Main Article Content

Abstract

In mathematics teaching and learning, mathematics tasks embedded in realistic contexts are crucial for developing mathematical concepts, procedures, and the application of mathematical knowledge. Despite this, mathematics teachers often encounter challenges in designing and implementing such realistic mathematics tasks. Therefore, this study aims to construct a learning trajectory to enhance preservice mathematics teachers' abilities to create and implement Realistic Mathematics Tasks (RMTs). Employing a design research methodology, the study comprises three phases: preliminary design, teaching experiment, and retrospective analysis. The data presented in this article are from the first cycle, encompassing all three phases. The research involved four fourth-year preservice mathematics teachers from Sanata Dharma University in Yogyakarta, Indonesia, participating in a preliminary experiment conducted over three months outside their regular coursework. Data were collected through pre-course written tests, observations, interviews, journal reflections, and analyses of the preservice teachers' work. The findings indicate that the learning trajectory effectively raised awareness among preservice teachers about key characteristics of realistic mathematics tasks. This heightened awareness was evident in their reflections and work. Additionally, observations of their teaching practices revealed that preservice teachers valued student reasoning in solving RMTs. However, they faced difficulties in classroom management and guiding students to construct new knowledge actively through their experiences in solving RMTs.

Keywords

Design Research Didactical Strategies Preservice Mathematics Teachers Realistic Mathematics Tasks

Article Details

How to Cite
Rianasari, V. F., & Guzon, A. F. H. (2024). Designing learning trajectory to support preservice mathematics teachers’ skills in creating and implementing realistic mathematics tasks. Journal on Mathematics Education, 15(3), 701–716. https://doi.org/10.22342/jme.v15i3.pp701-716

References

  1. Bakker, A., & van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Doing qualitative research: methodology and methods in mathematics education (Issue May, pp. 429–466). Springer. https://doi.org/10.1007/978-94-017-9181-6_16
  2. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. International Perspectives on the Teaching and Learning of Mathematical Modelling, 1, 15–30. https://doi.org/10.1007/978-94-007-0910-2_3
  3. Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55. https://doi.org/10.1007/s10649-012-9441-7
  4. Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. In Learning How to Teach Mathematical Modeling in School and Teacher Education. Springer International Publishing. https://doi.org/10.1007/978-3-319-68072-9
  5. Chan, C. M. E. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Conceptions of mathematical modelling. In S. G, K. G, B. W, & Brown J (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 405–413). Springer. https://doi.org/10.1007/978-94-007-6540-5_34
  6. Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26(2), 152–160. https://doi.org/10.1016/j.tate.2009.03.016
  7. 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_3
  8. Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. Van den Akker, K. P. E. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17–51). Routledge.
  9. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1–3), 111–129. https://doi.org/10.1023/a:1003749919816
  10. Große, C. S. (2014). Learning to solve story problems—supporting transitions between reality and mathematics. European Journal of Psychology of Education, 29(4), 619–634. https://doi.org/10.1007/s10212-014-0217-6
  11. Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems? ZDM - Mathematics Education, 53(4), 919–935. https://doi.org/10.1007/s11858-021-01224-7
  12. Hwang, J., & Ham, Y. (2021). Relationship between mathematical literacy and opportunity to learn with different types of mathematical tasks. Journal on Mathematics Education, 12(2), 199–222. https://doi.org/10.22342/JME.12.2.13625.199-222
  13. Isik, C., & Kar, T. (2012). The analysis of the problems posed by the pre-service teachers about equations. Australian Journal of Teacher Education, 37(9), 93–113. https://doi.org/10.14221/ajte.2012v37n9.1
  14. Jupri, A. (2015). The use of applets to improve Indonesian student performance in algebra. [Master thesis, University of Utrecht]. Utrecht University Repository.
  15. Kohar, A. W., Wardani, A. K., & Fachrudin, A. D. (2019). Profiling context-based mathematics tasks developed by novice PISA-like task designers. Journal of Physics: Conference Series, 1200(1). https://doi.org/10.1088/1742-6596/1200/1/012014
  16. Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225–250. https://doi.org/https://doi.org/10.1023/A:1016282811724
  17. Lee, N. H. (2013). Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Problem Posing and Task Design. In S. G, K. G, B. W, & B. J (Eds.), International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 415–425). Springer. https://doi.org/10.1007/978-94-007-6540-5_35
  18. Leiss, D., Plath, J., & Schwippert, K. (2019). Language and Mathematics - Key factors influencing the comprehension process in reality-based tasks. Mathematical Thinking and Learning, 21(2), 131–153. https://doi.org/10.1080/10986065.2019.1570835
  19. NCTM. (2000). Principles and standards for school mathematics. NCTM.
  20. Neef, N. A., Nelles, D. E., Iwata, B. A., & Page, T. J. (2003). Analysis of precurrent skills in solving mathematics story problems. Journal of Applied Behavior Analysis, 36(1), 21–33. https://doi.org/10.1901/jaba.2003.36-21
  21. Niss, M., Bruder, R., Planas, N., Turner, R., & Villa-Ochoa, J. A. (2017). Conceptualisation of the role of competencies, knowing and knowledge in mathematics education research. In Proceedings of the 13th International Congress on Mathematical Education: ICME-13 (pp. 235-248). Springer International Publishing.
  22. Nuthall, G. (2004). Analysis of why research has failed to bridge the theory-practice gap. Harvard Educational Review, 74(3), 273–307.
  23. Nyman, R. (2017). Interest and engagement: Perspectives on mathematics in the classroom. [Doctoral dissertation, Gothenburg University]. Gothenburg University Publications Electronic Archive (GUPEA).
  24. OECD. (2016). PISA 2015 results (volume I): Excellence and equity in education. OECD Publishing.
  25. OECD. (2019). PISA 2018 results: Combined executive summaries volume I, II & III. OECD Publishing.
  26. OECD. (2023). PISA 2022 Results (Volume I). OECD. https://doi.org/10.1787/53f23881-en
  27. Prediger, S., & Krägeloh, N. (2015). Low achieving eighth graders learn to crack word problems: a design research project for aligning a strategic scaffolding tool to students’ mental processes. ZDM - Mathematics Education, 47(6), 947–962. https://doi.org/10.1007/s11858-015-0702-7
  28. Pusat Asesmen dan Pembelajaran. (2020). AKM dan Implikasinya pada Pembelajaran. Kementerian Pendidikan dan Kebudayaan.
  29. Santrock, J. W. (2021). Educational psychology (7th ed.). McGraw Hill LLC.
  30. Şengül, S., & Katranci, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia - Social and Behavioral Sciences, 174(262), 1983–1990. https://doi.org/10.1016/j.sbspro.2015.01.864
  31. Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50(1–2), 301–314. https://doi.org/10.1007/s11858-017-0898-9
  32. Sevinc, S., & Lesh, R. (2021). Preservice mathematics teachers’ conceptions of mathematically rich and contextually realistic problems. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-021-09512-5
  33. Siswono, T. Y. E., Kohar, A. W., Hartono, S., & Rosyidi, A. H. (2018). An innovative training model for supporting in-service teachers’ understanding on problem-solving knowledge for teaching. Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education, 321–332.
  34. Stacey, K. (2015). The Real World and the Mathematical World. In K. Stacey & R. Turner (Eds.), Assessing Mathematical Literacy (pp. 57–84). Springer International Publishing. https://doi.org/10.1007/978-3-319-10121-7_3
  35. Stoyanova, E. N., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Mathematics Education Research Group of Australia.
  36. Sullivan, P., Knott, L., & Yang, Y. (2015). The relationships between task design, anticipated pedagogies, and student learning. In A. Watson & M. Ohtani (Eds.), Task Design in Mathematics Education: An ICMI Study 22 (pp. 83–114). Springer International Publishing. https://doi.org/10.1007/978-3-319-09629-2_3
  37. van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessments problems in mathematics. For the Learning of Mathematics, 25(2), 2–9.
  38. van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Vol. 4, Issue 3, pp. 713–717). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_170
  39. Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM - Mathematics Education, 52(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4
  40. Widjaja, W., & Dolk, M. (2010). Building, supporting, and enhancing teachers’ capacity to foster mathematical learning: insights from Indonesian classroom. In Y. Shimizu, Y. Sekiguchi, & K. Hino (Eds.), Proceedings of the 5th East Asia Regional Conference on Mathematics Education (pp. 332–339). EARCOME.
  41. Wijaya, A. (2008). Design Research in Mathematics Education Indonesian Traditional Games as Preliminaries in Learning Measurement of Length. [Master thesis, University of Utrecht]. Utrecht University Repository.
  42. Wijaya, A. (2015). Context-based mathematics tasks in Indonesia: Toward better practice and achievement. [Doctoral dissertation, University of Utrecht]. Utrecht University Repository. https://ro.ecu.edu.au/theses/885/
  43. Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015a). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
  44. Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015b). Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks. Mathematics Education Research Journal, 27(4), 637–662. https://doi.org/10.1007/s13394-015-0157-8