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JTAM (Jurnal Teori dan Aplikasi Matematika)
Published by Universitas Muhammadiyah Mataram
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
Mathematics
Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model pembelajaran matematika di sekolah dasar sampai perguruan tinggi berbasis pendekatan konstruktivis (PMRI/RME, PBL, CTL, dan sebagainya), (2) Pengembangan media pembelajaran matematika berbasis ICT dan Non-ICT, dan (3) Penelitian atau pengembangan/design research di bidang pendidikan matematika, statistika, analisis matematika, komputasi matematika, dan matematika terapan.
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Articles 23 Documents
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Search results for , issue "Vol 9, No 1 (2025): January" : 23 Documents clear
Metric Coloring of Pencil Graphs Adawiyah, Robiatul; Pujiyanto, Arif; Kristiana, Arika Indah; Dafik, Dafik; Prihandini, Rafiantika Megahniah; Susanto, Susanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27242

Abstract

A graph is defined as an ordered pair (V,E), where V is a non-empty set of elements called vertices, and E is a set of edges that are finite and may be empty. Each edge connects two distinct vertices from V(G). Let f:V(G)→{1,2,3,…,k} be a coloring of the vertices of graph G, where two adjacent vertices can be colored with the same color. Considering the set of color classes Π={C_1,C_2,…,C_k}, for a vertex v in G, the color representation of v is a k-vector r(Π)=(d(v,C_1 ),d(v,C_2 ),…,d(v,C_k )),, where d(v,C_1 )=min⁡{d(v,c)∶c∈C_1}. If r(u | Π )≠r(v | Π ) for every two adjacent vertices u and v in G, the coloring is called a metric coloring of G. Thus, it can be concluded that two adjacent vertices u and v can be colored with the same color if their metric code conditions are different. The minimum number of the metric coloring is called as metric chromatic number. The goal of this research is analizing the metric chromatic number of the pencil graph. This graph was chosen because no previous research had been carried out on this graph. The proof begins by determining the lower bound, then determining the upper bound by checking coloring function and checking the metric coloring function and the metric code function of each vertex. In this research, we got the exact value of metric chromatic number of several type of pencil graph.
The Urgency of Developing Teaching Modules Based on Ethnomatics Learning for Numeracy Skills Fitriani, Fitriani; Baharuddin, Muhammad Rusli; Patmaniar, Patmaniar; Wafda, Andi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26846

Abstract

Numeracy is one of the essential foundational skills that students must master, yet the 2018 Programme for International Student Assessment (PISA) survey revealed that Indonesian students ranked 72nd out of 79 countries in numeracy skills, reflecting low mathematical literacy globally. This issue often stems from the presentation of mathematical material that is abstract and less relevant to everyday life contexts. This study aims to develop a teaching module based on ethnomathematics learning that integrates the local culture of Luwu to improve students' numeracy skills. This research employs the research and development (R&D) method with the 4D model, encompassing the stages of Define, Design, Develop, and Disseminate. In the Define stage, a needs analysis and identification of local cultural potential were conducted. In the Develop stage, the module was validated by experts using validation sheets to assess the relevance of the material, completeness of information, and clarity of presentation. The module's practicality was evaluated through questionnaires and observations to assess its ease of use and effectiveness in learning. The results indicate that the teaching module based on ethnomathematics learning is both valid and practical. The module achieved high validity based on expert assessments covering material relevance, completeness of information, and clarity of presentation. The module's practicality was measured through teacher and student responses, reflecting its ease of use and effectiveness in enhancing student engagement in numeracy learning. In conclusion, the teaching module based on ethnomathematics learning has proven effective in improving students' numeracy skills and successfully integrating local cultural values into learning. This study contributes to the development of relevant, meaningful, and contextual teaching materials in mathematics education.
The GSTAR (1;1) Modelling with Three Combination of the Grid Sizes and Spatial Weight Matrix in Forest Fires Cases Ayyash, Muhammad Yahya; Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27543

Abstract

One of the models that is utilized in spatio-temporal analysis is known as the Generalized Space-Time Autoregressive (GSTAR). This model incorporates two dimensions, namely the geographical and temporal aspects of the situation. This approach assists in the identification of patterns and correlations between data by taking into account both spatial and temporal elements. From modeling the confidence level of forest fire hotspot cases in Kubu Raya and its surrounds using the GSTAR (1;1) model with three different combinations of grids and special weight matrices, the purpose of this study is to discover which combination of grids and spatial weight matrices is the most effective. The results of diagnostic tests and the degrees of MAPE accuracy are used to determine which model is the most suitable. The data was obtained from the FIRMS-NASA platform, ranging from January 2014 to August 2024. A grid with a dimension of 1.25 x 1.25 degrees and a rook contiguity weight matrix is a combination of grids and spatial weight matrices that meet the white noise assumption, according to the findings of the study. This conclusion is based on the diagnostic test. As a result, the combination of a grid with a size of 1.25 x 1.25 and a rook contiguity weight matrix is the best in this modeling. This combination has a MAPE of 11.797%, which indicates that this model has a good level of accuracy. 
GARITA Media: Students' Mathematical Communication in Solving Contextual Problems Cholily, Yus Mochamad; Rosyadi, Alfiani Athma Putri; Suciati, Nur; Usmiyatun, Usmiyatun
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26404

Abstract

Based on observation results, the mathematical communication skills of 6th-grade elementary school students are still relatively low. This can be seen during classroom learning activities or when taking exams, when they are faced with contextual story problems they have difficulty understanding and solving them. The implementation of this research activity aims to see effect GARITA media and the mathematical communication skills of 6th-grade elementary school students, as shown through the results of contextual problem assignment scores. Apart from looking at the connection between GARITA media and mathematical abilities, this research was conducted to increase students' understanding in solving contextual problems. GARITA media is a media in the form of story images which have the role of helping to illustrate the problems in story problems, making it easier for students to understand the content of contextual problems and solve them. This research uses quantitative methods with quasi-experiments. The population of this study were students at SD Muhammadiyah 3 IKROM Wage Sidoarjo. This research activity took data from 29 Zahrawi 6th grade students as the control group and 30 Haitam 6th grade students as the experimental group. The result of this research data was obtained by carrying out a post-test in the form of a contextual question test and a student response questionnaire. The data analysis techniques used in this research are normality test, homogeneity test, and hypothesis test. This shows a significant difference in the mathematical communication skills of students who received treatment using GARITA assistance with students who did not receive treatment. The homogeneity test result shows that homogeneity data based on post-test data shows a figure < 0,05. Hypothesis testing shows a significant influence based on the result of the independent sample t-test < 0,05. So, the result of this research indicates that GARITA media can influence the improvement of students' mathematical communication skills in solving contextual problems. 
Enhancing Weather Forecasting in Bandar Lampung: A Hybrid SARIMA-LSTM Approach Kurniasari, Dian; Salsabila, Anindya Dafa; Usman, Mustofa; Warsono, Warsono
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27188

Abstract

Indonesia’s tropical climate, marked by rainy and dry seasons, is increasingly affected by extreme weather events driven by climate change. Rising temperatures, shifting rainfall patterns, and sea-level rise have intensified health risks such as malaria, dengue hemorrhagic fever (DHF), and gastrointestinal infections. Accurate weather forecasting is essential for mitigating these challenges and informing risk management strategies. This study develops and evaluates a hybrid SARIMA-LSTM model for weather forecasting in Bandar Lampung, integrating time series analysis with deep learning to enhance predictive accuracy. SARIMA captures seasonal variations, while LSTM models nonlinear relationships, offering a robust approach to forecasting complex weather patterns. The SARIMA (6,1,0)(3,1,0)26 model was selected for its effective seasonal representation and combined with LSTM to leverage its capability in modelling nonlinear dependencies. Hyperparameter optimization using grid search further improved model performance. Two data partitioning approaches were tested: 70%-30% and 80%-20% splits for training and testing, respectively. The SARIMA-LSTM hybrid model demonstrated superior performance with the 80%-20% split, achieving MSE, RMSE, and MAPE values of 0.1174, 0.3426, and 0.0104%, respectively. The model accurately forecasted weather conditions over 21 weeks, aligning closely with observed trends and effectively capturing seasonal patterns. These findings underscore the model’s potential to support public health strategies, including disease outbreak mitigation for malaria and DHF, and enhance disaster preparedness in flood-prone areas.
Numerical Simulation of Fluid Flow in the Narrow Strait with Density Differences Usman, Tarmizi; Ikhwan, Muhammad; Zulfataya, Muhammad; Adami, Farhan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27252

Abstract

This study investigates the dynamics of fluid flow through a narrow strait connecting two large water bodies with different densities using numerical simulations. The research focuses on understanding how density-driven currents develop and interact in a confined channel, particularly the role of lateral density contrasts and the influence of gravitational and geostrophic forces. A semi-implicit numerical method is employed to efficiently model the complex flow dynamics while ensuring stability. The simulation results are analyzed using visualizations of the flow fields, which highlight the evolution of density-driven currents, vortex formation, and geostrophic adjustments over time. The findings reveal that denser water from the western basin flows toward the eastern basin, lowering the sea surface in the west and raising it in the east. Over time, the Coriolis force causes the bottom flow to deflect southward and the returning surface flow to shift northward, leading to geostrophic equilibrium. Transient vortices emerge within the strait, while stationary vortices form in the outflow regions, underscoring the interplay between gravitational forces, density contrasts, and rotational effects. These findings offer important insights into the hydrodynamic behavior of narrow straits, which are common in nature. The results can help improve the understanding of flow patterns in similar environments, such as fjords, estuaries, and channels, and may contribute to studies on sediment transport, nutrient mixing, and renewable energy potential in density-driven systems. 
Multigroup Analysis on Partial Least Square-Structural Equation Modeling in Modeling College Students' Saving Behavior Asaliontin, Lisa; Sumarminingsih, Eni; Solimun, Solimun; Sepriadi, Hanifa; Iriany, Atiek; Hamdan, Rosita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27692

Abstract

This study aims to determine the factors that influence college students' saving behavior, with gender as a moderating variable. The analysis used is Partial Least Square-Structural Equation Modeling (PLS-SEM) with Multigroup Analysis. This study was conducted on 200 college students in City X who were selected by purposive sampling. Data collection was carried out using a structured questionnaire that measures Perceived Benefits, Perceived Ease of Use, Saving Intentions, and Saving Behavior. Confirmatory Factor Analysis (CFA) and Bootstrapping were used to validate the measurement model and structural relationships. The results showed that Perceived Benefits and Perceived Ease had a significant effect on Saving Intentions and Saving Behavior. In addition, Saving Intentions had a significant effect on Saving Behavior. This relationship applies to both male and female groups, with a determination coefficient of 86.2% for males and 86.7% for females. Moderation analysis shows that gender moderates the relationship between Perceived Benefits and Saving Behavior, as well as between Perceived Ease and Saving Behavior. These findings highlight the importance of considering gender differences in efforts to improve students' savings behavior. 
Dynamical Analysis of Discrete-Time Modified Leslie-Gower Predator-Prey with Fear Effect Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus; Kusumawinahyu, Wuryansari Muharini
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26515

Abstract

It has been studied that fear plays a significant role in establishing ecological communities, influencing biodiversity, and preserving ecological balance in predator-prey interactions. In this study, it is proposed a discrete-time predator-prey model that takes the fear effect into account that is derived by using Euler method. Objective of this study is analyzing the model by linearization. Similar to the continuous model properties, the trivial fixed point and the predator-free fixed point are both unstable. The discrete model differs from the continuous model in that the stability of the interior fixed point and the free prey fixed point is affected by the time step size. Using numerical methods, we examine period-doubling bifurcations related to interior fixed point and prey-free point that are impacted by time step size.
A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance Novkaniza, Fevi; Putri, Irene Devina; Kafi, Rahmat Al; Devila, Sindy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27837

Abstract

This study develops and applies the Poisson-Gamma Hierarchical Generalized Linear Model (PGHGLM) to address the challenge of determining accurate and fair premium rates in vehicle insurance. The PGHGLM models a mixture distribution for the response variable, influenced by random effects, and employs a logarithmic link function. Parameter estimation is conducted using the maximum likelihood method. However, since analytical estimation is not feasible, the numerical conjugate gradient method, specifically the Fletcher-Reeves algorithm, is utilized. The implementation of the PGHGLM uses the longitudinal Claimslong dataset, incorporating driver age as a covariate. The main contribution of this research lies in integrating a priori risk classification with a posteriori adjustment based on longitudinal claim frequency data. For datasets without covariates, trend parameters are incorporated into the model. For datasets with covariates, such as driver age, the average claim frequency is computed for each age category. Results show that posteriori premium rates increase with rising claim frequency from the previous year, with higher claim frequencies leading to larger rate adjustments in the subsequent year. Through the PGHGLM, a posteriori premium rate estimates are obtained for each age group of vehicle insurance policyholders. This study demonstrates the practical application of the PGHGLM in calculating precise premium rates. By analyzing a longitudinal vehicle insurance dataset, the model generates annual a posteriori premium rates tailored to age groups. These findings underscore the PGHGLM’s robust methodological framework and its potential to enhance premium fairness, enable risk-adjusted pricing, and better tailor insurance products to diverse policyholder profiles. 
Trace of the Positive Integer Powers (n-1)-Tridiagonal Toeplitz Matrix n×n Aryani, Fitri; Wati, Fitri Ambar; Marzuki, Corry Corazon; Zukrianto, Zukrianto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27387

Abstract

The trace of a matrix is obtained by summing the elements along the main diagonal of a square matrix. The matrix used in this study is a Toeplitz (n-1)-tridiagonal matrix of order n×n. The aim of this research is to determine the general form or formula for the trace of a Toeplitz (n-1)-tridiagonal matrix of order n×n raised to a positive integer power. This research is quantitative, with the research instrument being the collection of data from the multiplication of Toeplitz (n-1)-tridiagonal matrices starting from order 3×3 from powers 2 through 10. This process continues up to order 6×6 from powers 2 through 10, until the pattern becomes apparent. The results of the research are two general forms of the powers of the Toeplitz (n-1)-tridiagonal matrix of order n×n: one for odd positive integer powers and another for even positive integer powers, both of which have been proven using mathematical induction. Furthermore, by using the definition of the trace of a matrix obtained two general forms for the trace of the Toeplitz (n-1)-tridiagonal matrix of order n×n are also derived: one for odd positive integer powers and another for even positive integer powers from the general form of the matrix power. Given the application of these two general forms in example problems with the order 8x8 for powers 12 and 21.

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