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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.
Arjuna Subject : -
Articles 540 Documents
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Modeling Zero-Inflated Poisson Invers Gaussian Regression Bayesian Approach Jannah, Berliana; Wardhani, Ni Wayan Surya; Sumarminingsih, Eni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34068

Abstract

Deaths due to dengue hemorrhagic fever (DHF) remains one of the most pressing public health issues in Indonesia, especially in urban areas such as Semarang City, which has a high population density and diverse environmental conditions that potentially increase the risk of transmission and death from DHF. This study aims to model the number of DHF in Semarang City using a Bayesian-based Zero-Inflated Poisson Inverse Gaussian Regression (ZIPIGR) approach. The research data was obtained from the Semarang City Health Office and the Central Statistics Agency (BPS) in 2024, with the response variable being the number of DHF deaths and five predictor variables. The data showed overdispersion and a high proportion of zeros (around 50%), indicating the presence of excess zeros in count data with a small sample size. The Bayesian ZIPIGR method was chosen because it can produce more stable parameter estimates than classical methods such as Maximum Likelihood Estimation (MLE), especially for data with complex likelihood functions, small sample sizes, and many zero values. Parameter estimation was performed using Gibbs Sampling simulation in the Markov Chain Monte Carlo (MCMC) framework. The results show that the Bayesian ZIPIGR model performs better than the MLE ZIPIGR model based on the Root Mean Square Error (RMSE) value. Factors that significantly influence DHF mortality are population density, slum area, and number of health workers. These results confirm that regional density and health worker capacity play an important role in increasing the risk of DHF mortality in urban areas. The developed model has been proven to be highly accurate in modeling count data with excess zero characteristics and makes an important contribution to health policy formulation. In practical terms, this model can be used to improve early warning systems and DHF control strategies in densely populated urban areas such as the city of Semarang.
Mathematics Learning Activities using Vignette Activity Sequence (VAS) and Braille Clock for Visually Impaired Students Maghfiroh, Diva Lailatul; Damayanti, Nia Wahyu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34839

Abstract

Mathematics learning for students with visual impairments is often challenging because many concepts are visual in nature, including units of time that require an understanding of the spatial position of clock hands. This condition requires a more concrete, tactile, and structured learning approach so that concepts can be understood meaningfully. This study aims to describe how Vignette Activity Sequence (VAS) based mathematics learning with braille clock media supports the understanding of time unit concepts in students with visual impairments. This study uses a double case study qualitative approach with two subjects, one with low vision and one with full blind student, selected through purposive sampling. The intervention lasted for one month through a series of VAS sessions that integrated contextual narratives, tactile exploration, and manipulative activities using braille clocks. Data were obtained through observation, semi-structured interviews, and documentation, then analyzed using the Miles and Huberman interactive model. The results showed that VAS helped both subjects understand the relationship between the movement of the short hand and the rotation of the long hand, albeit at different rates of development. The low vision subject was quicker to recognize numbers and understand time units, while the totally blind subject showed gradual improvement in tactile orientation and number touching strategies. Both experienced increased accuracy in reading time and moving the clock hands after attending repeated sessions. These findings confirm that the integration of VAS and braille clocks provides an effective and inclusive multisensory learning experience for students with visual impairments.
Dimensionality Reduction Evaluation of Multivariate Time Series of Consumer Price Index in Indonesia Valentika, Nina; Sumertajaya, I Made; Wigena, Aji Hamim; Afendi, Farit Mochamad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34151

Abstract

Multivariate time series (MTS) analysis of the Consumer Price Index (CPI) in Indonesia often encounters challenges such as outliers, missing data, and inter-variable correlations. Principal Component Analysis (PCA) is a practical approach for dimensionality reduction; however, its performance may vary depending on the data characteristics. This study is a quantitative comparative study that integrates empirical analysis and Monte Carlo simulation based on a first-order Vector Autoregressive (VAR(1)) model to evaluate three PCA approaches: Classical PCA, Robust PCA (RPCA), and PCA of MTS. These methods were applied to weekly price data of eight strategic food commodities across 70 districts and cities in Indonesia. The evaluation employed three criteria: (1) dimensionality reduction efficiency (empirical and simulation), (2) reconstruction accuracy measured using Root Mean Square Error (RMSE) (empirical), and (3) robustness to outliers and inter-variable correlations (simulation). Empirical results indicate that Classical PCA (lag 1) and RPCA (lag 1) are both efficient and effective in reducing dimensionality with minimal information loss. Using the first three principal components, all three methods were able to explain at least 85% of the total variance, with lag 1 identified as optimal. Simulation results reveal that RPCA (lag 1) provides the most stable and consistent performance in the presence of outliers, while Classical PCA (lag 2) performs better under conditions of high inter-variable correlation and a low proportion of outliers. These findings suggest that robust covariance estimation can improve the accuracy of dimensionality reduction and enhance the stability of multivariate time-series analysis for food price data in Indonesia.
Innovative Mathematics Learning: The Impact of Augmented Reality and Ethnomathematics on Communication Skills Tamur, Maximus; Jehadus, Emilianus; Jackaria, Potchong M.; Castulo, Nilo Jayoma; Ngao, Ayubu Ismail
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34363

Abstract

The integration of digital technology with a cultural approach has become an important innovation in mathematics education to enhance meaningful learning. However, there is still limited research combining Augmented Reality (AR) with ethnomathematics to strengthen students' mathematical communication skills. This study aims to analyze the impact of Augmented Reality and ethnomathematics-based learning on students' mathematical communication skills. The study employed an experimental design involving 60 seventh-grade students selected randomly from eight classes at SMP Negeri 6 Langke Rembong, Ruteng, Indonesia, during the 2024/2025 academic year. The research instrument consisted of a five-item mathematical communication test, which was validated through expert judgment and empirical testing, and demonstrated satisfactory reliability based on internal consistency analysis. SPSS and CMA software were used to support data analysis. A t-test was conducted to examine differences in mathematical communication ability between the experimental and control groups after fulfilling prerequisite assumptions. The findings indicate that the integration of AR and ethnomathematics significantly improved students’ ability to express mathematical ideas clearly, both orally and in written form. Additionally, students showed higher levels of cultural engagement and appreciation, which positively contributed to the development of their communication skills. This study recommends the integration of AR and ethnomathematics as a sustainable innovation in mathematics learning and suggests further research to explore its application across diverse mathematical topics and broader educational contexts.
Application of Kernel Nonparametric Biresponse Regression with the Nadaraya-Watson Estimator in Poverty Analysis in South Sulawesi Husain, Hartina; Nisardi, Muhammad Rifki; Sasolo, Ryo Hartawan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33543

Abstract

Poverty is a complex social issue that requires in-depth analysis to identify its contributing factors. South Sulawesi, as one of the provinces in Indonesia, continues to face various challenges in poverty alleviation. This study is a quantitative research that aims to model the poverty rate and poverty severity index using a biresponse nonparametric kernel regression with the Nadaraya-Watson estimator and Gaussian kernel function. The analysis is based on 2024 data form the Central Bureau of Statistics (BPS), which includes poverty indicators as response variables and socio-economic factors, processed using R Studio 2025. The nonparametric biresponse kernel regression analysis yielded optimal bandwidths of h_1=0,188; h_2=0,083; h_3=0,159; and h_4=0,028. Model accuracy is demonstrated by a Generalized Cross-Validation (GCV) value of 5.515 and a Mean Squared Error (MSE) of 0.585, indicating high stability and low prediction error. The model demonstrates adaptive accuracy in simultaneously modeling the two response variables and highlights the strength of kernel-based biresponse regression as an evidence-based tool for policymakers to design targeted, region-specific poverty alleviation strategies.
Arithmetic Adventure: A Role-Playing Game to Support Students’ Mathematical Thinking on Arithmetic Sequences Nurrosyadah, Naqiyyah; Susanti, Ely; Somakim, Somakim
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35260

Abstract

This study aims to develop an educational Role-Playing Game (RPG) entitled Arithmetic Adventure: The Mystery of Polaria Village to support students’ mathematical thinking on arithmetic sequences. The research employed a Development Research approach using the ADDIE model, which consists of Analyze, Design, Development, Implementation, and Evaluation stages. The subjects were 10th-grade students of SMA Negeri 10 Palembang who had implemented the Merdeka Curriculum. Data were collected through expert validation, student practicality questionnaires, and mathematical thinking ability tests. The results indicated that the RPG obtained an overall average validity score of 4.45, categorized as very valid in terms of content, construct, language, and ICT aspects. Practicality testing showed an average percentage of 86.25%, placing the RPG in the very practical category. Furthermore, the potential effect test revealed that 48.6% of students achieved good, 28.6% very good, and 22.9% fair in mathematical thinking ability, showing improvements in specializing, generalizing, conjecturing, and convincing. These findings demonstrate that Arithmetic Adventure is a valid, practical, and potentially effective educational game for supporting students’ mathematical thinking in arithmetic sequences. The study provides theoretical contributions by reinforcing the role of RPGs in fostering mathematical thinking and practical contributions by offering an innovative alternative medium for mathematics learning. 
The Severe Stunting Cases of Children in Central Java Province Explained by Negative Binomial Regression Model Widiyanto, Rhendy K. P.; Fauzi, Fatkhurokhman; Fauzan, Achmad; Kurnia, Anang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34846

Abstract

Severe stunting, or very short stature among children, remains a critical public health concern in Central Java Province. Robust statistical modelling is essential to identify the key factors associated with these cases and to guide targeted interventions. This study employs count regression models with an offset variable to analyze the factors influencing severe stunting cases across districts in Central Java. By using 2023 official data in districts level taken from the Ministry of Home Affairs and the Statistics Indonesia, we initially utilize a Poisson regression model in this study. However, due to evidence of overdispersion, a Negative Binomial regression model was adopted. Backward elimination was then applied to obtain the most parsimonious model. The Negative Binomial regression successfully addressed overdispersion. Five factors were identified as having a statistically significant influence on severe stunting cases: (1) the proportion of pregnant mothers with Chronic Energy Deficiency receiving nutritious food supplements, (2) the percentage of toddlers (6-23 months) receiving complementary nutritious food, (3) the proportion of households with access to good sanitation, (4) Gross Domestic Product per capita, and (5) the number of local healthcare facilities. These factors have negative relation to the stunting rates, meaning improving these factors will reduce the rates of severe stunting. The findings provide a validated statistical model for severe stunting and offer clear policy directions. To mitigate severe stunting, local governments should prioritize: enhancing nutritious food support for pregnant mothers and toddlers, improving household sanitation, stimulating local economic growth, and increasing accessibility to healthcare facilities.
Geostatistical Co-Kriging Approach for Estimating Total Coliform Bacteria in the Rivers of DKI Jakarta Salsabila, Salwa; Sirodj, Dwi Agustin Nuriani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34391

Abstract

Spatial statistics and geostatistics are essential for analyzing spatially distributed data, particularly in environmental studies where data gaps are prevalent. However, limited studies have applied multivariate geostatistical approaches, particularly Co-Kriging (CK), to assess microbial contamination in tropical urban river systems, where pollution patterns are highly variable and data gaps are frequent. This study employs CK, a multivariate geostatistical interpolation technique, to estimate Total Coliform Bacteria concentrations in the rivers of DKI Jakarta, Indonesia. Total Coliform Bacteria served as the primary variable, with Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) incorporated as secondary variables. A total of 120 sampling points were analyzed, with data collected by Dinas Lingkungan Hidup DKI Jakarta during the second monitoring period in June 2022. Semivariogram modelling identified the Gaussian model as the best fit, yielding the lowest root mean square error (RMSE) of 11.468, which performed better than both the Spherical and Exponential models. Model performance was further evaluated through Leave-One-Out Cross-Validation (LOOCV), in which one data point was systematically removed and re-estimated in multiple iterations to calculate the residuals and assess model accuracy. The CK analysis was performed using RStudio software. CK predictions closely matched observed concentrations, demonstrating strong model performance. At unsampled locations, the estimated mean Total Coliform Bacteria concentration was 7.711 × 10⁶ MPN/100 ml with a standard deviation of 4.406 × 10⁶ MPN/100 ml. The high variance indicates substantial spatial heterogeneity, likely driven by data outliers, weak spatial autocorrelation in COD, and low correlations between Total Coliform–COD and BOD–COD pairs. These findings highlight the potential of geostatistical CK to provide reliable spatial predictions of microbial contamination in urban river systems, thereby supporting evidence-based water quality monitoring and management in densely populated regions. The insights generated in this study can help environmental authorities in DKI Jakarta optimize monitoring strategies, prioritize pollution hotspot interventions, and strengthen urban river health management to protect public health and guide sustainable urban water governance.
Optimization of Rice Production Forecasting using Hybrid ANN-PSO Windasari, Wahyuni; Nugraheni, Anggit Gusti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34879

Abstract

Rice production is a critical component in sustaining national food security, especially Indonesia. The availability of sufficient, affordable, and equitable food is a major challenge for Indonesia. One approach to addressing this challenge is by developing reliable and accurate models for predicting food production. In this study, a hybrid approach that combines Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) algorithms is used to optimize the performance of modeling and prediction of rice production in Central Java, Indonesia. This study uses secondary data in the form of monthly time series data from the Central Java Provincial Statistics Agency (BPS), Meteorology, Climatology, and Geophysics Agency (BMKG), and satellite imagery data with an observation period from January 2019 to December 2024. The input variables in this study include harvested area, precipitation, number of rainy days, atmospheric pressure, wind speed, NDWI, and NDVI while the output variable is rice production in Central Java. The test results using the ANN model provided an RMSE value of 0.1312 and a MSE of 0.0172, while the ANN-PSO model provided an RMSE value of 0.0259 and a MSE of 0.00067. These results indicate that the PSO algorithm is able to optimize the performance of the ANN model in predicting rice production in Central Java. 
Transformation of Junior High School Mathematics Learning: Integration of Interactive Student Worksheet and Virtual Reality Based on Deep Learning Approach Istihapsari, Vita; Kusuma, Jaka Wijaya
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33737

Abstract

Mathematics learning in junior high schools still faces challenges in building active student engagement, deep conceptual understanding, and the application of technology during the learning process. This study aims to describe the transformation of the implementation of mathematics learning in junior high schools through the integration of interactive Student Worksheets (LKPD) and Virtual Reality (VR) based on the Deep Learning approach. The research employed a qualitative descriptive method, with data collected through classroom observations and interviews involving four classes of grade VII students and interviews with four grade VII mathematics teachers from four different junior high schools. Before implementation, all research instruments including the interactive LKPD, VR media assisted by Artsteps, observation sheets, and interview guidelines were validated by three experts in mathematics education and educational technology, and the results were categorized as very valid. Data were analyzed using the Miles and Huberman model, consisting of four stages: data collection, data reduction, data presentation, and conclusion drawing. The result of this study is that the application of the Deep Learning approach supported by interactive LKPD and VR media received a positive response from teachers and students. Interactive LKPD and VR Media effectively support the Deep Learning stages, namely (1) Introduction of material with context, (2) In-depth presentation of material, (3) Project-based assignments, (4) Discussion and collaboration, (5) In-depth reflection, (6) Provision of constructive feedback, (7) Competency-based assessment (8) Use of technology in learning, (9) Independent learning and self-regulation, (10) Evaluation and development on an ongoing basis. The implementation of learning is in line with the principles of Deep Learning, namely knowledge connectedness, active involvement, critical and reflective thinking, problem-based learning, collaboration, and intrinsic motivation; and also in line with the Deep Learning learning experience, namely understanding, applying and reflecting. These results show that the integration of interactive LKPD and VR media can be an effective strategy to transform mathematics learning at the junior high school level.

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