How are students’ reflective thinking for problem solving?

Year 2020, , 1135 - 1146, 15.09.2020

Muhammad Kholid , Cholis Sa'dıjah , Erry Hidayanto Hendro Permadi

https://doi.org/10.17478/jegys.688210

Cited By: 14

Abstract

Mathematics students with a reflective thinking tend to have self-confidence in solving mathematics easily. In recent years, however, there have not been the results of the researches that classify students’ reflective thinking for solving non-routine questions of Analytical Geometry questions, in particular. The present research paper reveals the new classification of the students’ reflective thinking for solving the problems. These are solving Analytical Geometry which can cause the students’ confusion to apply their reflective thinking. The classification of the study comprises four components. It employed a descriptive-qualitative approach. The amounts of the subjects were 21 out of 140 students who used their reflective thinking for solving questions. The data collection consisted of test, observation, and in-depth interview. The data validation employed a method triangulation technique. The results of the study show there are three classification of reflective thinking, namely: assumptive, virtual, and connective. The three classifications differ in the way they deal with confusion. Meanwhile, the three classifications have similarities. The students tended to use all of the reflective thinking components although there were a few indicators that were not realized maximally. These were making a plan before solving the problems, using an efficient way, and relating among concepts. The factor is students play an inactive role or low active in reflective thinking. Moreover, they think that the most important thing is answering the questions correctly and they do not understand the purposes of the problem. Therefore, the students need to get the treatments.

Keywords

analytic geometry, non-routine questions, reflective thinking

Supporting Institution

Directorate of Research and Community Service (DRPM BRIN) the Republic of Indonesia

Thanks

The authors are very grateful to Director of Directorate of Research and Community Service (DRPM BRIN) the Republic of Indonesia on research funding 2020.

References

• Agustan, J. D., & Siswono, T. Y. E. (2017). Profile of Male-Field Dependent (FD) Prospective Teacher’s Reflective Thinking in Solving Contextual Mathematical Problem. AIP Conference Proceedings, 1867, 020034–1. https://doi.org/10.1063/1.4994437
• Agustan, S., Juniati, D., & Siswono, T. Y. E. (2017). Profile of male-field dependent (FD) prospective teacher’s reflective thinking in solving contextual mathematical problem. AIP Conference Proceedings, 1867(March 2018). https://doi.org/10.1063/1.4994437
• Ambrose, L. J., & Ker, J. S. (2014). Levels of Reflective Thinking and Patient Safety: an Investigation of The Mechanisms That Impact on Student Learning in a Single Cohort Over a 5 Year Curriculum. Advances in Health Sciences Education, 19(3), 397–411. https://doi.org/10.1007/s10459-013-9470-8
• Aytekin, C., Baltaci, S., Aktunkaya, B., Kiymaz, B., & Yildiz, A. (2016). A Scale to Determine Parents’ Expectation from Mathematics Education (Peme): Development, Reliability and Validity. Journal of Kirsehir Education Faculty, 17(3), 397–411.
• Bardach, E., & Patashnik, E. M. (2019). A Practical Guide for Policy Analysis: The Eightfold Path to More Effective Problem Solving. CQPress.
• 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).
• Chee, Y. S., & Mehrotra, S. (2012). Reflective, reflexive guided appropriation: Facilitating teacher adoption of game based learning in classrooms. Proceedings of the 6th European Conference on Games Based Learning: ECGBL, 109.
• 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. http://www.iier.org.au/iier25/dervent.pdf
• Dündar, S., & Yaman, H. (2015). How do Prospective Teachers Solve Routine and Non-Routine Trigonometry Problems? International Online Journal of Educational Sciences, 7(2), 41–57.
• Eccles, D. W., & Arsal, G. (2017). The Think Aloud Method: What is It and How Do I Use It? Qualitative Research in Sport, Exercise and Health, 9(4), 514–531. https://doi.org/10.1080/2159676X.2017.1331501
• Fielding, N. G. (2012). Triangulation and Mixed Methods Designs: Data Integration With New Research Technologies. Journal of Mixed Methods Research, 6(2), 124–136. https://doi.org/10.1177/1558689812437101
• Gencel, I. E., & Saracaloğlu, A. S. (2018). The Effect of Layered Curriculum on Reflective Thinking and on Self-Directed Learning Readiness of Prospective Teachers. International Journal of Progressive Education, 14(1), 8–20. https://doi.org/10.29329/ijpe.2018.129.2
• Ghanizadeh, A. (2017). The Interplay Between Reflective Thinking, Critical Thinking, Self-Monitoring, and Academic Achievement in Higher Education. Higher Education, 74(1), 101–114. https://doi.org/10.1007/s10734-016-0031-y
• Ghanizadeh, A., & Jahedizadeh, S. (2017). Validating the Persian Version of Reflective Thinking Questionnaire and Probing Iranian University Students’ Reflective Thinking and Academic Achievement. International Journal of Instruction, 10(3), 209–226. https://doi.org/10.12973/iji.2017.10314a
• Gurol, A. (2011). Determining the Reflective Thinking Skills of Pre-Service Teachers in Learning and Teaching Process. Energy Education Science and Technology Part B: Social and Educational Studies, 3(3), 387–402.
• Halpem, D. F. (2013). Thought and Knowledge: An Introduction to Critical Thinking. Psychology Press.
• Handayani, U. F., Sa’Dijah, C., Sisworo, Sa’Diyah, M., & Anwar, L. (2020). Mathematical creative thinking skill of middle-ability students in solving contextual problems. AIP Conference Proceedings, 2215(April), 060007-1-060007–7. https://doi.org/10.1063/5.0000645
• 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. https://doi.org/10.29333/iji.2019.12236a
• Hidayat, W., & Husnussalam, H. (2019). The Adversity Quotient and Mathematical Understanding Ability of Pre-service Mathematics Teacher. Journal of Physics: Conference Series, 1315(1), 8–13. https://doi.org/10.1088/1742-6596/1315/1/012025
• Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372–400.
• 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
• Hsieh, P. H., & Chen, N. S. (2012). Effects of Reflective Thinking in the Process of Designing Software on Students’ Learning Performances. Turkish Online Journal of Educational Technology, 11(2), 88–99.
• Kaleliog˘lu, F. (2015). A New Way of Teaching Programming Skills to K-12 Students: Code.org. Computers in Human Behavior Journal, 52, 200–210. https://doi.org/https://doi.org/10.1016/j.chb.2015.05.047
• Kholid, M. N., Sadijah, C., Hidayanto, E., Permadi, H., & Firdareza, R. M. F. (2020). Pupils’ Reflective Thinking in Solving Linear Equation System Problem. Journal for the Mathematics Education and Teaching Practices, 1(1), 19–27.
• King, F., Goodson, L., & Rohani, F. (1997). Higher Order Thinking Skills. A publication of the Educational Services Program.
• Laurillard, D. (2016). The Educational Problem That MOOCs could Solve: Professional Development for Teachers of Disadvantaged Students. Research in Learning Technology, 24(March), 1–17. https://doi.org/10.3402/rlt.v24.29369
• Miller, D. I., & Halpern, D. F. (2014). The New Science of Cognitive Sex Differences. Trends in Cognitive Sciences, 18(1), 37–45. https://doi.org/https://doi.org/10.1016/j.tics.2013.10.011
• Mohamed, M., & Johnny, J. (2010). Investigating Number Sense Among Students. Procedia - Social and Behavioral Sciences, 8, 317–324. https://doi.org/https://doi.org/10.1016/j.sbspro.2010.12.044
• Önder, E. (2016). Causes of School Failure From Teacher and Student’S Perspective. International Journal on New Trends in Education and Their Implications, 7(2), 9–22.
• Özsoy, G., & Ataman, A. (2009). The Effect of Metacognitive Strategy Training on Mathematical Problem Solving Achievement. International Electronic Journal of Elementary Education, 1(2), 68–82.
• Pagano, M. (2009). Beyond Reflection Through an Academic Lens : Refraction and International Experiential Education. The Interdisciplinary Journal of Study Abroad Reflection, 18, 217–229.
• Pennington, R. (2011). Reflective Thinking in Elementary Preservice Teacher Portfolios: Can It Be Measured and Taught? Journal of Educational Research and Practice, 1(1), 37–49. https://doi.org/10.5590/JERAP.2011.01.1.03
• Pradana, L. N., Sholikhah, O. H., Maharani, S., Kholid, M. N., & Surakarta, U. M. (2020). Virtual Mathematics Kits ( VMK ): Connecting Digital Media to Mathematical Literacy. International Journal of Emerging Technologies in Learning (IJET), 15(3), 234–241. https://doi.org/https://doi.org/10.3991/ijet.v15i03.11674
• Pressley, M., Roehrig, A. D., Raphael, L., Dolezal, S., Bohn, C., Mohan, L., Wharton-McDonald, R., Bogner, K., & Hogan, K. (2003). Teaching Processes in Elementary and Secondary Education. In Handbook of Psychology (pp. 153–175). https://doi.org/https://doi.org/10.1002/0471264385.wei0708
• 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. https://doi.org/10.5539/ies.v10n5p13
• Purnomo, R. C., Sunardi, Yuliati, N., Yudianto, E., Mahfut, M., & Sa’dijah, C. (2020). Anxiety: How was the process of the undergraduate students who were in visualization level in constructing the definition? Journal of Physics: Conference Series, 1465(012049), 1–10. https://doi.org/10.1088/1742-6596/1465/1/012049
• 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. https://doi.org/10.17478/JEGYS.552091
• Rieger, A., Radcliffe, B. J., & Doepker, G. M. (2013). Practices for Developing Reflective Thinking Skills Among Teachers. Kappa Delta Pi Record, 49(4), 184–189. https://doi.org/10.1080/00228958.2013.845510
• Rohmah, M., & Sutiarso, S. (2018). Analysis problem solving in mathematical using theory Newman. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 671–681. https://doi.org/10.12973/ejmste/80630
• 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. https://doi.org/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. https://doi.org/10.17478/jegys.565454
• Sandie, S., Purwanto, P., Subanji, S., & Hidayanto, E. (2019). Student Difficulties in Solving Covariational Problems. International Journal of Humanities and Innovation (IJHI), 2(2), 25–30. https://doi.org/10.33750/ijhi.v2i2.38
• Satjatam, P., Sarintip, R., & Teerachai, N. (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
• Schneider, W., & Artelt, C. (2010). Metacognition and Mathematics Education. ZDM - International Journal on Mathematics Education, 42(2), 149–161. https://doi.org/10.1007/s11858-010-0240-2
• Sholihah, U., Nusantara, T., Sa’Dijah, C., & Susanto, H. (2019). The Ability of Students’ Visual Thinking in Solving Integral Problems. Journal of Physics: Conference Series, 1157(3). https://doi.org/10.1088/1742-6596/1157/3/032090
• Siswono, T. Y. E. (2011). Level of Students Creative Thinking in Classroom Mathematics. Educational Research and Reviews, 6(7), 548–553.
• Sivaci, S. Y. (2017). The Relationship between Reflective Thinking Tendencies and Social Problem Solving Abilities of Pre-Service Teachers. Journal of Education and Training Studies, 5(11), 21. https://doi.org/10.11114/jets.v5i11.2273
• Stoltz, paul G. (1997). Adversity Quotient: Turning Obstacles into Opportunities. John Wiley & Sons, Inc. Suharna, H. (2018). Teori Berpikir Reflektif dalam Menyelesaikan Masalah Matematika (1st ed.). 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.
• Sumaji, Sa’Dijah, C., Susiswo, & Sisworo. (2020). Mathematical communication process of junior high school students in solving problems based on APOS theory. Journal for the Education of Gifted Young Scientists, 8(1), 197–221. https://doi.org/10.17478/jegys.652055
• Sumitro, N. K., Sa’dijah, C., Raharjo, S., & Rahardi, R. (2019). The emergence of metacognitive activities through the scaffolding interaction. International Journal of Recent Technology and Engineering, 8(1C2), 665–671.
• Susandi, A. D., & Widyawati, S. (2017). Proses Berpikir dalam Memecahkan Masalah Logika Matematika Ditinjau dari Gaya Kognitif Field Independent dan Field Dependent. 1(1), 93–113. https://doi.org/10.25217/jn.v1i1
• Taşkin Can, B., & Yildirim, C. (2014). The instrument for determining the levels of reflective thinking among elementary school students. Educational Research and Reviews, 9(1), 9–16. https://doi.org/10.5897/ERR12.093
• Whalen, K., & Paez, A. (2019). Development of a new framework to guide, assess, and evaluate student reflections in a university sustainability course. Teaching and Learning Inquiry, 7(1), 55–77. https://doi.org/10.20343/teachlearninqu.7.1.5
• Yang, Y., van Aalst, J., Chan, C. K. K., & Tian, W. (2016). Reflective Assessment in Knowledge Building by Students with Low Academic Achievement. International Journal of Computer-Supported Collaborative Learning, 11(3), 281–311. https://doi.org/10.1007/s11412-016-9239-1
• 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. https://doi.org/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.
• Zhang, X. H., Kubota, K., Kubota, M., & Li, K. (2019). Teacher’s Developmental Stages of Exploring Thinking Tools in a Blended Learning Environment. International Conference on Blended Learning, 186–202. https://doi.org/https://doi.org/10.1007/978-3-030-21562-0_16