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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 Spatio-Temporal Precipitation Patterns in East Kalimantan using Space-Time Kriging and Median Polish-Based Spatio-Temporal Kriging Jannah, Friendtika Miftaqul; Fitriani, Rahma; Pramoedyo, Henny
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.v9i3.30642

Abstract

Precipitation variability presents significant challenges for disaster risk reduction and water resource management, particularly in flood and drought-prone regions such as East Kalimantan. This study aims to develop and evaluate two statistical approaches for spatio-temporal precipitation modeling: spatio-temporal kriging (ST-Kriging) and spatio-temporal median polish kriging (ST-MPK). Using monthly precipitation data obtained from seven observation stations provided by BMKG and BPS for the period 2021 to 2023, both models were assessed using performance metrics. ST-Kriging employed a simple sum-metric semivariogram model that combines exponential spatial and Gaussian temporal components. This model achieved an RMSE of 84.05, MAE of 69.95, and MAPE of 52.67%. Meanwhile, ST-MPK model, incorporating robust median polish decomposition and ST-Kriging of residuals, produced a lower MAPE of 44.83% with higher RMSE (122.44) and MAE (91.35). This suggests that while ST-Kriging offers better absolute error performance, ST-MPK provides greater relative accuracy and improved robustness to outliers, critical advantages for modeling precipitation in regions undergoing environmental shifts, where anomalies and extremes are increasingly common. These findings highlight ST-MPK’s potential to produce more reliable forecasts under irregular precipitation conditions, supporting early warning systems and informed water resource planning. Scientifically, this research contributes a robust modeling framework suitable for data-scarce and outlier-prone contexts. Practically, it can aid policymakers in designing adaptive flood mitigation strategies and sustainable water management policies tailored to the evolving climate realities of East Kalimantan.
Analysis Dynamics Model Predator-Prey with Holling Type III Response Function and Anti-Predator Behavior Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F. V.; Meirista, Etriana; Nurhayati, Nurhayati
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.v9i3.31533

Abstract

Understanding predator-prey dynamics is essential for maintaining ecological balance and biodiversity. Classical models often fail to capture complex biological behaviors such as prey defense mechanisms and nonlinear predation effects, which are vital for accurately describing real ecosystems. In light of this, there is a growing need to incorporate behavioral and functional complexity into mathematical models to better understand species interactions and their long-term ecological outcomes. This study aims to develop and analyze a predator-prey model that integrates two key ecological features: a Holling type III functional response and the anti-predator behavior exhibited by prey. The model assumes a habitat with limited carrying capacity to reflect environmental constraints. We formulate a nonlinear system of differential equations representing the interaction between prey and predator populations. The model is examined analytically by identifying equilibrium points and analyzing their local stability using the Routh-Hurwitz criteria. A literature-based theoretical analysis is supplemented with numerical simulations to validate and illustrate population dynamics. The model exhibits three equilibrium points: a trivial solution (extinction), a predator-free equilibrium, and a non-trivial saddle point representing coexistence. The non-trivial equilibrium best reflects ecological reality, indicating stable coexistence where prey consumption is balanced by reproduction, and predator mortality aligns with energy intake. Numerical simulations show that prey populations initially grow rapidly, then decline as they reach carrying capacity, while predator populations grow after a time lag and eventually stabilize. The results are further supported by the eigenvalue analysis, confirming local asymptotic stability. The proposed model realistically captures predator-prey dynamics, demonstrating that the inclusion of anti-predator behavior and a Holling type III response significantly affects population trajectories and system stability. This framework provides a more ecologically valid approach for studying long-term species coexistence and highlights the importance of incorporating behavioral responses in ecological modeling.
Prediction of Dow Jones Index, US Inflation, and Interest Rate with Kernel Estimator and Vector Error Correction Model Mardianto, M. Fariz Fadillah; Syahzaqi, Idruz; Permana, Made Riyo Ary; Makhbubah, Karina Rubita; Vanisa, Davina Shafa; Afifa, Fitriana Nur
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.v9i2.28460

Abstract

The Dow Jones Industrial Average (DJIA) is the oldest running U.S. stock market index, established by Dow Jones & Company under Charles Dow. Comprising thirty major publicly traded companies, the DJIA is a key indicator of macroeconomic health, reflecting investor confidence and economic stability. This study applies a quantitative research approach to forecast DJIA stock prices, inflation, and U.S. interest rates using time series analysis. Two forecasting methods are compared: Vector Error Correction Model (VECM) and Kernel regression. VECM, a parametric approach, estimates both short- and long-term relationships among economic variables, while Kernel regression, a nonparametric technique, effectively captures complex, nonlinear relationships without strict model assumptions. The results indicate that the Gaussian Kernel method provides the most accurate predictions, achieving a Mean Absolute Percentage Error (MAPE) of 5.72%. The analysis also shows that despite annual fluctuations, the DJIA has exhibited a steady growth trend from 2009 to 2024, with both its starting and ending prices increasing over time. This research is significant for investors, policymakers, and financial analysts, offering insights into market trends and economic indicators. By providing a reliable forecasting model, it aids in better decision-making regarding stock market investments and economic policies.
The use of Traditional Games to Increase Interest in Learning Multiplication in Class 4 Primary School Students in the City of Bandung Pratiwi, Intan Aprilianti; Dallyono, Ruswan; Kurniawan, Dede Trie; Yuniarti, Yeni
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.v9i3.29721

Abstract

Learning multiplication is challenging for fourth-graders of an elementary school in Bandung in terms of the subject when they learn it at school. Some students exhibit no curiosity in mathematics, despite the fact that curiosity is a significant part of learning effectively. This study aims to examine students’ responses on the use of traditional games as a way to grip the minds of pupils in learning multiplication with creative and constructive methods. With the use of the case study approach, the findings are presented through a descriptive analysis through a number of tables which are made from the responses to the questionnaires. The subjects were 30 fourth-grade students. The data were collected through questionnaires and documents with the help of the descriptive statistical methods for the analysis to represent the results in numerical and tabular formats. The conclusion drawn from the research is that the dakon game, the most traditional one, as a learning medium was perceived to be able to bring a remarkable change in students' interest to learn multiplication.
Comparing the Accuracy of Markov Switching – AR and Prophet Models in Predicting the Blue Bird Stock Prices Yulianty, Sherly; Mangku, I Wayan; Budiarti, Retno
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.v9i2.30096

Abstract

One form of investment asset that is in high demand for profit is stocks. However, stock prices fluctuate, so a mathematical model is needed to model the movement and calculate stock price predictions. Stock price movements often form several groups (states) of change, so the Markov Switching Autoregressive (MS-AR) model can be used to model and calculate stock price predictions. In addition, stock price movements often contain trend and seasonal patterns, so the Prophet model can be used to model movements and calculate stock price predictions. In this study, the Prophet model is modified by generating random numbers that spread normally with parameter values obtained from the error value of the Prophet base model. This study aims to compare the performance of the MS-AR model with the Prophet model in predicting BIRD stock prices. This research is a quantitative study with secondary data in the form of BIRD stock closing price data for the period 11 February 2023 to 11 February 2024. In this study, two models, MS-AR and Prophet, were built separately. In the MS-AR model, it is necessary to pay attention to the assumptions of the data used, namely normal distribution and stationary. In the Prophet model, there are no special assumptions like those of the MS-AR model, but the Prophet model is good for data containing trends and seasonal patterns. The results of this study show that among the MS-AR models, the MS(2)-AR(3) model is the best model. In addition, the results show that the modified Prophet model performs better than the basic Prophet model. The goodness of model performance is measured by the Mean Absolute Percentage Error (MAPE) metric, with MAPE values for each model being 5.54% for MS(2)-AR(3), 3.38% for the Prophet base model, and 2.88% for Prophet modification. Based on the MAPE value, the Prophet (modified) model is able to predict the closing price of shares better than the MS(2)-AR(3) and Prophet (basic) models. The results of this study can be used by investors as a measuring tool in reading and determining stock price predictions.
Portfolio Optimization using Shariah-Compliant Asset Pricing Model in Indonesia Qudratullah, Mohammad Farhan; Hanafi, Syafiq Mahmadah; Sunaryati, Sunaryati
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.v9i2.29168

Abstract

This paper develops portfolio optimization using the Shariah-Compliant Asset Pricing Model (SCAPM) which maximizes the Sharpe ratio by considering investors' prevention of risk. There are four approaches to developing portfolio optimization (SCAPM without interest rates, SCAPM with zakah rate, SCAPM with nominal gross domestic product growth (GDP), and SCAPM with inflation). This is a quantitative study that implements these models in the Islamic capital market in Indonesia, namely Islamic stocks included in the Jakarta Islamic Index (JII) for the period January 2011-December 2018. Based on the results of the Kendall W concordance test, this study found that the four SCAPM optimum portfolios have a very high level of conformity for return, risk, and performance at a 95% confidence level. In terms of the plot and ratio of return and risk, based on the investor's prevention of risk: the optimum portfolio 1 (risk-seeker) and the optimum portfolio 3 (risk-neutral) tend to give the same results and these portfolios were more efficient than the optimum portfolio 2 (risk-averter). This study contributes to the existing literature in the area of mathematics and the Islamic capital market, specifically in terms of the optimal Sharia-compliant portfolio. It is the first study developing, implementing, and testing the optimal portfolio with four approaches SCAPM based on the investors' prevention of risk in Indonesia.
Naïve Bayes Algorithm: Analysis of Student Group Assignment Project Patterns in Mathematics Learning Dewi, Wardhani Utami; Vahlia, Ira; Linuhung, Nego
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.v9i3.30459

Abstract

Effective collaboration in mathematics learning is essential for developing students' critical thinking and problem-solving skills; however, identifying patterns that lead to successful group collaboration remains challenging. This study aims explicitly to identify and classify the patterns of student group assignment completion in the Logic and Sets course using the Naïve Bayes algorithm. Survey data from 65 mathematics education students were analyzed using a quantitative approach and machine learning techniques. Attributes such as group size, task completion time, participation, contribution strategies, and communication effectiveness were collected via structured questionnaires. Data analysis involved preprocessing, model training using Naïve Bayes, and validation through accuracy and posterior probability analysis. Results indicated that the Naïve Bayes model accurately distinguished groups with very good (A) and fairly good (B) performance, achieving 84.62% accuracy. Groups achieving an A grade typically featured balanced participation and open communication strategies, whereas groups graded B exhibited uneven participation and passive members. This research significantly contributes by demonstrating how data-driven predictive analytics can support instructors in monitoring and enhancing collaborative learning processes in mathematics courses. Future research could further refine predictive accuracy by incorporating additional factors such as leadership style and collaborative technologies, potentially integrating the model into learning management systems for real-time evaluation and intervention.
Mathematical Semiotics in Primary Learning: Helping Prospective Teachers Understand Mathematical Representations Purwasih, Ratni; Irawan, Edi; Minasyan, Sona
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.v9i3.30835

Abstract

Mathematics learning in elementary schools is often faced with the challenge of bridging abstract concepts with participants' concrete experiences. One of the reasons is the difficulty in understanding and using mathematical signs and symbols appropriately. Semiotic representation of mathematics, which involves symbols, diagrams and notations as visual and conceptual aids, is an important approach in overcoming these challenges. This study aims to explore the ability of prospective elementary school teachers to understand and use semiotic representations of mathematics, especially in the context of number patterns. A qualitative approach with a hermeneutic phenomenological design was chosen to understand prospective teachers' experiences, views, and thought processes in interpreting and using mathematical symbols. The researcher used written tests and semi-structured interviews as data collection techniques to explore the semiotic representations used in mathematical problem solving. The participants were grouped based on the results of the initial ability test, and six of them were selected as research subjects. Data analysis used the Interpretive Phenomenology Analysis (IPA) method with the help of NVivo 14 Plus software, which allows researchers to systematically manage and analyze qualitative data. The results of this study are expected to provide insight into prospective teachers' understanding of symbolic representation in mathematics learning and the challenges they face, which can be the basis for designing more effective learning strategies in the context of mathematics education in primary schools. Using a descriptive qualitative approach, data were obtained through observation and analysis of problem solving activities involving symbolic and visual representations. The results of the study are expected to provide insight into the importance of semiotic training in prospective teacher education, so that they are able to convey mathematical concepts meaningfully and contextually.
The Effect of Mathematics Learning Interest and Social Skill on Algebraic Reasoning Sucipto, Lalu; Syawahid, Muhammad; Afika, Dini Safitri Nur; Kasim, Marini
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.v9i2.28245

Abstract

Algebraic reasoning plays a role in mathematical thinking. Understanding factor affective of algebraic reasoning is essential for improving mathematics education. This study aims to examine the effect of learning interest and social skills on students' algebraic reasoning. We conducted a quantitative study using a correlational design, employing questionnaires and a test as data collection methods. We selected 202 students from the Islamic state of junior high school in Mataram as a research sample using a simple random technique. The study used an algebraic reasoning test, a learning interest questionnaire, and a social skills questionnaire as research instruments. The data was analyzed using descriptive data and inferential analysis. Descriptive data consist of categorical descriptive and statistical descriptive. Inferential analysis used a multiple regression including prerequisite tests (normality, linearity, multicollinearity and heteroscedasticity) and hypothetical tests using t-test for partial and F-test for simultaneous. The result showed that learning interest has no effect on students algebraic reasoning (t-test =0,055, sig. = 0,957 > 0,05). Meanwhile, the social skills have an effect on students algebraic reasoning (t-test =2,943, sig. = 0,004 < 0,05). In addition, learning interest and social skill simultaneously have an effect on algebraic reasoning (F-test = 4,345, sig. = 0,014 < 0,05). The result also confirmed that learning interest and social skills have a 4,2% of contribution to increasing students algebraic reasoning. To improve the students learning interest and social skill, teacher should be encouraged in designing interactive learning and collaborative learning approaches, such as group discussions, peer tutoring, and cooperative problem-solving.
A Comparison of Multivariate Adaptive Regression Spline and Spline Nonparametric Regression on Life Expectancy in Indonesia Pratama, Bagas Shata; Suliyanto, Suliyanto; Mardianto, M. Fariz Fadillah; Sediono, Sediono
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.v9i3.29413

Abstract

Life expectancy is a key indicator of a population’s overall health and well-being. It also reflects the effectiveness of government efforts in improving public welfare. Despite various initiatives by both the government and society to improve life expectancy in Indonesia, significant disparities remain. This quantitative study aims to support these efforts by analyzing factors influencing life expectancy in Indonesia using data from the Indonesian Central Agency of Statistics (BPS) in 2023. A comparative analysis was conducted using two methods: Multivariate Adaptive Regression Spline (MARS) and Spline Nonparametric Regression. The results show that the MARS model outperforms the Spline model, achieving a lower Mean Squared Error (MSE) of 1.183 and a higher R-Square of 82.7%. Key variables significantly influencing life expectancy include access to decent housing, access to safe drinking water, per capita expenditure, and the Gini ratio. The findings not only confirm the presence of complex interactions among predictor variables effectively captured by the MARS method, but also contribute to the existing literature by emphasizing the importance of socioeconomic determinants in health outcomes. From a policy perspective, the results suggest that government strategies should prioritize improving access to basic needs and reducing inequality. These insights can guide targeted, data-driven interventions aimed at enhancing life expectancy in Indonesia.

Page 45 of 54 | Total Record : 540

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