Reflective thinking begins with repeated confusion and evaluation to solve a problem. There are four aspects to reflective thinking, namely techniques, monitoring, insight, and conceptualization. However, the problem-solvers’ reflective thinking characteristics in mathematical problems have not been discovered. The study describes the reflective thinking characteristics of proficient mathematics prospective teachers based on four aspects. The qualitative research was conducted at Universitas Muhammadiyah Surakarta with a total of 64 reflective thinkers. Data collected by test, observation sheets, and interview methods. The tests were administered twice. The instruments developed has been through the validation process and declared valid. Data analyzed through the stages of reduction, presentation, and verification. We successfully conclude that proficient mathematics prospective teachers have complete and consistent reflective thinking characteristics. Further research can be focused on the characteristics of reflective thinking based on another aspect.


Characteristics; Reflective thinking; Analytical geometry

Full Text:



Agustan, S., Juniati, D., & Siswono, T. Y. E. (2017). Reflective thinking in solving an algebra problem: A case study of field independent-prospective teacher. Journal of Physics: Conference Series, 893(1). doi:10.1088/1742-6596/893/1/012002

Aytekin, C., Baltaci, S., & Yildiz, A. (2018). Investigation of Parents ’ Expectations from Mathematics Education in Turkey. ACta Didactica Napocensia, 11(3), 59–78.

Baltaci, S., Yildiz, A., & Özcakir, B. (2016). The Relationship between Metacognitive Awareness Levels, Learning Styles, Genders and Mathematics Grades of Fifth Graders. Journal of Education and Learning, 5(4), 78. doi:10.5539/jel.v5n4p78

Basol, G., & Gencel, I. E. (2013). Reflective Thinking Scale: A Validity and Reliability Study. In Kuram Ve Uygulamada Egitim Bilimleri (Vol. 13, Issue 2, pp. 941–946).

Callan, G. L., Marchant, G. J., Finch, W. H., & German, R. L. (2016). Metacognition, strategies, achievement, and demographics: Relationships across countries. Kuram ve Uygulamada Egitim Bilimleri, 16(5), 1485–1502. doi:10.12738/estp.2016.5.0137

Charters, E. (2003). The Use of Think-Aloud Methods in Qualitative Research an Introduction to Think-Aloud Methods. Brock Education: A Journal of Educational Research and Practice, 12(2), 68–82. doi:10.26522/brocked.v12i2.38

Dewey, J. (1933). How We Think: A Restatement of The Relation of Reflective Thinking to The Educative Process (1st ed.). D.C. HEATH AND COMPANY.

Djasuli, M., Sa’dijah, C., Parta, I. N., & Candra, T. D. (2017). Students’ Reflective Abstraction in Solving Number Sequence Problems. International Electronic Journal of Mathematics Education, 12(3), 621–632.

Habermas, J. (2015). Knowledge and human interests. John Wiley & Sons.

Hidajat, F. A., Sa’dijah, C., Sudirman, & Susiswo. (2019). Exploration of Students ’ Arguments to Identify Perplexity from Reflective Process on Mathematical Problems. International Journal of Instruction, 12(2), 573–586.

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. doi:10.1007/s11423-011-9202-9

Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40.

Magiera, M. T., & Zawojewski, J. S. (2011). Characterizations of Social-Based Context Associated With Students’ Awareness, Evaluation, and Regulation of Their Thinking During Small-Group Mathematical Modeling. Jpurnal for Research in Mathematics Education, 42(5), 486–520.

Maharani, S., Kholid, M. N., Pradana, L. N., & Nusantara, T. (2019). Problem Solving in the Context of Computational Thinking. Infinity Journal, 8(2), 109–116. doi:10.22460/infinity.v8i2.p109-116

Mojžišová, A., & Pócsová, J. (2019). Automatic Test Generator for Analytic Geometry. 2019 20th International Carpathian Control Conference (ICCC). doi:10.1109/CarpathianCC.2019.8765961

Nigrini, M. J., & Karstens, W. (2019). Using analytic geometry to quantify the period-to-period changes in an array of values. Managerial Auditing Journal. doi:10.1108/MAJ-09-2017-1640

Purnomo, D., & Bekti, S. (2017). Patterns Change of Awareness Process, Evaluation, and Regulation on Mathematics Student. International Electronic Journal of Mathematics Education, 12(3), 715–733.

Purnomo, D., Nusantara, T., Subanji, S., & Rahardjo, S. (2017). The Characteristic of the Process of Students’ Metacognition in Solving Calculus Problems. International Education Studies, 10(5), 13. doi:10.5539/ies.v10n5p13

Putranta, H., & Jumadi. (2019). Physics Teacher Efforts of Islamic High School in Yogyakarta to Minimize Students’ Anxiety When Facing The Assessment of Physics Learning Outcomes. Journal for the Education of Gifted Young Scientists, 7(2), 119–136. doi:10.17478/JEGYS.552091

Rodgers, C. (2002). Defining Reflection:Another look at John Dewey and Reflective thinking. Teachers College Record,104, 104(4), 842–866.

Sa’dijah, C., Sa’diyah, M., Sisworo, & Anwar, L. (2020). Students’ Mathematical Dispositions Towards Solving HOTS Problems Based on FI and FD Cognitive Style. AIP Conference Proceedings, 2215(April), 060025-1-060025–060027. doi:10.1063/5.0000644

Sagala, R., Nuangchalerm, P., Saregar, A., & El Islami, R. A. Z. (2019). Environment-friendly education as a solution to against global warming: A case study at Sekolah Alam Lampung, Indonesia. Journal for the Education of Gifted Young Scientists, 7(2), 85–97. doi:10.17478/jegys.565454

Sarid, A. (2012). Systematic Thinking on Dialogical Education. Educational Philosophy and Theory, 44(9), 926–941. doi:10.1111/j.1469-5812.2011.00757.x

Schön, A. D. (1992). The Reflective Practioner: How Professionals Think in Action. London: Routledge. doi:10.4324/9781315237473

Sezer, R. (2008). Integration of Critical Thinking Skills into Elementary School Teacher Education Courses in Mathematics. Education, 128(3), 349–363.

Suharna, H. (2018). Teori Berpikir Reflektif dalam Menyelesaikan Masalah Matematika (1st ed.). Yogyakarta: DEEPUBLISH.

Suharna, H., Hairun, Y., Abdullah, I. H., Alhaddad, I., Afandi, A., Ardiana, & Sari, D. P. (2020). The Reflective Thinking Elementary Student in Solving Problems Based on Mathematic Ability. International Journal of Advanced Science and Technology, 29(6), 3880–3891.

Thompson, S., & Thompson, N. (2018). The Critically Reflective Practitioner. Macmillan International Higher Education.

Tutticci, N., Ryan, M., Coyer, F., & Lewis, P. (2018). Collaborative facilitation of debrief after high-fidelity simulation and its implications for reflective thinking: student experiences. Studies in Higher Education, 43(9), 1–14. doi:10.1080/03075079.2017.1281238

Zayyadi, M., Nusantara, T., Hidayanto, E., Sulandra, I. M., & Sa’dijah, C. (2020). Content and Pedagogical Knowledge of Prospective Teachers in Mathematics Learning: Commognitive Framework. Journal for the Education of Gifted Young Scientists, 8(March), 515–532. doi:10.17478/jegys.642131

Zehavi, N., & Mann, G. (2005). Instrumented Techniques and Reflective Thinking in Analytic Geometry. The Montana Mathematics Enthusiast, 2(22), 1551–3440.


Article Metrics

Abstract view : 348 times
PDF - 110 times


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.