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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 24 Documents
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Search results for , issue "Vol 9, No 2 (2025): April" : 24 Documents clear
Integrated Differentiated Learning Social-Emotional Competence: An Innovative Solution to Numeracy Skills Gunawan, Gunawan; Pertiwi, Budi Wahyu; Ferdianto, Ferry; Akhsani, Lukmanul
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.v9i2.28286

Abstract

A crucial aspect in various disciplines is numeracy skills. The purpose of the study was to determine the difference in the average social-emotional competence and numeracy skills of students before and after the implementation of differentiated learning that integrated social-emotional competence. The research was conducted at SMP Negeri Satu Atap 1 Cimanggu, Cilacap. The sample in this study was selected using the saturated slicing technique involving 22 grade VIII students. The type of research is an experimental study that uses a pre-experimental design with a one-group pre-test post-test method. The data collection techniques used include observation, tests, and questionnaires. There are 20 questions in the questionnaire. Data analysis was carried out quantitatively using paired sample t-tests and descriptive statistics. Before conducting the analysis, a prerequisite test was carried out using a normality test to test the distribution of data. The results of the study showed that the numeracy skills had a significance value of 0.200 (>0.05) and the social-emotional competence had a significance value of 0.11 (>0.05) which showed that the data was normally distributed. The results of the analysis showed that the value of the t-test of numeracy was 49.423 (t-test > ttable), with a significance value (2-tailed) < 0.05 (0.00 < 0.05). For KSE, the statistical value of the t-test was 27.54 with a very small p-value (5.75×10⁻¹⁸) indicating that there is a significant difference in the average value of numeracy skills and KSE before and after the implementation of integrated differentiation learning KSE. Integrated differentiation learning KSE can be applied to improve numeracy skills. The results of this study can be used as a solution to overcome the low mathematical numeracy skills of students.
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.
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. 
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. 
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.
Estimation of Tail Value at Risk for Bivariate Portfolio using Gumbel Copula Fransiska, Fransiska; Sulistianingsih, Evy; Satyahadewi, Neva
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.v9i2.29952

Abstract

Investing in the stock market involves complex risks, especially under extreme and unpredictable conditions. While Value at Risk (VaR) is a widely used risk measure, it has limitations in capturing tail-end risks. This study employs Tail Value at Risk (TVaR) using the Gumbel Copula approach, which effectively models upper-tail dependence in return distributions—an aspect often overlooked by traditional linear correlation methods. This quantitative research utilizes copula-based Monte Carlo simulation. The data consists of daily closing prices of PT Adaro Energy Indonesia Tbk (ADRO) and PT Indo Tambangraya Megah Tbk (ITMG) from July 3, 2023, to July 30, 2024. The analysis begins with return calculation and tests for autocorrelation and homoskedasticity. The Gumbel Copula parameter is estimated using Kendall’s Tau, resulting in a dependence parameter of 1.7791. Based on this, 1,000 simulations are conducted to generate new return data that reflect extreme dependencies between the two stocks. An optimal portfolio is constructed using the Mean-Variance Efficient Portfolio (MVEP) method, assigning weights of 31.61% to ADRO and 68.39% to ITMG. TVaR is then calculated from the simulated portfolio returns. The results show increasing TVaR values at higher confidence levels: 2.08%, 2.64%, 3.14%, and 4.11% for 80%, 90%, 95%, and 99%, respectively. These findings demonstrate that TVaR provides more accurate insights into potential losses in extreme market conditions, supporting investors in developing more informed and risk-sensitive portfolio strategies.
Forest Fires in Peatlands Analyzed from Various Perspectives: Spatial, Temporal, and Spatial-Temporal Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri; Ayyash, Muhammad Yahya; Pratiwi, Hesty
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.v9i2.28884

Abstract

Peatland fires are characterized by the compaction of organic matter below the soil surface. If dry conditions occur, the organic matter can burn, making it difficult to extinguish the fire. This study aims to analyze peatland forest fires with three perspectives, namely temporal, spatial, and spatial-temporal. The data used is the confidence level data of hotspots in forest fires in Kubu Raya Regency, West Kalimantan from January 2014 to December 2023. The methodology used includes collecting fire data from satellite imagery and prepocessing the data. Furthermore, three different data analyzes were carried out, namely temporal, spatial, and spatial-temporal analysis. The results of the study obtained three perspectives, namely from the time period, handling of forest fire cases because they have an impact on the future as seen from the ARIMA model. Regarding spatiality, the distribution of hotspots spread to surrounding areas that were heavily affected by hotspots as seen from the contour map using Kriging interpolation. Finally, regarding spatiality and temporality, forest fire projections show that locations that are close together and have a history of being affected by forest fires have a strong potential for the distribution of forest fire cases as seen from the GSTAR space-time model.
Analyzing Multiclass Land Cover and Spatial Point Patterns on Sentinel-2 Imagery Using Machine Learning and Deep Learning Nabilah, Muna Faizatun; Fauzan, Achmad
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.v9i2.29683

Abstract

Land cover conversion around educational centers, such as universities, is an inevitable consequence of increasing urban activity. The development of boarding houses, commercial zones, and other infrastructure often follows the expansion of academic institutions. To support sustainable spatial planning, early identification of land cover and analysis of spatial distribution patterns are crucial for zoning regulation and infrastructure management. This study focuses on classifying land cover and analyzing spatial patterns around Universitas Riau (UNRI) using Sentinel-2 satellite imagery with a 10-meter spatial resolution. The research applied a supervised classification approach, utilizing spectral bands—specifically Near-Infrared (NIR) and Short-Wave Infrared (SWIR)—as explanatory variables. The response variable was land cover, categorized into vegetation, non-vegetation, and water. Three machine learning models—Support Vector Machine (SVM), Naïve Bayes (NB), and Backpropagation Neural Network (BNN)—were compared based on overall accuracy and the Kappa coefficient. The models were trained and tested using a stratified 80-20 data split to ensure a balanced evaluation. Among the models, SVM demonstrated the highest accuracy, achieving an average of 91.15% in 2022 and 83.90% in 2023 with minimal variance, confirming its reliability for land cover classification. Spatially, non-vegetation areas were concentrated near major access routes and facilities, highlighting the influence of infrastructure development on land conversion. The study also identified potential growth zones within a 3–5 km radius from UNRI, emphasizing the need for anticipatory and sustainable land use policies. These findings support the formulation of spatial strategies aligned with Law No. 26 of 2007 on Spatial Planning and offer valuable insights for guiding urban development around academic hubs.
Spatial Panel Regression Modelling of Rainfall in Indonesia Saniyawati, Fang You Dwi Ayu Shalu; Astutik, Suci; Pramoedyo, Henny
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.v9i2.29882

Abstract

Rainfall is amount of water that falls to the earth's surface in the form of rain during a certain period of time, usually measured in millimeters. Rainfall data in Indonesia usually includes temporal and spatial dimensions, so the appropriate method for its analysis is spatial panel regression analysis. This study aims to identify factors that influence the amount of rainfall in Indonesia. This type of research is quantitative using secondary data from the central statistics agency website. The predictor variables used include air temperature, sunshine radiation, humidity, wind speed, and air pressure, while the response variable is amount of rainfall in 34 provinces in Indonesia. Spatial panel regression analysis is carried out using maximum likelihood estimation, which is used to estimate the regression coefficient and intercept that maximizes the likelihood of the existing data. Based on the lagrange multiplier test, spatial autocorrelation was found in the lag, so the appropriate model is SAR-FE. This model can overcome spatial autocorrelation by taking into account spatial interactions between locations, as well as controlling unobserved heterogeneity through fixed effects. The results show that sunshine radiation, humidity, and wind speed have significant effect on the amount of rainfall in Indonesia. The AIC value of SAR-FE model (-4.352594×〖10〗^(-13)) is smaller than SEM-FE model (-1.642001×〖10〗^(-12)), indicating that SAR-FE model is better at explaining the data.

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