Main Article Content

Abstract

Fraction learning has gained significant attention in mathematics education research, with a growing body of literature addressing the instructional challenges inherent in teaching fractions effectively. Establishing a solid conceptual foundation in fractions is critical to fostering broader mathematical proficiency, yet many students continue to struggle with core fractional concepts. This study addresses these issues by integrating a real-world context—Musi Rawas tourism—into fraction instruction, targeting pre-service elementary teachers enrolled in an elementary mathematics education program. Adopting a design research methodology, specifically a validation study, the study progresses through three structured phases: preliminary design, design experiments (encompassing pilot and teaching experiments), and retrospective analysis. Data collection involved teaching materials, observational checklists, and documentation to capture the instructional dynamics and learning outcomes. The study’s primary contribution is a localized instructional theory for teaching fractions within a tourism context, organized across five progressive learning activities: problem identification in the Gegas Water Lake tourism setting, contextual model development, model-based problem-solving, context-specific solution formulation, and abstraction of mathematical conclusions. This framework offers an innovative pedagogical approach, illustrating the potential for enhancing fraction learning through contextualized instruction in tourism, with detailed insights into the methodology and outcomes presented in the full study.

Keywords

Design Research Fraction Gegas Water Lake Tourism Local Instructional Theory Multiplication of Fractions

Article Details

How to Cite
Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024). Learning fraction with vacation: Integrating Musi Rawas tourism in designing learning trajectory on fraction. Journal on Mathematics Education, 15(4), 1153–1174. https://doi.org/10.22342/jme.v15i4.pp1153-1174

References

  1. Alkhateeb, M. A. (2019). Common errors in fractions and the thinking strategies that accompany them. International Journal of Instruction, 12(2), 399-416. https://doi.org/10.29333/iji.2019.12226a
  2. Anwar, L., Budayasa, I. K., Amin, S. M., & de Haan, D. (2012). Eliciting mathematical thinking of students through Realistic Mathematics Education. Journal on Mathematics Education, 3(1), 55-70. http://dx.doi.org/10.22342/jme.3.1.620.55-70
  3. Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. https://doi.org/10.1016/j.jecp.2012.06.004
  4. Braithwaite, D. W., & Siegler, R. S. (2024). A unified model of arithmetic with whole numbers, fractions, and decimals. Psychological Review, 131(2), 431–455. https://doi.org/10.1037/rev0000440
  5. Brown, E. L., Stark, K., Vesely, C., & Choe, J. (2023). “Acting often and everywhere:” Teachers’ emotional labor across professional interactions and responsibilities. Teaching and Teacher Education, 132, 104227. https://doi.org/10.1016/j.tate.2023.104227
  6. Bueddefeld, J., & Duerden, M. D. (2022). The transformative tourism learning model. Annals of Tourism Research, 94, 103405. https://doi.org/10.1016/j.annals.2022.103405
  7. Bush, J. B. (2021). Software‐based intervention with digital manipulatives to support student conceptual understandings of fractions. British Journal of Educational Technology, 52(6), 2299-2318. https://doi.org/10.1111/bjet.13139
  8. Chai, Y., Dai, B., Zhang, Y., & Wang, Y. (2024). Partnerships in educational tourism in China: a power perspective. Journal of Sustainable Tourism, 1-18. https://doi.org/10.1080/09669582.2024.2346789
  9. Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64, 293-316. https://doi.org/10.1007/s10649-006-9036-2
  10. Choe, Y., & Kim, N. (2024). From the classroom to the Living Lab for developing competencies in tourism higher education. Journal of Hospitality, Leisure, Sport & Tourism Education, 35, 100511. https://doi.org/10.1016/j.jhlste.2024.100511
  11. Dole, S., & Geiger, V. (2020). Numeracy across the curriculum: Research-based strategies for enhancing teaching and learning. Routledge. https://doi.org/10.4324/9781003116585
  12. Domínguez, A., Saenz-de-Navarrete, J., De-Marcos, L., Fernández-Sanz, L., Pagés, C., & Martínez-Herráiz, J. J. (2013). Gamifying learning experiences: Practical implications and outcomes. Computers & Education, 63, 380-392. https://doi.org/10.1016/j.compedu.2012.12.020
  13. Espinoza-Figueroa, F., Vanneste, D., Alvarado-Vanegas, B., Farfan-Pacheco, K., & Rodriguez-Giron, S. (2021). Research-based learning (RBL): Added-value in tourism education. Journal of Hospitality, Leisure, Sport & Tourism Education, 28, 100312. https://doi.org/10.1016/j.jhlste.2021.100312
  14. Farrell, B. H., & Twining-Ward, L. (2004). Reconceptualizing tourism. Annals of tourism research, 31(2), 274-295. https://doi.org/10.1016/j.annals.2003.12.002
  15. Feng, Y., & Zhao, Y. (2024). Exploring teaching pathways for deep learning and smart tourism based on project-based learning: A case study of the deep learning course at Guilin tourism university. Pacific International Journal, 7(3), 6-10. https://doi.org/10.55014/pij.v7i3.607
  16. Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Kluwer Academic Publishers.
  17. Günter, K. P., Ahnesjö, I., & Gullberg, A. (2023). “I try to encourage my students to think, read, and talk science” intelligible identities in university teachers' figured worlds of higher education biology. Journal of Research in Science Teaching, 60(6), 1195-1222. https://doi.org/10.1002/tea.21829
  18. Hanna, G. (2020). Mathematical proof, argumentation, and reasoning. In S. Lerman (eds), Encyclopedia of Mathematics Education (pp. 561-566). Springer. https://doi.org/10.1007/978-3-030-15789-0_102
  19. Hunt, J. H., Silva, J., & Lambert, R. (2019). Empowering students with specific learning disabilities: Jim's concept of unit fraction. Journal of Mathematical Behavior, 56(2019), 100738. https://doi.org/10.1016/j.jmathb.2019.100738
  20. Jannah, A. F., & Prahmana, R. C. I. (2019). Learning fraction using the context of pipettes for seventh-grade deaf-mute student. Journal for the Education of Gifted Young Scientists, 7(2), 299-321. https://doi.org/10.17478/jegys.576234
  21. Jarrah, A. M., Wardat, Y., & Gningue, S. (2022). Misconception on addition and subtraction of fractions in seventh-grade middle school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), em2115. https://doi.org/10.29333/ejmste/12070
  22. Johnston, O., Wildy, H., & Shand, J. (2023). Student voices that resonate–Constructing composite narratives that represent students’ classroom experiences. Qualitative Research, 23(1), 108-124. https://doi.org/10.1177/14687941211016158
  23. Kalogeropoulos, P., Russo, J.A., & Liyanage, A. (2024). Values alignment as teacher craft for effective mathematics teaching and learning. In Y. Dede, G. Marschall, P. Clarkson (eds), Values and Valuing in Mathematics Education (pp. 149-168). Springer. https://doi.org/10.1007/978-981-99-9454-0_8
  24. Kilic, C. (2015). Analyzing pre-service primary teachers' fraction knowledge structures through problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 11(6),1603–1619. https://doi.org/10.12973/eurasia.2015.1425a
  25. Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge. https://doi.org/10.4324/9781003008057
  26. Lee, J. E., & Lee, M. Y. (2023). How elementary prospective teachers use three fraction models: their perceptions and difficulties. Journal of Mathematics Teacher Education, 26(4), 455-480. https://doi.org/10.1007/s10857-022-09537-4
  27. Lenz, K., Reinhold, F., & Wittmann, G. (2024). Topic specificity of students’ conceptual and procedural fraction knowledge and its impact on errors. Research in Mathematics Education, 26(1), 45-69. https://doi.org/10.1080/14794802.2022.2135132
  28. Malone, T. W., & Lepper, M. R. (2021). Making learning fun: A taxonomy of intrinsic motivations for learning. In R. E. Snow, M. J. Farr (eds), Aptitude, Learning, and Instruction (pp. 223-254). Routledge. https://doi.org/10.4324/9781003163244
  29. Marleny, A. S., Zukardi, & Putri, R. I. I. (2024). Systematic literature review: Development of PISA mathematics minimum competency assessment questions in tourism contexts. AIP Conference Proceedings, 3052(1), 020076. https://doi.org/10.1063/5.0201041
  30. Mavrikis, M., Rummel, N., Wiedmann, M., Loibl, K., & Holmes, W. (2022). Combining exploratory learning with structured practice educational technologies to foster both conceptual and procedural fractions knowledge. Educational technology research and development, 70(3), 691-712. https://doi.org/10.1007/s11423-022-10104-0
  31. Meryansumayeka, Putri, R. I. I., & Zulkardi. (2019). How students learn fraction through pempek lenjer context. Journal of Physics: Conference Series, 1166(1), 012028. https://dx.doi.org/10.1088/1742-6596/1166/1/012028
  32. Misquitta, R. (2011). A review of the literature: Fraction instruction for struggling learners in mathematics. Learning Disabilities Research & Practice, 26(2), 109-119. https://doi.org/10.1111/j.1540-5826.2011.00330.x
  33. Moyo, M., & Machaba, F.M. (2021). Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator. Pythagoras, 42(1), a602. https://doi.org/10.4102/pythagoras.v42i1.602
  34. Ne, L. I. (2005). Cooking With Fractions Word Problems. Scholastic. https://www.scholastic.com/content/dam/parents/migrated-assets/printables/pdfs/problem-solving-and-cooking-printable_v2.pdf
  35. Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326985ep4001_3
  36. Olson, T. A., & Olson, M. (2013). The importance of context in presenting fraction problems to help students formulate models and representations as solution strategies. NCSM Journal of Mathematics Education Leadership, 14(2), 38-47. https://www.researchgate.net/profile/Melfried-Olson-2/publication/265599148_The_importance_of_context_in_presenting_fraction_problems_to_help_students_formulate_models_and_representations_as_solution_strategies/links/55a58e6d08ae00cf99c97ba1/The-importance-of-context-in-presenting-fraction-problems-to-help-students-formulate-models-and-representations-as-solution-strategies.pdf
  37. Pierce, R. (2021). Decimals, Fractions, and Percentages. Math Is Fun. https://www.mathsisfun.com/decimal-fraction-percentage.html
  38. Plomp, T. (2013). Educational design research: An introduction. In T. Plomp, N. Nieveen (eds), Educational Design Research (pp. 10-51). SLO
  39. 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
  40. Prediger, S., Quabeck, K., & Erath, K. (2022). Conceptualizing micro-adaptive teaching practices in content-specific ways: Case study on fractions. Journal on Mathematics Education, 13(1), 1–30. https://doi.org/10.22342/jme.v13i1.pp1-30
  41. Purnomo, Y. W., Pasri, Aziz, T. A., Shahrill, M., & Prananto, I. W. (2022). Students’ failure to understand fraction multiplication as part of a quantity. Journal on Mathematics Education, 13(4), 681–702. https://doi.org/10.22342/jme.v13i4.pp681-702
  42. Rau, M. A., & Matthews, P. G. (2017). How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions. ZDM, 49, 531-544. https://doi.org/10.1007/s11858-017-0846-8
  43. 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
  44. Safriani, W., Munzir, S., Duskri, M., & Maulidi, I. (2019). Analysis of students' errors on the fraction calculation operations problem. Al-Jabar: Jurnal Pendidikan Matematika, 10(2), 307-318. http://dx.doi.org/10.24042/ajpm.v10i2.5224
  45. Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, 40, 927-939. https://doi.org/10.1007/s11858-008-0125-9
  46. Shanty, N. O. (2023). Fifth grade students' learning of multiplication of fractions based on Realistic Mathematics Education. Doctoral Dissertation. Middle East Technical University. https://hdl.handle.net/11511/104825
  47. Sidney, P. G., & Alibali, M. W. (2017). Creating a context for learning: Activating children's whole number knowledge prepares them to understand fraction division. Journal of Numerical Cognition, 3(1), 31–57. https://doi.org/10.5964/jnc.v3i1.71
  48. Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive psychology, 62(4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001
  49. Soto-Andrade, J. (2020). Metaphors in mathematics education. In S. Lerman (eds), Encyclopedia of Mathematics Education (pp. 619-625). Springer. https://doi.org/10.1007/978-3-030-15789-0_113
  50. Streefland, L. (2012). Fractions: A realistic approach. In T. P. Carpenter, E. Fennema, T. A. Romberg (eds), Rational Numbers (pp. 289-325). Routledge. https://doi.org/10.4324/9780203052624
  51. Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024a). Mathematics in tourism of Musi Rawas regency. AIP Conference Proceedings, 3052(1), 020013. https://doi.org/10.1063/5.0201021
  52. Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024b). Students’ cognitive processes in understanding fractions through the tourist context. Jurnal Pendidikan Matematika, 18(1), 27–38. https://doi.org/10.22342/jpm.v18i1.pp27-38
  53. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In S. Lerman (eds), Encyclopedia of Mathematics Education (pp. 713-717). Springer. https://doi.org/10.1007/978-3-030-15789-0_170
  54. Van Galen, F. (2013). Contexts and models in mathematics education. The First South East Asia Design/Development Research (SEA-DR) International Conference (pp. 12-21). Universitas Sriwijaya. http://eprints.unsri.ac.id/2538/
  55. Van Galen, F., Feijs, E., Figueiredo, N., Gravemeijer, K., Van Herpen, E., & Keijzer, R. (2008). Fractions, percentages, decimals and proportions. Sense Publishers.
  56. Wang, H. H., Hong, Z. R., She, H. C., Smith, T. J., Fielding, J., & Lin, H. S. (2022). The role of structured inquiry, open inquiry, and epistemological beliefs in developing secondary students’ scientific and mathematical literacies. International Journal of STEM Education, 9(1), 14. https://doi.org/10.1186/s40594-022-00329-z
  57. Webb, D. C., Van der Kooij, H., & Geist, M. R. (2011). Design research in the Netherlands: Introducing logarithms using realistic mathematics education. Journal of Mathematics Education at Teachers College, 2(1), 708. https://doi.org/10.7916/jmetc.v2i1.708
  58. Wortha, S. M., Bloechle, J., Ninaus, M., Kiili, K., Lindstedt, A., Bahnmueller, J., ... & Klein, E. (2020). Neurofunctional plasticity in fraction learning: An fMRI training study. Trends in Neuroscience and Education, 21, 100141. http://dx.doi.org/10.1016/j.tine.2020.100141
  59. Xu, C., Di Lonardo Burr, S., McNally-Edwards, N., McShane, C., Wan, L., & Wylie, J. (2024). A holistic investigation of fraction learning: examining the hierarchy of fraction skills, misconceptions, mathematics anxiety and response confidence. Journal of Cognitive Psychology, 36(7), 815-833. https://doi.org/10.1080/20445911.2024.2388907
  60. Zulkardi, Nusantara, D. S., & Putri, R. I. I. (2021). Designing PISA-like task on uncertainty and data using Covid-19 context. Journal of Physics: Conference Series, 1722(1), 012102. https://doi.org/10.1088/1742-6596/1722/1/012102

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