Article Sidebar

Download
PDF
Statistic
Read Counter : 172 Download : 63

Downloads

Download data is not yet available.

Main Article Content

Abstract

The Iceberg Design framework has been utilized to represent the progression of students’ mathematical understanding, moving from informal, contextually grounded reasoning toward formal mathematical abstraction. This study investigates how prospective mathematics teachers develop Iceberg Designs within the Realistic Mathematics Education (RME) framework, a model that enhances contextual learning and supports mathematical literacy. Thirty prospective mathematics teachers from Universitas Negeri Surabaya participated in this qualitative study, collaboratively designing Iceberg models as part of their coursework. Data from document analysis, interviews, and observations were evaluated using content analysis, the research evaluated the depth and coherence of their designs across four key components: situational contexts which evaluates the relevance and variety of real-world situations, model-of representations which examines the assistance of mathematical representation to connect the context into mathematical concept, model-for abstractions which assess the use of mathematical models toward formalization, and formal mathematical concepts which assess the mathematical ideas being explicitly involved. The findings reveal significant variation in the quality and completeness of the Iceberg Designs. Models for equivalent ratios and quadratic equations exhibited strong integration, using multiple, varied contexts to bridge situational and formal mathematical understanding effectively. Conversely, designs for fraction multiplication and quadrilateral area conservation were often surface level, relying on a single, underdeveloped context that hindered abstraction. Importantly, the study underscores the potential of Iceberg Designs to support the Sustainable Development Goals (SDGs), particularly in fostering critical thinking, practical problem-solving, and meaningful contextual learning for high quality of education (SDG 4) and decent work for sustainable economic growth (SDG 8). These insights indicate the need for deeper integration of RME principles in teacher education and curriculum development through sustained investment in this area.

Keywords

Iceberg Design Mathematical Literacy Prospective Teachers Realistic Mathematics Education SDGs

Article Details

Creative Commons License

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

How to Cite
Sari, Y. M., Fiangga, S., El Milla, Y. I., Shahrill, M., & Yanti, L. P. (2025). Prospective teachers’ iceberg designs in realistic mathematics education approach: Connecting mathematics and the SDGs. Journal on Mathematics Education, 16(3), 981–1000. https://doi.org/10.22342/jme.v16i3.pp981-1000
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Abrahamson, D., & Zolkower, B. (2020). Reinventing realistic mathematics education at Berkeley—Emergence and development of a course for pre-service teachers. In M. van den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands Didactics of Mathematics (pp. 255–277). Springer Open. https://doi.org/10.1007/978-3-030-20223-1_14
  2. Ariati, C., J. D. H. A., & Suparman, S. (2023). The effect of realistic mathematics education in enhancing Indonesian students’ mathematical reasoning ability: A meta-analysis. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(2), 324. https://doi.org/10.31764/jtam.v7i2.12493
  3. Boswinkel, N., & Moerlands, F. (2003). Het topje van de ijsberg. In K. Groenewegen (Ed.), Nationale Rekendagen 2002 - een praktische terugblik (pp. 103–114). Freudenthal Instituut. https://www.fi.uu.nl/publicaties/literatuur/5467.pdf
  4. Denscombe, M. (2010). The good research guide: For small-scale social research projects (Open UP Study Skills). McGraw-Hill. https://doi.org/10.1371/journal.pone.0017540
  5. Dilekçi, A., & Karatay, H. (2023). The effects of the 21st century skills curriculum on the development of students’ creative thinking skills. Thinking Skills and Creativity, 47, 101229. https://doi.org/10.1016/j.tsc.2022.101229
  6. Engelbrecht, J., B. M. C., & Kaiser, G. (2023). Will we ever teach mathematics again in the way we used to before the pandemic? ZDM – Mathematics Education, 55(1), 1–16. https://doi.org/10.1007/s11858-022-01460-5
  7. Fauziah, A., Putri, R. I. I., & Zulkardi. (2022). Collaborative learning through lesson study in PMRI training for primary school pre-service teacher: The simulation of polygon matter. Infinity Journal, 11(1), 1-16. https://doi.org/10.22460/infinity.v11i1.p1-16
  8. Fiangga, S., Khabibah, S., Amin, S. M., & Ekawati, R. (2021). A learning design analysis of the pre-service teachers’ mathematics pedagogical content knowledge. Journal of Physics: Conference Series, 1899(1), 012153. https://doi.org/10.1088/1742-6596/1899/1/012153
  9. Freudenthal, H. (1991). Revisiting Mathematics Education. Kluwer Academic.
  10. Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602
  11. Homavazir, M., & Homavazi, Z. (2024). STEM education: Present status and future direction. AG Volumes, 1, 148-159. https://agvolumes.com/Books-AG/index.php/AGvolumes/article/view/17/16
  12. Jana, A., & Rout, R. (2021). Preparedness of the libraries to address the recent pandemic: A case study on 100 top academic institutes of India. DESIDOC Journal of Library & Information Technology, 41(3), 175–183. https://doi.org/10.14429/djlit.41.03.16466
  13. Khairunnisak, C., Johar, R., Maulina, S., Zubainur, C. M., & Maidiyah, E. (2024). Teachers’ understanding of realistic mathematics education through a blended professional development workshop on designing learning trajectory. International Journal of Mathematical Education in Science and Technology, 55(4), 805–828. https://doi.org/10.1080/0020739X.2022.2038800
  14. Llinares, S. (2021). Instructional quality of mathematics teaching and mathematics teacher education. Journal of Mathematics Teacher Education, 24, 1–3. https://doi.org/10.1007/s10857-021-09488-2
  15. Maass, K., Geiger, V., Ariza, M. R., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM - Mathematics Education, 51(6), 869–884. https://doi.org/10.1007/s11858-019-01100-5
  16. Martinez, M. V., Castro-Superfine, A., & Stoelinga, T. (2022). A curriculum-based approach to learning trajectories in middle school Algebra. REDIMAT - Journal of Research in Mathematics Education, 11(1), 5-32. https://doi.org/10.17583/redimat.5539
  17. Milles, M., & Huberman, A. (2014). Qualitative data analysis: A methods sourcebook. Sage Publications.
  18. Novita, R., & Herman, T. (2021). Digital technology in learning mathematical literacy, Can it helpful? Journal of Physics: Conference Series, 1776(1), 012027. https://doi.org/10.1088/1742-6596/1776/1/012027
  19. OECD. (2022). PISA 2022 Results (Volume I). OECD. https://doi.org/10.1787/53f23881-en
  20. Palupi, E. L., Kohar, A. W., Ekawati, R., Fiangga, S., & Masriyah, M. (2022). Unpacking primary teachers’ initial knowledge of realistic mathematics education: A case of iceberg model of fraction division. In Eighth Southeast Asia Design Research (SEA-DR) & the Second Science, Technology, Education, Arts, Culture, and Humanity (STEACH) International Conference (SEADR-STEACH 2021) (pp. 245-250). Atlantis Press. https://doi.org/10.2991/ASSEHR.K.211229.038
  21. Palupi, E. L., Susanah, S., Hidayat, D., Fiangga, S., & Masriyah, M. (2020). Workshop merancang pembelajaran daring berbantuan Edmodo dan Cloud di masa COVID-19 untuk KKG Gugus 02 Kranggan Mojokerto [Workshop on designing online learning assisted by Edmodo and Cloud during COVID-19 for KKG Gugus 02 Kranggan Mojokerto]. Jurnal Anugerah: Jurnal Pengabdian kepada Masyarakat Bidang Keguruan dan Ilmu Pendidikan, 2(2), 101-108. https://doi.org/10.31629/anugerah.v2i2.2739
  22. Pandra, V., Kartowagiran, B., & Sugiman. (2021). Mathematics test development by item response theory approach and its measurement on elementary school students. Turkish Journal of Computer and Mathematics Education, 12(5), 464-483. https://turcomat.org/index.php/turkbilmat/article/view/994/782
  23. Polit, D. F., & Beck, C. T. (2010). Generalization in quantitative and qualitative research: Myths and strategies. International Journal of Nursing Studies, 47(11), 1451-1458. https://doi.org/10.1016/j.ijnurstu.2010.06.004
  24. Prahmana, R. C. I., Sagita, L., Hidayat, W., & Utami, N. W. (2020). Two decades of realistic mathematics education research in Indonesia: A survey. Infinity Journal, 9(2), 223–246. https://doi.org/10.22460/infinity.v9i2.p223-246
  25. Pramudiani, P., Herman, T., Turmudi, Dolk, M., & Terlouw, B. (2022). What do Indonesian and Dutch teachers find challenging when implementing realistic mathematics education. Jurnal Pendidikan Matematika, 17(1), 103-120. https://doi.org/10.22342/jpm.17.1.20097.103-120
  26. Priatna, N., Lorenzia, S., & Widodo, S. A. (2020). STEM education at junior high school mathematics course for improving the mathematical critical thinking skills. Journal for the Education of Gifted Young Scientists, 8(3), 1173-1184. https://doi.org/10.17478/jegys.728209
  27. Rahmawati & Ranti, M. G. (2021). Development of realistic mathematics education (RME) model based on HOTS problems for the topic of ratio. Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 5(2), 281-293. https://doi.org/10.31331/medivesveteran.v5i2.1674
  28. Risdiyanti, I., Zulkardi, Putri, R. I. I., Prahmana, R. C. I., & Nusantara, D. S. (2024). Ratio and proportion through realistic mathematics education and Pendidikan Matematika Realistik Indonesia approach: A systematic literature review. Jurnal Elemen, 10(1), 158–180. https://doi.org/10.29408/jel.v10i1.24445
  29. Sembiring, R. K. (2010). Pendidikan Matematika Realistik Indonesia (PMRI): Perkembangan dan tantangannya [Indonesian Realistic Mathematics Education (IRME): Developments and challenges]. Journal on Mathematics Education, 1(1), 11-16. https://core.ac.uk/download/pdf/267823332.pdf
  30. Tanujaya, B., Mumu, J., & Margono, G. (2017). The relationship between higher order thinking skills and academic performance of student in mathematics instruction. International Education Studies, 10(11), 78-85. https://files.eric.ed.gov/fulltext/EJ1159551.pdf
  31. Thornhill-Miller, B., Camarda, A., Mercier, M., Burkhardt, J. M., Morisseau, T., Bourgeois-Bougrine, S., ... & Lubart, T. (2023). Creativity, critical thinking, communication, and collaboration: Assessment, certification, and promotion of 21st century skills for the future of work and education. Journal of Intelligence, 11(3), 54. https://doi.org/10.3390/jintelligence11030054
  32. Ulfah, A. S., Yerizon, & Arnawa, I. M. (2020). Preliminary research of mathematics learning device development based on Realistic Mathematics Education (RME). Journal of Physics: Conference Series, 1554(1), 012027. https://doi.org/10.1088/1742-6596/1554/1/012027
  33. United Nations. (2015). Transforming our world: The 2030 agenda for sustainable development. United Nations.
  34. United Nations. (2023). The 17 Goals - Sustainable Development Goals. United Nations. https://sdgs.un.org/goals
  35. van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc
  36. Webb, D. C. (2017). The iceberg model: Rethinking mathematics instruction from a student perspective. In L. West & M. Boston (Eds.), Annual Perspectives in Mathematics Education: Reflective and Collaborative Processes to Improve Mathematics Teaching (pp. 201–209). NCTM.
  37. Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics Teaching in the Middle School, 14(2), 110-113. https://doi.org/10.5951/MTMS.14.2.0110
  38. Zolkower, B., B. A. M. P. S., & Gallego, M. F. (2020). From the bottom up—Reinventing realistic mathematics education in Southern Argentina. In International Reflections on the Netherlands Didactics of Mathematics (pp. 133–166). Springer. https://doi.org/10.1007/978-3-030-20223-1_9
  39. Zulkardi, Putri, R. I. I., & Wijaya, A. (2020). Two decades of realistic mathematics education in Indonesia. In M. van den Heuvel-Panhuizen (ed.), International reflections on the Netherlands Didactics of Mathematics (pp. 325–340). Springer Open. https://doi.org/10.1007/978-3-030-20223-1_18