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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Pendidikan Matematika (Jupitek) Jurnal Magister Pendidikan Matematika (JUMADIKA) Science Map Journal Pattimura International Journal of Mathematics (PIJMath) Amalgamasi: Journal of Mathematics and Applications
Bustan, Ariestha Widyastuty
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Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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ETHNOMATHEMATICS: THE CONCEPT OF WEIGHTED GRAPHS IN THE TRADITIONAL GAME OF DAM Bustan, Ariestha Widyastuty; Mahmud, Rauman; Gafur, Anuwar Kadil A; Salmin, Munazat
Jurnal Magister Pendidikan Matematika (JUMADIKA) Vol 6 No 2 (2024): Jurnal Magister Pendidikan Matematika (JUMADIKA)
Publisher : Prodi Magister Pendidikan Matematika Pascasarjana Universitas Pattimura Ambon

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/jumadikavol6iss2year2024page89-95

Abstract

This research integrates graph theory concepts with the traditional game of DAM originating from North Maluku, particularly in Ternate City. An ethnomathematics approach is employed to bridge mathematics education with the preservation of local culture. The DAM game is represented as a weighted graph, where game stones serve as vertices, and the lines connecting the stones represent edges with weights corresponding to the number of steps between stones. Using ethnographic methods, the study observes the rules, strategies, and mathematical aspects of the DAM game. Findings reveal that strategies for capturing opponent stones can be represented as vertex deletion and edge addition in the graph. Additionally, the shortest path with minimum weight in the weighted graph is used to determine optimal strategies for players to reach the opponent's first row. This research enriches mathematics education through cultural approaches while supporting the preservation of traditional games as local cultural heritage
BILANGAN TERHUBUNG PELANGI LOKASI PADA GRAF KEMUDI DAN GRAF JARING Mahmud, Rauman; Bustan, Ariestha Widyastuty
Science Map Journal Vol 7 No 1 (2025): Science Map Journal
Publisher : Jurusan Pendidikan MIPA FKIP Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/jmsvol7issue1pp6-13

Abstract

Konsep bilangan terhubung pelangi lokasi pada graf merupakan salah satu inovasi dalam teori pewarnaan graf yang menggabungkan konsep pewarnaan titik pelangi dan dimensi partisi pada graf. Konsep ini bertujuan untuk menentukan bilangan bulat positif terkecil sehingga terdapat pewarnaan- pelangi lokasi pada graf yang memungkinkan setiap titik memiliki kode pelangi yang unik. Dalam penelitian ini, kami mengkaji bilangan terhubung pelangi lokasi pada graf kemudi dan graf jaring. Hasil dari kedua graf menunjukkan bahwa jumlah titik pemotong berbanding lurus dengan bilangan terhubung pelangi lokasi pada graf kemudi dan graf jarring.
EKSPLORASI BILANGAN TERHUBUNG PELANGI LOKASI PADA GRAF ULAR SEGITIGA Bustan, Ariestha Widyastuty; Hi Dahlan, Akmal; Kharie, Diyah Safitri Qammariyah
Amalgamasi: Journal of Mathematics and Applications Vol. 4 No. 1 (2025): Amalgamasi: Journal of Mathematics and Applications
Publisher : Universitas Pasifik Morotai

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55098/amalgamasi.v4.i1.pp11-15

Abstract

The concept of the locating rainbow connection number in a graph is an innovation in graph coloring theory that combines the ideas of rainbow vertex coloring and partition dimension in graphs. This concept aims to determine the smallest positive integer such that there exists a locating rainbow -coloring of the graph, allowing each vertex to have a unique rainbow code. In this study, we investigate the locating rainbow connection number of the triangle snake graph. The method employed involves analyzing the graph’s structure and constructing rainbow vertex-paths that ensure the uniqueness of the rainbow code for each vertex. The results show that, for graphs of order greater than five, the locating rainbow vertex-connection number of a triangle snake graph is equal to the number of cut-vertices in the graph
EKSPLORASI ETNOMATEMATIKA TERHADAP TRANSFORMASI GEOMETRI PADA BATIK MALEFO Bustan, Ariestha Widyastuty; Salmin, Munazat; Talib, Taufan
Jurnal Pendidikan Matematika (JUPITEK) Vol 4 No 2 (2021): Jurnal Pendidikan Matematika (JUPITEK)
Publisher : Program Studi Pendidikan Matematika FKIP Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/jupitekvol4iss2pp87-94

Abstract

Abstract mathematical concepts require using objects around the student's environment to make mathematical concepts more concrete. One of the objects around that can be used is a cultural object. In particular, the approach that links mathematics with culture is the ethnomathematical approach. This study explores the ethnomathematics of the geometric transformation material on malefo batik, a typical batik of Ternate City. This type of research is qualitative research with an ethnographic approach. Data was collected using literature study, observation, interview, and documentation methods. The subject of this research is the owner of the Malefo batik gallery. The data obtained in this study came from direct observation, interviews with research subjects, and document results. The results of the study found that the motifs used in malefo batik can be a concrete example of the types of geometric transformations, namely the translational type of geometric transformation on the clove and machete flower arrangement batik motifs, the type of reflection on the clove flower motif, nutmeg, salawaku, parang and coconut flowers, the type of dilatation in the dodia batik motif, as well as the rotation type in the clove and clove flower motifs. The examples represented in Malefo batik can then be recommended as an alternative learning media to understand the material of geometric transformation better
EFEKTIVITAS MODEL PEMBELAJARAN TUTOR SEBAYA DENGAN PENGGUNAAN LKS TERHADAP HASIL BELAJAR SISWA DALAM MENYELESAIKAN SOAL CERITA PADA MATERI KELILING DAN LUAS LINGKARAN Bustan, Ariestha Widyastuty; Samsi, Hasan; Ruhama, Mustafa A. H
Jurnal Magister Pendidikan Matematika (JUMADIKA) Vol 1 No 2 (2019): Jurnal Magister Pendidikan Matematika (JUMADIKA)
Publisher : Prodi Magister Pendidikan Matematika Pascasarjana Universitas Pattimura Ambon

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (560.084 KB) | DOI: 10.30598/jumadikavol1iss2year2019page51-58

Abstract

This research is an experimental research which aims to determine the effectiveness of peer tutoring learning models with the use of LKS on student learning outcomes in solving the story problems in the material around and the area of ​​the circle. The population in this study were all eighth grade students of SMP Negeri 1 Kota Ternate and samples that were randomly taken were class VIIIA students as an experimental class which amounted to 27 students and class VIIIB as a control class totaling 30 students. Data collection is done through tests of student learning outcomes with 5 items as instruments that have been validated by the validator. The analysis of the data used is 5-scale PAP, homogeneity test, normality test, the Mann-Whitney test and hypothesis test. The results of the calculation of the initial homogeneity test obtained F count = 1.29 less than Ftable = 1.90, then the two data are homogeneous. In the normality test the final test data is obtained χ2 count> tabel2 tables or 9.90> 7.82 for the experimental class and χ2 count> χ2 tables or 10.56> 7.82 for the control class, meaning that the two group data are not normally distributed, so used non parametric statistical tests. The non parametric test used is the Mann-Whitney test, from the calculation results obtained by Zhitung = -4.14 with Ztable = ± 1.96 at a significant level () = 0.05, Accept H0 if -Zt ≤ ZH ≤ + Zt and Reject H0 if ZH> Zt or ZH <-Zt. Because ZH <Zt (-4.14 <-1,96), then H0 is rejected and H1 is accepted, meaning that there are differences in student learning outcomes between the experimental class and the control class in class VII students of SMP Negeri 1 Ternate City. Thus, there are differences in learning outcomes in class VIII students of SMP Negeri 1 Kota Ternate who use peer tutoring learning models with the use of LKS and those who do not use the learning model. Based on the mean, level of mastery obtained by the experimental class and the control class, as well as student activities and responses to peer tutoring learning models with the use of LKS, it can be concluded that the application of peer tutoring learning models with the use of effective LKS to improve student learning outcomes material around and area of ​​circle
THE LOCATING RAINBOW CONNECTION NUMBERS OF LOLLIPOP AND BARBELL GRAPHS Bustan, Ariestha Widyastuty; Talib, Taufan; Laamena, Novita Serly; Saputra, Lamanisa Rasid; Nurhayati, Nurhayati
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2727-2738

Abstract

The concept of the locating rainbow connection number of a graph is an innovation in graph coloring theory that combines the concepts of rainbow vertex coloring and partition dimension on graphs. This concept aims to determine the smallest positive integer such that there exists a locating rainbow -coloring on the graph, ensuring that every vertex has a unique rainbow code. In this study, we investigate the locating rainbow connection number of the lollipop graph and barbell graph . Using a literature study method, hypotheses were formulated and proven through theoretical analysis. The results show that and .
Value at Risk Prediction for the GJR-GARCH Aggregation Model Nurhayati, Nurhayati; Apriani, Wiwin; Bustan, Ariestha Widyastuty
Pattimura International Journal of Mathematics (PIJMath) Vol 1 No 1 (2022): Pattimura International Journal of Mathematics (PIJMath)
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (470.401 KB) | DOI: 10.30598/pijmathvol1iss1pp01-06

Abstract

Volatility is the level of risk faced due to price fluctuations. The greater the volatility brings, the greater the risk. We need a measure such as Value at Risk (VaR) and volatility modeling to overcome this. The most frequently used volatility model in the financial sector is GARCH. However, this model is still unable to accommodate the asymmetric nature, so the GJR-GARCH model was developed. In addition, this study also used aggregation returns with two assets in them. This study aimed to determine the VaR prediction for the GJR-GARCH(1.1) aggregation model and its comparison with the GARCH(1.1) aggregation model. The results obtained indicate that the prediction of volatility using the GJR-GARCH(1.1) aggregation model is more accurate than the GACRH(1.1) aggregation model because it has a correct VaR value that is close to the given confidence level.
Penerapan Metode Structural Equation Modelling dengan Path Analysis untuk Menganalisis Pengaruh Motivasi Orang Tua dan Kondisioning Rumah terhadap Akhlak (Mandiri, Kerja Keras, dan Tanggung Jawab) Siswa Mayawi; Bustan, Ariestha Widyastuty; Nurhayati; Fitriawati, Andi; Salmin, Munazat
Amalgamasi: Journal of Mathematics and Applications Vol. 1 No. 1 (2022): Amalgamasi: Journal of Mathematics and Applications
Publisher : Universitas Pasifik Morotai

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55098/amalgamasi.v1.i1.pp18-24

Abstract

Membentuk akhlak merupakan hal mendasar dan paling penting dalam penyelenggaraan pendidikan. Orang tua sebagai bagian dari penyelenggara pendidikan informal harus selalu mengajarkan pendidikan akhlak seperti nasihat, bimbingan, disiplin, dan arahan yang berlandaskan nilai-nilai ajaran. Khususnya bagaimana orang tua memberikan motivasi kepada anaknya serta memberikan kondisi lingkungan keluarga atau pengondisian rumah yang baik dalam membentuk akhlak seorang anak agar memiliki kemandirian, kerja keras dan tanggung jawab. Data pada penelitian ini menggunakan data akhlak mulia siswa sekolah menengah pertama yang dianalisis menggunakan SEM dengan Path Analysis. Terdapat 5 variabel manifest yaitu motivasi orang tua, kondisioning rumah, kemandirian, kerja keras dan tanggung jawab. Motivasi orang tua dan kondisioning rumah berpengaruh terhadap kemandirian dan tanggung jawab siswa. Adapun motivasi orang tua dan kondisoning rumah juga secara tidak lagsung berpengaruh terhadap kerja keras siswa. Selanjutnya kemandirian berpengaruh langsung terhadap tanggung jawab siswa dan kamandirian serta tanggung jawab juga berpengaruh secara langsung terhadap kerja keras siswa. Dari hasil Uji Goodness of Fit terhadap model pada gambar di atas menunjukkan probabilitas nilai chi-square di atas 0,05. Adapun semua nilai GFI, AGFI, TLI dan CFI diatas 0,9 serta nilai RMSEA dibawah 0,08 sehingga dapat disimpulkan bahwa model diatas didukung oleh data atau model tersebut fit
Co-Authors Andi Fitriawati Anuwar Kadir Abdul Gafur Apriani, Wiwin Hi Dahlan, Akmal Kharie, Diyah Safitri Qammariyah Laamena, Novita Serly Mahmud, Rauman Mayawi Mustafa A. H. Ruhama, Mustafa A. H. Nurhayati Nurhayati Nurhayati Salmin, Munazat Samsi, Hasan Saputra, Lamanisa Rasid Taufan Talib