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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 565 Documents
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Analysis of Creative Thinking Ability in Solving Problems Based on Students' Learning Styles Medyasari, Larasati Tiara; Zaenuri, Zaenuri; Dewi, Nuriana Rachmani; Wijayanti, Kristina
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.v10i2.35253

Abstract

Mathematical creative thinking ability plays a crucial role in helping students solve everyday problems. This study aimed to assess students' creative thinking abilities by categorizing them into auditory, visual, and kinesthetic learning styles based on various indicators of mathematical creative thinking ability. This study aims to assess students' creative thinking abilities by categorizing them into auditory, visual, and kinesthetic learning styles based on four indicators of mathematical creative thinking abilities, namely fluency, flexibility, novelty, and elaboration. This research is a qualitative descriptive study. The data collection methods used in this study include tests to determine students’ mathematical creative thinking abilities, interviews, and documentation. The research findings were analyzed and classified into categories representing visual, auditory, and kinesthetic learning styles, with one research subject selected from each category out of 31 students. The results of the research are students with a visual learning style could solve problems fluently and efficiently while drawing accurate conclusions. Additionally, visual learners could approach problems in multiple ways and solve them independently with innovative thinking. Students with an auditory learning style could interpret problems but required more communication skills to effectively convey their ideas, draw appropriate conclusions, or evaluate the problems encountered. Lastly, students with a kinesthetic learning style required additional assistance in solving problems and responding to the given indicators.
Mathematical Model of Joint Life Term Insurance Premiums under Inflation, Interest Rate, and Dependent Mortality Habel, Ine Febrianti; Purnaba, I Gusti Putu; Budiarti, Retno
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.v10i2.35690

Abstract

Multilife insurance refers to a contract that covers two or more lives simultaneously, with joint life insurance representing a key form in which the benefit is paid upon the first death among the insured individuals. The lifetimes of insured individuals are typically not independent, as they may be influenced by shared environmental, health, or behavioral factors, leading to mortality dependence. Inflation and interest rates also play critical roles in determining the present value of benefits and premiums. However, most previous studies have examined either mortality dependence or macroeconomic effects in isolation. This study aims to develop a comprehensive mathematical model for determining joint life term insurance premiums that simultaneously incorporates mortality dependence through the Gumbel copula and interest rate and inflation through the Fisher equation. The model integrates demographic and economic risk components within a unified actuarial valuation framework, providing a more realistic representation of premium dynamics under varying financial conditions. Simulation results indicate that premiums incorporating inflation are consistently higher than those without inflation, whereas higher nominal interest rates result in lower premium levels. These findings reflect the theoretical relationship between inflation, real interest rates, and the time value of money. The study further introduces an elasticity-based analysis that quantifies the sensitivity of premiums to changes in inflation and interest rates, demonstrating nonlinear yet economically meaningful responses across different age structures of insured spouses. The results highlight the importance of jointly modeling mortality dependence and economic variables to enhance pricing accuracy and fairness in life insurance. The proposed model offers practical relevance for actuaries in premium determination, assists insurers in risk management and product design, and supports the development of resilient pricing strategies under inflationary and interest.
Understanding Spatial Variability of Human Development Index in Aceh: A Geographically Weighted Regression Approach Mardalena, Selvi; Rahayu, Latifah; Sasmita, Novi Reandy; Hayati, Raihan; Nisa, Arhamun; Ummah, Nurul; Yasmirullah, Septia Devi Prihastuti
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.v10i2.35734

Abstract

The Human Development Index (HDI) is an important indicator in measuring people's quality of life, which includes education, health and economic dimensions. In Aceh Province, HDI achievements show inequality between regions, especially between coastal and inland areas. This study employs a quantitative spatial analysis to examine socio-economic determinants of HDI across districts using the Geographically Weighted Regression (GWR). The analysis utilized 2023 secondary data from the Central Bureau of Statistics (BPS), integrating HDI with key indicators of labor conditions, poverty, education, health, and regional economic performance. The global linear regression model was compared with GWR models using adaptive Gaussian and bisquare kernel weighting function, with model selection based on the Akaike Information Criterion (AIC). The results show that the GWR model with an Adaptive Gaussian Kernel weighting function outperformed the global regression model, indicating strong spatial non- stationarity in the relationships between HDI and its determinants. The average years of schooling, labor force participation rate, open unemployment rate, percentage of poverty, life expectancy, expenditure per capita, gross regional domestic product, and expected years of schooling have a significant effect on HDI in Aceh, but their contribution varies across districts. This study contributes to the literature by providing spatially explicit evidence to support region-based development policies, emphasizing the need for differentiated interventions to reduce interregional inequality and promote more equitable human development across Aceh Province.
Innovation in Numeracy Learning Through Immersive Media for Pre-Service Teachers in Professional Education Rohimah, Siti Maryam; Indriyani, Yuni; Nugraha, Eggie; Subaryo, Subaryo
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.v10i2.36651

Abstract

This research presents an innovative approach to numeracy instruction for pre-service elementary school teachers using holographic images. The primary contribution is the integration of low-cost, mobile-based holographic prototyping within teacher education to enhance spatial reasoning, foster interdisciplinary learning, and support experiential pedagogy. This research aims to analyze prospective teachers' perspectives on holographic media in numeracy learning, with a focus on their experiences in designing and evaluating hologram prototypes for classroom use. A qualitative methodology was adopted, involving 59 pre-service teachers from an elementary teacher education program. Data collection utilized questionnaires and semi-structured interviews, with thematic analysis employed to identify key patterns and themes. Participants engaged in an iterative design process, developing and testing several holographic prototypes, which resulted in a truncated pyramid configuration optimized for mobile-based projection. The analysis identified four principal themes: interdisciplinary applicability, pedagogical strategies for young learners, development of holographic problem-solving skills, and improved spatial–structural understanding. The findings suggest that holographic learning activities enhance student engagement, deepen conceptual understanding, and strengthen both spatial and collaborative skills. This study extends the literature on numeracy and STEM education by illustrating the effective integration of immersive holographic media into pre-service teacher training as a practical and pedagogically valuable instructional innovation. 
The Spread of Academic Boredom Model in the Context of Mathematics Lessons: Epidemiological Approach Suzana, Yenny; Irwansyah, Budi; Setambah, Mohd Afifi Bahurudin; Mulyono, Mulyono; Maulida, Iyana
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.v10i2.35443

Abstract

Boredom in educational contexts seems to be a universal academic emotion, and one that is frequently experienced by students across age groups, educational needs, and ethnicity However, despite its significance in the context of mathematics lessons, academic boredom is rarely studied, especially in terms of mathematical modeling. This article proposes a dynamic model of the spread of academic boredom in the context of mathematics lessons using an epidemiological approach, taking a case study in the middle school students. This model divides the student population into four subpopulations or compartments: susceptible (S), exposed (E), infected (I), and recovered (R) from academic boredom in the context of mathematics lessons. The transition process between subpopulations or compartments is influenced by social interactions between students. By using theoretical assumptions that refer to general patterns of social behavior dynamics in adolescents and consideration of the educational context, we explore the model behavior for the spread of academic boredom in the context of mathematics lessons using sensitivity analysis and scenario-based simulation methods. The simulation results indicate that the strength of social interactions between students significantly influences the spread of academic boredom in the context of mathematics lessons. The results of this study provide insights for the policy makers in the middle school students in designing more effective strategies to mitigate academic boredom among students, especially in the context of mathematics lesson. This study opens up opportunities for further, more empirical research by incorporating actual data regarding the decisions of students why they have academic boredom.
Exchange Rate Prediction of BRICS Countries against US Dollar Based on Multiresponse Fourier series Estimator Mardianto, M. Fariz Fadillah; Maulidya, Utsna Rosalin; Ginzel, Bryan Given Christiano; Putra, Mochamad Rasyid Aditya; Pusporani, Elly; Miswan, Nor Hamizah
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.v10i2.36983

Abstract

The dominance of the US dollar (USD) as the global reserve currency has begun to face structural challenges since the 2007-2008 financial crisis, which triggered the strengthening of the BRICS alliance. Although this alliance now controls 35% of the world's GDP and is actively pursuing de-dollarization, analysis of the volatility of their collective currencies is often limited to univariate parametric models that fail to capture inter-country dependencies and complex periodic fluctuation patterns. This study aims to fill this gap by applying a nonparametric multiresponse Fourier series regression to simultaneously model the interdependence of the five major BRICS currencies against the USD. Using weekly secondary data from June 2009 to February 2025 (817 observations) from investing.com, this study positions time as the predictor and the exchange rates of the five BRICS currencies as the response. The analysis results show that the best estimation model is obtained through a sine function without a trend component with an optimal oscillation parameter k=1, based on a minimum Generalized Cross Validation (GCV) value of 0.000702363. The prediction results from the training data produce a MAPE value of 4.7521%, which classifies the analysis as highly accurate. These findings strategically support the validation of the de-dollarization movement, providing a predictive instrument for developing countries to reduce their dependence on the USD, as well as strengthening the bargaining position of Eastern economies in a more multipolar international financial order.
Bayesian Logistic Regression for Inhomogeneous Poisson Point Process: A Case Study of Post-Harvest Facilities in Sidenreng Rappang Husain, Ahmad; Sam, Marwan; Jamaluddin, Sri Rezki Wahdania
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.v10i2.35956

Abstract

Understanding the spatial distribution of post-harvest infrastructure is crucial for improving the efficiency and resilience of agricultural supply chains, particularly in major food-producing regions. This study aims to extend the estimating equations based on the logistic regression likelihood within the Bayesian framework to model the spatial intensity of an Inhomogeneous Poisson Point Process (IPP). The proposed approach integrates prior information into the logistic regression likelihood by constructing posterior distributions, enabling a more comprehensive inference by quantifying parameter uncertainty. In contrast to conventional maximum likelihood (ML) estimation, which produces only point estimates, the Bayesian method provides a probabilistic characterization of parameter estimates using the Markov Chain Monte Carlo (MCMC) approach, specifically the Gibbs Sampling algorithm, to approximate posterior distributions. The methodological framework is applied to the spatial distribution of post-harvest rice facilities in Sidenreng Rappang Regency, Indonesia. The analysis is based on georeferenced observational data obtained from local goverment records and agricultural statistics, processed usign Geographic Information System (GIS) tools and statistical software. Spatial covariates include the proportion of paddy field area per village (Z_1), rice producing area (Z_2), and distance to the nearest Bulog warehouse (Z_3 ). The results indicate that Z₁ and Z₃ significantly affect the spatial intensity of post-harvest facilities, where areas with larger paddy field proportions are more likely to host such facilities, while increasing distance from Bulog reduces the likelihood of facility presence. The posterior trace and density plots demonstrate good convergence and mixing, confirming the reliability of the Gibbs Sampling procedure. Model comparison through the Akaike Information Criterion (AIC) and likelihood values shows that the Bayesian approach yields a substantially lower AIC, ten times smaller than the ML-based logistic regression, indicating superior model fit and computational efficiency. The findings suggest that integrating Bayesian inference into the IPP logistic framework enhances model interpretability and robustness, particularly in accounting for uncertainty and prior knowledge. The study underscores the practical importance of spatial modeling for agricultural infrastructure planning and offers a flexible computational framework applicable to other spatial point pattern analyses across diverse domains.
Air Temperature Prediction in Sleman Yogyakarta using Fourier Series and Markov Switching Syahzaqi, Idrus; Riefky, Muhammad; Cahyoko, Fajar Dwi; Nahar, Muhammad Hafidzuddin; Pratama, Fachriza Yosa; Mardianto, Muhammad Fariz Fadillah
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.v10i2.35371

Abstract

Global warming increases the urgency of accurate local temperature forecasting, particularly in Sleman, Yogyakarta, a region characterized by diverse topography and high exposure to climate-related risks such as volcanic activity, agricultural vulnerability, and rapid urbanization. Such conditions increase the urgency for localized predictive models that can support agricultural planning, energy management, and disaster preparedness. This research used quantitative approach with a comparative predictive modelling design to predict the weekly average air temperature in Sleman by comparing two models: the Fourier Series regression and the Markov Switching Autoregressive (MSAR) model. The Fourier Series was selected for its ability to capture smooth seasonal and periodic behavior typical of climatological data, whereas the MSAR model was employed to accommodate regime shifts and nonlinear structural variations. The dataset comprises 127 weekly observations from January 2023 to June 2025 (BMKG), the data were split into 70% training and 30% testing. Model performance was assessed using GCV, MSE, MAE, MAPE, and residual diagnostics. Results show that the Fourier Series model performs substantially better, achieving lower GCV (0.3520), MSE (0.00415 training; 0.00114 testing), and MAE (0.34015 training; 0.12940 testing), as well as lower MAPE (1.26% training; 0.47% testing). In contrast, the MSAR model yields higher errors with GCV (0.5747), MSE (0.9113 training; 0.4686 testing), MAE (0.8005 training; 0.5512 testing), and MAPE (1.96% training; 1.34% testing). These results indicate that Sleman’s temperature dynamics characterized by stable oscillatory patterns with minimal regime shifts are more effectively captured through harmonic decomposition. The study reinforces the importance of periodic modeling for mixed-topography regions like Sleman and recommends future research integrating additional climatic variables, hybrid statistical–machine-learning frameworks, and longer time spans to improve responsiveness to extreme events and nonlinear atmospheric behavior.
Trajectories of Cannibalism Interaction with Holling Type II and Monod–Haldane Functional Responses Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F. V.; Meirista, Etriana
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.v10i2.36659

Abstract

The stability and equilibrium behavior of predator–prey systems involving cannibalistic interactions is crucial for explaining the long-term sustainability of ecological communities. This study aims to analyze the dynamics of a modified predator–prey model by incorporating cannibalism in predators as a self-regulating mechanism influencing population control. This study is a literature-based research, and the instruments employed are non-physical in nature, including a mathematical model, mathematical analysis tools, and numerical computation frameworks. The research methodology employs literature review and analysis of a model formulated as a system of nonlinear differential equations.  This system describes the population dynamics of two prey species and one predator species exhibiting cannibalistic tendencies. Analytical and numerical approaches are utilized to determine equilibrium points, evaluate local stability, and assess the effects of density-dependent mortality and cannibalistic behavior on ecosystem balance. The results show that the proposed predator–prey model admits one trivial equilibrium, five semi-trivial equilibrium, and one coexistence equilibrium. The coexistence equilibrium is locally asymptotically stable and satisfies the Routh–Hurwitz stability criterion. Simulation numeric the cannibalism parameter and density-dependent mortality rates play a significant role in stabilizing the predator population dynamics. When the mortality coefficient increases, the predator population decreases toward a lower equilibrium point, while the prey population slightly increases due to reduced predation pressure. Eigenvalue analysis reinforces these findings by confirming the system's compliance with the Routh–Hurwitz stability conditions. Ecological implications, these findings suggest that cannibalistic behavior in predators acts as a natural feedback mechanism to regulate population density, enhance ecosystem stability, and support the long-term sustainability of predator–prey interactions. The cannibalistic character of the predator species does not necessarily lead to species extinction, but can instead facilitate a sustainable and balanced coexistence within the ecosystem.
Forecasting Rice Prices in Indonesia Using a Hybrid HWES-MLP Time Series Prediction Model Supriadin, Supriadin; Haris, M. Al; Amri, Saeful; Abas, Hafiza; Fadugba, Sunday Emmanuel
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.v10i2.35445

Abstract

Rice is the main staple food for the majority of the Indonesian population. However, the fluctuation in rice prices and future uncertainty emphasize the importance of forecasting rice prices, thus requiring a forecasting model capable of providing accurate predictions. Various previous forecasting methods have been limited in capturing the combination of linear and non-linear patterns in rice price data, spurring the need for a more comprehensive hybrid approach. This research applies a quantitative approach by utilizing secondary data sourced from publications of the Central Statistics Agency (BPS) of Indonesia. This study aims to forecast rice prices in Indonesia using a hybrid approach combining Holt–Winters Exponential Smoothing (HWES) with Multilayer Perceptron (MLP). The hybrid model is designed to overcome the limitations of the Holt-Winters Exponential Smoothing method, which can only capture linear patterns such as trend and seasonality, by adding the Multilayer Perceptron method to capture non-linear patterns that cannot be handled by the linear approach. The dataset comprises monthly rice prices in Indonesia from January 2010 to December 2024, while the period of January–December 2025 is used as the prediction period. The data analysis process was carried out using the software R-Studio and Minitab, which provide a variety of features to support time series modeling. The results indicate that the most effective method for forecasting rice prices in Indonesia is the Hybrid Holt Winters Exponential Smoothing (α = 0.5; β = 0.3; γ = 0.3)-Multilayer Perceptron (12-12-1), which achieved the highest accuracy with a MSE of 9666.12, a RMSE of 310.9117, and a MAPE of 1.9949%. This finding indicates that the Hybrid HWES-MLP approach is highly capable of capturing rice price data patterns. Thus, this model holds significant potential to be utilized as a benchmark supporting government policy in maintaining rice price stability, market intervention, and optimizing the management of national rice reserves stock.

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