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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
Control Strategies for HIV/AIDS-Hepatitis B Coinfection using Optimal Control Approach and Cost-Effectiveness Analysis Annisa, Winda Nur; Bakhtiar, Toni; Silalahi, Bib Paruhum
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.v9i2.29601

Abstract

HIV/AIDS and Hepatitis B are infectious diseases caused by viruses, sharing similar transmission mechanisms. This study seeks to determine the most effective and cost-efficient strategies for controlling the spread of these diseases by utilizing a modified HIV/AIDS-Hepatitis B coinfection model with various control variables. The model divides the total population into nine subpopulations, each representing a specific disease state. Based on these classifications, the model incorporates four key control variables, namely Hepatitis B vaccination program, Hepatitis B treatment, HIV/AIDS treatment, and public health education program. The research employs optimal control theory and the Pontryagin Maximum Principle to address the optimal control problem to minimize infection rates and implementation costs over a specific periode. The Hamilton function integritas the dynamic system and cost function. The model is analyzed through simulations using parameter values from previous studies, then optimizing control variables to generate a numerically solved system of differential equations that uses Scilab 2024 software. Simulation result show that the optimal combination of four control strategies reduces HIV/AIDS-Hepatitis B infection by 79,2% in under ten years. Furthermore, the cost-effectiveness of different strategies is evaluated using the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) indicates that single control strategies are more cost-efficient, while combining all four strategies is more expensive. However, successful implementation depends on financial constraints (limited vaccination and ARV treatment), healthcare infrastructure (availability of testing facilities), and public compliance with health education programs. Consequently, the proposed strategies are recommended for policymakers, with consideration of associated costs to ensure feasibility.
Spatio-Temporal Median Polish Kriging with ARIMA Integration for Monthly Precipitation Interpolation in East Kalimantan Jannah, Friendtika Miftaqul; Fitriani, Rahma; 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.v9i2.29570

Abstract

Precipitation can lead to disasters like droughts and floods, necessitating accurate interpolation methods. Traditional spatio-temporal kriging often struggles with outliers, which can reduce estimation reliability. This study develops spatio-temporal median polish kriging, which separates spatial and temporal components to improve interpolation accuracy, particularly in handling outliers. Unlike conventional kriging, this method integrates median polish kriging for robust spatial interpolation and ARIMA for capturing temporal trends, making it more effective in dynamic precipitation pattern estimation. The study utilizes precipitation data from seven observation posts in East Kalimantan (2021–2023). The data is processed using a combination of spatial, temporal, and spatial-temporal modeling approaches to capture precipitation variations accurately. For spatial interpolation, the study applies kriging in median polish spatial effects. The best semivariogram model for spatial effects is exponential, which is used to characterize spatial dependencies. To capture temporal effects of median polish, the study employs ARIMA(1,2,0), which models precipitation trends over time and helps manage temporal fluctuations. For residuals of median polish interpolation, the study applies spatio-temporal kriging, using a simple sum-metric model as the best approach to integrate both spatial and temporal dependencies. The semivariograms selected for spatial, temporal, and joint dependencies follow a gaussian structure. The interpolation results reveal that precipitation increases toward the west, with precipitation patterns also showing an increasing trend over time. These findings demonstrate the model’s capability in capturing spatial and temporal precipitation variations while addressing potential outliers through the median polish approach. By utilizing a robust statistical framework, the model reduces the influence of extreme values, leading to more reliable precipitation estimates. However, this study utilizes only seven observation posts. The limited number of observation posts may introduce uncertainty in regions distant from measurement stations and affect the model's accuracy. Therefore, further research should test this model by applying it to different geographical regions with a more extensive dataset.
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.
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.
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.
The Effect of GEMAS on Mathematical Problem-Solving and Critical-Thinking Abilities Lukman, Hamidah Suryani; Setiani, Ana
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.v9i2.29659

Abstract

This research focuses on the development of gamification-based mathematics teaching materials specifically designed to improve the problem-solving and critical mathematical thinking skills of junior high school students in the form of GEMAS (Junior High School Mathematics Game) and to test the product based on its validity, practicality, and effectiveness aspects. The ADDIE MODEL is used in the research and development of GEMAS. Previous research articles have discussed the stages of product development, validity testing, and practicality, so the focus mof this article only discusses its effectiveness test. Thus, the stages of the ADDIE model used in this article are also limited to the last two stages, namely Implementation and Evaluation. The study was conducted at two junior high schools in Sukabumi using a one-sample pretest-posttest design. The sample was 256 students from 10 study groups using cluster random sampling techniques. Data were collected through the Krulik-Rudnick problem-solving ability test instrument, the FRISCO critical-thinking ability test, and student response sheets that met the criteria of being very valid and highly reliable. Data were analyzed using a paired two-sample t-test at a significance level of alpha 5% and descriptive analysis. The results of the study showed that GEMAS met the criteria for effectiveness. This can be seen from the overall range of values between the average pretest and posttest of problem-solving ability which reached 43.75 and critical thinking ability which reached 47.00, as well as the n-gain value of both mathematical problem-solving ability and mathematical critical thinking ability of junior high school students has met the moderate improvement category (46-51%). 
Optimal Control Strategies for Syphilis and HIV/AIDS Coinfection Transmission with Cost-Effectiveness Analysis Cahyona, Dwizani Vinoma; Bakhtiar, Toni; Jaharuddin, Jaharuddin
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.v9i2.28571

Abstract

Syphilis and HIV/AIDS are global health problems with significant impacts on society. The combination of these two infections can worsen the prognosis of patients and increase the economic strain on the health system. This study aims to develop an optimal control model in managing the spread of syphilis and HIV/AIDS coinfection by considering HIV/AIDS treatment, syphilis treatment, and preventive measures through condom use as dynamic control variables. Pontryagin's maximum principle is used to derive the optimality conditions. To theoretically investigate the impact of the control measures, this study analyzed five strategies related to the implementation of these controls using Scilab-2024.0.0 for simulate and evaluate of their effectiveness. The simulation results show that the combination of three control interventions is more effective in decreasing the prevalence of syphilis and HIV/AIDS coinfection compared to the application of one type of control alone. This combination strategy significantly reduces the infection rate by up to 86.04%, emphasizing the importance of a multifaceted intervention approach rather than a single control measure. Furthermore, a cost-effectiveness analysis was conducted by comparing the costs and effectiveness of various control strategies to determine the most efficient and economically feasible option. The results of the comparison indicate that although integrated intervention is the most effective strategy in minimizing infection rates, a strategy that focuses only on preventive measures through the use of condoms is a more efficient option when considering the balance between budget limitations and control effectiveness.
Through the Teacher's Lens: Perspectives on Integrating Higher-Order Thinking Skills into Mathematics Instruction Gradini, Ega; Noviani, Julia; Samsudin, Syafiza Saila
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.v9i2.30074

Abstract

The integration of Higher-Order Thinking Skills (HOTS) in mathematics instruction holds significant potential to deepen students’ conceptual understanding and fostering analytical thinking. However, its implementation is often hindered by gaps in teacher competency, curricular limitations, and outdated assessment methodologies. This study aims to explore mathematics teachers’ perspective on HOTS integration by examining four dimensions: understanding, perceived need, implementation challenges, and classroom practices. A descriptive survey design was employed, involving 186 junior and senior high school teachers selected through stratified random sampling. Data were collected via a structured questionnaire and analyzed using descriptive and inferential statistics, including Pearson correlation. Findings reveals a noticeable gap between teachers’ conceptual understanding of HOTS and its practical application in the classroom. While teachers acknowledge the importance of HOTS and frequently incorporate problem-solving and analytical activities, practical application is inconsistent due to time constraints, insufficient training, and limitation of resources. Differences were observed across teaching levels and school types: private and senior high school teachers, showing stronger understanding and more frequent HOTS integration. Weak correlation among understanding, perceived need, and practice indicate that awareness alone does not ensure effective implementation. These findings underscore the need for systematic support, targeted professional development, and policy reforms to bridge the gap between theory and practice. The study contributes to educational practice by highlighting actionable areas for institutional support and inform policy development aimed at enhancing the integration of HOTS in mathematics education.
Patterns of Student Thinking Interaction in Group Discussion: The Effect of Explorative Interaction on Understanding Statistical Concepts Syarifudin, Syarifudin; Haris, Abd.; Nurrahmah, Nurrahmah
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.v9i2.30091

Abstract

This study aims to analyze patterns of students' thinking interaction during group discussions in statistics learning and examine their impact on conceptual understanding, particularly across different levels of academic ability. A qualitative approach was employed using discourse and interaction analysis. Data were collected through classroom observations, video/audio recordings, transcription of student discussions, students' written work, and in-depth interviews. These instruments enabled comprehensive documentation and triangulation of students' verbal and behavioral interactions. Twelve junior high school students were selected and categorized into high, medium, and low academic ability groups. Discourse structures were analyzed using the Sinclair & Coulthard model (to identify classroom discourse moves) and Mercer's framework (to detect exploratory and cumulative talk). Furthermore, interaction patterns were categorized using the ICAP model—which distinguishes passive, active, constructive, and interactive engagement—and Bales’ Interaction Process Analysis (IPA), which classifies social-emotional and task-related behaviors in small groups. The findings revealed that groups with explorative interaction patterns demonstrated deeper conceptual understanding, facilitated by active questioning, argument construction, and peer clarification. In contrast, static interaction groups were characterized by passive reception and rote learning, while counterproductive groups showed fragmented participation and communication breakdowns. These results confirm the vital role of interaction quality in supporting conceptual development. The novelty of this study lies in its integration of discourse- and interaction-based frameworks to reveal how different thinking dynamics shape learning outcomes in heterogeneous academic groups. Practically, the study highlights the importance of scaffolding, open-ended questioning, and structured facilitation to promote argumentation-rich discussions. These strategies are essential for fostering critical thinking and improving students’ understanding of statistics concepts. 

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