Hypothetical Learning Trajectory Based on Realistic Mathematics Education in SPLDV Material: Implementation to Accommodate Differences in Junior High School Students' Initial Abilities
Abstract
This study stems from the challenge of understanding the concept of SPLDV, which is generally still procedural and lacks meaning, as well as the diversity of students' initial abilities that influence their thinking processes and problem-solving strategies. The research method used was qualitative descriptive within the framework of Didactical Design Research (DDR) at SMP Muhammadiyah 5 Surakarta with three ninth-grade students representing high, medium, and low initial abilities as subjects. Data were collected through SPLDV concept comprehension tests and in-depth interviews. The results showed that the application of RME-based HLT helped students understand concepts gradually, starting from real contexts, situational models, mathematical models, to formal representations. Students with high initial abilities were able to fulfill all of Polya's problem-solving indicators, including the evaluation stage. Students with medium initial abilities were able to understand the problem and develop a plan but were not consistent in evaluating the results. Meanwhile, students with low initial abilities were only able to identify basic information without being able to model or implement a solution strategy. Overall, RME-based HLT proved to be effective in facilitating differences in students' initial abilities and improving their understanding of SPLDV concepts through a structured and contextual learning path.
References
Agusta, E. S. (2020). Peningkatan Kemampuan Matematis Siswa Melalui Pendekatan Pendidikan Matematika Realistik. ALGORITMA: Journal of Mathematics Education, 2(2), 145–165. https://doi.org/10.15408/ajme.v2i2.17819
Astuti, W., & Wijaya, A. (2021). Learning trajectory berbasis proyek pada materi definisi himpunan. Jurnal Riset Pendidikan Matematika, 7(2), 254–266. https://doi.org/10.21831/jrpm.v7i2.16483
Benu, R. S. M., Nifu, A. B., & Ndolu, S. W. (2024). Analisis Hypothetical Learning Trajectory (HLT) Pada Mata Kuliah Pembelajaran Matematika SD Mahasiswa PGSD. DIKDAS MATAPPA: Jurnal Ilmu Pendidikan Dasar, 7(3), 454–464.
Daulay, L. A., Yustinaningrum, B., Pasaribu, F. T., Manurung, S. L., & Putri, E. (2025). Development of a Module with a RME Approach on the Topic Systems of Linear Equations in Two Variables. Al-Ta Lim Journal, 32(2), 162–171. https://doi.org/10.15548/jt.v32i2.986
Diaz, M. E., & Marlina, R. (2024). SMP PADA MATERI SISTEM PERSAMAAN LINEAR DUA VARIABEL ( SPLDV ). 10(1), 112–118.
Harahap, H. M., & Lubis, R. (2019). Efetivitas pendekatan pembelajaran matematika realistik (PMR) terhadap kemampuan pemecahan masalah matematis siswa SMP Negeri 7 Padangsidimpuan. Jurnal MathEdu (Mathematic Education Journal), 2(2), 105–113. https://doi.org/10.58230/27454312.698
Haryaty, N., & Anggo, M. (2019). Analisis Metakognisi Siswa dalam Memahami Konsep Sistem Persamaan Linear Dua Variabel Ditinjau Dari Kemampuan Awal Siswa. Jurnal Pembelajaran Berpikir Matematika, 4(1), 57–66.
Herawati, E. D., & Sopiany, H. N. (2023). Analisis Hypothetical Learning Trajectory Siswa SMK Pada Materi SPLDV Ditinjau dari Mathematic Anxiety. Seminar Nasional Matematika Dan Pendidikan Matematika (Sesiomadika) 2023, 6379, 631–642.
Hidayati, I., Deciku, B., & Azizah, T. (2022). Hypothetical Learning Trajectory Sistem Persamaan Linear Dua Variabel Berbasis Realistic Mathematics Education. Juring (Journal for Research in Mathematics Learning), 5(2), 109–118.
Indriyani Fitri Hidayat, E., Asih Vivi Yandhari, I., & Pamungkas Alamsyah, T. (2020). Efektivitas Pendekatan Realistic Mathematics Education(RME) Untuk Meningkatkan Kemampuan PemahamanKonsep Matematika Siswa Kelas V. Jurnal Ilmiah Sekolah Dasar, 4(1), 106–113. ttps://ejournal.undiksha.ac.id/index.php/JISD/index
Maftuh, M. S., & Yustitia, V. (2021). Pendekatan Realistic Mathematics Education Pada Materi Bentuk Aljabar. Inomatika, 3(1), 16–26. https://doi.org/10.35438/inomatika.v3i1.239
Marselina, S., & Roesdiana, L. (2019). Analisis Kemampuan Pemecahan Masalah Matematis Siswa SMP pada Materi SPLDV Ditinjau dari Kemampuan Awal Matematika. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 3(2), 207. https://doi.org/10.31331/medivesveteran.v3i2.771
Maspupah, A., & Purnama, A. (2020). Analisis Kesulitan Siswa MTs Kelas VIII Dalam Menyelesaikan Soal Cerita Sistem Persamaan Linear Dua Variabel (SPLDV) Ditinjau Dari Perbedaan Gender. Jurnal Cendekia : Jurnal Pendidikan Matematika, 4(1), 237–246. https://doi.org/10.31004/cendekia.v4i1.193
Nuraida, I., & Amam, A. (2019). Hypothetical Learning Trajectory in Realistic Mathematics Education To Improve the Mathematical Communication of Junior High School Students. Infinity Journal, 8(2), 247–258. https://doi.org/10.22460/infinity.v8i2.p247-258
Oktoviani, V., Widoyani, W. L., & Ferdianto, F. (2019). Analisis Kemampuan Pemahaman Matematis Siswa SMP pada Materi Sistem Persamaan Linear Dua Variabel. Edumatica: Jurnal Pendidikan Matematika, 09(April), 39–45.
Palinussa, A. L., & Tamalene, H. (2021). PERBEDAAN HASIL BELAJAR MATEMATIKA MATERI SPLDV PADA SISWA SMP DI KOTA AMBON. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(2), 951–963.
Pebrianti, W., & Puspitasari, N. (2023). Kemampuan Pemahaman Konsep pada Materi Sistem Persamaan Linear Dua Variabel Ditinjau dari Perbedaan Gender Siswa SMP Kelas VIII. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 2(1), 55–70. https://doi.org/10.31980/powermathedu.v2i1.2733
Sari, P. P., & Lestari, D. A. (2020). ANALISIS KESULITAN SISWA SMP DALAM MENYELESAIKAN SOAL CERITA PADA MATERI SISTEM PERSAMAAN LINEAR DUA. Jurnal Cendekia: Jurnal Pendidikan Matematika, 04(01), 286–293.
Sektiwulan, A., Kirana, A., Ningrum, P., & Rohman, W. (2024). Pengembangan Modul Matematika Berbasis RME Bermuatan Soal HOTS untuk Siswa SMP. 6(2), 1359–1368.
Suryadi, D. (2010). Penelitian Pembelajaran Matematika Untuk Pembentukan Karakter Bangsa. Seminar Nasional Matematika Dan Pendidikan Matematika, November, 1–14.
Susanti, Y., Friansah, D., S, A. E., Studi, P., Matematika, P., & Pgri, S. (2020). PENGEMBANGAN MEDIA PEMBELAJARAN BERBASIS REALISTIC MATHEMATICS EDUCATION MENGGUNAKAN APLIKASI MACROMEDIA FLASH PADA MATERI SPLDV. Indiktika : Jurnal Inovasi Pendidikan Matematika, 3(1), 60–70.
Umam, M. A., & Zulkarnaen, R. (2022). Analisis Kemampuan Pemahaman Konsep Matematis Siswa Dalam Materi Sistem Persamaan Linear Dua Variabel. Jurnal Educatio FKIP UNMA, 8(1), 303–312. https://doi.org/10.31949/educatio.v8i1.1993
Utami, A. J. L., & Kusumah, Y. S. (2023). ANALISIS KEMAMPUAN PEMAHAMAN KONSEP MATEMATIS PADA MATERI SISTEM PERSAMAAN LINEAR DUA VARIABEL. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1385–1392. https://doi.org/https://doi.org/10.24127/ajpm.v12i1.6985
Utami, M. R. P., Zulkardi, Susanti, E., & Meryansumayeka. (2024). Desain Pembelajaran Materi Sistem Persamaan Linear Dua Variabel dengan Konteks Wisata Jakabaring Palembang Designing Learning Materials for Systems of Linear Equations in Two Variables in the Context of Jakabaring Tourism in Palembang. Edumatica:JurnalPendidikanMatematika, 14(03), 243–258.
