Learning trajectory for equivalent fraction learning: An insight
DOI:
https://doi.org/10.30862/jhm.v5i1.233Keywords:
Design Research, Equivalent Fractions, HLT, MeasurementAbstract
Equivalent fraction is a sub-topic of fractions that highly contributes to explaining the basic concepts of fractions. However, this topic is one of the most challenging topics for students as it involves an advanced and formal concept and various representations. This study aims to present the preliminary result of the learning trajectory on equivalent fractions. This design research consisted of three stages: preparation, implementation, and retrospective analysis. The learning trajectory in the form of a hypothetical learning trajectory (HLT) was designed in the context of measuring cups. The data was collected through documentation, interviews, and class observations. The HLT was implemented to investigate students’ actual learning trajectories. The findings showed that the measuring cup context assists students to easily perceive those different fractions may have the same quantity (equivalent fractions). The learning trajectory consists of two activities. The first one aims to introduce a measurement concept of fractions to students. The second one aims to help students construct the concept of equivalent fractions. Finally, the study findings contribute to further development of learning trajectory on equivalent fractions.References
Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. CD- β Press.
Doorman, L. M. (2005). Modeling motion: From trace graphs to instantaneous change. Wilco Press.
Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publisher
Hacker, D. J., Kiuhara, S. A., & Levin, J. R. (2019). A metacognitive intervention for teaching fractions to students with or at-risk for learning disabilities in mathematics. ZDM - Mathematics Education, 51(4), 601–612. https://doi.org/10.1007/s11858-019-01040-0
Haris, D., & Putri, R. I. I. (2011). The role of context in third graders’ learning of area measurement. Journal on Mathematics Education, 2(1), 55-66. https://doi.org/10.22342/jme.2.1.778.55-66
Kara, M., Simon, M. A., & Placa, N. (2018). An empirically-based trajectory for fostering abstraction of equivalent-fraction concepts: A study of the Learning Through Activity research program. Journal of Mathematical Behavior, 52, 134–150. https://doi.org/10.1016/j.jmathb.2018.03.008
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
Pedersen, P. L., & Bjerre, M. (2021). Two conceptions of fraction equivalence. Educational Studies in Mathematics, 107(1), 135–157. https://doi.org/10.1007/s10649-021-10030-7
Putri, R. I. I. (2011). Improving mathematics communication ability of student in grade 2 through PMRI approach. Presented at International Seminar and the Fourth National Conference on Mathematics Education, 21-23 July 2011, Universitas Negeri Yogyakarta, Yogyakarta.
Putri, R. I. I., & Zulkardi. (2017). Fraction in shot-put: A learning trajectory. AIP Conference Proceedings, 1868, 050005. https://doi.org/10.1063/1.4995132
Putri, R. I. I., Zulkardi, Setyorini, N. P., Meitrilova, A., Permatasari, R., Saskiyah, S. A., & Nusantara, D. S. (2021). Designing a healthy menu project for Indonesian junior high school students. Journal on Mathematics Education, 12(1), 133–146. https://doi.org/10.22342/jme.12.1.13239.133-146
Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.5951/jresematheduc.26.2.0114
Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14, 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
Streefland, L. (1991). Fractions in realistic mathematics education, A paradigm of developmental research. Kluwer Academic Publishers
Wijaya, A., Elmaini, & Doorman, M. (2021). A learning trajectory for probability: A case of game-based learning. Journal on Mathematics Education, 12(1), 1–16. https://doi.org/10.22342/jme.12.1.12836.1-16
Wilkins, J. L. M., & Norton, A. (2018). Learning progression toward a measurement concept of fractions. International Journal of STEM Education, 5(1), 1-11. https://doi.org/10.1186/s40594-018-0119-2
Wong, M. (2010). Equivalent fractions: Developing a pathway of students’ acquisition of knowledge and understanding. Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 673-680). Fremantle: MERGA
Zulkardi, & Putri, R. I. I. (2010). Pengembangan blog support untuk membantu siswa dan guru matematika Indonesia belajar Pendidikan Matematika Realistik Indonesia (PMRI) [Developing a support blog to help Indonesian mathematics students and teachers learn Indonesian Realistic Mathematics Education (IRME)]. Jurnal Inovasi Perekayasa Pendidikan (JIPP), 2(1), 1-24.
Zulkardi, Putri R. I. I., & Wijaya A. (2020). Two decades of realistic mathematics education in Indonesia. In van den Heuvel-Panhuizen M. (eds), International Reflections on the Netherlands Didactics of Mathematics. ICME-13 Monographs (pp. 325-340). Springer
Zulkardi. (2002). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Doctoral Dissertation. University of Twente, Enshede, Netherland.
Downloads
Published
How to Cite
Issue
Section
License
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Journal of Honai Math Posting Your Article Policy at http://journalfkipunipa.org/index.php/jhm/about
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with Journal of Honai Math agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-NC-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
