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Abstract

In educational settings, reflective thinking is often overlooked, with an excessive emphasis on final answers, resulting in students needing more ability to evaluate and reconstruct their problem-solving processes. The ability for reflective thinking is required by students in solving problems, including numerical problems. This study uses a qualitative approach to focus on field-independent students' numerical problem-solving processes. The data collection technique begins by administering the Group Embedded Figures Test (GEFT), a valid and reliable numeracy problem instrument, and conducting in-depth interviews. Two students with similar initial mathematical abilities and field-independent cognitive styles were selected as research subjects. Findings reveal that these students face challenges such as lengthy problem descriptions and a lack of confidence but gradually develop strategies, emphasizing repeated problem analysis, concept interconnections, and error awareness. Researcher-provided scaffolding facilitates critical reflection, enabling the construction of new ideas. These results have practical implications for teachers, suggesting the need to design lessons that cater to diverse cognitive styles, providing more complex problems to field-independent students to enhance their problem-solving skills.

Keywords

Field Independent Student Numeracy Problems Reflective Thinking Process Scaffolding

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Setiyani, 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
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References

  1. Ahmad, H., & Latif, A. (2021). Development of student worksheets assisted by GeoGebra application in improving higher-order thinking ability in mathematics learning. Journal of Physics: Conference Series, 1882(1), 12048. https://10.1088/1742-6596/1882/1/012048
  2. Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33–52. https://doi.org/10.1007/s10857-006-9005-9
  3. Ariyana, I. K. S., & Suardipa, I. P. (2023). Strategy for Developing Numeracy Skill of Elementary School Students Based on Constructivism Theory. International Conference on Elementary Education, 5(1), 315–324.
  4. Baker, S. G., Patel, N., Von Gunten, C., Valentine, K. D., & Scherer, L. D. (2020). Interpreting politically-charged numerical information: The influence of numeracy and problem difficulty on response accuracy. Judgment and Decision Making, 15(2), 203–213. https://doi.org/10.1017/S193029750000735X
  5. Basol, G., & Evin Gencel, I. (2013). Reflective Thinking Scale: A Validity and Reliability Study. Educational Sciences: Theory and Practice, 13(2), 941–946. https://files.eric.ed.gov/fulltext/EJ1017318.pdf
  6. Bell, A., Kelton, J., McDonagh, N., Mladenovic, R., & Morrison, K. (2011). A critical evaluation of the usefulness of a coding scheme to categorise levels of reflective thinking. Assessment & Evaluation in Higher Education, 36(7), 797–815. https://doi.org/10.1080/02602938.2010.488795
  7. Bruine de Bruin, W., & Slovic, P. (2021). Low numeracy is associated with poor financial well-being around the world. Plos One, 16(11), e0260378. https://scholarsbank.uoregon.edu/xmlui/bitstream/handle/1794/26967/journal.pone.0260378.pdf?sequence=1&isAllowed=y
  8. Chen, M. A., Hwang, G., & Chang, Y. (2019). A reflective thinking‐promoting approach to enhancing graduate students’ flipped learning engagement, participation behaviors, reflective thinking and project learning outcomes. British Journal of Educational Technology, 50(5), 2288–2307. https://doi.org/10.1111/bjet.12823
  9. Choy, S. C., & San Oo, P. (2012). Reflective thinking and teaching practices: A precursor for incorporating critical thinking into the classroom? International Journal of Instruction, 5(1). https://dergipark.org.tr/en/download/article-file/59759
  10. Creswell, J. W., & Clark, V. L. P. (2017). Designing and conducting mixed methods research. Sage publications. https://doc1.bibliothek.li/acd/FLMF050277.pdf
  11. Darling-Hammond, L. (2019). A license to teach: Building a profession for 21st century schools. Routledge.
  12. Dubinsky, E. (1991). Constructive aspects of reflective abstraction in advanced mathematics. In Epistemological foundations of mathematical experience (pp. 160–202). Springer. https://doi.org/10.1007/978-1-4612-3178-3_9
  13. Dwiyanti, W., Waluya, S. B., & Walid, W. (2022). Reflective thinking in solving number theory problem: A case study of pre-service teacher in terms of cognitive style. AIP Conference Proceedings, 2577(1). https://doi.org/10.1063/5.0096137
  14. Gagatsis, A., & Patronis, T. (1990). Using geometrical models in a process of reflective thinking in learning and teaching mathematics. Educational Studies in Mathematics, 21(1), 29–54. https://doi.org/10.1007/BF00311014
  15. Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM, 47, 531–548. https://doi.org/10.1007/s11858-015-0708-1
  16. Ghanizadeh, A. (2017). The interplay between reflective thinking, critical thinking, self-monitoring, and academic achievement in higher education. Higher Education, 74, 101–114. https://doi.org/10.1007/s10734-016-0031-y
  17. Gittens, C. A. (2015). Assessing numeracy in the upper elementary and middle school years. Numeracy, 8(1), 3. http://dx.doi.org/10.5038/1936-4660.8.1.3
  18. Goos, M., Geiger, V., & Dole, S. (2013). Designing rich numeracy tasks. ICMI Study 22: Task Design in Mathematics, 589–597. https://hal.science/hal-00834054
  19. Goos, M., Geiger, V., & Dole, S. (2014). Transforming professional practice in numeracy teaching. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming mathematics instruction: multiple approaches and practices (pp. 81–102). Springer. https://doi.org/10.1007/978-3-319-04993-9_6
  20. Gürol, 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).
  21. Hamer, S., & Collinson, G. (2014). Achieving evidence-based practice: A handbook for practitioners. Elsevier Health Sciences.
  22. Hamidah, K., & Suherman, S. (2016). Proses Berpikir Matematis Siswa dalam Menyelesaikan Masalah Matematika di tinjau dari Tipe Kepribadian Keirsey. Al-Jabar: Jurnal Pendidikan Matematika, 7(2), 231–248. http://dx.doi.org/10.24042/ajpm.v7i2.38
  23. Hidayat, N., Usodo, B., & Saputro, D. R. S. (2021). Reflective thinking ability of junior high school students in relations and function problems. Journal of Physics: Conference Series, 1776(1), 12024. https://10.1088/1742-6596/1776/1/012024
  24. Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16, 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3
  25. Hodnik Čadež, T., & Manfreda Kolar, V. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89, 283–306. https://doi.org/10.1007/s10649-015-9598-y
  26. Hong, Y.-C., & Choi, I. (2011). Three dimensions of reflective thinking in solving design problems: A conceptual model. Educational Technology Research and Development, 59, 687–710. https://doi.org/10.1007/s11423-011-9202-9
  27. Indefenso, E. E., & Yazon, A. D. (2020). Numeracy level, mathematics problem skills, and financial literacy. Universal Journal of Educational Research, 8(10), 4393–4399. https://10.13189/ujer.2020.081005
  28. Jain, P., & Rogers, M. (2019). Numeracy as Critical Thinking. Adults Learning Mathematics, 14(1), 23–33. https://files.eric.ed.gov/fulltext/EJ1232382.pdf
  29. Kahtz, A. W., & Kling, G. J. (1999). Field‐dependent and Field‐independent Conceptualisations of Various Instructional Methods with an Emphasis on CAI: a qualitative analysis. Educational Psychology, 19(4), 413–428. https://doi.org/10.1080/0144341990190403
  30. Kember, D., McKay, J., Sinclair, K., & Wong, F. K. Y. (2008). A four‐category scheme for coding and assessing the level of reflection in written work. Assessment & Evaluation in Higher Education, 33(4), 369–379. https://doi.org/10.1080/02602930701293355
  31. 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
  32. Kim, M. C., & Hannafin, M. J. (2011). Scaffolding problem solving in technology-enhanced learning environments (TELEs): Bridging research and theory with practice. Computers & Education, 56(2), 403–417. https://doi.org/10.1016/j.compedu.2010.08.024
  33. Kim, Y., & Silver, R. E. (2016). Provoking reflective thinking in post observation conversations. Journal of Teacher Education, 67(3), 203–219. https://doi.org/10.1177/00224871166371
  34. Kitchener, K. S. (1984). Educational goals and reflective thinking. The Educational Forum, 48(1), 74–95. https://doi.org/10.1080/00131728309335882
  35. Kusmaryono, I., Ubaidah, N., & Basir, M. A. (2020). The role of scaffolding in the deconstructing of thinking structure: A case study of pseudo-thinking process. Infinity Journal, 9(2), 247-262. https://doi.org/10.22460/infinity.v9i2.p247-262
  36. Lee, H.-J. (2005). Understanding and assessing preservice teachers’ reflective thinking. Teaching and Teacher Education, 21(6), 699–715. https://doi.org/10.1016/j.tate.2005.05.007
  37. Liljedahl, P. (2015). Numeracy task design: A case of changing mathematics teaching practice. ZDM, 47, 625–637. https://doi.org/10.1007/s11858-015-0703-6
  38. Mamonto, K., Juniati, D., & Siswono, T. Y. E. (2018). Understanding fraction concepts of Indonesian junior high school students: A case of field independent and field dependent students. Journal of Physics: Conference Series, 947(1), 12058. https://10.1088/1742-6596/947/1/012058
  39. 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
  40. Megawati, L. A., & Sutarto, H. (2021). Analysis numeracy literacy skills in terms of standardized math problem on a minimum competency assessment. Unnes Journal of Mathematics Education, 10(2), 155–165. https://doi.org/10.15294/ujme.v10i2.49540
  41. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. sage.
  42. Mirzaei, F., Phang, F. A., & Kashefi, H. (2014). Assessing and improving reflective thinking of experienced and inexperienced teachers. Procedia-Social and Behavioral Sciences, 141, 633–639. https://doi.org/10.1016/j.sbspro.2014.05.111
  43. Muhaimin, L. H., Dasari, D., & Kusumah, Y. S. (2023). Numeracy-Ability, Characteristics of Pupils in Solving the Minimum Competency Assessment. Jurnal Program Studi Pendidikan Matematika, 12(1), 697–707. http://dx.doi.org/10.24127/ajpm.v12i1.6396
  44. Noer, S. H. (2020). The analysis of reflective thinking ability in junior high school students. Journal of Physics: Conference Series, 1521(3), 32024. https://10.1088/1742-6596/1521/3/032024
  45. Pagano, M., & Roselle, L. (2009). Beyond reflection: Refraction and international experiential education. Frontiers: The Interdisciplinary Journal of Study Abroad, 18(1), 217–229. https://doi.org/10.36366/frontiers.v18i1.263
  46. Puntambekar, S. (2022). Distributed scaffolding: scaffolding students in classroom environments. Educational Psychology Review, 34(1), 451–472. https://doi.org/10.1007/s10648-021-09636-3
  47. Putra, Y. Y., Zulkardi, Z., & Hartono, Y. (2016). Pengembangan soal matematika model PISA konten bilangan untuk mengetahui kemampuan literasi matematika siswa [Development of PISA-Style Mathematics Items on Number Content to Assess Students' Mathematical Literacy Skills]. Jurnal Elemen, 2(1), 14–26. https://doi.org/10.29408/jel.v2i1.175
  48. Rahmi, N., & Zubainur, C. M. (2020). Students’ mathematical reflective thinking ability through scaffolding strategies. Journal of Physics: Conference Series, 1460(1), 12022. doi:10.1088/1742-6596/1460/1/012022
  49. 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, 12041. https://10.1088/1742-6596/947/1/012041
  50. Richard, C. B. (2010). The Evaluation of Reflective Learning Practice: Preparing College Students for Globalization. ERIC.
  51. Rokaya, B. B. (2021). Constructive Learning Approach in Mathematics Education: Challenges and Possibilities. Academic Journal of Mathematics Education, 4(1), 1–6.
  52. Salido, A., & Dasari, D. (2019). The analysis of students’ reflective thinking ability viewed by students’ mathematical ability at senior high school. Journal of Physics: Conference Series, 1157(2), 22121. https://10.1088/1742-6596/1157/2/022121
  53. Samuels, M., & Betts, J. (2007). Crossing the threshold from description to deconstruction and reconstruction: using self‐assessment to deepen reflection. Reflective Practice, 8(2), 269–283. https://doi.org/10.1080/14623940701289410
  54. Schleicher, A. (2013). Developing educational policies in a holistic skills framework. In Educational policy innovations: Levelling up and sustaining educational achievement (pp. 29–48). Springer. https://doi.org/10.1007/978-981-4560-08-5_3
  55. Scott, F. (2016). An investigation into students’ difficulties in numerical problem solving questions in high school biology using a numeracy framework. European Journal of Science and Mathematics Education, 4(2), 115–128.
  56. Sezer, R. (2008). Integration of critical thinking skills into elementary school teacher education courses in mathematics. Education, 128(3), 349–363.
  57. Sriwongchai, A., Jantharajit, N., & Chookhampaeng, S. (2015). Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand. International Education Studies, 8(11), 77–87. http://dx.doi.org/10.5539/ies.v8n11p77
  58. Steen, L. A. (2001a). Mathematics and democracy: The case for quantitative literacy. NCED Princeton, NJ. https://www.proquest.com/openview/a073c8de293dd2c224a48c3d99148440/1?pq-origsite=gscholar&cbl=35418
  59. Steen, L. A. (2001b). Mathematics and numeracy: Two literacies, one language. The Mathematics Educator, 6(1), 10–16. https://math.nie.edu.sg/ame/matheduc/tme/tmeV6_1/Doc%20p2.pdf
  60. Suharna, H., Abdullah, I., & Angkotasan, N. (2022). Proses Akomodasi Mahasiswa dalam Menyelesaikan Masalah Kalkulus Berdasarkan Karakter Proses Berpikir Reflektif. [Student Accommodation Process in Solving Calculus Problems Based on the Characteristics of Reflective Thinking Process]. Jurnal Pendidikan Guru Matematika, 2(2). https://doi.org/10.33387/jpgm.v2i2.4627
  61. Surbeck, E. (1991). Assessing Reflective Responses in Journals. Educational Leadership, 48(6), 25–27.
  62. Thanheiser, E. (2010). Investigating further preservice teachers’ conceptions of multidigit whole numbers: Refining a framework. Educational Studies in Mathematics, 75, 241–251. https://doi.org/10.1007/s10649-010-9252-7
  63. Thayer-Bacon, B. (2000). Constructive thinking versus critical thinking: A classroom comparison. Philosophical Inquiry in Education, 13(1), 21–39.
  64. Tout, D., & Gal, I. (2015). Perspectives on numeracy: Reflections from international assessments. ZDM, 47, 691–706. https://doi.org/10.1007/s11858-015-0672-9
  65. Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher–student interaction: A decade of research. Educational Psychology Review, 22, 271–296. https://doi.org/10.1007/s10648-010-9127-6
  66. Watson, A., & Mason, J. (2006). Mathematics as a constructive activity: Learners generating examples. Routledge.
  67. Witkin, H. A., Moore, C. A., Goodenough, D. R., & Cox, P. W. (1977). Field-dependent and field-independent cognitive styles and their educational implications. Review of Educational Research, 47(1), 1–64. https://doi.org/10.3102/00346543047001001
  68. Xiao, F., Barnard-Brak, L., Lan, W., & Burley, H. (2019). Examining problem-solving skills in technology-rich environments as related to numeracy and literacy. International Journal of Lifelong Education, 38(3), 327–338. https://doi.org/10.1080/02601370.2019.1598507
  69. Yuek Ming, H., & Abd Manaf, L. (2014). Assessing learning outcomes through students’ reflective thinking. Procedia-Social and Behavioral Sciences, 152, 973–977. https://doi.org/10.1016/j.sbspro.2014.09.352
  70. 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
  71. Zevenbergen, R. (2004). Technologizing numeracy: Intergenerational differences in working mathematically in new times. Educational Studies in Mathematics, 56, 97–117. https://doi.org/10.1023/B:EDUC.0000028399.76056.91

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