Analysis of students’ relational critical thinking abilities using an in-depth learning approach
DOI:
https://doi.org/10.59672/ijed.v7i2.6121Keywords:
Critical thinking, Deep learning, Rasch model, Taxonomy of SOLO HOTS-MunaliAbstract
Achieving the Golden Age Indonesia 2045 vision requires advancing human resources, particularly among educators. This is due to low PISA scores, a test of academic ability and critical thinking skills. This research is urgent because it aims to improve educator quality through a deep learning approach. This study aims to analyze students' Relational Critical Thinking (RCT) abilities in mathematics using a deep learning approach. This study employs a quantitative methodology using the Rasch model for data analysis. The research population includes Senior High Schools and Islamic Senior High Schools in Banten Province, with participants selected through random sampling. Data were collected using Google Forms with 15 essay questions on relational critical thinking. The results: 103 students (27.54%) fall into the developing RCT category, 152 students (40.64%) fall into the basic RCT category, and 119 students (31.82%) fall into the incompetent RCT category. These findings demonstrate that students' RCT abilities in mathematics are largely at the basic and incompetent levels. Deep learning can enhance students' RCT. This study recommends that educators consistently implement deep learning project-based learning approaches and use a valid critical thinking instrument.
Downloads
References
Agustika, G. N. S., & Diputra, K. S. (2025). Effectiveness of hybrid project-based learning with digital portfolios in enhancing mathematics pedagogical content knowledge. Indonesian Journal of Educational Development (IJED), 6(2), 293–308. https://doi.org/10.59672/ijed.v6i2.4923
Anisa Amalia Maisaroh, & Sri Untari. (2024). Transformation of character education through government policies in Indonesia towards the golden era generation 2045. Journal of Government Policy, 7(47), 18–30.
Baghaei, P. (2009). Understanding the Rasch model. Mashhad: Mashhad Islamic Azad University Press.
Bell, S. (2010). Project-based learning for the 21st century: Skills for the future. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 83(2), 39–43. https://doi.org/10.1080/00098650903505415
Bhismantara, B. S., Yakub Iskandar, M., Wijayanti, H. T., Widiastuti, A., Wulandari, T., & Rokhim, H. N. (2024). Efforts to improve teacher competence in the utilisation of technology in learning activities. 9(1). https://doi.org/10.34125/jmp.v9i1.331
Bond, T. G., & Fox, C. M. (2013). Applying the Rasch model: Fundamental measurement in the human sciences. Psychology Press.
Burcu Tunç, E. (2023). Assessing the psychometric properties of the brief resilience scale: A Rasch model. International Journal of Eurasian Education and Culture, 8(23). https://doi.org/10.35826/ijoecc.789
Chalkiadaki, A. (2018). A systematic literature review of 21st century skills and competencies in primary education. International Journal of Instruction, 11(3), 1–16. https://doi.org/10.12973/iji.2018.1131a
Chan, S. W., Ismail, Z., & Sumintono, B. (2014). A Rasch model analysis on secondary students’ statistical reasoning ability in descriptive statistics. Procedia - Social and Behavioral Sciences, 129, 133–139. https://doi.org/10.1016/j.sbspro.2014.03.658
Choir, M. N. A. C. (2025, December 24). Average TKA scores plummet: A warning alarm for education. 1–2.
Christensen, K. B., Makransky, G., & Horton, M. (2017). Critical values for yen’s q 3: identification of local dependence in the Rasch model using residual correlations. Applied Psychological Measurement, 41(3), 178–194. https://doi.org/10.1177/0146621616677520
Darwis, R. H., Alimuddin, ✉, & Patimbangi, A. (2024). Journal of learning and development studies higher order thinking and critical thinking skills in problem-based learning environments: a systematic review. Journal of Learning and Development Studies, 4(2), 21–33. https://doi.org/10.32996/jlds
Davidowitz, B., & Potgieter, M. (2016). Use of the Rasch measurement model to explore the relationship between content knowledge and topic-specific pedagogical content knowledge for organic chemistry. International Journal of Science Education, 38(9), 1–20. https://doi.org/10.1080/09500693.2016.1196843
Feri, M., Nur Ismiati, Widya Rahmawati Al-Nur, & Farah Nabila Akbar. (2025). Implementing deep learning approaches in primary education: A literature review. Jurnal VARIDIKA, 178–194. https://doi.org/10.23917/varidika.v37i2.12151
Feriyanto, F., & Anjariyah, D. (2024). Deep learning approach through meaningful, mindful, and joyful learning: A Library Research. Electronic Journal of Education, Social Economics and Technology, 5(2), 208–212. https://doi.org/10.33122/ejeset.v5i2.321
Fullan, M., Quinn, J., & McEachen, J. (2018). Deep learning: Engage the world, change the world. Deep Learning: Engage the World Change the World., xvii, 187–xvii, 187.
Huang, W. D., Loid, V., & Sung, J. S. (2024). Reflecting on gamified learning in medical education: a systematic literature review grounded in the Structure of Observed Learning Outcomes (SOLO) taxonomy 2012—2022. BMC Medical Education, 24(1). https://doi.org/10.1186/s12909-023-04955-1
Hyytinen, H., Jämsä, M., Tuononen, T., & Kleemola, K. (2025). A systematic-narrative review of performance-based assessments of critical thinking in higher education. Assessment and Evaluation in Higher Education, 50(8), 1293–1310. https://doi.org/10.1080/02602938.2025.2553341
Ilyana Ismarau Tajuddin, N., Abas, U.-H., Azhar Aziz, K., Nor Haizan Nor, R., Aziyatul Izni, N., Nuruddin Sudin, M., Aqilah Hazirah Mohd Anim, N., & Md Noor, N. (2025). Content validity assessment using aiken’s v: Knowledge integration model for blockchain in higher learning institutions. IJACSA) International Journal of Advanced Computer Science and Applications, 16(6), 2025. www.ijacsa.thesai.org
James, M. D. R., Carlson, J. E., Ackerman, T. A., & The. (1979). When unidimensional data are not unidimensional. Eric, 1–24.
Jeet, G., & Pant, S. (2023). Creating joyful experiences for enhancing meaningful learning and integrating 21st century skills. International Journal of Current Science Research and Review, 06(02). https://doi.org/10.47191/ijcsrr/V6-i2-05
Kang, H. A., Su, Y. H., & Chang, H. H. (2018). A note on monotonicity of item response functions for ordered polytomous item response theory models. British Journal of Mathematical and Statistical Psychology, 71(3), 523–535. https://doi.org/10.1111/bmsp.12131
KOCA, B. U., & TATLI, C. (2022). A study on the deep (Meaningful) learning perceptions of the teacher candıdates in the philosophy of education course carried out with distance education. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 10(2), 769–779. https://doi.org/10.18506/anemon.1096710
Lewis. R, A. (1985). Three coefficients for analyzing the reliability and validity of ratings. Educational and Psychological Measurement, 45(1), 131–142. https://doi.org/https://doi.org/10.1177/0013164485451012
Loyens, S. M. M., van Meerten, J. E., Schaap, L., & Wijnia, L. (2023). Situating higher-order, critical, and critical-analytic thinking in problem- and project-based learning environments: A systematic review. Educational Psychology Review, 35(2). https://doi.org/10.1007/s10648-023-09757-x
Made, N., Svari, F. D., & Arlinayanti, K. D. (2024). Changing the paradigm of education through the utilisation of technology in the global era. Jayapangus Press Metta: Multidisciplinary Science Journal, 4. https://jayapanguspress.penerbit.org/index.php/metta
Marton, F., & Saljo, K. (1976). Symposium: Learning processes and strategies-ii on qualitative differences in learning-ii outcome as a function of the learners' conception of the task. British Journal of Educational Psychology, 46(1947), 115–127.
Masayu Andayanie, L., Syahriandi Adhantoro, M., Purnomo, E., & Tribuana Kurniaji, G. (2025). Implementation of deep learning in education: Towards mindful, meaningful, and joyful learning experiences. Journal of Deep Learning | e, 1(1), 47–56. https://journals2.ums.ac.id/index.php/jdl
Medriati, R., Risdianto, E., Purwanto, A., & Kusen, K. (2022). Rasch model analysis on the development of digital learning model using moocs in practical courses at university. AL-ISHLAH: Jurnal Pendidikan, 14(1), 269–282. https://doi.org/10.35445/alishlah.v14i1.1192
Mohamad, M. M., Sulaiman, N. L., Sern, L. C., Mohd, K., & Salleh. (2015). Measuring the validity and reliability of research instruments.
Mudrika, P. A., Syaifuddin, M., & Azmi, R. D. (2024). HOTS critical thinking and math problem-solving skills on wordwall-assisted problem-based learning model. European Journal of Education and Pedagogy, 5(3), 44–50. https://doi.org/10.24018/ejedu.2024.5.3.835
Muhammad, I., Marina Angraini, L., Darmayanti, R., & Sugianto, R. (2023). Students’ interest in learning mathematics using augmented reality: Rasch model analysis. Edutechnium Journal of Educational Technology, 1(1), 89–99. https://www.edutechnium.com/journal
Munali. (2023). Assessment of student performance based on HOTS with the solo-munali taxonomy in mathematics subjects (1st ed.). CV. Kamila Press Lamongan.
Munali, & Alifah, S. (2024a). Analysis of summative model statistics questions. Lebesgue: Scientific Journal of Mathematics Education, Mathematics, and Statistics, 5(3), 1319–1334. https://doi.org/10.46306/lb.v5i3
Munali, & Alifah, S. (2024b). Steam learning: Miniature suspension bridge. ijcd: Indonesian Journal of Community Dedication, 2(3), 394–401.
Munali, & Alifah, S. (2025). Deep learning: A comprehensive framework for building collaborative problem solving. Education is the cognitive ability of students. The cognitive abilities of indonesian students. Lumbung Inovasi: Journal of Community Service, 10(2), 435–447. https://doi.org/https://doi.org/10.36312/linov.v10i2.2874
Munali, Dewi, S., Alifah, S., & Hapsari, S. (2025). Deep learning model approach project-based learning. December, 10(4), 1125–1138. https://doi.org/10.36312/vb141e09
Nizar Zulfikar, R., Ralmugiz, U., Fatmawati, A., Aba, M. M., Syarief, N. H., & Ketty, F. (2025). Unlocking higher order thinking with react strategy: An effective solution for 21st century learning. JTMT: Journal Tadris Matematika, 6(1), 15–21. https://doi.org/10.47435/jtmt.v6i1.3722
Nur Kartika, S., Maftuhah Hidayati, Y., Puji Rahmawati, F., Muhammadiyah Surakarta, U., Yani, J. A., & Tengah, J. (2026). Analysis of critical thinking in mathematics learning for solving Higher Order Thinking Skills (HOTS) problems in elementary school students. Teorema: Teori Dan Riset Matematika, 11(1), 99–106. https://doi.org/10.25157/teorema.v10i1.20022
Pastoriko, W., Fabian, F. M., & Ying, K. Y. (2024). The effect of scaffolding-based digital instructional media on higher-order thinking skills. Journal on Mathematics Education, 15(4), 1077–1094. https://doi.org/10.22342/jme.v15i4.1077-1094
Permatasari, M., & Murdiono, M. (2022). The urgency of political ethics of pancasila for the millennial generation towards golden Indonesia 2045. European Journal of Social Sciences Studies, 7(4), 26–46. https://doi.org/10.46827/ejsss.v7i4.1253
Prihantoro, P., Joko Prayitno, H., & Artha Kusumaningtyas, D. (2025). Deep learning: Policies, concepts, and implementation in senior high schools in indonesia. Journal of Deep Learning, 1(1). https://journals2.ums.ac.id/index.php/jdl
Puskurjar. (2025). Deep learning. https://www.deeplearningbook.org/contents/convnets.html
Putri, R. (2024). Educational innovation using deep learning models in Indonesia. Journal of Citizenship and Political Education (JPKP), 2(2), 69–77.
Rahayu, R., Iskandar, S., & Abidin, Y. (2022). 21st century learning innovations and their implementation in Indonesia. Journal Basicedu, 6(2), 2099–2104. https://doi.org/10.31004/basicedu.v6i2.2082
Santun Naga, D. (2012). Score theory in mental measurement (2nd ed.). PT Nagarani Citrayasa.
Sepriyanti, N., Nelwati, S., Kustati, M., & Afriadi, J. (2022). The effect of 21st-century learning on higher-order thinking skills (HOTS) and numerical literacy of science students in Indonesia based on gender. Journal of Indonesian Science Education, 11(2), 314–321. https://doi.org/10.15294/jpii.v11i2.36384
Sofyan, Kurniati, E., Widana, I. W., Sabariah, & Binti Muhammad, M. (2026). Development and validation of multimedia-based learning product instruments: SEM and Rasch model approaches. Indonesian Journal of Educational Development (IJED), 7(1), 82–95. https://doi.org/10.59672/ijed.v7i1.6343
Solihin, R. R., Susanto, T. T. D., Fauziyah, E. P., Yanti, N. V. I., & Ramadhania, A. P. (2024). The efforts of the indonesian government in increasing teacher quality based on pisa results in 2022: a literature review. Education Science Perspective, 38(1), 57–65. https://doi.org/10.21009/pip.381.6
Sumintoro, Bambang & Widhiarso, W. (2015). Application of the Rasch model for social science research (B. Trim, Ed.; II). TrimKom Publishing House.
Tabatabaee-Yazdi, Mona. et al., Motallebzadeh, K., Ashraf, H., & Baghaei, P. (2018). Development and validation of a teacher success questionnaire using the Rasch model. International Journal of Instruction, 11(2), 129–144. https://doi.org/10.12973/iji.2018.11210a
Taufik, Nurtamam, M. E., Dewanto, & Santosa, T. A. (2025). The effectiveness of deep learning-based pjbl on students’ scientific and critical thinking skills at Indonesia. Jurnal Penelitian Pendidikan IPA, 11(9), 228–236. https://doi.org/10.29303/jppipa.v11i9.12857
Tennant, A., & Conaghan, P. G. (2007). The Rasch measurement model in rheumatology: What is it and why use it? When should it be applied, and what should one look for in a Rasch paper? Arthritis Care & Research, 57(8), 1358–1362. https://doi.org/10.1002/art.23108
Wahyuni, S., Hindun, I., & Nurwidodo, N. (2024). Improving the quality of implementation of project-based learning in science teachers at muhammadiyah schools in Batu City addresses various learning problems. 9(3), 706–723.
Wang, C., Zheng, P., Zhang, F., Qian, Y., Zhang, Y., & Zou, Y. (2022). Exploring quality evaluation of innovation and entrepreneurship education in higher institutions using deep learning approach and fuzzy fault tree analysis. Frontiers in Psychology, 12(January), 1–16. https://doi.org/10.3389/fpsyg.2021.767310
Wang, Q., & Abdullah, A. H. (2024). Enhancing students’ critical thinking through mathematics in higher education: A systemic review. SAGE Open, 14(3). https://doi.org/10.1177/21582440241275651
Weng, C., Chen, C., & Ai, X. (2023). A pedagogical study on promoting students’ deep learning through design-based learning. International Journal of Technology and Design Education, 33(4), 1653–1674. https://doi.org/10.1007/s10798-022-09789-4
Widana, I. W., Sumandya, I. W., Sukendra, K., Sudiarsa, I. W. (2020). Analysis of conceptual understanding, digital literacy, motivation, divergent thinking, and creativity on the teacher's skills in preparing HOTS-based assessments. Jour of Adv Research in Dynamical & Control Systems, 12(8), 459-466. https://doi.org/10.5373/JARDCS/V12I8/20202612
Widana, I. W. & Ratnaya, I. G. (2021). Relationship between divergent thinking and digital literacy on teacher ability to develop HOTS assessment. Journal of Educational Research and Evaluation, 5(4), 516-524. https://doi.org/10.23887/jere.v5i4.35128
Zhang, J.-L. (2020). The application of human comprehensive development theory and deep learning in innovation education in higher education. Frontiers in Psychology, 11(July), 1–11. https://doi.org/10.3389/fpsyg.2020.01605
Zhu, Q., & Zhang, H. (2022). teaching strategies and psychological effects of entrepreneurship education for college students majoring in social security law based on deep learning and artificial intelligence. Frontiers in Psychology, 13(March), 1–17. https://doi.org/10.3389/fpsyg.2022.779669
Zulyusri, Z., Elfira, I., Lufri, L., & Santosa, T. A. (2023). Literature study: Utilization of the pjbl model in science education to improve creativity and critical thinking skills. Journal of Science Education Research, 9(1), 133–143. https://doi.org/10.29303/jppipa.v9i1.2555
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Munali, Siti Alifah, Imam Suseno, Tatan Zenal Mutakin, Shinta Dewi, Lusiana Wulansari, Sri Hapsari

This work is licensed under a Creative Commons Attribution 4.0 International License.
This is an Open Access article distributed under the terms of Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.








