TY  - JOUR
T1  - Thinking Beyond the Equations: A Deep Dive into Reflective Thinking for Mathematics Learning
AU  - Kuncoro, Krida
AU  - Hidayat, Angga
AU  - Nadzeri, Mohamad Basri
AU  - Juandi, Dadang
AU  - Hendriyanto, Agus
AU  - Meirani, Fajar
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.17275/per.25.75.12.5
JF  - Participatory Educational Research
JO  - PER
PB  - Özgen KORKMAZ
WT  - DergiPark
SN  - 2148-6123
SP  - 310
EP  - 334
VL  - 12
IS  - 5
LA  - en
AB  - Reflective thinking is a cognitive process that involves re-examining issues to overcome challenges in problem-solving. In the context of mathematics education, it serves not only as a tool for error correction but also as a means of fostering deeper conceptual understanding and self-regulation. This study aims to assess current research on reflective thinking within the field of mathematics education. To explore this, relevant keywords such as "reflective thinking" and "mathematics education" were used in literature searches. A systematic literature review (SLR) was conducted to enhance our understanding of the topic, focusing on articles indexed in the ERIC and Scopus databases. Following the PRISMA guidelines, we carefully evaluated 101 articles published between 2018 and 2024, eliminating duplicates and irrelevant content. Ultimately, 23 articles were selected based on predefined criteria. The findings reveal that reflective thinking is an ongoing and dynamic process that positively impacts academic achievement. The review highlights the significant role of reflective thinking in various areas, including problem-solving, creative idea generation, task completion, learning enhancement, decision-making, and the development of both systematic and conceptual skills. In conclusion, this study emphasizes the essential role of reflective thinking in mathematics education, underscoring its importance in improving educational practices and outcomes. Furthermore, reflective thinking not only enhances individual cognitive skills but also promotes collaborative and interactive learning environments, encourages reflective teaching practices among educators, and strengthens lifelong learning dispositions, all of which are crucial for holistic educational development.
KW  - mathematics education
KW  - reflective thinking
KW  - systematics literature review
CR  - Afshar, H. S., & Rahimi, M. (2016). Reflective thinking, emotional intelligence, and speaking ability of EFL learners: Is there a relation? Thinking Skills and Creativity, 19, 97–111. https://doi.org/10.1016/j.tsc.2015.10.005
CR  - Akdemir, E. (2018). Investigating the reflective thinking skills of students for problem solving. The Turkish Online Journal of Educational Technology, 1, 774–780. Retrieved from https://eric.ed.gov/?id=ED595226
CR  - Aldahmash, A. H., Alshalhoub, S. A., & Naji, M. A. (2021). Mathematics teachers’ reflective thinking: Level of understanding and implementation in their professional practices. PloS One, 16(10), e0258149. https://doi.org/10.1371/journal.pone.0258149
CR  - Ball, D. L., & Bass, H. (2002). Toward a practice-based theory of mathematical knowledge for teaching. Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group, 3–14. Canadian Mathematics Education Study Group.
CR  - Barnham, C. (2015). Quantitative and qualitative research: Perceptual foundations. International Journal of Market Research, 57(6), 837–854. https://doi.org/10.2501/IJMR-2015-070
CR  - Baron, J. (1981). Reflective thinking as a goal of education. Intelligence, 5, 291–309. Elsevier. https://doi.org/10.1016/0160-2896(81)90021-0
CR  - Benz, C. (2016). Reflection: An opportunity to address different aspects of professional competencies in mathematics education. Mathematics Education in the Early Years: Results from the POEM2 Conference, 2014, 419–435. https://doi.org/10.1007/978-3-319-23935-4_23
CR  - Broza, O., Lifshitz, A., & Atzmon, S. (2022). Exploring a model to develop critical reflective thought among elementary school math preservice teachers. Journal of Education, 202(4), 406–415. https://doi.org/10.1177/0022057421998336
CR  - Chamdani, M., Yusuf, F. A., Salimi, M., & Fajari, L. E. W. (2022). Meta-analysis study: The relationship between reflective thinking and learning achievement. Journal on Efficiency and Responsibility in Education and Science, 15(3), 181–188. https://doi.org/10.7160/eriesj.2022.150305
CR  - Changwong, K., Sukkamart, A., & Sisan, B. (2018). Critical thinking skill development: Analysis of a new learning management model for Thai high schools. Journal of International Studies, 11(2). https://doi.org/10.14254/2071-8330.2018/11-2/3
CR  - Chasanah, C., & Usodo, B. (2020). The effectiveness of learning models on written mathematical communication skills viewed from students’ cognitive styles. European Journal of Educational Research, 9(3), 979–994. https://doi.org/10.12973/eu-jer.9.3.979
CR  - Clarà, M., Mauri, T., Colomina, R., & Onrubia, J. (2019). Supporting collaborative reflection in teacher education: a case study. European Journal of Teacher Education, 42(2), 175–191. https://doi.org/10.1080/02619768.2019.1576626
CR  - Cornito, C., & Caingcoy, M. (2021). Reflective habits of the mind: A systematic literature review. International Journal of Research Publication and Reviews. https://dx.doi.org/10.5281/zenodo.3953324
CR  - Demir, S. (2015). Evaluation of critical thinking and reflective thinking skills among science teacher candidates. Journal of Education and Practice, 6(18), 17–21. Retrieved from https://www.iiste.org/Journals/index.php/JEP/article/view/23611
CR  - Deringöl, Y. (2019). The relationship between reflective thinking skills and academic achievement in mathematics in fourth-grade primary school students. International Online Journal of Education and Teaching, 6(3), 613–622. Retrieved from https://iojet.org/index.php/IOJET/article/view/532
CR  - Dervent, F. (2015). The effect of reflective thinking on the teaching practices of preservice physical education teachers. Issues in Educational Research, 25(3), 260–275. Retrieved from http://www.iier.org.au/iier25/dervent.html
CR  - Dewey, J. (1933). How we think. A restatement of the relation of reflective thinking to the educative process. DC Heath and Company
CR  - Dreyfus, T. (2002). Advanced mathematical thinking processes. In Advanced mathematical thinking (pp. 25–41). Springer. https://doi.org/10.1007/0-306-47203-1_2
CR  - Dubinsky, E. (2002). Reflective abstraction in advanced mathematical thinking. In Advanced mathematical thinking (pp. 95–126). Springer. https://doi.org/10.1007/0-306-47203-1_7
CR  - Egmir, E., & Ocak, İ. (2020). Prediction level of the fourth grade students’ scientific attitudes on reflective thinking skills for problem solving. Open Journal for Educational Research, 4(2), 87–102. https://doi.org/10.32591/coas.ojer.0402.02087e
CR  - Erdogan, F. (2019). Effect of cooperative learning supported by reflective thinking activities on students’ critical thinking skills. Eurasian Journal of Educational Research, 19(80), 89–112. https://doi.org/10.14689/ejer.2019.80.5
CR  - Erdoğan, F. (2020). The relationship between prospective middle school mathematics teachers’ critical thinking skills and reflective thinking skills. Participatory Educational Research, 7(1), 220–241. https://doi.org/10.17275/per.20.13.7.1
CR  - Farnila, Y., Johar, R., & Usman, U. (2021). Students’ reflective thinking process in mathematical problem-solving reviewed from self-confidence. AIP Conference Proceedings, 2331(1). https://doi.org/10.1063/5.0042223
CR  - Fitriati, F., Novita, R., & Johar, R. (2020). Exploring the usefulness of rich mathematical tasks to enhance. Cakrawala Pendidikan [Educational Horizons], 39(2), 346–358. https://doi.org/10.21831/cp.v39i2.24047
CR  - Flora, J. (2023). Demystifying Preservice Teacher Reflective Thinking: A Systematic Literature Review. Doctor of Education (EdD), 213. Retrieved from https://digitalcommons.georgefox.edu/edd/213/
CR  - Gelter, H. (2003). Why is reflective thinking uncommon. Reflective Practice, 4(3), 337–344. https://doi.org/10.1080/1462394032000112237
CR  - Gökçe, S., & Yenmez, A. A. (2023). Ingenuity of scratch programming on reflective thinking towards problem solving and computational thinking. Education and Information Technologies, 28(5), 5493–5517. https://doi.org/10.1007/s10639-022-11385-x
CR  - Gough, D. (2007). Weight of evidence: a framework for the appraisal of the quality and relevance of evidence. Research Papers in Education, 22(2), 213–228. https://doi.org/10.1080/02671520701296189
CR  - Gourlet, P., Eveillard, L., & Dervieux, F. (2016). The research diary, supporting pupils’ reflective thinking during design activities. IDC, 206–217. https://doi.org/10.1145/2930674.2930702
CR  - Hendriana, H., Putra, H. D., & Hidayat, W. (2019). How to design teaching materials to improve the ability of mathematical reflective thinking of senior high school students in Indonesia? Eurasia Journal of Mathematics, Science and Technology Education, 15(12), em1790. https://doi.org/10.29333/ejmste/112033
CR  - Hidajat, F. A., & Sa’dijah, C. (2019). Exploration of students’ arguments to identify perplexity from reflective process on mathematical problems. International Journal of Instruction, 12(2), 573–586. https://doi.org/10.29333/iji.2019.12236a
CR  - Hong, Y.-C., & Choi, I. (2011). Three dimensions of reflective thinking in solving design problems: a conceptual model. Educational Technology Research and Development, 59(5), 687–710. https://doi.org/10.1007/s11423-011-9202-9
CR  - Kalelioğlu, F. (2015). A new way of teaching programming skills to K-12 students: Code. org. Computers in Human Behavior, 52, 200–210. https://doi.org/10.1016/j.chb.2015.05.047
CR  - Katrancı, Y., & Şengül, S. (2020). The evaluation of inquiry learning skills towards math of middle school students in terms of inquiring, evaluating, reasoning, and reflective-thinking skills for problem-solving. Egitim ve Bilim [Education and Science], 45(201). https://doi.org/10.15390/EB.2020.7765
CR  - Kholid, M. N., Sa’Dijah, C., Hidayanto, E., & Permadi, H. (2022a). Students’ reflective thinking pattern changes and characteristics of problem solving. Reflective Practice, 23(3), 319–341. https://doi.org/10.1080/14623943.2021.2025353
CR  - Kholid, M. N., Telasih, S., Pradana, L. N., & Maharani, S. (2021). Reflective thinking of mathematics prospective teachers’ for problem solving. Journal of Physics: Conference Series, 1783(1), 12102. IOP Publishing. https://doi.org/10.1088/1742-6596/1783/1/012102
CR  - Kholid, M., Sa’dijah, C., Hidayanto, E., & Permadi, H. (2020). How are students’ reflective thinking for problem solving? Journal for the Education of Gifted Young Scientists, 8(3), 1135–1146. https://doi.org/10.17478/jegys.688210
CR  - Kholid, M., Swastika, A., Ishartono, N., Nurcahyo, A., Lam, T. T., Maharani, S., … Wijaya, A. P. (2022b). Hierarchy of students’ reflective thinking levels in mathematical problem solving. Acta Scientiae [Journal of Science], 24(6), 24–59. https://doi.org/10.17648/acta.scientiae.6883
CR  - Kizilkaya, G., & Askar, P. (2009). The development of a reflective thinking skill scale towards problem solving. Egitim ve Bilim [Education and Science], 34(154), 82. Retrieved from https://eb.ted.org.tr/index.php/EB/article/view/550
CR  - Leung, D. Y. P., & Kember, D. (2003). The relationship between approaches to learning and reflection upon practice. Educational Psychology, 23(1), 61–71. https://doi.org/10.1080/01443410303221
CR  - Liao, H.-C., & Wang, Y. (2019). Reflective thinking scale for healthcare students and providers—Chinese version. Social Behavior and Personality: An International Journal, 47(2), 1–10. https://doi.org/10.2224/sbp.7671
CR  - Mann, K., Gordon, J., & MacLeod, A. (2009). Reflection and reflective practice in health professions education: a systematic review. Advances in Health Sciences Education, 14(4), 595–621. https://doi.org/10.1007/s10459-007-9090-2
CR  - McLeod, G. A., Vaughan, B., Carey, I., Shannon, T., & Winn, E. (2020). Pre-professional reflective practice: Strategies, perspectives and experiences. International Journal of Osteopathic Medicine, 35, 50–56. https://doi.org/10.1016/j.ijosm.2019.11.005
CR  - Mefoh, P. C., Nwoke, M. B., Chukwuorji, J. C., & Chijioke, A. O. (2017). Effect of cognitive style and gender on adolescents’ problem solving ability. Thinking Skills and Creativity, 25, 47–52. https://doi.org/10.1016/j.tsc.2017.03.002
CR  - Miettinen, R. (2000). The concept of experiential learning and John Dewey’s theory of reflective thought and action. International Journal of Lifelong Education, 19(1), 54–72. https://doi.org/10.1080/026013700293458
CR  - Minott, M. A. (2011). The impact of a course in reflective teaching on student teachers at a Local University College. Canadian Journal of Education, 34(2), 131–147. Retrieved from https://journals.sfu.ca/cje/index.php/cje-rce/article/view/530
CR  - Muntazhimah, M., Turmudi, T., & Prabawanto, S. (2021). The relation between prior knowledge and students’ mathematics reflective thinking ability. Journal of Physics: Conference Series, 1731(1), 12043. IOP Publishing. https://doi.org/10.1088/1742-6596/1731/1/012043
CR  - NCTM. (2000). Principles and standards for school mathematics. Reston: NCTM.
CR  - Ng, C. S. L., & Tan, C. (2006). Investigating Singapore pre-service teachers’ ill-structured problem-solving processes in an asynchronous online environment: Implications for reflective thinking. New Horizons in Education, 54, 1–15. Retrieved from https://www.learntechlib.org/p/105588/
CR  - Okoli, C., & Schabram, K. (2010). A guide to conducting a systematic literature review of information systems research. Available at SSRN 1954824. https://doi.org/10.2139/ssrn.1954824
CR  - Orakcı, Ş. (2021). Exploring the relationships between cognitive flexibility, learner autonomy, and reflective thinking. Thinking Skills and Creativity, 41, 100838. https://doi.org/https://doi.org/10.1016/j.tsc.2021.100838
CR  - Ozyildirim-Gumus, F., & Ozyildirim, G. (2020). Reflective thinking and probabilistic thinking: an example of elementary school students. Acta Didactica Napocensia [Napocensia Didactic Act], 13(1), 43–56. https://doi.org/10.24193/adn.13.1.5
CR  - Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., Shamseer, L., Tetzlaff, J. M., Akl, E. A., & Brennan, S. E. (2021). The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ, 372. https://doi.org/10.1136/bmj.n71
CR  - Paul, R. W. (1990). Critical and reflective thinking: A philosophical perspective. Dimensions of Thinking and Cognitive Instruction (pp. 445-494). Hillsdale, N.J.: L. Erlbaum.
CR  - Phan, H. P. (2009). Exploring students’ reflective thinking practice, deep processing strategies, effort, and achievement goal orientations. Educational Psychology, 29(3), 297–313. https://doi.org/10.1080/01443410902877988
CR  - Porntaweekul, S., Raksasataya, S., & Nethanomsak, T. (2016). Developing reflective thinking instructional model for enhancing students’ desirable learning outcomes. Educational Research and Reviews, 11(6), 238–251. https://doi.org/10.5897/ERR2015.2380
CR  - Prediger, S. (2005). Developing reflectiveness in mathematics classrooms—An aim to be reached in several ways. ZDM, 3(37), 250–257. https://doi.org/10.1007/s11858-005-0017-1
CR  - Procter, L. (2020). Fostering critically reflective thinking with first-year university students: early thoughts on implementing a reflective assessment task. Reflective Practice, 21(4), 444–457. https://doi.org/10.1080/14623943.2020.1773421
CR  - Ramdani, R., Syamsuddin, A., & Sirajuddin, S. (2019). Development of mathematical module-problem solving approach to train student’s reflective thinking. Pedagogical Research, 4(4), em0040. https://doi.org/10.29333/pr/5861
CR  - Rodgers, C. (2002). Defining reflection: Another look at John Dewey and reflective thinking. Teachers College Record, 104(4), 842–866. https://doi.org/10.1111/1467-9620.00181
CR  - Sa’dijah, C., Kholid, M. N., Hidayanto, E., & Permadi, H. (2021). Are there differences in reflective thinking between male and female prospective mathematics teachers? 7th International Conference on Research, Implementation, and Education of Mathematics and Sciences (ICRIEMS 2020), 344–351. Atlantis Press. https://doi.org/10.2991/assehr.k.210305.050
CR  - Salido, A., Suryadi, D., Dasari, D., & Muhafidin, I. (2020). Mathematical reflective thinking strategy in problem-solving viewed by cognitive style. Journal of Physics: Conference Series, 1469(1), 12150. IOP Publishing. https://doi.org/10.1088/1742-6596/1469/1/012150
CR  - Saracoglu, M. (2022). Reflective thinking and inquiry skills as predictors of self-efficacy in teaching mathematics. Problems of Education in the 21st Century, 80(1), 213–231. https://doi.org/10.33225/pec/22.80.213
CR  - Sarican, G., & Akgunduz, D. (2018). The impact of integrated STEM education on academic achievement, reflective thinking skills towards problem solving and permanence in learning in science education. Cypriot Journal of Educational Sciences, 13(1), 94–113. https://doi.org/10.18844/cjes.v13i1.3322
CR  - Satriawan, M. A., Budiarto, M. T., & Siswono, T. Y. E. (2018). Students’ relational thinking of impulsive and reflective in solving mathematical problem. Journal of Physics: Conference Series, 947(1), 12030. IOP Publishing. https://doi.org/10.1088/1742-6596/947/1/012030
CR  - Setiyani, S. B., Waluya, Y. L., & Cahyono, A. N. (2022). Mathematical reflective thinking process of prospective elementary teachers review from the disposition in numerical literacy problems. International Journal of Educational Methodology, 8(3), 405–420. https://doi.org/10.12973/ijem.8.3.405
CR  - Setiyani, S., Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2024). Construction of reflective thinking: A field independent student in numerical problems. Journal on Mathematics Education, 15(1), 151–172. https://doi.org/10.22342/jme.v15i1.pp151-172
CR  - Slavin, R. E. (2019). Educational psychology: Theory and practice. London: Pearson.
CR  - Strohmaier, A. R., MacKay, K. J., Obersteiner, A., & Reiss, K. M. (2020). Eye-tracking methodology in mathematics education research: A systematic literature review. Educational Studies in Mathematics, 104(2), 147–200. https://doi.org/10.1007/s10649-020-09948-1
CR  - Sudirman, A., Gemilang, A. V., Kristanto, T. M. A., Robiasih, R. H., Nugroho, A. D., Karjono, J. C. S., Lestari, T., Widyarini, T. L., Prastanti, A. D., & Susanto, M. R. (2024). Reinforcing reflective practice through reflective writing in higher education: A systematic review. International Journal of Learning, Teaching and Educational Research, 23(5), 454–474. https://doi.org/10.26803/ijlter.23.5.24
CR  - Syamsuddin, A., Haking, H., Tonra, W. S., & Syukriani, A. (2023). Designing worksheets to improve reflective thinking for elementary school students on the solid figure subject. Academic Journal of Interdisciplinary Studies, 12(2), 349-366. https://doi.org/10.36941/ajis-2023-0054
CR  - Syamsuddin, A., Juniati, D., & Siswono, T. Y. E. (2020). Understanding the problem solving strategy based on cognitive style as a tool to investigate reflective thinking process of prospective teacher. Universal Journal of Educational Research, 8(6), 2614–2620. https://doi.org/10.13189/ujer.2020.080644
CR  - Taggart, G. L., & Wilson, A. P. (2005). Promoting reflective thinking in teachers: 50 action strategies. Corwin Press.
CR  - Tall, D. (2002). The psychology of advanced mathematical thinking. In Advanced mathematical thinking (pp. 3–21). Springer. https://doi.org/10.1007/0-306-47203-1_1
CR  - Titus, A., & Muttungal, P. V. (2024). Reflective thinking in school: A systematic review. International Journal of Evaluation and Research in Education, 13(2), 742-751. https://doi.org/10.11591/ijere.v13i2.26573
CR  - Toraman, Ç., Orakci, S., & Aktan, O. (2020). Analysis of the relationships between mathematics achievement, reflective thinking of problem solving and metacognitive awareness. International Journal of Progressive Education, 16(2), 72–90. https://doi.org/10.29329/ijpe.2020.241.6
CR  - Viera, A. J., & Garrett, J. M. (2005). Understanding interobserver agreement: the kappa statistic. Fam Med, 37(5), 360–363. Retrieved from https://pubmed.ncbi.nlm.nih.gov/15883903/
CR  - Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In Advanced mathematical thinking (pp. 65–81). Springer. https://doi.org/10.1007/0-306-47203-1_5
CR  - Xiao, Y., & Watson, M. (2019). Guidance on conducting a systematic literature review. Journal of Planning Education and Research, 39(1), 93–112. https://doi.org/10.1177/0739456X17723971
CR  - Yasin, M., Fakhri, J., Faelasofi, R., Safi’i, A., Supriadi, N., Syazali, M., & Wekke, I. S. (2020). The effect of SSCS learning model on reflective thinking skills and problem solving ability. European Journal of Educational Research, 9(2), 743–752. https://doi.org/10.12973/eu-jer.9.2.743
CR  - Yilmaz, D., & Turan, H. (2020). Self-efficacy beliefs of pre-service teachers in teaching first reading and writing and mathematics. Participatory Educational Research, 7(1), 257–270. https://doi.org/10.17275/per.20.15.7.1
CR  - Zehavi, N., & Mann, G. (2005). Instrumented techniques and reflective thinking in analytic geometry. The Mathematics Enthusiast, 2(2), 83–92. https://doi.org/10.54870/1551-3440.1025
CR  - Zwozdiak-Myers, P. (2018). The teacher’s reflective practice handbook: Becoming an extended professional through capturing evidence-informed practice. Routledge. https://doi.org/10.4324/9780203118733
UR  - https://doi.org/10.17275/per.25.75.12.5
L1  - https://dergipark.org.tr/en/download/article-file/3978717
ER  -