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Simulating the Movement of Planets in the Solar System Using a Linear System Nurul Fadhilah; Muarief, Muchammad; Aningtias, Rizka Fitri
International Journal of Technology and Modeling Vol. 2 No. 1 (2023)
Publisher : Etunas Sukses Sistem

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.63876/ijtm.v2i1.95

Abstract

This article discusses the simulation of planetary movements in the solar system using a linear system-based approach. Mathematical models of solar systems often involve non-linear differential equations, which include the complexity of gravitational interactions between planets and other celestial bodies. However, to simplify the calculation and analysis process, a linear approach can be used with certain assumptions. In this study, the motion of the planets is modeled using Newtonian mechanical principles adapted into a linear equation system. The simulation is carried out by utilizing numerical computing software to calculate the position and speed of the planet in a certain time span. The simulation results show that the linear system approach is able to represent the basic motion of the planet with an adequate degree of accuracy on short time scales, but it shows limitations in predicting complex dynamics, such as orbital resonance or the gravitational influence of small bodies. This approach is suitable for educational applications, where visualization of planetary movements can help understand the basic principles of orbital dynamics. These findings emphasize the importance of choosing the right simulation method according to the purpose, both for scientific and educational purposes. The study suggests the development of a hybrid model that combines a linear approach with non-linear elements to improve accuracy without losing computational efficiency.  
The Effect of Critical Thinking Skills and Mathematical Connection Skills on Students’ Ability To Solve Hots Problems Izzati, Nurma; Muarief, Muchammad
JPMI (Jurnal Pendidikan Matematika Indonesia) Vol 11, No 1 (2026): Volume 11 Number 1, March 2026
Publisher : STKIP Singkawang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26737/jpmi.v11i1.8505

Abstract

This study was conducted to explore the extent of the impact of students' critical thinking skills and mathematical connections in solving HOTS-type problems. Using a quantitative approach with a causal relationship model, this study took the subjects of grade VIII students at SMP Negeri 2 Sumber for the 2025/2026 school year period. From the total existing population, as many as 38 students were selected as a representative sample determined through the cluster random sampling method. All primary data were collected using a description test instrument that had passed validity and reliability tests to measure critical thinking competence, connection skills, and students' success in answering high-level questions. The data was then processed in depth through path analysis techniques with the help of SPSS 21 software.The main findings in this study reveal that critical thinking skills have a very strong direct influence on students' HOTS scores, which is evidenced by a beta value of 0.602 and a significance level of p < 0.001. However, quite contrasting results were found on the mathematical connection variable. This variable did not have a significant impact directly on students' ability to solve HOTS questions (beta = 0.115; p = 0.395). Furthermore, the results of the mediation test showed that no empirical evidence was found regarding the indirect influence of critical thinking on solving HOTS problems through the intermediary of mathematical connection ability. Simultaneously, the two independent variables tested in this model contributed 40.4% in explaining the variation in students' HOTS ability. This indicates that there are still around 59.6% of other factors outside of this study that also affect student achievement. In conclusion, these findings emphasize that the critical thinking factor is the most dominant and crucial element in supporting the success of junior high school students when facing complex mathematical problems.Pengaruh Kemampuan Berpikir Kritis dan Kemampuan Koneksi Matematis terhadap Kemampuan Siswa dalam Menyelesaikan Soal HOTSABSTRAKStudi ini dilakukan untuk mendalami sejauh mana dampak dari kecakapan berpikir kritis serta koneksi matematis siswa dalam menuntaskan soal-soal bertipe HOTS. Menggunakan pendekatan kuantitatif dengan model hubungan kausal, penelitian ini mengambil subjek siswa kelas VIII di SMP Negeri 2 Sumber untuk periode tahun ajaran 2025/2026. Dari total populasi yang ada, sebanyak 38 peserta didik terpilih sebagai sampel representatif yang ditentukan melalui metode cluster random sampling. Seluruh data primer dikumpulkan menggunakan instrumen tes uraian yang telah melewati uji validitas serta reliabilitas guna mengukur kompetensi berpikir kritis, kemampuan koneksi, dan keberhasilan siswa dalam menjawab soal-soal tingkat tinggi. Data tersebut kemudian diolah secara mendalam lewat teknik analisis jalur (path analysis) dengan bantuan perangkat lunak SPSS 21.Temuan utama dalam penelitian ini mengungkap bahwa kemampuan berpikir kritis memiliki pengaruh langsung yang sangat kuat terhadap perolehan skor HOTS siswa, yang dibuktikan dengan nilai beta sebesar 0,602 dan tingkat signifikansi p < 0,001. Namun, hasil yang cukup kontras ditemukan pada variabel koneksi matematis. Variabel tersebut justru tidak memberikan dampak signifikan secara langsung terhadap kemampuan siswa dalam menyelesaikan soal-soal HOTS (beta = 0,115; p = 0,395). Lebih lanjut, hasil uji mediasi menunjukkan bahwa tidak ditemukan bukti empiris mengenai adanya pengaruh tidak langsung antara berpikir kritis terhadap penyelesaian soal-soal HOTS melalui perantara kemampuan koneksi matematis.Secara simultan, kedua variabel independen yang diuji dalam model ini menyumbang andil sebesar 40,4% dalam menjelaskan variasi kemampuan HOTS peserta didik. Hal ini mengindikasikan bahwa masih terdapat sekitar 59,6% faktor lain di luar penelitian ini yang turut memengaruhi capaian siswa. Sebagai kesimpulan akhir, temuan ini mempertegas bahwa faktor berpikir kritis merupakan elemen yang paling dominan dan krusial dalam mendukung keberhasilan siswa tingkat menengah pertama saat menghadapi persoalan matematika yang kompleks.Kata Kunci:Kemampuan berpikir kritis matematis; kemampuan koneksi matematis; soal HOTS