KaydedilenlerDerginizi ekleyin

Dergiler / Journal for the Mathematics Education and Teaching Practices / 2026 / Volume: 1 Issue: 1

Pupils’ reflective thinking in solving linear equation system problem

Muhammad Noor Kholıd(UNIVERSITAS MUHAMMADIYAH SURAKARTA)0000-0002-7215-3239
Cholis Sa'dıjah(Universitas Negeri Malang)0000-0002-0264-8578
Erry Hidayanto(Universitas Negeri Malang)
Hendro Permadi(Universitas Negeri Malang)
Rizka Mafida Feby Fırdareza(UNIVERSITAS MUHAMMADIYAH SURAKARTA)
Sayfa
—
Yayın Tarihi
2020-06-15
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is necessary to develop reflective thinking skills in pupils with low mathematical abilities.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Reflective thinking begins with perplexity.
📊
Temel Bulgular & Veri:The qualitative research employed 46 Indonesian reflective thinkers.
💡
Sonuç & Katkı:It is necessary to develop reflective thinking skills in pupils with low mathematical abilities.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:pupils’ reflective thinking · mathematical abilities · linear equation system problems

Abstract

Reflective thinking begins with perplexity. Efforts to overcome perplexity by involving the experience and knowledge. In the process of reflective thinking, problem solvers need to use mathematical abilities. The research reveals pupils’ reflective thinking in solving Linear Equation System (LES) problem in term of their mathematical abilities. The qualitative research employed 46 Indonesian reflective thinkers. A reflective thinker is a pupil employes experience and knowledge in solving LES problem. The instruments have been validated by mathematicians and education experts. Data collected by some methods among others: test, observation, and in-depth interview. Triangulation conducted as data validation process. We successfully concluded that different mathematical abilities provide differences in pupils' reflective thinking for solving LES problems. It is necessary to develop reflective thinking skills in pupils with low mathematical abilities.

🔖

Bu Makaleye Atıf Yap

Kholıd, M. N., Sa'dıjah, C., Hidayanto, E., Permadi, H., Fırdareza, R. M. F. (2020). Pupils’ reflective thinking in solving linear equation system problem. Journal for the Mathematics Education and Teaching Practices, Volume: 1 Issue: 1. https://ajindex.com/articles/1153504

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (39)

  1. Afshar, H. S., & Farahani, M. (2018). Inhibitors to EFL Teachers’ Reflective Teaching and EFL Learners’ Reflective Thinking and the Role of Teaching Experience and Academic Degree in Reflection Perception. Reflective Practice: International and Multidisciplinary Perspectives, 19(1), 46–67. https://doi.org/https://doi.org/10.1080/14623943.2017.1351353
  2. Annisavitri, R., Sa’dijah, C., Qohar, A., Sa’Diyah, M., & Anwar, L. (2020). Analysis of Mathematical Literacy Test as A Problem-Solving Ability Assessment of Junior High School Students. AIP Conference Proceedings 2215 - 060002, 060002-1-060002–060007. https://doi.org/https://doi.org/10.1063/5.0000648
  3. Bishop, J. P. (2012). “She’s Always Been the Smart One. I’ve Always Been the Dumb One”: Identities in the Mathematics Classroom. Journal for Research in Mathematics Education, 43(1), 34–74. https://doi.org/10.5951/jresematheduc.43.1.0034
  4. Cavanagh, M. (2011). Active Learning in Higher Education. Social and Behaviour Science And, 12(1), 23–33. https://doi.org/https://doi.org/10.1177%2F1469787410387724
  5. 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.
  6. DiDonato, N. C. (2013). Effective Self- and Co-Regulation in Collaborative Learning Groups: An Analysis of How Students Regulate Problem Solving of Authentic Interdisciplinary Tasks. Instructional Science, 41, 25–47. https://doi.org/https://doi.org/10.1007/s11251-012-9206-9
  7. Dubinsky. (2002). Reflective Abstraction in Advanced Mathematical Thinking. In Mathematics Education Library (pp. 95–126). https://doi.org/https://doi.org/10.1007/0-306-47203-1_7
  8. 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
  9. 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
  10. Hanley, P., Slavin, R., & Elliott, L. (2015). Thinking, Doing, Talking Science: Evaluation Report and Executive Summary.
  11. 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
  12. 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
  13. Howlett, C., Ferreira, J.-A., & Blomfield, J. (2015). Teaching Sustainable Development in Higher Education: Building Critical, Reflective Thinkers Through an Interdisciplinary Approach. International Journal of Sustainability in Higher Education, 17(3), 305–321.
  14. 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.
  15. Huang, H.-M., Rauch, U., & Liaw, S.-S. (2010). Investigating Learners’ Attitudes Toward Virtual Reality Learning Environments: Based on A Constructivist Approach. Computers & Education, 55(3), 1171–1182. https://doi.org/https://doi.org/10.1016/j.compedu.2010.05.014
  16. Ikram, M., Purwanto, Parta, I. N., & Susanto, H. (2020). Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591–611. https://doi.org/https://doi.org/10.17478/jegys.665836
  17. Kaune, C. (2006). Reflection and Metacognition in Mathematics Education - Tools for The Improvement of Teaching Quality. ZDM - International Journal on Mathematics Education, 38(4), 350–360. https://doi.org/10.1007/BF02652795
  18. Kulkarni, V. B. (2017). Overview of Reasons of Lack of Motivation in the Students of Indian Engineering Education. 2017 International Conference on Transforming Engineering Education (ICTEE), 1–5. https://doi.org/https://doi.org/10.1109/ICTEED.2017.8585628
  19. Mann, E. L., Chamberlin, S. A., & Graefe, A. K. (2017). The Prominence of Affect in Creativity: Expanding the Conception of Creativity in Mathematical Problem Solving. In Creativity and Giftedness. Advances in Mathematics Education (pp. 57–73). Springer.
  20. Oliver, M. (2011). Technological Determinism in Educational Technology Research: Some Alternative Ways of Thinking About the Relationship Between Learning and Technology. Journal of Computer Assisted Learning, 27, 373–384. https://doi.org/https://doi.org/10.1111/j.1365-2729.2011.00406.x
  21. 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.
  22. Parmin, Saregar, A., Deta, U. A., & El Islami, R. A. Z. (2020). Indonesian Science Teachers’ Views on Attitude, Knowledge, and Application of STEM. Journal for the Education of Gifted Young Scientists, 8(1), 17–31. https://doi.org/https://doi.org/10.17478/jegys.647070
  23. Pravesti, C. A., Wiyono, B., Moenindyah, D., & Triyono. (2020). Examining The Effects of Guidance and Counseling Services to The Self-Regulated Learning for College Students. Journal for the Education of Gifted Young Scientists, 8(1), 33–45. https://doi.org/https://doi.org/10.17478/jegys.664548
  24. 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
  25. Radovic, D., Black, L., Williams, J., & Salas, C. E. (2018). Towards Conceptual Coherence in the Research on Mathematics Learner Identity: A Systematic Review of the Literature. Educational Studies in Mathematics, 99, 21–42. https://doi.org/https://doi.org/10.1007/s10649-018-9819-2
  26. Ramasamy, R., & Puteh, M. (2018). Bar Model Method for Higher Order Thinking Skills Questions in Mathematics for Dual Language Program Pupils. International Journal of Academic Research in Business and Social Sciences, 8(9), 1456–1462. https://doi.org/http://dx.doi.org/10.6007/IJARBSS/v8-i9/4855
  27. Rodgers, C. (2002). Defining Reflection:Another look at John Dewey and Reflective thinking. Teachers College Record,104, 104(4), 842–866. https://surreyfp.wikispaces.com/file/view/defining+reflection-Rogers.pdf
  28. 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
  29. Sammons, P., Gu, Q., Day, C., & Ko, J. (2011). Exploring the Impact of School Leadership on Pupil Outcomes: Results from a Study of Academically Improved and Effective Schools in England. International Journal of Educational Management, 25(1), 83–101. https://doi.org/https://doi.org/10.1108/09513541111100134
  30. Sandt, S. van der. (2007). Research Framework on Mathematics Teacher Behaviour: Koehler and Grouws’ Framework Revisited. Eurasia Journal of Mathematics, Science & Technology Education, 3(4), 343–350.
  31. Sezer, R. (2008). Integration of Critical Thinking Skills into Elementary School Teacher Education Courses in Mathematics. Education, 128(3), 349–363.
  32. Stahlberg, N., Mosler, S., & Schlüter, M. (2016). Writing, Calculating and Peer Feedback in a Mathematically-oriented Course for Process Engineers: Raising Motivation and Initiating Processes of Thinking and Learning. Journal of Academic Writing, 6(1), 84–97. https://doi.org/http://dx.doi.org/10.18552/joaw.v6i1.285
  33. Stark, R., & Krause, U. M. (2009). Effects of reflection prompts on learning outcomes and learning behaviour in statistics education. Learning Environments Research, 12(3), 209–223. https://doi.org/10.1007/s10984-009-9063-x
  34. Suharna, H. (2018). Teori Berpikir Reflektif dalam Menyelesaikan Masalah Matematika (1st ed.). DEEPUBLISH.
  35. 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
  36. Titikusumawati, E., Sa’dijah, C., As’ari, A. R., & Susanto, H. (2013). The Effectiveness of The Integration of Open-Ended and Collaborative (OE-C) Learning Strategies in Reducing Gaps of Elementary School Students’ Creative Thinking Skills. Elementary Education Online, 19(1), 198–207. https://doi.org/10.17051/ilkonline.2020.
  37. Van Haneghan, J. P., & Baker, L. (1989). Cognitive Monitoring in Mathematics. In Cognitive Strategy Research (pp. 215–238). Springer. https://doi.org/10.1007/978-1-4613-8838-8_9
  38. 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
  39. Zehavi, N., & Mann, G. (2005). Instrumented Techniques and Reflective Thinking in Analytic Geometry. The Montana Mathematics Enthusiast, 2(22), 1551–3440.