Learning trajectory in mathematics education for geometry topic

Authors

  • Ika Muji Wahyuni Universitas Sebelas Maret
  • Mardiyana Mardiyana Universitas Sebelas Maret
  • Yuli Bangun Nursatin Universitas Sebelas Maret
  • Farida Nurhasanah Universitas Sebelas Maret

DOI:

https://doi.org/10.29407/jmen.v11i1.24268

Keywords:

learning trajectory, pembelajaran, matematika, geometri

Abstract

Penelitian ini bertujuan untuk mengkaji learning trajectory dalam pembelajaran matematika, khususnya pada materi geometri, menggunakan metode Systematic Literature Review (SLR) dengan analisis bibliometrik melalui perangkat Vosviewer. Learning trajectory merupakan pendekatan strategis yang memetakan langkah-langkah pembelajaran secara progresif untuk mencapai pemahaman konseptual yang lebih baik. Materi geometri dipilih karena sifatnya abstrak dan memerlukan representasi visual untuk memfasilitasi pemahaman peserta didik. Metode SLR digunakan untuk menganalisis tren penelitian, teori yang mendasari, serta implementasi learning trajectory pada pembelajaran geometri. Data diambil dari artikel jurnal terindeks dalam database seperti Google Scholar, Scopus, dan Web of Science. Analisis dengan Vosviewer digunakan untuk memvisualisasikan hubungan antara konsep, kata kunci, dan topik utama yang sering muncul. Hasil analisis menunjukkan bahwa learning trajectory berperan penting dalam mendukung pemahaman geometri melalui pendekatan berbasis visualisasi, manipulasi objek, dan diskusi kolaboratif. Temuan juga mengidentifikasi tiga tema utama: (1) desain learning trajectory berbasis masalah (problem-based learning), (2) pengintegrasian teknologi dalam pembelajaran geometri, dan (3) peran asesmen formatif dalam memvalidasi proses pembelajaran. Kesimpulan dari penelitian ini menegaskan bahwa penggunaan learning trajectory yang dirancang dengan cermat dapat meningkatkan efektivitas pembelajaran geometri. Penelitian ini diharapkan dapat memberikan kontribusi bagi pendidik dan peneliti untuk meningkatkan kualitas pembelajaran matematika melalui pendekatan yang lebih terstruktur dan berbasis data.

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References

Ali, S., DiPaola, D., Lee, I., Hong, J., & Breazeal, C. (2021, 2021). Exploring generative models with middle school students Conference on Human Factors in Computing Systems - Proceedings, https://doi.org/10.1145/3411764.3445226

Altche, F., & Fortelle, A. (2017, 2017). An LSTM network for highway trajectory prediction IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, https://doi.org/10.1109/ITSC.2017.8317913

Bu, X., Dai, X., & Hou, R. (2023). Data‐driven iterative learning trajectory tracking control for wheeled mobile robot under constraint of velocity saturation. IET Cyber‐Systems and Robotics.

Can, D. (2020). Supporting Learning Trajectories for the Development of Number Concept: Digital Games. Kuramsal Eğitimbilim, 13(4), 663–684. https://doi.org/10.30831/akukeg.692165

Clara, A., Brizuela, B. M., Blanton, M., Sawrey, K., Gardiner, A. M., & Newman-owens, A. (2021). A learning trajectory in Kindergarten and first grade students' thinking of variable and use of variable notation to represent indeterminate quantities.

Clements, D. H., & Sarama, J. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Lawrence Erlbaum Associates Publishers.

Domu, I., & Mangelep, N. O. (2020). The Development of Students' Learning Material on Arithmatic Sequence Using PMRI. Approach, 196(Ijcse), 426–432. https://doi.org/10.2991/aer.k.201124.076

Gallagher, M. A., Parsons, S. A., & Vaughn, M. (2022). Adaptive teaching in mathematics: a review of the literature. Educational Review, 74(2), 298–320. https://doi.org/10.1080/00131911.2020.1722065

Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. Educational Design Research.

Hendrik, A. I., Ekowati, C. K., & Samo, D. D. (2020). Kajian Hypothetical Learning Trajectories dalam Pembelajaran Matematika di Tingkat SMP. Fraktal: Jurnal Matematika Dan Pendidikan Matematika, 1(1), 1–11. https://doi.org/10.35508/fractal.v1i1.2683

Hmelo-Silver, C. E. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3

Lantakay, C. N., Senid, P. P., Blegur, I. K. S., & Samo, D. D. (2023). Hypothetical Learning Trajectory: Bagaimana Perannya dalam Pembelajaran Matematika di Sekolah Dasar? Griya Journal of Mathematics Education and Application, 3(2), 384–393. https://doi.org/10.29303/griya.v3i2.329

Lee, M. Y., & Lee, J. E. (2021). A learning trajectory as a scaffold for pre-service teachers' noticing of students' mathematical understanding. International Journal of Science and Mathematics Education, 19(3), 539–558. https://doi.org/10.1007/s10763-020-10062-0

Litkowski, E. C., Duncan, R. J., Logan, J. A. R., & Purpura, D. J. (2020). When do preschoolers learn specific mathematics skills? Mapping the development of early numeracy knowledge. Journal of Experimental Child Psychology, 195, 104846. https://doi.org/10.1016/j.jecp.2020.104846

Liu, C., Yang, H., Fu, J., & Qian, X. (2022, 2022). Learning Trajectory-Aware Transformer for Video Super-Resolution Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, https://doi.org/10.1109/CVPR52688.2022.00560

Morais, R., Le, V., Tran, T., Saha, B., Mansour, M., & Venkatesh, S. (2019, 2019). Learning regularity in skeleton trajectories for anomaly detection in videos Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, https://doi.org/10.1109/CVPR.2019.01227

Mousoulides, N., & Sriraman, B. (2020). Encyclopedia of Mathematics Education. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-94-007-4978-8

NCTM. (2000). Principles and standards for school mathematics. Author.

Nursyahidah, F., Saputro, B. A., Albab, I. U., & Aisyah, F. (2020). Pengembangan Learning Trajectory Based Instruction Materi Kerucut Menggunakan Konteks Megono Gunungan. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 47–58. https://doi.org/10.31980/mosharafa.v9i1.591

Pacchiano, A., Saha, A., & Lee, J. (2023). Dueling RL: Reinforcement Learning with Trajectory Preferences. Proceedings of Machine Learning Research, 206, 6263–6289.

Putri, N. S., Sridana, N., Junaidi, J., & Hikmah, N. (2023). Pengaruh Learning Trajectory Terhadap Hasil Belajar Matematika Siswa Kelas VII SMP Negeri 2 Sakra Tahun Ajaran 2021/2022. Jurnal Ilmiah Profesi Pendidikan, 8(1), 391–396. https://doi.org/10.29303/jipp.v8i1.1189

Rich, K. M., Binkowski, T. A., Strickland, C., & Franklin, D. (2018, 2018). Decomposition: A K-8 computational thinking learning trajectory ICER 2018 - Proceedings of the 2018 ACM Conference on International Computing Education Research, https://doi.org/10.1145/3230977.3230979

Rokhmawati, L. N., Ratnaningsih, N., & Ni'mah, K. (2023). ATURAN PENJUMLAHAN DAN PERKALIAN DALAM KAIDAH PENCACAHAN. BAGAIMANAKAH DESAIN HYPOTHETICAL LEARNING TRAJECTORY BERBASIS RME? JPMI (Jurnal Pembelajaran Matematika Inovatif, 6(3), 937–950. https://doi.org/10.22460/jpmi.v6i3.17321

Sari, D. L., Fitriani, D. A., Khaeriyah, D. Z., Hartono, & Nursyahidah, F. (2022). Hypothetical Learning Trajectory pada Materi Peluang: Konteks Mainan Tradisional Ular Naga. Mosharafa: Jurnal Pendidikan Matematika, 11(2), 203–214. https://doi.org/10.31980/mosharafa.v11i2.699

Schult, J., Mahler, N., Fauth, B., & Lindner, M. A. (2022). Did students learn less during the COVID-19 pandemic? Reading and mathematics competencies before and after the first pandemic wave. School Effectiveness and School Improvement, 33(4), 544-563. https://doi.org/10.1080/09243453.2022.2061014

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205

Towe, M. M., & Julie, H. (2020). Developing learning trajectories with the RME of phytagorean theorem. Journal of Physics: Conference Series, 1470(1). https://doi.org/10.1088/1742-6596/1470/1/012027

Wandanu, R. H., Mujib, A., & Firmansyah. (2020). Hypothetical Learning Trajectory berbasis Pendidikan Matematika Realistik untuk Mengembangkan Kemampuan Pemecahan Masalah Matematis Siswa. Jurnal MathEducation Nusantara, 3(2), 8–16.

Wang, L., Wang, K., Pan, C., Xu, W., Aslam, N., & Hanzo, L. (2021). Multi-Agent Deep Reinforcement Learning-Based Trajectory Planning for Multi-UAV Assisted Mobile Edge Computing. IEEE Transactions on Cognitive Communications and Networking, 7(1), 73–84. https://doi.org/10.1109/TCCN.2020.3027695

Wang, S., Bao, Z., Culpepper, J. S., & Cong, G. (2021). A Survey on Trajectory Data Management, Analytics, and Learning. ACM Computing Surveys, 54(2), 1–36. https://doi.org/10.1145/3440207

Wu, H., Lyu, F., Zhou, C., Chen, J., Wang, L., & Shen, X. (2020). Optimal UAV Caching and Trajectory in Aerial-Assisted Vehicular Networks: A Learning-Based Approach. IEEE Journal on Selected Areas in Communications, 38(12), 2783–2797. https://doi.org/10.1109/JSAC.2020.3005469

Yao, Z., Yu, J., & Ding, J. (2021). Contrastive learning of graph encoder for accelerating pedestrian trajectory prediction training. IET Image Processing, 15(14), 3645–3660. https://doi.org/10.1049/ipr2.12185

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Published

2025-05-31

How to Cite

Wahyuni, I. M. ., Mardiyana, M., Nursatin, Y. B. ., & Nurhasanah, F. . (2025). Learning trajectory in mathematics education for geometry topic. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 11(1), 147-159. https://doi.org/10.29407/jmen.v11i1.24268

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