Covid 19. AIP Conference Proceedings, 2468. https://doi.org/10.1063/5.0102598

Low, K. C., Mohamad, S. S., Chong, S. L., Abd Rahman, M. A., Purnomo, E. P., & Gunsuh, A. (2024). Improving university students’ critical thinking and problem-solving skills: How problem-based learning works during COVID-19 pandemic? Journal of Advanced Research in Applied Sciences and Engineering Technology, 37(2), 165–176. https://doi.org/10.37934/araset.37.2.165176

Maciejewski, W., & Star, J. R. (2019). Justifications for choices made in procedures. Educational Studies in Mathematics, 101(3), 325–340. https://doi.org/10.1007/s10649-019-09886-7

Muharram, M. R. W., Prabawanto, S., & Jupri, A. (2019). Analysis of students’ critical thinking skill of fractions on primary school. Journal of Physics: Conference Series, 1157(3). https://doi.org/10.1088/1742-6596/1157/3/032119

Nuryanti, L., Zubaidah, S., & Diantoro, M. (2018). Analisis kemampuan berpikir kritis siswa smp. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 3(2), 155–158. https://doi.org/10.17977/jptpp.v3i2.10490

Obeng, B. A., Banson, G. M., Owusu, E., & Owusu, R. (2024). Analysis of senior high school students’ errors in solving trigonometry. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2385119

Payadnya, I. P. A. A., & Wibawa, K. A. (2021). Students’ higher-order thinking skills in discrete mathematics during covid-19 pandemic. Journal of Physics: Conference Series, 1957(1). https://doi.org/10.1088/1742-6596/1957/1/012012

Pratiwi, A. N., Aisyah, N., & Kamran, M. (2023). STEM-based approach : A learning design to improve critical thinking skills. 14(1), 225–237.

Razfy, M., & Pradipta, T. R. (2022). Analysis of mathematical critical thinking ability viewed from students’ self-confidence post-covid-19 pandemic. Edumaspul - Jurnal Pendidikan, 6(2), 1850–1855. https://doi.org/10.23960/jpmipa/v23i3.pp904-917

Setiawan, A., Malik, A., Suhandi, A., & Permanasari, A. (2018). Effect of Higher Order Thinking Laboratory on the Improvement of Critical and Creative Thinking Skills. IOP Conference Series: Materials Science and Engineering, 306(1), 012008. https://doi.org/10.1088/1757-899X/306/1/012008

Shang, J., Zhang, L., Hu, R., Ma, S., Zeng, J., Yuan, M., & Sun, J. (2018). How to support fraction learning with math game “Run fraction”: Theory, design and application. ICCE 2018 - 26th International Conference on Computers in Education, Extended Summary Proceedings, 20–22. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060073563&partnerID=40&md5=e0770fe3a5ff48be660be04c1ee10d1b

Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the learning through activity research program. Journal of Mathematical Behavior, 52, 122–133. https://doi.org/10.1016/j.jmathb.2018.03.004

Solikhin, M., & Fauziah, A. N. M. (2021). Analisis kemampuan berpikir kritis siswa smp pada pelajaran ipa saat pembelajaran daring selama pandemi covid-19. Pensa E-Jurnal : Pendidikan Sains, 9(2), 188–192. https://ejournal.unesa.ac.id/index.php/pensa/article/view/38060

Syarifuddin, H., & Ismail, R. N. (2023). Optimizing students ’ mathematical critical and creative thinking skills through the flip-a-team model with e-learning. 14(1), 133–140.

Tamila, R., Febrian, F., & Tambunan, L. R. (2020). Analisis kemampuan berpikir kritis dalam menyelesaikan masalah matematika pada materi pecahan kelas vii smp 10 tanjungpinang. Student Online Journal (SOJ) UMRAH - Keguruan Dan Ilmu Pendidikan, 1(1), 588–597. https://soj.umrah.ac.id/index.php/SOJFKIP/article/view/334