Electronic Theses and Dissertation
Universitas Syiah Kuala
DISSERTATION
MODEL MATEMATIKA PERILAKU BELAJAR SISWA
Pengarang
Mutiawati - Personal Name;
Dosen Pembimbing
Marwan - 197111251999031003 - Dosen Pembimbing I
Rahmah Johar - 197011171998032002 - Dosen Pembimbing II
Mailizar - 198105252006041002 - Dosen Pembimbing III
Yusrizal - 195212311982031020 - Penguji
Salmawaty - 196110091991022001 - Penguji
Nomor Pokok Mahasiswa
1909300070022
Fakultas & Prodi
Fakultas Pasca Sarjana / Doktor Matematika dan Aplikasi Sains (S3) / PDDIKTI : 44001
Subject
Kata Kunci
Penerbit
Banda Aceh : Fakultas Pasca Sarjana., 2023
Bahasa
No Classification
-
Literature Searching Service
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RINGKASAN
Perilaku belajar dapat didefinisikan sebagai bentuk kesiapan mental yang dimiliki oleh siswa dalam mengadopsi bentuk dan metode pembelajaran baik secara teoritis maupun praktis berupa kecakapan, keaktifan, kreativitas, motivasi belajar yang dikembangkan secara stabil baik di dalam kelas maupun melalui interaksi sosial siswa di luar kelas. Hasil kajian systematic literature review dari 10 database elektronik terhadap 504 artikel diketahui bahwa perilaku belajar siswa dipengaruhi oleh 19 faktor seperti motivasi belajar, sikap terhadap pembelajaran, fleksibilitas strategi pembelajaran, kesempatan belajar, hambatan perubahan siswa, gaya belajar, pembelajaran mandiri, kemampuan akademik, latar belakang pendidikan, umur, intervensi negatif, kontrol perilaku, emosi, keadaan internal siswa, paparan lingkungan digital, lingkungan belajar, keterlibatan dalam pembelajaran, ketekunan, dan efikasi diri.
Intervensi untuk dapat menilai perilaku belajar siswa membutuhkan alat ukur yang valid. Validitas isi diuji menggunakan Aiken Index [V], dilanjutkan dengan analisis konstruk dengan uji Exploratory Factor Analysis (EFA) dan Confirmatory Factor Analysis (CFA). Hasil validasi isi diperoleh nilai rata-rata validitas Necessity of Items (CVR) = 0,803, Relevancy of Items (S-CVI) = 0,824, dan Clarity of Items (I-CVIs) =0,826. Hasil uji EFA mengungkapkan KMO masing-masing 0,805, 0,789, dan 0,759. Hasil akhir uji CFA menghasilkan 48 item yang valid dan menunjukkan model yang fit. Sub skala A berupa perilaku belajar di dalam kelas terdiri dari 17 item (RMSEA = 0.062; GFI= 0.922; CFI=0.953; NFI=0.919; dan TLI=0.939). Subskala B terdapat 19 item terkait motivasi belajar siswa (RMSEA = 0,037; GFI= 0,940; CFI=0,971; NFI=0,911; dan TLI=0,964) dan subskala C terkait interaksi sosial siswa di luar kelas terdapat 12 item (RMSEA = 0,035; GFI= 0,967; CFI=0,987; dan TLI=0,983). Hasil uji reliabilitas menunjukkan nilai Cronbach's Alpha masing-masing sebesar 0,851 (baik), 0,723 (dapat diterima), dan 0,685 (sedang).
Model dibangun melalui analogi penyebaran perilaku belajar dengan penularan penyakit menular yaitu dengan model Susceptible-Exposed-Infectious-Recovered (SEIR). Pembentukan model matematika dilakukan dalam dua bentuk model yaitu model 1 berupa model matematika yang menggambarkan perilaku belajar siswa secara umum dan model 2 berupa model matematika yang menunjukkan perilaku belajar siswa Boarding School dan Non-Boarding School. Pada pemodelan 1, populasi siswa dibagi kedalam enam kompartemen, sedangkan pada pemodelan 2 populasi siswa dibagi ke dalam delapan kompartemen. Pembentukan model matematika perilaku belajar digunakan model persamaan differensial biasa tidak linear, dengan ketentuan jika R_01 maka perilaku menyimpang sangat mungkin untuk mempengaruhi populasi. Analisis kestabilan ditentukan berdasarkan nilai eigen dari Matriks Jacobian. Hasil pengujian didapat titik ekuilibrium bebas perilaku menyimpang E_1 merupakan stabil asimtotik lokal.
Hasil model simulasi model 1 menunjukkan bahwa puncak kerentanan pada kelompok siswa yang tidak berinteraksi sosial di luar kelas meningkat pesat pada dua hari pertama dan mulai stabil ketika melewati hari ke-150. Berbeda dengan kelompok siswa rentan yang berinteraksi sosial di luar kelas mengalami peningkatan setelah melewati hari ke-1 dan mulai stabil setelah hari ke-250. Selain itu, nilai T_i kasus penambahan siswa terpengaruh perilaku menyimpang di SMP N 6 Banda Aceh turun menjadi 0 pada hari ke-21, sedangkan di SMP N 19 Percontohan Banda Aceh turun menjadi 0 pada hari ke-25. Hasil simulasi model menyimpulkan bahwa penyebaran perilaku belajar menyimpang yang terjadi di SMP SMP N 19 Percontohan Banda Aceh lebih lambat dan lebih tahan lama. Sebaran perilaku belajar siswa di SMP N 6 Banda Aceh stabil pada hari ke-198, sedangkan di SMP N 19 Percontohan Banda Aceh stabil pada hari ke-201.
Hasil simulasi model 2 model matematika matematika perilaku belajar antara SMP Boarding School dan SMP Non-Boarding School diketahui perubahan perilaku belajar siswa rentan dari kedua sekolah tersebut dimulai pada hari pertama pengecekan simulasi dan mencapai titik 0 pada hari ke-120. Kondisi awal simulasi dipketahui bahwa siswa yang terpengaruh perilaku belajar menyimpang di SMP Boarding lebih sedikit dibandingkan dengan SMP Non-Boarding School. Namun, kondisi akhir siswa terpengaruh perilaku belajar menyimpang di di SMP Boarding School lebih banyak dibandingkan dengan siswa di SMP Non-Boarding School. Pada saat simulasi terlihat bahwa pergerakan grafik pada SMP Boarding School mengalami peningkatan lebih lambat. Hal inilai yang menyebabkan penyebaran perilaku belajar menyimpang yang terjadi di SMP Boarding School lebih stabil dibandingkan dengan SMP Non-Boarding School.
Kata Kunci: Perilaku Belajar, SEIR, Motivasi Belajar dan Interaksi Sosial
SUMMARY Learning behavior can be interpreted as a form of mental readiness possessed by students in adopting learning forms and methods both theoretically and practically in the form of skills, activeness, creativity, and learning motivation which are developed stably both in the classroom and through students' social interactions outside the classroom. The results of a systematic literature review of 10 electronic databases on 504 articles found that student learning behavior is influenced by 19 factors such as learning motivation, attitudes towards learning, the flexibility of learning strategies, learning opportunities, barriers to student change, learning styles, independent learning, academic ability, background educational background, age, negative intervention, behavior control, emotion, student's internal state, exposure to the digital environment, learning environment, involvement in learning, effort, and self-efficacy. Interventions to be able to assess student learning behavior require a valid measurement tool. Content validity was tested using the Aiken Index [V], followed by construct analysis using Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) tests. The results of content validation obtained an average validity value of Necessity of Items (CVR) = 0.803, Relevancy of Items (S-CVI) = 0.824, and Clarity of Items (I-CVIs) = 0.826. The EFA test results revealed a KMO of 0.805, 0.789, and 0.759 respectively. The final results of the CFA test produced 48 valid items and showed a fit model. The A sub-scale in the form of learning behavior in the classroom consists of 17 items (RMSEA = 0.062; GFI = 0.922; CFI = 0.953; NFI = 0.919; and TLI = 0.939). In the B subscale, there are 19 items related to student learning motivation (RMSEA = 0.037; GFI = 0.940; CFI = 0.971; NFI = 0.911; and TLI = 0.964) and in the C subscale related to students' social interactions outside the classroom, there are 12 items (RMSEA = 0.035; GFI = 0.967; CFI = 0.987; and TLI = 0.983). The results of the reliability test showed Cronbach's Alpha values of 0.851 (good), 0.723 (acceptable), and 0.685 (moderate) respectively. The model was built through the analogy of the spread of learning behavior with the transmission of infectious diseases, namely the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The formation of the mathematical model is carried out in two forms, namely model 1 in the form of a mathematical model that describes student learning behavior in general, and model 2 in the form of a mathematical model that shows the learning behavior of students in Boarding Schools and Non-Boarding Schools. In model 1, the student population is divided into six compartments, while in model 2 the student population is divided into eight compartments. The formation of a mathematical model of learning behavior uses a non-linear ordinary differential equation model, with the condition that if R_01 then the deviant behavior is very likely to affect the population. The stability analysis is determined based on the eigenvalues of the Jacobian Matrix. The test results show that the deviant behavior-free equilibrium point E_1 is locally asymptotically stable. The results of the model 1 simulation show that the peak of vulnerability in groups of students who do not interact socially outside the classroom increases rapidly in the first two days and begins to stabilize when it passes the 150th day. In contrast to the group of vulnerable students who interact socially outside the classroom, it has increased after the 1st day and begins to stabilize after the 250th day. In addition, the T_i value for the case of additional students affected by deviant behavior at SMP N 6 Banda Aceh fell to 0 on the 21st day, while at SMP N 19 Pilot Banda Aceh it fell to 0 on the 25th day. The results of the model simulation concluded that the spread of deviant learning behaviors that occurred in the Banda Aceh Pilot SMP N 19 was slower and more durable. The distribution of student learning behavior at SMP N 6 Banda Aceh was stable on day 198, while at SMP N 19 Pilot Banda Aceh it was stable on day 201. The simulation results of model 2 of the mathematical model of learning behavior between SMP Boarding Schools and SMP Non-Boarding Schools show that changes in the learning behavior of vulnerable students from the two schools started on the first day of checking the simulation and reached point 0 on the 120th day. The initial condition of the simulation is that it is known that fewer students are affected by deviant learning behavior at boarding schools than at non-boarding schools. However, the final condition of students affected by deviant learning behavior at boarding school junior high schools was more than students at non-boarding school junior high schools. At the time of the simulation, it can be seen that the graphical movement at the SMP Boarding School has increased more slowly. This is what causes the spread of deviant learning behavior that occurs in boarding school junior high schools to be more stable than non-boarding school junior high schools. Keywords: Learning Behavior, SEIR, Learning Motivation and Social Interaction
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