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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 577 Documents
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Modelling the Prevalence of Stunting in Toddlers Aged 6 – 23 Months in Indonesia with Approaches Multivariate Adaptive Regression Splines and Generalized Additive Model Aflaha, Nabila Shafa; Oktavia, Sabrina Salsa; Kurniawan, Ardi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35644

Abstract

Stunting remains a major global public health issue, marked by growth failure caused by long-term nutritional deficiencies in early childhood. In Indonesia, stunting prevalence among children under five was reported at 21.5% in 2023. This study employs an analytical observational approach with a cross-sectional design to examine nutritional factors associated with stunting among children aged 6–23 months in Indonesia, using Multivariate Adaptive Regression Splines (MARS) and Generalized Additive Models (GAM). Secondary data were obtained from the 2024 Indonesian Nutritional Status Survey (SSGI), encompassing 36 provinces. Stunting prevalence was defined as the response variable, while predictor variables included the consumption of animal-source protein, sweetened beverages, unhealthy foods, and the lack of fruit and vegetable intake. The analysis began with descriptive statistics and was followed by MARS and GAM modelling. Model performance was assessed using the coefficient of determination (R²) and Root Mean Square Error (RMSE). The findings indicate that the GAM model outperformed MARS, achieving a higher R² 0.7734 and a lower RMSE 2.5968, compared to MARS with an R² of 0.7319 and an RMSE of 2.8249. While MARS effectively identified structural changes through hinge functions, GAM offered greater modelling flexibility via smooth functions. Among the examined factors, animal-source protein intake showed the strongest association with stunting, followed by the consumption of sweetened beverages and unhealthy foods, whereas inadequate fruit and vegetable intake exhibited a weaker relationship. Overall, both approaches were effective, although GAM demonstrated superior predictive capability for provincial-level stunting analysis.
Students’ Cognitive Load in Understanding Linear Equation in One Variable Rofiq, Ainur; Sudirman, Sudirman; Muksar, Makbul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.36034

Abstract

Cognitive load is the mental effort made by students in their working memory to process information received. This study aims to describe the cognitive load of students in understanding linear equation in one variable material. The research method used is qualitative with a case study type of research. The research was conducted at a junior high school in Malang. The research subjects were two active students selected based on the recommendation of the mathematics teacher in the class. Data were collected through observation sheets, interviews, and student reflection sheets, then analyzed using data reduction, data presentation, and conclusion drawing techniques. The results showed that students experienced intrinsic, extraneous, and germane cognitive load. Intrinsic cognitive load occurred when faced with complex problems and story problems that required the processing of several concepts at once, such as equations, integer operations, distributive properties, and algebraic operations. Students experienced extraneous cognitive load because they did not have sufficient prerequisite knowledge due to the teacher providing apersepsi that did not help activate students' prior knowledge. Students misunderstood the definition of a linear equation in one variable and only memorized the rules for moving terms because the teacher used inappropriate terms in their explanation. Students were confused in understanding simple example questions because the teacher explained too quickly without giving students time to understand. Students' attention was divided because the teacher gave examples in the workbook, while the steps to solve the problems were written on the board. Students were unable to complete the exercises because the teacher did not pay attention to their understanding. Germane cognitive load occurred because students' understanding was procedural. This was because the teacher's learning strategy did not support the formation of knowledge schemas. These findings have implications for teachers to design learning that takes into account students' working memory capacity.
Measuring the Impact of APOS Theory-Based Contextual Mathematics Assignments on the Mathematical Communication Skills of Prospective Teacher Students Jaya, Ilham; Nurkhasyanah, Alfiyanti; Fitria, Anna; Salsabila, Ismi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.36568

Abstract

Mathematical communication skills are essential for conveying ideas, interpreting symbols, and linking abstract concepts to contextual phenomena. This study aims to measure the effectiveness of applying APOS theory-based contextual tasks in improving the mathematical communication skills of prospective teacher students. This study uses a quasi-experimental design with a non-equivalent control group model, involving an experimental class that receives contextual task-based learning using the APOS theory approach and a control class that follows conventional learning. The instrument used was a mathematical communication skills test covering five main indicators, namely the ability to express ideas in writing, use representations, explain procedures, relate concepts to real contexts, and construct mathematical arguments. The data were analyzed using the Rasch model, normality test, homogeneity test, independent t-test, score improvement analysis, and PLS-SEM-based structural modeling. The results indicate that the instrument demonstrates strong validity and reliability, as reflected by average Infit and Outfit MNSQ values of 1.00, item reliability of 0.89, and person reliability of 0.84. Significant differences were found between the experimental and control groups across all indicators of mathematical communication skills, with higher posttest mean scores in the experimental group (76.10) compared to the control group (49.87), as well as greater learning gains in the experimental group (N-Gain 68.27%) than in the control group (33.18%). The structural model further confirms the positive contribution of APOS theory to mathematical communication skills, particularly in explaining procedures (β = 0.323) and using mathematical representations (β = 0.257). Overall, this study confirms that the application of APOS theory-based contextual tasks is effective in strengthening the mathematical communication skills of prospective teachers and provides important implications for the development of a more contextual and meaningful mathematics education curriculum. 
Random Forest-Based Modeling of Life Expectancy in Central Kalimantan Puspitorini, Mega; Ayu, Regina Wahyudyah Sonata; Monita, Dita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35399

Abstract

This study investigates key socioeconomic determinants of life expectancy (LE) and develops a regional-level predictive model using the Random Forest regression approach for regencies and municipalities in Central Kalimantan Province during 2016–2023. Although life expectancy is a core indicator of human development, empirical studies employing machine learning methods at the sub-provincial level in Indonesia remain limited. Using secondary data from Statistics Indonesia (BPS), this study examines the relationship between LE and selected indicators related to education, sanitation, health infrastructure, economic conditions, and demography. The Random Forest model exhibits robust predictive performance, achieving MAE values of approximately 0.29–0.30 and coefficients of determination (R²) ranging from 0.71 to 0.74 across different evaluation schemes. Feature importance analysis identifies mean years of schooling as the most influential determinant of life expectancy, followed by access to proper sanitation and the availability of health facilities. These results highlight the prominent role of human capital and basic infrastructure in shaping regional health outcomes. By integrating machine learning techniques with regional socioeconomic data, this study extends existing life expectancy research in Indonesia through a data-driven modeling framework. Overall, this study supports evidence-based planning by highlighting priority intervention areas to improve life expectancy and human development in Central Kalimantan.
Forecasting Indonesia’s Export Revenue through a Vector Autoregressive Exogenous Approach Sudarwanto, Sudarwanto; Puteri, Syafa Marisha; Santi, Vera Maya; Alwansyah, Muhammad Arib
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.36760

Abstract

The Vector Autoregressive with Exogenous Variables (VARX) model extends the conventional VAR framework by explicitly incorporating external macroeconomic drivers, offering a more structurally informed approach to export forecasting. This study contributes to the literature by introducing a disaggregated modeling strategy that treats oil and gas exports and non-oil and gas exports as separate endogenous components, an aspect that has been largely overlooked in previous studies on Indonesia’s export performance. By positioning VARX as a system-based forecasting tool rather than a purely statistical extension, this research provides an updated methodological perspective on export revenue analysis. Using monthly data from January 2015 to December 2024, this study evaluates several VARX specifications that integrate the rupiah–US dollar exchange rate and West Texas Intermediate (WTI) crude oil prices as exogenous variables. Model selection is conducted based on a combination of information criteria and forecasting performance indicators, leading to the identification of VARX(5,6) as the most suitable specification. The inclusion of exogenous variables is shown to substantially enhance predictive accuracy, confirming the relevance of external economic shocks in shaping Indonesia’s export revenue dynamics. Empirical results indicate that WTI oil prices exert a significant causal influence on export revenue, while the exchange rate effect becomes meaningful when jointly evaluated with oil prices and endogenous export components. The selected VARX(5,6) model demonstrates strong forecasting performance, achieving a MAPE of 5.60% and an nRMSE of 6.40%. From a policy standpoint, these findings suggest that export planning and stabilization policies should explicitly account for global oil price volatility and exchange rate interactions. The proposed VARX framework can therefore serve as a practical analytical tool for policymakers to anticipate short-term export fluctuations and design responsive trade and macroeconomic strategies under external uncertainty.
Bridging Cultural Contexts and Digital Innovation in Mathematics Learning: A Meta-Analytic of Augmented Reality Supported Ethnomathematics Maximus Tamur; Muhammad Afrilianto; Potchong M. Jackaria; Nilo Jayoma Castulo; Ayubu Ismail Ngao
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.v10i3.34065

Abstract

The integration of cultural perspectives into Mathematics Education has expanded significantly alongside the rapid development of Augmented Reality (AR). While prior reviews have separately examined digital innovation in mathematics learning or the role of ethnomathematics in culturally responsive pedagogy, no previous meta-analysis has systematically synthesized empirical evidence at the intersection of augmented reality and ethnomathematics. This study addresses that gap by providing the first quantitative synthesis of the effectiveness of AR-supported ethnomathematics across educational levels, thereby bridging cultural context and digital innovation within a single analytical framework. Using a meta-analytic approach, quantitative findings from 21 empirical studies (selected from an initial pool of 101 studies indexed in Google Scholar and Scopus) were synthesized using a random-effects model in Comprehensive Meta-Analysis (CMA). The overall effect size was large and positive (ES = 1.10), demonstrating that AR-supported ethnomathematics substantially improves students’ mathematics learning outcomes compared to conventional approaches. Moderator analyses revealed significant heterogeneity, with stronger effects observed in interventions that integrated interactive and contextually immersive AR features and at the primary and secondary education levels. The magnitude of the effect (ES = 1.10) indicates not merely statistical significance but strong practical relevance, suggesting that integrating culturally grounded mathematical contexts with immersive AR technology can meaningfully enhance conceptual understanding, engagement, and knowledge retention. For curriculum development, these findings support the systematic incorporation of AR-based ethnomathematical modules into mathematics syllabi, particularly in culturally diverse settings. Rather than positioning digital innovation as a supplementary tool, the results advocate for its structural integration into culturally responsive curriculum design. Future research should employ longitudinal and mixed-method designs to examine the sustainability of these effects and to explore how evolving digital innovations influence students’ cognitive and affective learning trajectories over time.
Comparative Evaluation of Eigenvector Selection in Eigenvector Spatial Filtering using a Gradient Boosting Machine for PM2.5 Concentration Prediction Putri Nisrina Az-Zahra; Anik Djuraidah; Erfiani Erfiani
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.v10i3.38883

Abstract

Spatial dependence remains a critical issue in spatial data analysis. To address this issue, various eigenvector selection methods within the Eigenvector Spatial Filtering (ESF) framework have been proposed. However, these methods often do not provide explicit information regarding the individual contribution of each spatial component, limiting model interpretability, particularly when dealing with a large number of candidate eigenvectors and complex models. In addition, ESF has limitations in capturing nonlinear relationships and complex interactions inherent in spatial data, while its integration with advanced feature selection methods within machine learning frameworks remains underexplored. This quantitative empirical study aims to evaluate different eigenvector selection methods within ESF integrated with a Gradient Boosting Machine (GBM) model for predicting PM2.5 concentrations in DKI Jakarta. Data were collected from 100 monitoring stations across five administrative regions for the first half of 2025. Spatial eigenvectors were derived from a spatial weights matrix and selected using four methods: positive eigenvalues, Moran’s Index significance, LASSO regression, and SHAP values obtained from the GBM model. Model performance was assessed using both 10-fold random cross-validation and spatial blocked cross-validation to evaluate predictive accuracy and spatial generalization. The results showed that adding spatial eigenvectors significantly improved the model performance compared to models without spatial components. Under 10-fold cross-validation, the SHAP-based selection method achieved the highest predictive accuracy (R² = 0.619), effectively capturing spatial dependence and nonlinear relationships. The SHAP method demonstrated robustness by selecting stable and consistent spatial components across different regions. These findings highlight the methodological advantage of integrating ESF with machine learning and SHAP-based feature selection, offering a more interpretable and robust framework for spatial modelling. Practically, the improved prediction of PM2.5 concentrations can support more accurate air quality assessments and inform environmental management strategies in urban areas.
Application of Ensemble Bagging Support Vector Machine for Early Detection of Childhood Stunting Alfiyah Hanun Nasywa; Solimun Solimun; Achmad Efendi; Adji Achmad Rinaldo Fernandes; Celia Sianipar; Fachira Haneinanda Junianto
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.v10i3.36005

Abstract

Stunting is a significant public health issue in Indonesia, characterized by a child's height being below the age standard. Maternal knowledge and family economic level are key factors influencing children's nutritional status, thus requiring accurate classification methods for early stunting risk detection. This study aims to develop a machine learning-based classification model for stunting risk using Support Vector Machine (SVM) with a quadratic polynomial kernel and evaluate its performance improvement through the ensemble Bagging SVM approach. Primary data were collected from 100 mothers of children under five, using a five-point Likert scale questionnaire to assess maternal knowledge (X₁) and family economic level (X₂). The SVM model was constructed using a quadratic polynomial kernel and compared to Bagging SVM, which applies bootstrap resampling and majority voting. Model performance was evaluated using accuracy, sensitivity, and specificity. The basic SVM model yielded 85% accuracy, 90% sensitivity, and 80% specificity. The SVM Bagging approach showed performance improvements, with 95% accuracy, 100% sensitivity, and 94% specificity. These results indicate that SVM Bagging reduces misclassification. The SVM Bagging approach was more effective than a single SVM in classifying stunting risk. The novelty and scientific contribution of this study lie in applying ensemble machine learning methods, particularly Bagging SVM, to enhance early detection of stunting risk. This method offers a reliable solution for improving stunting risk classification accuracy and strengthening targeted nutrition interventions in Indonesia.
Comparison of Mack Chain-Ladder and Bootstrap Methods for Claim Reserve Estimation under IFRS 17 in Lampung General Insurance Tiara Yulita; Putri Isnaini Cahyaning Baiti; Dila Tirta Julianty; Ayu Sofia; Dwi Mahrani; M. Naufal Athaatmaja
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.v10i3.38485

Abstract

Claim  reserves are funds set aside by insurance companies to pay for reported claims (RBNS) as well as claims that have not yet been reported (IBNR), and they are crucial because they directly affect the financial health of the company. In 2024, there were customer complaints in Lampung regarding delays in claim payments by general and life insurance companies. Therefore, this study uses claim data from general insurance companies in Lampung for the period 2013–2024. The novelty of this study lies in comparing the Mack Chain Ladder analytical method and the Bootstrap simulation method for estimating claim reserves within the IFRS 17 framework using regional insurance data from Lampung, which has not been widely explored in previous studies. This study aims to estimate claim reserves and estimate the Liability for Incurred Claims (LIC),The objective of this study is to compare claim reserve values using an analytical approach (Mack Chain-Ladder) and a simulation approach (Bootstrap), implemented in accordance with the International Financial Reporting Standard (IFRS) 17. The IFRS 17 components to be calculated include the Liability for Incurred Claims (LIC) , Best Estimate Liability (BEL), and Risk Adjustment (RA) under IFRS 17. . Accurate estimation of claim reserves and the implementation of IFRS 17 play a vital role in ensuring the sustainability of insurance companies. The Mack Chain-Ladder (MCL) method is used to obtain equations for the expected value and variance of future claims as well as the prediction error rate. Meanwhile, the Bootstrap method generates numerous simulated claim datasets that reflect various possible scenarios. The advantage of the simulation approach is its ability to provide a full predictive distribution, which can be used to estimate the risk adjustment under IFRS 17. The empirical results show that the estimated claim reserve using the Mack Chain-Ladder (MCL) method is 234,740,644, while the Bootstrap method with 5.000 simulations produces a reserve range ofIn addition, this study also discusses methods for calculating capital requirements based on Value at Risk and for estimating risk adjustment using risk measures applied to the simulated distribution of claim liabilities over the contract period. 233,158,004-236,320,156. These results provide empirical insights into claim reserve estimation and support the implementation of IFRS 17 in regional insurance companies by calculating the BEL, RA, and LIC values, whose results are based on the claim reserve calculation .
Computational Analysis of Xception and ConvMixer Architecture in Classification of Skin Disease Images using Geometric Transformation Maya Isafa Sam Saputri; Sugiyarto Surono; Aris Thobirin
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.v10i3.37037

Abstract

This research seeks to evaluate and contrast the effectiveness of two deep learning models, Xception and ConvMixer, for classification of skin disease images. An experimental methodology was employed using the Massive Skin Disease. The data is divided into training, validation, and test data with a ratio of 80:10:10. The pre-processing stage includes resizing, normalization, and the application of geometric augmentation to improve visual variation in the training data. Both models were trained using equalized parameters so that comparisons were made objectively. The models were assessed through several evaluation metrics, including loss, accuracy, precision, recall, and F1-score metrics in a multi-class classification scheme. The results showed that Xception obtained a test accuracy of 99,70%, while ConvMixer achieved 94,60%. Additionally, Xception exhibits faster convergence and more stable inter-class performance consistency, while ConvMixer excels in compute time efficiency. This study contributes in the form of a comparative analysis of two modern architectures with training parameters that are equalized in the classification of skin diseases. However, the study is still limited to the use of a partial class and a single dataset, so further testing is needed to ensure the generalization capabilities of the model over a wider range of scenarios.

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