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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 590 Documents
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Analysis of Prospective Teachers' Self-Training Needs Regarding Mathematical Software Adaptation Supriyo Supriyo; Ani Afifah; Rani Darmayanti; Syed Muhammad Yousaf Farooq
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37325

Abstract

In the modern educational landscape, the integration of technology into mathematics education is crucial, and prospective teachers are expected to be not only passive users but also adaptive developers of digital content. Despite being labeled as the "digital generation," a paradox has emerged where general technological proficiency does not equate to competence in specialized mathematics software. This study addresses the self-paced training needs of prospective mathematics teachers at Universitas PGRI Wiranegara, aiming to improve their ability to adapt learning software effectively. Using a qualitative descriptive approach, data were collected through questionnaires and in-depth interviews with final-year students, with the instruments validated through expert assessment and data triangulation to ensure reliability and accuracy. The study revealed a significant gap in technological proficiency: 88% of respondent demonstrated proficiency in basic visualization techniques, but only 4% mastered advanced features such as scripting. Analysis of self-paced learning patterns highlighted issues such as fragmented learning, reactive learning, and high cognitive load, underscoring the urgent need for a structured, project-based self-paced training roadmap. This roadmap will guide prospective teachers from understanding mathematical abstractions to effectively implementing digital functions, empowering them to become competent digital content developers and increasing the effectiveness of their teaching in technologically integrated classrooms. 
Development of Leapfrog-Hansen Numerical Model to Simulate One-Dimensional Dam-Break Flow Qalbi Hafiyyan; Irene Anggraini; Puspita Rahmasari; Azwa Nirmala
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.38595

Abstract

This study is a computational study aimed at developing and validating a numerical model for simulating one-dimensional dam-break flow. Dam construction, in addition to providing benefits to the community in terms of flood control, irrigation, and clean water sources, also carries the potential for disaster. Disasters can occur when dams fail or collapse. Dam failures can generate catastrophic flooding that threatens infrastructure, the environment, and human life. Therefore, numerical modeling is an important approach for understanding the characteristics of dam-break flow to support flood mitigation efforts following dam failure. The proposed model is developed using the Leapfrog finite-difference method, known for its simplicity. However, the conventional Leapfrog method is prone to numerical oscillations when handling discontinuities and shock waves in dam-break simulations. The novelty of this research lies in the development of a Leapfrog–Hansen numerical model for one-dimensional dam-break flow simulation by integrating the Hansen numerical filter into the conventional Leapfrog finite-difference scheme to improve stability while maintaining computational simplicity. The governing shallow water equations were solved using the proposed Leapfrog–Hansen model and applied to several hypothetical one-dimensional dam-break scenarios with varying downstream water depths. The performance of the developed model was evaluated by comparing its numerical simulation results with Stoker's analytical solution, which is often used as a benchmark in numerical modeling of one-dimensional dam-break flow. The comparison results show that the Leapfrog–Hansen model accurately reproduces the water surface profiles predicted by the analytical solution. The Leapfrog-Hansen model yielded relatively small Mean Absolute Error (MAE) values of 0.032 to 0.062, indicating high accuracy in reproducing dam-break flows. In addition, the developed model successfully reduces numerical oscillations in the conventional Leapfrog scheme and accurately captures flow discontinuities, shock-wave propagation, and wet-dry conditions, while maintaining simulation stability. These findings demonstrate that the proposed Leapfrog–Hansen model provides a simple, stable, and accurate alternative for simulating one-dimensional dam-break flows and has potential applications in flood-propagation analysis, preliminary dam-break hazard assessment, and other hydraulic studies related to flood risk mitigation.
Hybrid Approach for Class Imbalance Handling using Adaptive Weighted Oversampling and Instance Hardness-Based Undersampling Hartono Hartono; Erianto Ongko; Muhammad Khahfi Zuhanda
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.36972

Abstract

Class imbalance remains a major challenge in multi-class classification, where existing hybrid resampling methods often combine oversampling and undersampling in a loosely coupled manner, without explicitly coordinating minority enrichment and majority reduction. In this experimental study, we propose a novel hybrid resampling method, Adaptive Weighted Oversampling and Instance Hardness-Based Undersampling (AWO-IHU), which differs from existing hybrid approaches by explicitly aligning boundary-aware minority oversampling with instance hardness-based majority undersampling. Rather than independently applying oversampling and undersampling, the proposed method integrates both processes through a coordinated design guided by classification difficulty to improve decision boundary quality. Methodologically, AWO-IHU first applies adaptive weighted oversampling to emphasize informative minority instances near class boundaries, followed by instance hardness-based undersampling that selectively removes redundant majority samples using an ensemble-based difficulty estimation. The experimental evaluation is conducted using multiple benchmark datasets with varying numbers of instances, attributes, and classes. Classification performance is evaluated using Accuracy, Precision, Recall, and Cohen’s Kappa, enabling a comprehensive assessment of overall correctness, minority sensitivity, and agreement beyond chance under class imbalance. Experimental results show that AWO-IHU consistently outperforms SMOTE, Random Undersampling, and conventional hybrid sampling methods. In particular, the proposed method achieves perfect or near-perfect Recall values up to 1.0, while maintaining high Precision values above 0.89 and producing the highest Cohen’s Kappa values up to 0.86. These findings demonstrate that explicitly coordinating minority enrichment with difficulty-aware majority reduction yields more reliable decision boundary learning and improved generalization in imbalanced multi-class classification. 
Geographically Weighted Panel Regression Analysis of Poverty Determinants in Central Java Province, Indonesia Diva Aprilia Trisha Utami; Gangga Anuraga; Artanti Indrasetianingsih; Hani Brilianti Rochmanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37624

Abstract

The Geographically Weighted Panel Regression (GWPR) model combines panel and spatial data to capture geographic heterogeneity by allowing variable effects to differ by location. This quantitative study examines poverty rates in Central Java Province from 2022 to 2024 using GWPR, analyzing secondary data from 35 districts/cities provided by the Central Java Provincial Statistics Agency (BPS). Independent variables include Gross Regional Domestic Product (GRDP), labor force participation, minimum wage, literacy, school participation, sanitation, and clean water access. This study examines the spatial–temporal determinants of poverty in Central Java Province using a spatial-panel modeling approach. Panel regression analysis was first conducted, and the Chow, Hausman, and Lagrange Multiplier tests identified the Random Effect Model (REM) as the most appropriate global specification. However, evidence of spatial heterogeneity suggested that global parameters could not adequately capture interregional differences. To address this limitation, Geographically Weighted Panel Regression (GWPR) was employed to simultaneously model spatial and temporal variation. Estimation was performed using Weighted Least Squares with a bisquare kernel, and the optimal bandwidth was selected through Cross-Validation, yielding a minimum CV value of 0.0038 with a bandwidth of 9. The GWPR model achieved a markedly higher R² (0.9996) than REM (0.5628), indicating superior capacity to represent localized structural variation. The range of Local R² values (0.242–0.898) demonstrates heterogeneous model fit and reduces concerns of overfitting, with bandwidth selection functioning as a nonparametric regularization mechanism. These findings highlight the importance of spatially adaptive poverty policies tailored to district-specific socioeconomic conditions in Central Java Province, Indonesia. 
A Mathematical Model of Wasting–Stunting Dynamics with Age-Dependent Nutritional Recovery in Children under Five Nur Rahmi; Wahyuni Ekasasmita; Muhammad Rifki Nisardi; Ahmad Fajri; Muhammad Fadhil Nurahmad; Hartina Husain; Ahmad Husain
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.39083

Abstract

Childhood wasting and stunting remain major public health challenges, yet their long-term interaction at the population level remains insufficiently understood. This study develops a deterministic compartmental model to investigate wasting–stunting dynamics among children under five years of age in Indonesia by classifying the population into four nutritional states: well-nourished, moderately wasted, severely wasted, and stunted. An important feature of the model is the incorporation of age-dependent recovery weighting based on infant population proportion, allowing recovery rates to differ between infants and older children according to demographic composition. Model parameters are estimated using nonlinear least-squares calibration based on aggregated national prevalence data from Indonesia during 2013–2024. Concurrent wasting–stunting is incorporated implicitly within the stunting dynamics to maintain model parsimony. The analysis includes threshold, local stability, and normalized sensitivity analyses. The calibrated model produced a residual error of approximately 8.77×〖10〗^(-3), indicating good agreement with observed prevalence data. Numerical simulations show declining and stabilizing behavior for severe wasting, whereas stunting remains persistent over time. Threshold analysis indicates that the condition R_W<1 is associated with decay of wasting dynamics and convergence toward equilibrium. Sensitivity analysis indicates that deterioration and progression toward stunting dominate long-term dynamics, while infant-related recovery parameters exhibit relatively low sensitivity rankings. These findings suggest that reducing wasting alone may not substantially lower stunting prevalence and highlight the importance of integrated interventions targeting both acute and chronic undernutrition pathways.
Mathematical Problem-Solving Ability Viewed from Self-Emotions: Case Study through Problem-Based Learning Syafruddin Kaliky; Sufyani Prabawanto; Wahyudin Wahyudin; Syaidah Baharuddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.36974

Abstract

Problem-solving ability is a skill that individuals must possess in the process of planning, making plans, implementing plans, and reviewing the correctness of the solutions obtained. However, many students still have difficulty solving the given problems. Self-emotion is an important factor in problem-solving because it is related to positive and negative emotions in responding to the questions given. To stimulate problem-solving abilities and control self-emotions, the PBL model is applied. The objectives of this study are (1) to describe students' problem-solving abilities in terms of self-emotions through the PBL model, and (2) to link mathematical problem-solving abilities with students' self-emotions. The study was conducted in a junior high school class VIII-H in West Bandung, Indonesia with 33 students. This study used a mixed qualitative-quantitative approach. For quantitative research, a One-Group Pretest-Posttest design was used. Data collection methods used a self-emotion questionnaire sheet, test questions, and semi-structured interviews. Data analysis was performed using SPSS 24 and NVIVO 12 software. This study shows that self-emotions play a significant role in students' mathematical problem-solving abilities through the application of Problem-Based Learning (PBL). Quantitative results indicate an increase in problem-solving abilities from pre-test to post-test in students with both positive and negative emotions, with better final outcomes in students with positive emotions. Qualitatively, students with positive emotions were able to systematically fulfill all stages of problem-solving according to Polya, while students with negative emotions only fulfilled some indicators and showed limitations in reflection and justification of solution steps. These findings confirm that PBL is not only effective in improving mathematical problem-solving abilities but also helps manage students' emotions during the learning process. Thus, the Problem-Based Learning model not only contributes to improving mathematical problem-solving abilities but also plays a role in managing and suppressing students' negative emotions during the learning process. Therefore, PBL can be recommended as an effective learning model for developing mathematical problem-solving abilities while supporting students' emotional regulation in mathematics learning. 
Pertamina Geothermal Energy Stock Price Prediction and Risk Analysis: ARIMA-GARCH and VaR with Cornish-Fisher Expansion M. Fariz Fadillah Mardianto; Doni Muhammad Fauzi; Idrus Syahzaqi; Elly Pusporani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37866

Abstract

The geothermal energy sector makes a strategic contribution to supporting long-term domestic energy sustainability and attracts investor attention due to high market volatility. Therefore, analysis that can accurately describe stock price dynamics and risks is needed. This study aims to model and predict the share price of PT Pertamina Geothermal Energy (PGEO) and estimate the associated investment risk. This study uses a quantitative time series approach with ARIMA–GARCH modeling and the Value at Risk method using Cornish–Fisher Expansion. This study uses weekly closing price data for PGEO stocks from February 2023 to September 2025. The methods used include ARIMA-GARCH modeling for stock price prediction and Cornish–Fisher Expansion based Value at Risk to estimate investment risk. The results indicate that the ARIMA(2,2,0)–GARCH(2,0) model provides the most adequate representation of PGEO stock price dynamics and volatility, achieving an RMSE value of 258.33 and a MAPE of 16.21% as measures of forecasting performance. Meanwhile, risk measurement using the Cornish–Fisher Expansion Value at Risk method produced a VaR value that increased along with the holding period and confidence level, with a risk range of 8.21% to 19.95%. The novelty of this research lies in the integration of ARIMA–GARCH volatility modeling and the Value at Risk method using Cornish–Fisher Expansion, thereby providing a more comprehensive analytical framework for price prediction and investment risk estimation in renewable energy stocks. The findings of this study are expected to serve as an empirical reference for investors and policymakers in assessing potential risks and supporting more informed investment decisions within the renewable energy sector.
Application of Proportional Hazard and Additive Models in the Survival Analysis of Breast Cancer Patients Muhammad Bayu Nirwana; Tiara Fitri Adani; Kayla Argya Puruhita; Andreas Rony Wijaya; Hasih Pratiwi; Silvina Rosita Yulianti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37028

Abstract

Breast cancer is the most common type of cancer among women and one of the highest causes of death among other types of cancer. This study aims to evaluate the methodological advantages of additive hazard models over the multiplicative Cox model in identifying temporal risk factors for breast cancer survival. Using secondary data from 1458 patients and 10 covariates, applying three methods, Cox proportional hazards model, Lin-Ying additive hazard model, and Aalen additive hazard model. The proportional hazard assumption test indicated that Cox regression model did not fully satisfy the assumption; therefore, the Lin–Ying and Aalen additive models were applied. In the Lin–Ying models, hormonal therapy, radiotherapy, the Nottingham Prognostic Index (NPI), and tumor size were identified as significant predictors of survival, whereas in the Aalen model, significant factors also included age and chemotherapy in addition to those four covariates. These findings highlight that while the Cox model provides efficient estimation and interpretable hazard ratios, the Lin–Ying and Aalen models offer more robust alternatives when the proportional hazard assumption is violated. The Aalen model was selected based on the results of the Aalen plot. Overall, risk control efforts in breast cancer patients should focus on managing NPI scores and tumor size as well as ensuring appropriate therapies, particularly hormonal therapy and radiotherapy, which have been demonstrated to provide protective effects.
Analysis of Indonesia’s Gross Regional Domestic Product using a Spatially Filtered Unconditional Quantile Regression Approach Sri Amaliya; Anik Djuraidah; Budi Susetyo
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37875

Abstract

Analyzing Indonesia’s Gross Regional Domestic Product (GRDP) is crucial for understanding regional economic disparities characterized by heterogeneity and spatial dependence. However, previous studies using mean regression or standard Unconditional Quantile Regression (UQR) often ignore spatial dependence, potentially biasing distributional estimates. Substantively, this study aims to examine how socioeconomic factors influence regional economic performance across different levels of GRDP in Indonesia. To address the methodological gap, this study applies Spatially Filtered Unconditional Quantile Regression (SF-UQR), which captures heterogeneous effects across the GRDP distribution while accounting for spatial dependence. Using cross-sectional data of Indonesian districts and cities from Statistics Indonesia (BPS) in 2023, GRDP is specified as the response variable, with five explanatory variables: human development index, minimum wage, number of workers, original local government revenue, and poverty rate. The analysis compares UQR and SF-UQR across selected quantiles. The results reveal substantial heterogeneity. Human development index and original local government revenue consistently show positive effects, poverty rate negatively affects lower quantiles, minimum wage exhibits a shifting pattern, and number of workers is significant mainly at middle and upper quantiles. SF-UQR outperforms standard UQR, achieving an adjusted R² of 0,67 compared to 0,52 under UQR. Methodologically, this study highlights the relevance of incorporating spatial filtering into UQR when analyzing regional economic data characterized by spatial dependence, providing an alternative distributional perspective on regional economic dynamics. From a policy perspective, the findings indicate that development strategies should consider both distributional heterogeneity and spatial dependence. Overall, the results highlight the necessity of spatially informed and distribution-sensitive policy design to reduce regional economic disparities in Indonesia.
Hourly Wage Modeling in Indonesia using Spatial Durbin Model Approach Suliyanto Suliyanto; Dita Amelia; Ilham Maulana Al Hasri; Nashwa Carista
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.35666

Abstract

Hourly wage disparities in Indonesia reflect complex regional economic conditions that vary across provinces. These disparities are closely related to spatial factors, as economic conditions in one region may influence neighboring regions. This study aims to compare the performance of the Ordinary Least Squares (OLS) linear regression model and the Spatial Durbin Model (SDM) in identifying the determinants of hourly wages in Indonesia. The study uses secondary data from BPS Indonesia for 2023, covering 34 provinces. Predictor variables used including the poverty gap index, expected years of schooling, GRDP per capita, and the percentage of poor population. Spatial effects were examined using Moran’s I and the Breusch-Pagan test. The test results indicate the presence of both spatial dependence and heterogeneity in provincial hourly wages, suggesting that the OLS model is insufficient to capture spatial interactions between regions. Therefore, the Spatial Durbin Model is applied to accommodate both direct effects and spatial spillover effects. The empirical results of the SDM show that the poverty gap index and GRDP per capita have significant direct effects on hourly wages at the provincial level. In addition, the poverty gap index and expected years of schooling exhibit significant indirect effects. Model performance was evaluated using the coefficient of determination (R-Square), Mean Square Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results show that the Spatial Durbin Model outperforms the OLS model, as indicated by a higher R-Square value and lower MSE, MAE, and MAPE values. 

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