Learning Trajectories of Different Denominator Fractions with Ote-ote

Authors

DOI:

https://doi.org/10.31980/mosharafa.v13i4.2506

Keywords:

different denominator fractions, hypothetical learning trajectories, ote-ote

Abstract

Abstrak

Pecahan berpenyebut berbeda adalah subtopik pecahan yang sangat berkontribusi dalam menjelaskan konsep dasar pecahan. Namun, bagi siswa sekolah dasar menantang karena didasarkan dari konsep yang membutuhkan representasi beragam. Penelitian ini bertujuan untuk mengembangkan learning trajectories (LT) pada pecahan berpenyebut berbeda dengan konteks Ote-ote.  Ote-ote merupakan makanan khas Jawa Timur yang berbentuk mirip dengan lingkaran. Partisipan penelitian ini adalah 26 siswa kelas 5 Sekolah Dasar Negeri Jimbaran Wetan, Sidoarjo. Desain penelitian yang digunakan adalah desain research dengan tahapan: preparation, implementation, dan retropective analysis. Data dikumpulkan melalui lembar kerja siswa, observasi, dan tes. Teknis analisis data menggunakan triangulasi sumber. LT yang dikembangkan terdiri dari empat aktivitas, yaitu: (1) pengenalan pecahan, (2) penjumlahan pecahan berpenyebut sama (3) pecahan senilai, dan (4) penjumlahan pecahan berpenyebut berbeda. Aktivitas LT membangun pemahaman siswa mengenai pecahan berpenyebut berbeda, umumnya dalam kategori memuaskan.

Abstract

Different denominator fractions is a 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 a 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 a 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.

Author Biography

Fitria Wulandari, Universitas Muhammadiyah Sidoarjo

https://scholar.google.com/citations?user=B1ge01AAAAAJ&hl=id&oi=ao

References

Adelia, V., Putri, R. I. I., Zulkardi, Z., & Mulyono, B. (2022). Learning trajectory for equivalent fraction learning: An insight. Journal of Honai Math, 5(1), 47–60. https://doi.org/10.30862/jhm.v5i1.233

Afriansyah, E. A., & Turmudi, T. (2022). Prospective teachers’ thinking through realistic mathematics education based emergent modeling in fractions. Jurnal Elemen, 8(2), 605-618. https://doi.org/10.29408/jel.v8i2.5712

Adha, I., Zulkardi, Putri, R. I. I., & Somakim. (2024). When designer meets local culture: The promising learning trajectory on the surface area of polyhedron. Journal on Mathematics Education, 15(3), 945–960. https://doi.org/10.22342/jme.v15i3.pp945-960

Amo-Asante, K., & Bonyah, E. (2023). Building students’ conceptual understanding of operations on fractions using manipulatives: A junior high school perspective. Mediterranean Journal of Social & Behavioral Research, 7(3), 151–159. https://doi.org/10.30935/mjosbr/13381

Amuah, E., & Davis, E. K. (2023). 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, 27(2), 123–136. https://doi.org/10.1080/18117295.2023.2226546

Ayuningtyas, I. N., Amir, M. F., & Wardana, M. D. K. (2024). Elementary school students’ layers of understanding in solving literacy problems based on Sidoarjo context. Infinity Journal, 13(1), 157–174. https://doi.org/10.22460/infinity.v13i1.p157-174

Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts (4th ed.). Academic Press. https://doi.org/https://experts.umn.edu/en/publications/rational-number-concepts

Cabuquin, J., & Abocejo, F. (2024). Conceptual and procedural understanding in the division of algebraic fractions. Recoletos Multidisciplinary Research Journal, 12(1), 225–240. https://doi.org/10.32871/rmrj2412.01.17

Clements, D. H. (2014). Learning and Teaching Early Math. Routledge. https://doi.org/10.4324/9780203520574

Clements, D. H., & Sarama, J. (2020). Learning and teaching early math. In Learning and Teaching Early Math. Routledge. https://doi.org/10.4324/9781003083528

Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: Results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107(3), 525–545. https://doi.org/10.1007/s10649-021-10033-4

Febriani, R., Susanti, E., & Hapizah, H. (2023). Learning trajectory in the material of comparing and ordering fractions using paper folding for elementary school students. Al-Jabar : Jurnal Pendidikan Matematika, 14(2), 353. https://doi.org/10.24042/ajpm.v14i2.18046

Flores, M. M., Hinton, V. M., & Meyer, J. M. (2020). Teaching fraction concepts using the concrete-representational-abstract sequence. Remedial and Special Education, 41(3), 165–175. https://doi.org/10.1177/0741932518795477

Fuller, R. A. (1997). Elementary teachers’ pedagogical content knowledge of mathematics. Mid- Western Educational Researcher: https://scholarworks.bgsu.edu/mwer/vol10/iss2/3

Hearne, L. (2021). Investigating how learners use representations in understanding fractions-a semiotic perspective in a modelling classroom. (Stellenbosch : Stellenbosch University, 2021-12). https://doi.org/https://scholar.sun.ac.za/items/67084bb0-6511-49db-8f0c-bc9b684e04a6

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

Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology, 62, 101896. https://doi.org/10.1016/j.cedpsych.2020.101896

Kohen, Z., & Orenstein, D. (2021). Mathematical modeling of tech-related real-world problems for secondary school-level mathematics. Educational Studies in Mathematics, 107(1), 71–91. https://doi.org/10.1007/s10649-020-10020-1

Lerman, S. (2020). Encyclopedia of Mathematics Education (S. Lerman, Ed.). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0

Magfirotin, E. S., & Amir, M. F. (2024). Elementary School Students’ Conceptual and Procedural Knowledge in Solving Fraction Problems. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(1), 109–122. https://doi.org/10.15294/0m58xs24

Martin, K., & Hunt, J. H. (2022). Learning trajectory based fraction intervention: Building a mathematics education evidence base. Investigations in Mathematics Learning, 14(3), 235–249. https://doi.org/10.1080/19477503.2022.2105028

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook. In German Journal of Human Resource Management: Zeitschrift für Personalforschung (Vol. 28, Issue 4). https://doi.org/10.1177/239700221402800402

Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Evaluation Journal of Australasia, 3(2), 60–61. https://doi.org/10.1177/1035719X0300300213

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

Pramudiani, P., Herman, T., Turmudi, Dolk, M., & Doorman, M. (2022). How does a missing part become important for primary school students in understanding fractions? Journal on Mathematics Education, 13(4), 565–586. https://doi.org/10.22342/jme.v13i4.pp565-586

Ramadhan, M. H., Zulkardi, Z., & Putri, R. I. I. (2022). Designing learning trajectory for teaching fractions using pmri approach with a chessboard context. SJME (Supremum Journal of Mathematics Education), 6(2), 162–170. https://doi.org/10.35706/sjme.v6i2.5866

Ramadhani, R., Prahmana, R. C. I., Soeharto, & Saleh, A. (2024). Integrating traditional food and technology in statistical learning: A learning trajectory. Journal on Mathematics Education, 15(4), 1277–1310. https://doi.org/10.22342/jme.v15i4.pp1277-1310

Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students? Learning and Instruction, 65, 101264. https://doi.org/10.1016/j.learninstruc.2019.101264

Rizal, M., Siswono, T. Y. E., Nurdin, & Bitara, T. (2023). Students’ Learning Trajectory in Solving Fraction Problems: Cases of Boy and Girl Students in Junior High School. Studies in Learning and Teaching, 4(1), 157–169. https://doi.org/10.46627/silet.v4i1.212

Rosmayasari, R., Suryadi, D., Herman, T., Prabawanto, S., & Tin Lam, T. (2023). Students’ hypothetical learning trajectory (HLT) in learning fraction division calculation operations. Dinamika Jurnal Ilmiah Pendidikan Dasar, 14(2), 158. https://doi.org/10.30595/dinamika.v14i2.16819

Saili, J., Samuel, E. B., & Mukuka, A. (2023). Effect of visual-based instruction on elementary pre-service teachers’ conceptual understanding of fractions. Journal of Mathematics and Science Teacher, 3(1), em030. https://doi.org/10.29333/mathsciteacher/13063

Salsabila, I., Amir, M. F., & Wardana, M. D. K. (2022). A learning trajectory of integer addition and subtraction using the kempreng game context. Jurnal Elemen, 8(2), 556–571. https://doi.org/10.29408/jel.v8i2.5541

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Source: Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/https://doi.org/10.5951/jresematheduc.26.2.0114

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

Tarida, L., Anjarsari, E., Hasan, B., & Widayati, F. E. (2023). How does student learn mathematics through traditional food? (a hypothetical learning trajectory). Unnes Journal of Mathematics Education, 12(3), 205–212. https://doi.org/10.15294/ujme.v12i3.71337

Torres-Peña, R. C., Peña-González, D., & Ariza, E. A. (2024). Enhancing fraction learning through problem-solving and historical context: A didactic unit approach. Journal on Mathematics Education, 15(3), 815–834. https://doi.org/10.22342/jme.v15i3.pp815-834

Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.54870/1551-3440.1317

Wulandari, D., & Amir, M. F. (2022). Analysis of elementary school students’ difficulties in fraction addition. K R E A N O Creative-Innovative Mathematics (Education) Journal. https://doi.org/https://doi.org/10.15294/kreano.v13i1.35275

Downloads

Published

2024-10-30

How to Cite

Ainin, N. A. K., Amir, M. F., & Wulandari, F. (2024). Learning Trajectories of Different Denominator Fractions with Ote-ote. Mosharafa: Jurnal Pendidikan Matematika, 13(4), 1003–1018. https://doi.org/10.31980/mosharafa.v13i4.2506

Issue

Section

Articles

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.