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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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Spatial Fuzzy Clustering Algorithm for Optimizing Inclusive Da'wah Distribution Patterns Karim, Abdul; Adeni, Adeni; Riyadi, Agus; Mursyid, Achmad Yafik
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.30599

Abstract

This article aims to identify and analyse the potential for inclusive da'wah in Central Java Province, Indonesia, by focusing on three fundamental aspects that determine the success of the da'wah process: the subject, the object, and the environment of the da'wah. This research applies an empirical approach through a series of spatial clustering analyses using the fuzzy geographically weighted clustering (FGWC) method to determine the optimum number of clusters in mapping the potential for da'wah. FGWC is a spatial analysis method that combines the concept of fuzzy clustering with a geographically weighted approach, allowing for more flexible and contextual identification of distribution patterns based on location. This method was chosen for its ability to handle uncertainty in spatial data as well as considering geographical variations in clustering. The data used in this study came from the Ministry of Religious Affairs of the Republic of Indonesia and the Central Statistics Agency (BPS) of Central Java Province, covering demographic, social, and religious data from 35 districts/cities in Central Java. The results of the FGWC analysis show that the optimum number of clusters is two, with districts/cities in the second cluster identified as having higher da’wah potential. This is evidenced by six high-value variables in the second cluster, while the first cluster has only one high-value variable. These findings have significant implications for inclusive da'wah strategies in Central Java. These results can be used as a strategy for mapping priority da'wah areas, allocating effective resources, and developing a more contextualised da'wah approach according to the characteristics of each cluster. This research's originality lies in applying the FGWC method in the context of da'wah mapping. This article is the first to combine spatial analysis with a study of the potential for inclusive da'wah, thus contributing to developing an interdisciplinary approach in the study of contemporary Islam in Indonesia.
Spatial Clustering Regression in Identifying Local Factors in Stunting Cases in Indonesia Syam, Ummul Auliyah; Djuraidah, Anik; Syafitri, Utami Dyah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29803

Abstract

Stunting is a significant health problem in Indonesia with high spatial disparities between regions. This study applies the Spatial Clustering Regression (SCR) method to analyze spatial patterns and identify local factors influencing stunting. SCR is a method that combines spatial regression and clustering analysis simultaneously using a k-means clustering-based formulation and a penalty likelihood function motivated by the Potts model to encourage similar clustering in adjacent locations with regression parameter estimation done locally in areas that have similar characteristics. This quantitative study uses secondary data from the Central Bureau of Statistics in 2022 covering 510 districts/cities, with one response variable (percentage of stunting) and seven explanatory variables reflecting socioeconomic, health, and infrastructure conditions. The results show that SCR divides the region into four spatial clusters characterized by different local factors. Cluster 1 has the lowest percentage of stunting that is influenced by access to clean water, sanitation, and education, Cluster 2 by poverty rate, number of public health centers, access to clean water, and education, Cluster 3 by poverty and nutrition of pregnant women, and Cluster 4 is the most vulnerable area with the highest stunting rate with a significant influential factor which is access to sanitation. The SCR approach allows for easier and more in-depth interpretation of results than other spatial methods such as GWR, as it can capture complex spatial patterns in the form of regional clusterings. These results provide a strong basis for formulating region-specific intervention policies, such as poverty alleviation and sanitation improvement in Cluster 4, strengthening health services in Cluster 2, developing education and nutrition programs in Cluster 3, and maintaining and improving nutrition consumption in Cluster 1.
Multilevel Semiparametric Modeling with Overdispersion and Excess Zeros on School Dropout Rates in Indonesia Tarida, Arna Ristiyanti; Djuraidah, Anik; Soleh, Agus Mohamad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.30102

Abstract

This study aims to identify key factors influencing high school dropout rates in Indonesia by applying advanced statistical modeling that accounts for complex data characteristics. Dropout data often display overdispersion (variability greater than expected) and excess zeros (many students not dropping out), which, if ignored, can bias conclusions.  To address this, we compare parametric models, Zero-Inflated Poisson Mixed Model (ZIPMM), Zero-Inflated Generalized Poisson Mixed Model (ZIGPMM), and Zero-Inflated Negative Binomial Mixed Model (ZINBMM), with their semiparametric counterparts (SZIPMM, SZIGPMM, SZINBMM). The semiparametric models use B-spline functions to capture nonlinear relationships between predictors and dropout rates, with flexibility. Model performance was evaluated using Akaike Information Criterion (AIC) and Root Mean Square Error (RMSE) across 100 simulation repetitions to ensure robustness. Results show that the semiparametric ZIGPMM (SZIGPMM) outperformed other models, achieving the lowest average AIC (18969.62), suggesting the best trade-off between model fit and complexity. The optimal spline configuration used knot point 2 and order 3, with a Generalized Cross-Validation (GCV) score of 9.4107. Key predictors of dropout include school status (public or private), student-teacher ratio, distance from home to school, parental education level, parental employment status, and number of siblings. These findings provide actionable insights for education policymakers, emphasizing the need to address structural and socioeconomic barriers to reduce dropout rates effectively.
Identification of Demographic Factors Affecting Student Performance using Tree-Based Machine Learning Models Murwaningtyas, Chatarina Enny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.28815

Abstract

This study aims to identify key academic and demographic factors influencing student performance in the Logic and Set Theory course, particularly in the context of different learning modes during and after the COVID-19 pandemic. It adopts a quantitative exploratory design involving students from the 2020 to 2023 cohorts at Sanata Dharma University. Academic data (exam and assignment scores, course outcomes) and demographic data (e.g., parental education and income, region of origin, gender, and high school major) were collected from the academic system and supplemented via questionnaires. The dataset was cleaned, encoded, and normalized using RobustScaler, with class imbalance addressed through SMOTE. Descriptive statistics were used to explore initial data characteristics. Five tree-based machine learning models, Decision Tree, Random Forest, XGBoost, LightGBM, and CatBoost, were implemented within a pipeline that included preprocessing and model optimization using GridSearchCV with 5-fold cross-validation. Model evaluation employed multiple metrics, including accuracy, precision, recall, F1-score, AUC, and Average Precision. Results showed that XGBoost and CatBoost achieved the best performance (accuracy 92%, AUC 0.99) with balanced precision and recall across all four performance categories. Feature importance analysis indicated that exam and assignment scores were the strongest predictors, while demographic factors such as enrollment year, parental education, and income contributed moderately. Variables like gender, region, and high school major had minimal influence. This research demonstrates how machine learning can effectively integrate academic and demographic data, rather than analyzing them in isolation, to uncover nuanced patterns in student achievement. The findings support the development of data-driven educational interventions, such as preparatory learning modules, peer mentoring for underperforming groups, targeted academic advising for students from low-income or less-educated families, and flexible instructional strategies for cohorts affected by pandemic-related disruptions. 
Spatial Clustering Analysis of Hand, Foot, and Mouth Disease in Jakarta using Local Indicator of Spatial Association Cluster Map and K-Means Clustering Sabila, Fatsa Vidyaningtyas; Widyaningsih, Yekti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.30339

Abstract

Hand, Foot, and Mouth Disease (HFMD) is a infectious disease characterized by ulcers and blisters, primarily affecting children. The objective of this quantitative study is to identify areas with the highest HFMD cases (hotspot areas) in Jakarta in 2024 and to classify areas (districts) based on the number of HFMD cases and variables associated with the disease. The analysis employs the Local Indicator of Spatial Association (LISA) Cluster Map to detect spatial hotspots and K-Means Clustering to group districts by HFMD cases and related variables. LISA is a univariate method for detecting hotspots based on the local Moran’s Index that measures spatial dependence, whereas K-Means Clustering is a multivariate method for grouping individuals based on multiple variables. This study uses data from official government sources, including the number of HFMD cases, population density, average number of students per kindergarten, and average number of students per elementary school. The results of this study show that the LISA clustering reveals Kalideres and Cengkareng as High-High (H-H) clusters, while Tanah Abang, Menteng, and Senen form Low-Low (L-L) clusters. Makasar is classified as a Low-High (L-H) cluster. In contrast, the K-Means clustering groups districts into four clusters based on HFMD cases and related demographic factors, sorted in ascending order of HFMD cases. Areas with the lowest HFMD cases tend to have a moderate population density and fewer average number of students per kindergarten, while areas with the highest cases tend to have a lower population density but a higher average number of students per kindergarten. Areas classified as high cases HFMD by both methods, such as Cengkareng, should be prioritized for intervention. Cengkareng represents a district with the highest HFMD cases despite having a relatively low population density, along with a high average number of students per kindergarten and per elementary school. 
Portfolio Optimization for Rupiah Exchange Rate using Multidimensional Geometric Brownian Motion Model Masitah, Siti; Budiarti, Retno; Purnaba, I Gusti Putu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29953

Abstract

Exchange rate fluctuations are critical in ensuring economic stability and shaping foreign investment, while foreign currencies serve as asset and wealth diversification instruments. This study aims to predict foreign exchange rates with a multidimensional geometric Brownian motion model and determine the optimal portfolio fund allocation with the Markowitz model using the Moore-Pendrose method. The multidimensional GBM model was employed for its ability to capture the volatility and interdependence among multiple currencies, making it more suitable for multi-asset portfolios than univariate models. The Markowitz model was used to determine the optimal asset allocation that achieves a specified expected return with minimal risk, while the Moore-Penrose method was applied to address matrix inversion challenges in high-dimensional data. Using data from 2023 to April 2024 on the Indonesian rupiah against the Singapore Dollar (SGD), Chinese Yuan (CNY), and Euro (EUR), this study finds that the multidimensional GBM model effectively forecasts exchange rate movements, as indicated by MAPE values below 10% for each currency. "The optimal portfolio yields a risk of 0.28% and an expected return of 0.009%, with asset allocations of 90.3% in SGD, 8.2% in CNY, and 1.5% in EUR. The dominance of SGD in the optimal portfolio suggests it was the most favorable investment option against the rupiah during the study period. This reflects Singapore's strong economic fundamentals and strategic position as a global financial hub. These findings provide valuable insights for investors and financial analysts seeking to manage currency risk and enhance returns through data-driven diversification strategies.
Simulation-Based Pricing and Settlement Price Distributions of Indonesian Structured Warrants Sasongko, Leopoldus Ricky; Mahatma, Tundjung; Robiyanto, Robiyanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29282

Abstract

The Indonesian capital market has experienced significant growth, marked by the introduction of Structured Warrants (SWs) as innovative financial instruments. This study aims to develop a robust simulation-based pricing model for Indonesian Call SWs utilizing the Geometric Brownian Motion (GBM) framework and to determine their settlement price distributions. Monte Carlo simulations were employed to accurately capture the specific characteristics of Indonesian Call SWs, notably their average-price settlement mechanism and conversion rates. The results indicate that the settlement prices conform to a lognormal distribution, validating the GBM assumption and aligning with key trading metrics such as implied volatility, which is widely utilized in the Indonesian SW market. Additionally, the Symmetrical Auto Rejection rule, which imposes realistic constraints on underlying asset price movements, significantly enhances model realism and better reflects actual market conditions. The findings reveal that simulated Indonesian Call SW prices are slightly lower compared to values derived from the Black-Scholes model adjusted for conversion rates, highlighting opportunities for further refinement of pricing methodologies. Investors can leverage these insights to better assess risks and returns by anticipating volatility and price trends, with paying close attention to conversion rates and settlement mechanisms. Issuers may benefit from improved pricing accuracy, thus minimizing mispricing risks, while regulators can utilize this research to assess current market rules and design policies aimed at increasing market efficiency and transparency. 
The Future of Augmented Reality Immersive Technology-Based Mathematics Learning: A Meta-Analysis Study Tamur, Maximus; Subaryo, Subaryo; Marzuki, Marzuki; Ngao, Ayubu Ismail; Castulo, Nilo Jayoma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.31033

Abstract

Immersive technology with augmented reality (AR) as a didactic support has gone global and enriched the learning process with various packages of advantages. Although there have been many meta-analyses to test the aggregate effect of AR on students' academic performance, few have considered the duration of treatment as a moderator variable and also the comparison of the effect of AR in mathematics learning with other subjects. This study was conducted to. This random effect meta-analysis study was conducted to test the effectiveness of the application of immersive AR technology in learning by considering the duration of treatment and subject matter as research features and specifically identifying data from the Scopus database. This objective was achieved by examining 73 independent comparisons (n = 2822) that met the requirements and were identified from the Scopus database. The results of the CMA software-assisted analysis showed that the integration of immersive augmented reality technology in learning had a moderate effect (g = 0.75, p < 0.005) compared to learning conditions without AR. These results also add empirical validity to the relationship between categorical variables and the size of the research effect, as needed to understand research in the context of the application of AR in mathematics learning in the future. By clarifying the impact of AR implementation in mathematics learning, this study contributes to teachers to improve teaching effectiveness, enrich interactive learning media, and arouse students' interest and understanding of mathematical concepts in a more concrete and visual way. These findings also provide new directions for teachers, lecturers, stakeholders, and professionals in their efforts to develop a didactic framework by considering the duration of treatment in future AR applications.
Digital Teaching Material Transformation: Design Student Worksheets using GeoGebra Based on Local Wisdom by Pre-service Teachers Sugiarni, Rani; Jusniani, Nia; Rodríguez-Nieto, Camilo Andrés
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.31034

Abstract

The limited ability of teachers to design interesting digital mathematics teaching materials, as well as the context that is free from local participant wisdom, also causes misconceptions and difficulties in understanding mathematical concepts in depth for students. This study aims to analyze the ability of pre-service mathematics teachers to design student worksheets using the GeoGebra application based on local wisdom in mathematics learning. This study uses a qualitative method with a descriptive analytical approach to describe the ability of the pre-service mathematics study program to design student worksheets with Geogebra software based on local wisdom in mathematics learning. Participants in this study were in the pre-service mathematics education study program in West Java. The data collection technique used documentation in the form of student digital open material designs. The digital teaching materials designed by pre-service mathematics students are worksheets with GeoGebra software based on local wisdom. The research instruments were lecturer and teacher assessment sheets to ensure the feasibility of digital teaching materials and student response questionnaires for the practicality of the results of the digital teaching material plan used by students. The results of the study can be explained by the fact that the ability of students in the mathematics education study program to create digital open materials, namely student worksheets and GeoGebra software media, is worthy of the high category as assessed by lecturers and teachers. Meanwhile, the students' response to the socialization of digital open media design by students gave a positive response with a high category. Thus, students' digital teaching materials support meaningful mathematics learning for students with technology and local wisdom.
Development of Android-Based Game Media in Improving Students' Mathematical Literacy Suryani, Eka; Susanti, Ely; Aisyah, Nyimas
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.28323

Abstract

This research aims to develop an Android-based learning media to enhance junior high school students' mathematical literacy, particularly in understanding numbers. It employs a development research approach with a qualitative methodology supported by quantitative data. The research follows the Research and Development (R&D) method, adapted from the Plomp model. The innovation involves the creation of a game-based learning media using an Android platform. The game itself is a web-based application developed through Wordwall. The study's subjects consist of 26 seventh-grade students, selected from MTs GUPPI Sukamoro in Banyuasin Regency and Srijaya Negara Junior High School in Palembang City.  The data collection techniques used in this study included: (1) a validation sheet to assess the validity of the game product,  (2) a student response questionnaire consisting of 11 questions to assess the practicality of the game, (3) pretest and posttest to assess students' mathematical literacy, and (4) interviews conducted if issues arose after the game and test were administered. Data analysis was carried out using quantitative methods. The validity and practicality levels of the data are analyzed using percentages, while the test data is evaluated based on the N-gain value.  The results indicated that the Android-based game achieved a validity score of 77.54%, categorized as good. The data test results were 0.65 and 0.58, falling within the moderate criteria. Additionally, the classical average scores were 96.1% and 100%, with students achieving an average score of 84.69 and 83.88. These findings demonstrate that the Android-based learning media is both valid and effective in enhancing mathematical literacy on number concepts among seventh-grade students.

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