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Reflective Practice
International and Multidisciplinary Perspectives
Volume 25, 2024 - Issue 3
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Research Articles

Defragmenting students’ reflective thinking levels for mathematical problem solving: does it work?

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Pages 319-351 | Received 06 Oct 2023, Accepted 13 Feb 2024, Published online: 23 Feb 2024

References

  • 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(12002), 1–6. https://doi.org/10.1088/1742-6596/893/1/012002
  • Angel, H. F., & Seitz, R. J. (2016). Process of believing as fundamental brain function: The concept of credition. SFU Research Bulletin, 3, 1–20. https://doi.org/10.15135/2016.4.1.1-20
  • Bayar, M. F., & Kurt, U. (2021). The effect of using smart boards in science lessons on middle school students’ attitudes towards smartboards and reflective thinking skills. Educational Policy Analysis and Strategic Research, 16(3), 23–38. https://doi.org/10.29329/epasr.2021.373.2
  • 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
  • Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4 ed.). Sage Publication.
  • Damon, W., & Killen, M. (1982). Peer interaction and the process of change in children’s moral reasoning. Merrill-Palmer Quarterly, 28(3), 347–367.
  • 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 (IOJET), 6(3), 613–622.
  • 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.
  • Deshpande, D. S., Riccomini, P. J., Hughes, E. M., & Raulston, T. J. (2021). Problem solving with the Pythagorean Theorem: A think aloud analysis of secondary students with learning disabilities. Learning Disabilities, 19(1), 23–47.
  • Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process (1 ed.). D.C. Heath & Co Publishers.
  • Dwiyanti, W., Waluya, S. B., & Walid. (2022). Reflective thinking in solving number theory problem: A case study of pre-service teacher in terms of cognitive style. AIP Conference Proceedings, 2577(December). https://doi.org/10.1063/5.0096137
  • Eğmir, E., & Ocak, İ. (2020). The relationship between teacher candidates’ critical thinking standards and reflective thinking skills. International Journal of Progressive Education, 16(3), 156–170. https://doi.org/10.29329/ijpe.2020.248.12
  • Ekawati, M., & Asih, E. C. M. (2019). Mathematical reflective thinking process based on cognitive style. Journal of Physics, 1211(1), 012069. https://doi.org/10.1088/1742-6596/1211/1/012069
  • 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
  • Farnila, Y., Johar, R., & Usman. (2021). Students’ reflective thinking process in mathematical. The 2nd Science and Mathematics International Conference (SMIC 2020): Transforming Research and Education of Science and Mathematics in the Digital Age, 2331(1), 020024–1–020024–020026. https://doi.org/10.1063/5.0042223
  • Gatot, M. (2008). Pembelajaran matematika SD (elementary mathematics learning). Universitas Terbuka.
  • Habernas, J. (1971). Knowledge and human interests (1 ed.). John Wiley & Sons, Inc.
  • Harris, S., Sheth, S. A., & Cohen, M. S. (2008). Functional neuroimaging of belief, disbelief, and uncertainty. Annals of Neurology, 63(2), 141–147. https://doi.org/10.1002/ana.21301
  • Herna. (2016). Defragmentasi Struktur Berpikir Mahasiswa Untuk Memperbaiki Konstruksi Pseudo Benar Mahasiswa Dalam Memahami Konsep Limit Fungsi (Defragmenting Students’ Thinking Structures to Improve Students’ Pseudo-True Constructions in Understanding the Concept of F. Universitas Negeri Malang.
  • Hong, Y. C., & Choi, I. (2011). Three dimensions of reflective thinking in solving design problems: A conceptual model. Educational Technology Research & 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. The Turkish Online Journal of Educational Technology, 11(2), 88–99.
  • Jha, S. K. (2012). Mathematics performance of primary school students in Assam (India): An analysis using Newman procedure. International Journal of Computer Application in Engineering Sciences, 2(1), 17–21.
  • Kholid, M. N., Agustin, R. L., & Pradana, L. N. (2019). Effect of tps strategy with portfolio assessment and learning interest on mathematical learning achievement. International Journal of Scientific and Technology Research, 8(9), 616–620.
  • Kholid, M. N., Pradana, L. N., Maharani, S., & Swastika, A. (2022). Geogebra in project-based learning (geo-pjbl): A dynamic tool for analytical geometry course. Journal of Technology and Science Education, 12(1), 112–120. https://doi.org/10.3926/jotse.1267
  • Kholid, M. N., 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
  • Kholid, M. N., Sa’dijah, C., Hidayanto, E., & Permadi, H. (2022). Students’ reflective thinking pattern changes and characteristics of problem solving. Reflective Practice, 23(3), 319–341. https://doi.org/10.1080/14623943.2021.2025353
  • Kholid, M. N., Swastika, A., Ishartono, N., Nurcahyo, A., Lam, T. T., Maharani, S., Ikram, M., Murniasih, T. R., Majid, M., Wijaya, A. P., & Pratiwi, E. (2022). Hierarchy of students’ reflective thinking levels in mathematical problem solving. Acta Scientiae, 24(6), 24–59. https://doi.org/10.17648/acta.scientiae.6883
  • Khotimah, R. P., & Masduki, M. (2016). Improving teaching quality and problem solving ability through contextual teaching and learning in differential equations: A lesson study approach. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 1(1), 1–13. https://doi.org/10.23917/jramathedu.v1i1.1791
  • Khusna, A. H. (2021). Scaffolding based learning: Strategies for developing reflective thinking skills (A case study on random variable material in mathematics statistics courses). Journal of Physics: Conference Series, 1940(12093), 1–8. https://doi.org/10.1088/1742-6596/1940/1/012093
  • King, F. J., Goodson, L., & Rohani, F. (1997). Higher order thinking skills. A publication of the Educational Services Program.
  • Lai, A. F., & Yang, S. M. (2011). The learning effect of visualized programming learning on 6 th graders’ problem solving and logical reasoning abilities. Proceedings of the Electrical and Control Engineering (ICECE) International Conference on IEEE, Yichang, China. https://ieeexplore.ieee.org/document/6056908
  • Mardhiyatirrahmah, L., & Abdussakir, A. (2021). Restructuring of students’ thinking in junior high school through defragmentation for solving mathematical problems. Jurnal Ilmiah Kependidikan, 10(2), 95–102.
  • Masduki Kholid, M. N., & Khotimah, R. P. (2020). Exploring students’ problem-solving ability and response towards metacognitive strategy in mathematics learning. Universal Journal of Educational Research, 8(8), 3698–3703. https://doi.org/10.13189/ujer.2020.080849
  • Mayangsari, A. D., Labulan, P. M., & Rusdiana, R. (2021). Analisis Kesalahan Buku Teks Matematika Kelas Xi Sma/Ma Kurikulum 2013. Jurnal Magister Pendidikan Matematika (JUMADIKA), 3(2), 79–84. https://doi.org/10.30598/jumadikavol3iss2year2021page79-84
  • Mhlolo, M. K. (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science & Technology Education, 16(2), 176–191. https://doi.org/10.1080/10288457.2012.10740738
  • Moleong, L. (2007). Qualitative research methodology. PT Remaja Rosdakarya Offset.
  • Muntazhimah, M., Turmudi, T., & Prabawanto, S. (2021). The relation between prior knowledge and students’ mathematics reflective thinking ability. Journal of Physics, 1731(1), 012043. https://doi.org/10.1088/1742-6596/1731/1/012043
  • Musser, G. L., Burger, W. F., & Peterson, B. E. (2008). Mathematics for elementary teachers : A contemporary approach. Laurie Rosatone.
  • Musser, G. L., Burger, W. F., & Peterson, B. E. (2011). Mathematics for elementary teachers a contemporary approach (9 ed.). John Wiley & Sons, Inc.
  • Newman, M. A. (1983). Strategies for diagnosis and remediation. Harcourt, Brace Jovanovich.
  • Nurfatanah, Rusmono, & Nurjannah. (2018). Kemampuan Pemecahan Masalah Matematis Siswa Sekolah Dasar (Elementary School Students’ Mathematical Problem Solving Ability), Jakarta, Indonesia, 546–551. https://doi.org/10.31949/educatio.v9i2.4609
  • Özsoy, G., Kuruyer, H. G., & Çakiroğlu, A. (2015). Evaluation of students’ mathematical problem solving skills in relation to their reading levels. International Electronic Journal of Elementary Education, 8(1), 581–600.
  • Ozyildirim-Gumus, F., & Ozyildirim, G. (2020). Reflective thinking and probabilistic thinking: An example of elementary school students. Acta Didactica Napocensia, 13(1), 43–56. https://doi.org/10.24193/adn.13.1.5
  • Pradana, L. N., Sholikhah, O. H., Maharani, S., & Kholid, M. N. (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/10.3991/ijet.v15i03.11674
  • Putri, R. W., & Indrawatiningsih, N. (2023). Defragmenting student construction holes in solving system of absolute value equations. Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika, 6(2), 131–142.
  • Rachmat, A. (2008). Dos and Windows. https://www.slideshare.net/sinjo/doswindows-presentation
  • Radiusman, R. (2020). Studi literasi: Pemahaman konsep anak pada pembelajaran matematika (Literacy study: Children’s understanding of concepts in Mathematics Learning). FIBONACCI: Jurnal Pendidikan Matematika dan Matematika, 6(1), 1–8. https://doi.org/10.24853/fbc.6.1.1-8
  • Rasyid, M. A., Budiarto, M. T., & Lukito, A. (2018). Junior high school students’ reflective thinking on fraction problem solving: In case of gender differences. Journal of Physics: Conference Series, 947(1), 012041. https://doi.org/10.1088/1742-6596/947/1/012041
  • Ristekdikti. (2017). Rencana induk riset nasional tahun 2017-2045 (8 ed.). Kementerian riset, Teknologi, dan pendidikan tinggi.
  • Sachs, O., & Hirsch, J. (2008). A Neurology of Belief. Annals of Neurology, 63(2), 129–130. https://doi.org/10.1002/ana.21378
  • Sa’dijah, C., Kholid, M. N., Hidayanto, E., & Permadi, H. (2020). Reflective thinking characteristics: A study in the proficient mathematics prospective teachers. Infinity Journal, 9(2), 159–172. https://doi.org/10.22460/infinity.v9i2.p159-172
  • 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
  • Salido, A., Suryadi, D., Dasari, D., & Muhafidin, I. (2020). Mathematical reflective thinking strategy in problem-solving viewed by cognitive style. Journal of Physics, 1469(1), 012150. https://doi.org/10.1088/1742-6596/1469/1/012150
  • Saraçoğlu, M., & Kahyaoğlu, M. (2021). Learning and studying approaches as a predictor of reflective thinking skills towards problem-solving of secondary school students. International Journal of Education & Literacy Studies, 9(4), 132. https://doi.org/10.7575/aiac.ijels.v.9n.4p.132
  • Schon, D. A. (1992). The reflective practitioner: How professionals think in action (1 ed.). Routledge. https://doi.org/10.4324/9781315237473
  • Seitz, R. J., & Angel, H. F. (2020). Belief formation – a driving force for brain evolution. Brain and Cognition, 140(105548), 1–8. https://doi.org/10.1016/j.bandc.2020.105548
  • Shavit, P., & Moshe, A. (2019). The contribution of reflective thinking to the professional development of pre-service teachers. Reflective Practice, 20(4), 548–561. https://doi.org/10.1080/14623943.2019.1642190
  • Singh, P., Rahman, A. A., & Hoon, T. S. (2010). The Newman procedure for analyzing primary four pupils errors on written mathematical tasks: A Malaysian perspective. Procedia - Social & Behavioral Sciences, 8(5), 264–271. https://doi.org/10.1016/j.sbspro.2010.12.036
  • Skemp, R. R. (2006). Relational understanding and instrumental understanding. National Council of Teachers of Mathematics, 12(2), 88–95. https://doi.org/10.5951/MTMS.12.2.0088
  • Smith, E. E., & Kosslyn, S. M. (2014). Cognitive psychology: Mind and brain. Pearson Education.
  • Strenberg, R. J., & Strenberg, K. (2012). Cognitive psychology (6 ed.). Wadsworth Cengage Learning.
  • Subanji. (2007). Proses Berpikir Penalaran Kovariasional Pseudo dalam Mengkonstruksi Grafik Fungsi Kejadian Dinamik Berkebalikan. University of Surabaya.
  • Subanji. (2015). Teori Kesalahan Konstruksi Konsep dan Pemecahan Masalah Matematika. UM Press.
  • Subanji. (2016). Teori Defragmentasi Struktur Berpikir Dalam Mengkonstruksi Konsep dan Pemecahan Masalah Matematika (Defragmentation Theory of Thinking Structures in Constructing Concepts and Solving Mathematical Problems).
  • Sutama, S., Fuadi, D., Narimo, S., Hafida, S. H. N., Novitasari, M., Anif, S., Prayitno, H. J., Sunanih, S., & Adnan, M. (2022). Collaborative mathematics learning management: Critical thinking skills in problem solving. International Journal of Evaluation and Research in Education (IJERE), 11(3), 1015–1027. https://doi.org/10.11591/ijere.v11i3.22193
  • Sutarni, S., Sutama Prayitno, H. J., & Sutapa, A. (2023). Analysis of creative thinking skills in solving mathematics problems with high order thinking skill (HOTS) oriented at the elementary school level. AIP Conference Proceedings. https://doi.org/10.1063/5.0141697
  • Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia - Social & Behavioral Sciences, 8(5), 142–151. https://doi.org/10.1016/j.sbspro.2010.12.020
  • Tican, C., & Taspinar, M. (2015). The effects of reflective thinking-based teaching activities on pre-service teachers’ reflective thinking skills, critical thinking skills, democratic attitudes, and academic achievement. The Anthropologist, 20(1–2), 111–120. https://doi.org/10.1080/09720073.2015.11891730
  • Toh, T. L., Quek, K. S., & Tay, E. G. (2008). Problem solving in the mathematics classroom (junior college). National Institute of Education, Nanyang Technological University.
  • Tutticci, N., Coyer, F., Lewis, P. A., & Ryan, M. (2017). Validation of a reflective thinking instrument for third-year undergraduate nursing students participating in high-fidelity simulation. Reflective Practice, 18(2), 219–231. https://doi.org/10.1080/14623943.2016.1268115
  • Ulucinar Sagir, S., Aslan, O., Bertiz, H., & Oner Armagan, F. (2021). Investigation of the relationship between pre-service science teachers’ perceived self-efficacy in science teaching and disposition toward reflective thinking. European Journal of Science and Mathematics Education, 4(3), 331–345. https://doi.org/10.30935/scimath/9474
  • Usodo, B., Aulia, I. I., Wulandari, A. N., Sutopo Setiawan, R., Kurniawati, I., & Kuswardi, Y. (2020). Fragmentation of thinking structure and its impact to students’ algebraic concept construction and problem solving. Journal of Physics Conference Series, 1567(32006), 1–6. https://doi.org/10.1088/1742-6596/1567/3/032006
  • Wahab, A., Ahsan, M., & Busrah, Z. (2022). Defragmenting Struktur Berpikir Pemecahan Masalah Siswa Melalui Pemetaan Kognitif Berbasis Polya Pada Soal PISA (Defragmenting Students’ Problem-Solving Thinking Structures Through Polya-Based Cognitive Mapping of PISA Problems). Journal of Mathematics Learning Innovation, 1(1), 73–97. https://doi.org/10.35905/jmlipare.v1i1.3388
  • White, A. L. (2005). Active mathematics in classrooms: Finding out why children make mistakes - and then doing something to help them. Square One: Primary Journal of the Mathematical Association of New South Wales, 15(4), 15–19.
  • White, A. L. (2010). Numeracy, literacy and Newman’s error analysis. Journal of Science & Mathematics Education in Southeast Asia, 33(2), 129–148.
  • Wibawa, K. A., Nusantara, T., Subanji, & I. Nengah, P. (2018). Defragmentation of student’s thinking structures in solving mathematical problems based on CRA framework. Journal of Physics Conference Series, 1028(1), 1–7. https://doi.org/10.1088/1742-6596/1028/1/012150
  • Wibawa, K. A., Nusantara, T., Subanji, & I. Nengah, P. (2021). Rekonstruksi Kesalahan dan Perbaikan Struktur Berpikir Dalam Memecahkan Masalah Matematis (Error Reconstruction and Improvement of Thinking Structures in Solving Mathematical Problems). CV Confident.
  • Wibawa, K. A., Payadnya, I. P. A. A., Atmaja, I. M. D., & Simons, M. D. (2020). Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework. Beta: Jurnal Tadris Matematika, 13(2), 130–151. https://doi.org/10.20414/betajtm.v13i2.327
  • Wibawa, K. A., Subanji, & Chandra, T. D. (2013). Defragmenting Berpikir Pseudo dalam Memecahkan Masalah Limit Fungsi (Defragmenting Pseudo Thinking in Solving Function Limit Problems). Exchange of Experiences Teachers Quality Improvement Program.
  • Wulandari, S., & Gusteti, M. U. (2021). Defragmentation of preservice teacher’s thinking structures in solving higher order mathematics problem. Journal of Physics: Conference Series, 1940(1), 1–7. https://doi.org/10.1088/1742-6596/1940/1/012099
  • Yildiz Durak, H. (2020). The effects of using different tools in programming teaching of secondary school students on engagement, computational thinking and reflective thinking skills for problem solving. Technology, Knowledge and Learning, 25(1), 179–195. https://doi.org/10.1007/s10758-018-9391-y
  • Yorulmaz, A., Uysal, H., & Çokçaliskan, H. (2021). Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 239–259. https://doi.org/10.23917/jramathedu.v6i3.14349

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