DOI of the published article https://doi.org/10.31980/mosharafa.v13i4.2506
Learning Trajectories of Different Denominator Fractions with Ote-ote
Lintasan Belajar Pecahan Berpenyebut Berbeda dengan Ote-ote
DOI:
https://doi.org/10.21070/ups.8639Keywords:
different denominator fractions, hypothetical learning trajectories, Ote-oteAbstract
Different denominator fractions is subtopic of fractions that greatly contributes to explaining the basic concept of fractions. However, it is challenging for primary students because it is based on concept that requires multiple representations. This study aims to develop learning trajectories (LT) on different denominator fractions in the context of Ote-ote. Ote-ote is typical East Java food shaped similarly to a circle. The participants of this study were 26 grade 5 students from Sekolah Dasar Negeri Jimbaran Wetan, Sidoarjo. The study design used was research design with stages: preparation, implementation, and retrospective analysis. Data were collected through student worksheets, observation, and tests—technical data analysis using source triangulation. The developed LT consists of four activities, namely: (1) introduction of fractions, (2) addition of common denominator fractions, (3) equivalent fractions, and (4) addition of different denominator fractions. The LT activities construct students' understanding of different denominator fractions, generally in the satisfactory category.
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R. C. Torres-Peña, D. Peña-González, and E. A. Ariza, “Enhancing fraction learning through problem-solving and historical context: A didactic unit approach,” Journal on Mathematics Education, vol. 15, no. 3, pp. 815–834, Aug. 2024, doi: 10.22342/jme.v15i3.pp815-834.
P. B. Kalra, E. M. Hubbard, and P. G. Matthews, “Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children,” Contemp Educ Psychol, vol. 62, p. 101896, Jul. 2020, doi: 10.1016/j.cedpsych.2020.101896.
J. Cabuquin and F. Abocejo, “Conceptual and procedural understanding in the division of algebraic fractions,” Recoletos Multidisciplinary Research Journal, vol. 12, no. 1, pp. 225–240, Jun. 2024, doi: 10.32871/rmrj2412.01.17.
Y. Copur-Gencturk, “Teachers’ conceptual understanding of fraction operations: Results from a national sample of elementary school teachers,” Educational Studies in Mathematics, vol. 107, no. 3, pp. 525–545, Jul. 2021, doi: 10.1007/s10649-021-10033-4.
E. Amuah and E. K. Davis, “Strategies and procedural and conceptual knowledge of addition of unlike denominator fractions: The case of grade 8 children in two districts of the central region of ghana,” African Journal of Research in Mathematics, Science and Technology Education, vol. 27, no. 2, pp. 123–136, May 2023, doi: 10.1080/18117295.2023.2226546.
D. Wulandari and M. F. Amir, “Analysis of elementary school students’ difficulties in fraction addition,” K R E A N O Creative-Innovative Mathematics (education) Journal, 2022, doi: https://doi.org/10.15294/kreano.v13i1.35275.
A. M. Jarrah, Y. Wardat, and S. Gningue, “Misconception on addition and subtraction of fractions in seventh-grade middle school students,” Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 6, p. em2115, May 2022, doi: 10.29333/ejmste/12070.
M. J. Behr, R. Lesh, T. R. Post, and E. A. Silver, Rational number concepts. Academic Press, 1984. [Online]. Available: https://www.researchgate.net/publication/258510439
M. A. Simon, “Reconstructing mathematics pedagogy from a constructivist perspective,” Source: Journal for Research in Mathematics Education, vol. 26, no. 2, pp. 114–145, 1995, doi: https://doi.org/10.5951/jresematheduc.26.2.0114.
R. A. Fuller, “Elementary teachers’ pedagogical content knowledge of mathematics,” Mid- Western Educational Researcher:, 1997, [Online]. Available: https://scholarworks.bgsu.edu/mwer/vol10/iss2/3
D. H. Clements, Learning and Teaching Early Math. Routledge, 2014. doi: 10.4324/9780203520574.
A. Wijaya, M. van den Heuvel-Panhuizen, M. Doorman, and A. Robitzsch, “Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors,” The Mathematics Enthusiast, vol. 11, no. 3, pp. 555–584, Dec. 2014, doi: 10.54870/1551-3440.1317.
P. Pramudiani, T. Herman, Turmudi, M. Dolk, and M. Doorman, “How does a missing part become important for primary school students in understanding fractions?,” Journal on Mathematics Education, vol. 13, no. 4, pp. 565–586, Dec. 2022, doi: 10.22342/jme.v13i4.pp565-586.
F. Reinhold, S. Hoch, B. Werner, J. Richter-Gebert, and K. Reiss, “Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students?,” Learn Instr, vol. 65, p. 101264, Feb. 2020, doi: 10.1016/j.learninstruc.2019.101264.
D. H. Clements and J. Sarama, Learning and teaching early math. Routledge, 2020. doi: 10.4324/9781003083528.
I. Salsabila, M. F. Amir, and M. D. K. Wardana, “A learning trajectory of integer addition and subtraction using the kempreng game context,” Jurnal Elemen, vol. 8, no. 2, pp. 556–571, Jul. 2022, doi: 10.29408/jel.v8i2.5541.
V. Adelia, R. I. I. Putri, Z. Zulkardi, and B. Mulyono, “Learning trajectory for equivalent fraction learning: An insight,” Journal of Honai Math, vol. 5, no. 1, pp. 47–60, Mar. 2022, doi: 10.30862/jhm.v5i1.233.
R. Febriani, E. Susanti, and H. Hapizah, “Learning trajectory in the material of comparing and ordering fractions using paper folding for elementary school students,” Al-Jabar : Jurnal Pendidikan Matematika, vol. 14, no. 2, p. 353, Dec. 2023, doi: 10.24042/ajpm.v14i2.18046.
M. H. Ramadhan, Z. Zulkardi, and R. I. I. Putri, “Designing learning trajectory for teaching fractions using pmri approach with a chessboard context,” SJME (Supremum Journal of Mathematics Education), vol. 6, no. 2, pp. 162–170, Jul. 2022, doi: 10.35706/sjme.v6i2.5866.
M. Rizal, T. Y. E. Siswono, Nurdin, and T. Bitara, “Students’ Learning Trajectory in Solving Fraction Problems: Cases of Boy and Girl Students in Junior High School,” Studies in Learning and Teaching, vol. 4, no. 1, pp. 157–169, May 2023, doi: 10.46627/silet.v4i1.212.
R. Ramadhani, R. C. I. Prahmana, Soeharto, and A. Saleh, “Integrating traditional food and technology in statistical learning: A learning trajectory,” Journal on Mathematics Education, vol. 15, no. 4, pp. 1277–1310, Nov. 2024, doi: 10.22342/jme.v15i4.pp1277-1310.
L. Tarida, E. Anjarsari, B. Hasan, and F. E. Widayati, “How does student learn mathematics through traditional food? (a hypothetical learning trajectory),” Unnes Journal of Mathematics Education, vol. 12, no. 3, pp. 205–212, Oct. 2023, doi: 10.15294/ujme.v12i3.71337.
I. Adha, Zulkardi, R. I. I. Putri, and Somakim, “When designer meets local culture: The promising learning trajectory on the surface area of polyhedron,” Journal on Mathematics Education, vol. 15, no. 3, pp. 945–960, Sep. 2024, doi: 10.22342/jme.v15i3.pp945-960.
Sukasno, Zulkardi, R. I. I. Putri, and Somakim, “Learning fraction with vacation: Integrating Musi Rawas tourism in designing learning trajectory on fraction,” Journal on Mathematics Education, vol. 15, no. 4, pp. 1153–1174, Oct. 2024, doi: 10.22342/jme.v15i4.pp1153-1174.
Arthur. Bakker, Design research in statistics education : On symbolizing and computer tools = Ontwikkelingsonderzoek in het statistiekonderwijs : Over symboliseren en computertools. CD-ß, Center for Science and Mathematics Education, 2004.
S. Lerman, Encyclopedia of Mathematics Education. Cham: Springer International Publishing, 2020. doi: 10.1007/978-3-030-15789-0.
I. N. Ayuningtyas, M. F. Amir, and M. D. K. Wardana, “Elementary school students’ layers of understanding in solving literacy problems based on Sidoarjo context,” Infinity Journal, vol. 13, no. 1, pp. 157–174, Jan. 2024, doi: 10.22460/infinity.v13i1.p157-174.
M. Q. Patton, “Qualitative research and evaluation methods (3rd ed.),” Eval J Australas, vol. 3, no. 2, pp. 60–61, Dec. 2002, doi: 10.1177/1035719X0300300213.
M. B. Miles, A. M. Huberman, and J. Saldaña, Qualitative data analysis: A methods sourcebook, vol. 28, no. 4. 2014. doi: 10.1177/239700221402800402.
J. Saili, E. B. Samuel, and A. Mukuka, “Effect of visual-based instruction on elementary pre-service teachers’ conceptual understanding of fractions,” Journal of Mathematics and Science Teacher, vol. 3, no. 1, p. em030, Mar. 2023, doi: 10.29333/mathsciteacher/13063.
M. M. Flores, V. M. Hinton, and J. M. Meyer, “Teaching fraction concepts using the concrete-representational-abstract sequence,” Remedial and Special Education, vol. 41, no. 3, pp. 165–175, Jun. 2020, doi: 10.1177/0741932518795477.
K. Martin and J. H. Hunt, “Learning trajectory based fraction intervention: Building a mathematics education evidence base,” Investigations in Mathematics Learning, vol. 14, no. 3, pp. 235–249, Jul. 2022, doi: 10.1080/19477503.2022.2105028.
L. Hearne, “Investigating how learners use representations in understanding fractions-a semiotic perspective in a modelling classroom,” (Stellenbosch : Stellenbosch University, 2021-12), 2021, doi: https://scholar.sun.ac.za/items/67084bb0-6511-49db-8f0c-bc9b684e04a6.
P. L. Pedersen and M. Bjerre, “Two conceptions of fraction equivalence,” Educational Studies in Mathematics, vol. 107, no. 1, pp. 135–157, May 2021, doi: 10.1007/s10649-021-10030-7.
R. Rosmayasari, D. Suryadi, T. Herman, S. Prabawanto, and T. Tin Lam, “Students’ hypothetical learning trajectory (HLT) in learning fraction division calculation operations,” Dinamika Jurnal Ilmiah Pendidikan Dasar, vol. 14, no. 2, p. 158, Apr. 2023, doi: 10.30595/dinamika.v14i2.16819.
K. Amo-Asante and E. Bonyah, “Building students’ conceptual understanding of operations on fractions using manipulatives: A junior high school perspective,” Mediterranean Journal of Social & Behavioral Research, vol. 7, no. 3, pp. 151–159, Oct. 2023, doi: 10.30935/mjosbr/13381.
Z. Kohen and D. Orenstein, “Mathematical modeling of tech-related real-world problems for secondary school-level mathematics,” Educational Studies in Mathematics, vol. 107, no. 1, pp. 71–91, May 2021, doi: 10.1007/s10649-020-10020-1.
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