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All Journal Saintifik : Jurnal Matematika, Sains, dan Pembelajarannya Transformasi : Jurnal Pendidikan Matematika dan Matematika
Adhi Surya Nugraha
Program Studi Pendidikan Matematika, Universitas Sanata Dharma
Education Mathematics Physics Other

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ANALISIS KEMAMPUAN SPATIAL REASONING, VISUALISASI, DAN REPRESENTASI MATEMATIS PADA PENYELESAIAN SOAL GEOMETRI RUANG Adhi Surya Nugraha
TRANSFORMASI Vol 10 No 1 (2026): TRANSFORMASI: Jurnal Pendidikan Matematika dan Matematika
Publisher : Program Studi Pendidikan Matematika FMIPA Universitas PGRI Banyuwangi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36526/tr.v10i1.7674

Abstract

This study aims to describe the spatial reasoning, visualization, and mathematical representation abilities of Mathematics Education students in solving two spatial geometry problems. The study used a mix method with a descriptive approach. The subjects were 19 students from the class of 2025. Data collection was carried out by a test using two questions. The first question relates to determining the shortest path on the surface of a cube through unfolding, while the second question relates to determining the distance from a point to a plane on the cube. Subjects’ answers were categorized into four quality levels: category A (correct and complete answer), B (initial model is correct but incomplete), C (major strategy or representation error), and D (strategy cannot be operationally formalized). The data show that 9 subjects fell into category B, 9 subjects fell into category C, and 1 subject fell into category D. In the first question, the average subject had a moderate level of spatial reasoning and representation, with visualizations already quite apparent. Subjects tended to be able to construct mathematical visualizations and representations, although some had not yet provided a complete minimum justification. In the second question, the average subject had a low level of spatial reasoning and representation, with visualizations beginning to appear but lacking operational capabilities. Subjects experienced more fundamental difficulties, particularly in constructing planes, determining relevant distances, and formalizing relationships between lines. These results point to the need to emphasize representation translation, mathematical modeling, and argument validation in geometry learning.
Analisis RK4, Improved Euler, Adams-Bashforth dan ode45 pada Fase Jatuh Bebas Bungee Jumping menggunakan MATLAB Adhi Surya Nugraha
Saintifik: Jurnal Matematika, Sains, dan Pembelajarannya Vol 12 No 2 (2026): Saintifik: Jurnal Matematika, Sains, dan Pembelajarannya
Publisher : Universitas Sulawesi Barat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31605/saintifik.v12i2.675

Abstract

Fase awal bungee jumping dapat dimodelkan sebagai gerak jatuh dengan hambatan udara kuadratik. Model tersebut digunakan untuk membandingkan Runge-Kutta orde empat (RK4), Improved Euler, Adams-Bashforth orde empat, dan solver adaptif RK45 (ode45). Persamaan geraknya diturunkan dari Hukum II Newton dan memiliki solusi analitik, sehingga galat numerik dapat dihitung secara langsung. Simulasi memakai massa 68,1 kg, percepatan gravitasi 9,81 m/s², koefisien hambat 0,25 kg/m, dan interval waktu 0-10 detik. Tiga metode langkah tetap diuji pada h = 0,5, 1, dan 2 detik. Ode45 dijalankan dengan RelTol 10⁻¹⁰ dan AbsTol 10⁻¹². Pada kelompok langkah tetap, RK4 memberi galat terkecil dan orde konvergensi empiris yang mendekati empat. Adams-Bashforth masih kompetitif pada langkah kecil, tetapi galatnya bertambah lebih cepat ketika h diperbesar. Improved Euler menghasilkan galat terbesar dan menunjukkan orde empiris mendekati dua. Ode45 memberikan galat paling kecil karena langkah internalnya diatur secara adaptif. Hasil ini memperlihatkan bahwa pilihan metode perlu mempertimbangkan akurasi, ukuran langkah, dan cara solver mengendalikan galat.
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