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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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Mathematics and Mathematics Education Values: An Analysis of Implementability in Mathematics Learning at Madrasah Pardi, M. Habib Husnial; Alkusaeri, Alkusaeri
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.26633

Abstract

Integrating values into all aspects of the learning process for a particular subject is an important part of education. Students must not only develop cognitively, but the formation of attitudes and characters must also be in line with the overall educational goals. Mathematics, as one of the core subjects that students must learn, must also reflect the values embedded in it. The success of mathematics education can be assessed through the values conveyed during the learning process. This study aims to explore and analyze teachers' understanding of Mathematical Values and Values in Mathematics Education, as well as how these values are conveyed in the classroom. This study aims to explore and analyze teachers' understanding of Mathematical Values and Values in Mathematics Education, as well as how these values are conveyed in the classroom. This study uses a qualitative approach with a case study design. Data were collected through interview techniques from 4 mathematics teacher informants determined by percussive sampling techniques. Data analysis uses an intractic model in line with the data collection process through three activities simultaneously; (1) data condensation; (2) data display, and (3) drawing conclusions/verification. The results of the study indicate that teachers' understanding of Mathematics values [rational values] and Mathematics education values are very important in improving students' logical thinking skills, and providing a comprehensive understanding of mathematics in developing their problem-solving skills. In mathematics teaching practices, teachers convey mathematical values during problem-solving activities, where students must understand various mathematical equations, concepts, and methods. While Mathematics education values (MEV) are conveyed during the problem-solving phase and reinforced at the end of the teaching and learning activities.
Prediction of Air Temperature in East Java using Spatial Extreme Value with Copula Approach Sofro, A'yunin; Habibulloh, Wildan; Khikmah, Khusnia Nurul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25436

Abstract

The increase in world temperature or global warming is a form of imbalance in the average temperature on Earth. The increase in air temperature will increase the risk of disasters, which will occur more frequently in the future. Rising global temperatures are expected to cause changes that can have fatal consequences. To anticipate the dangers are predicted by predicting the future air temperature increase. One of the methods that can be used is spatial extreme value theory, which uses the Gaussian copula model approach and Student's t copula, where the choice of these two methods was based on the flexibility they offer in capturing tail dependencies due to their capacity to describe the dependence structure between many variables simultaneously. . This makes it possible to get a return level or predicted value of air temperature by considering the elements of location in it. This research discusses both approaches and uses the maximum likelihood estimation (MLE) and pseudo maximum likelihood estimation (PMLE) methods to estimate the parameters. In addition, since spatial elements need to be considered, the trend surface model is also used. Akaike information criterion (AIC) is used to determine the best model for predicting air temperature based on extreme n air temperature data in East Java Province from nine air temperature observation stations. The results show that the highest air temperature value is around the Banyuwangi temperature observation station located in Banyuwangi Regency in the next two-year return period. The AIC results show that the best model produced is the Gaussian copula approach with a smaller AIC value than the student's t-copula approach, which is 8.0174. This value used to compare the relative quality of different statistical models with a lower AIC value generally indicates a better-fitting model.This value with a lower AIC value generally indicates a better-fitting model.
Indonesian National Mortality Rates using the Whittaker-Henderson Graduation Method Setiady, Gabrielle Aretha; Kusnadi, Felivia
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.26316

Abstract

In this paper, we aim to present a graph depicting the quantified mortality rates for the entire population of Indonesia, derived from the 2019 World Health Organization (WHO) mortality data for Indonesia. First, the mortality rates which consisted of five-year age groups were interpolated to determine the rates for each individual age. Next, these rates were extrapolated to extend the data from age 85 up to age 110. The resulting crude rates were adjusted with the Whittaker-Henderson smoothing technique by utilizing Python and MS Excel. The refined results were then compared to the insured lives from the fourth Indonesian Mortality Rates Table (TMI IV). This assessment supplied the government with insights to help shape health policies and inform economic forecasts. The results indicated that male mortality rates were higher than those of females, although no significant difference was observed among the younger generation. On the contrary, mortality rates of old people were significantly greater compared to the insured lives which was due to WHO’s limited data availability and more comprehensive data collection process, compared to TMI IV’s insured lives through the underwriting process.
Optimizing Long-Term Meteorological Data Completeness in North Aceh, Indonesia: A Comparative Analysis of Interpolation Methods Sasmita, Novi Reandy; Saragih, Novita Sari; Rahayu, Latifah; Malfirah, Malfirah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27929

Abstract

More data in meteorological records is needed to ensure the accuracy of meteorological modeling, particularly in long-term datasets. This study aims to identify the most effective interpolation method for addressing missing data in North Aceh's meteorological dataset from 2010 to 2023, with a focus on the accuracy of methods applied across various meteorological variables. The study analyzed data from North Aceh Regency, Indonesia, comprising 25,565 daily observations of temperature, humidity, rainfall, sunshine duration, and wind speed. Missing values were interpolated using three methods: spline, stineman, and moving average interpolation. Performance was evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Squared Logarithmic Error (MSLE) across 10%, 20%, and 30% levels of simulated missing data. All analysis in this study were carried out using R-4.4.2 software. While spline interpolation performed reasonably well, it showed increased variability, especially for high-variance variables like rainfall. Moving average interpolation was less reliable, with error rates increasing alongside higher levels of missing data. In contrast, stineman interpolation consistently achieved the lowest error metrics across all levels of missing data, with MAE ranging from 0.219 to 0.6691, MSLE from 0.035 to 0.109, and RMSE from 1.247 to 2.245, demonstrating superior robustness. Stineman interpolation offers a highly effective approach for managing missing meteorological data in North Aceh’s long-term dataset, enhancing data reliability for meteorological modeling and decision-making in meteorological-sensitive sectors. This study provides practical recommendations for selecting optimal interpolation techniques, especially in regions with variable meteorological data quality.
Comparison of Nonparametric Path Analysis and Biresponse Regression using Truncated Spline Approach Azizah, Laila Nur; Rohma, Usriatur; Fernandes, Adji Achmad Rinaldo; Wardhani, Ni Wayan Surya; Astutik, Suci
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26739

Abstract

Nonparametric path analysis and biresponse nonparametric regression are two flexible statistical approaches to analyze the relationship between variables without assuming a certain form of relationship. This study compares the performance of the two methods with the truncated spline approach, which has the advantage of determining the shape of the regression curve through optimal selection of knot points. This study aims to evaluate the best model based on linear and quadratic polynomial degree with 1, 2, and 3 knot points. The model is applied to data with 100 samples and simulated data of various sample levels. The results show that the best model in nonparametric path analysis is a quadratic model with three knots, while the best model in biresponse nonparametric regression is a quadratic model with two knots. Biresponse nonparametric regression has a coefficient of determination of 88.8% which is higher than the nonparametric path analysis of 70.9%. The best biresponse nonparametric regression model is the model with quadratic order and two knots.
The Model of Students’ Emotional Intelligence of Professional Education Program in Indonesia Yanuarto, Wanda Nugroho; Setyaningsih, Eka; Suanto, Elfis; Isnawan, Mohamad Galang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27483

Abstract

Recently, there has been a noticeable increase in the significance of students' emotional intelligence (EI) and personality traits regarding self-awareness, self-management, and social awareness. This is to guarantee that their workforce is trained successfully and continuously produces good results. The aims of the study are as follows. (1) to assess how well the proposed model fits the students' data, and (2) to identify the connection between EI domains. The authors opted for a cross-sectional study design by questionnaire survei for EI domains. A total of 1,284 students were involved in this research. The purposive design procedure that resulted in the sample selection involved five departments within the Professional Educational Programs at Universitas Muhammadiyah Purwokerto in Indonesia. The structural model includes all of the interdependencies between the variables. Statistics for Windows 24.0 and Analysing Moment Structures (AMOS) 24 Version were utilized for data analysis. According to the findings, students' levels of self-awareness significantly affect their ability to self-manage in professional education programs, and vice versa. Thus, our study strengthened the idea that EI with an emotion-response process mask is a quality requirement for effective students in any kind of learning environment. 
XportID: Website for Clustering Indonesian Export Commodities by Destination Continent using Gaussian Mixture Model Lisanthoni, Angela; Trimono, Trimono; Prasetya, Dwi Arman
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27500

Abstract

Exports play a crucial role in driving economic growth and increasing foreign exchange reserves. However, Indonesia's export performance has not yet reached its optimal potential, as evidenced by an 11% decline in export value in 2023. The decrease is partly attributed to the limited range of export destination markets. Therefore, this study aims to analyze export trade patterns to identify the most ideal and potential market locations. The research will employ a quantitative approach, using secondary data from the Central Bureau of Statistics and the 2022 BACI dataset, focusing on the top 5 HS2 commodity types by highest export quantity. Clustering analysis is applied to group markets based on similar characteristics, identifying countries with high, medium, and low export potential for Indonesia’s export strategy. The research develops a website-based clustering system called XportID, utilizing a Gaussian Mixture Model (GMM) with the Expectation-Maximization (EM) algorithm to determine optimal cluster parameters. GMM is preferred for its flexibility and probabilistic system, providing more accurate results compared to distance-based methods. There will be 3, 4, and 5 clusters formed and then the best cluster will be selected by comparing the silhouette score obtained. Results show that the Asian continent has 5 clusters with the best value of 0.7035, the American continent has 3 clusters with the best value of 0.8165, the African continent has 3 clusters with the best value of 0.8534, the Australian continent has 3 clusters with the best value of 0.8540, and the European continent has 4 clusters with the best value of 0.8654. Overall results, the clustering system is categorized as strong structure with average value of 0.8185. Countries with high export potential include Malaysia, Philippines, South Korea, Brazil, Mexico, New Zealand, and Spain. Specifically in Africa, commodities related to HS2-15 show potential for growth.
Development of Ramsey RESET to Identify the Polynomials Order of Smoothing Spline with Simulation Study Nurdin, Muhammad Rafi Hasan; Fernandes, Adji Achmad Rinaldo; Sumarminingsih, Eni; Ullah, Muhammad Ohid
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26785

Abstract

Path  analysis is used to determine the effect of exogenous variables on endogenous variables. One of the assumptions in path analysis is the linearity assumption. The linearity assumption can be tested using Ramsey RESET. If the Ramsey RESET results show that all variables are non-linear then one of the alternative models that can be used is nonparametric smoothing spline. The smoothing spline method requires a smoothing spline polynomial order in estimating the nonparametric path analysis function. This polynomial order results in the smoothing spline method having good flexibility in data adjustment. The selection of the smoothing spline polynomial order becomes an obstacle because there is no test to determine the best order. Therefore, the purpose of this study is to find out how the value of V for order 3 and 4, develop Ramsey RESET to identify the best spline polynomial order, and evaluate the Ramsey RESET algorithm through simulation studies on various errors. The results of V values of order 3 and 4 can be obtained through the integral process and it is found that the higher the order, the value of V has a higher rank. Ramsey RESET development is done by modifying the second regression using nonparametric regression functions of order 2, 3, and 4. The simulation study results show that the classical Ramsey RESET can be used to detect linear shapes well because it is not affected by the value of the error variance. However, the classical Ramsey RESET has limitations in detecting non-linear forms other than quadratic and cubic forms so that other forms such as smoothing spline are needed. In testing non-linear models, the lowest p value is obtained in the form that matches the actual conditions, this can be interpreted that the modified Ramsey RESET can detect non-linear forms with spline polynomial orders well. The contribution of this research is to provide a test to identify the best smoothing spline polynomial order using Ramsey RESET modification
Mathematical Modeling of Stunting with the Influence of Nutritional Intervention Himmah, Elok Faiqotul; Kaestria, Rommi; Riana, Riana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26817

Abstract

The high number of stunting in Central Kalimantan with a prevalence that is still quite far from the WHO threshold, which is 26.9%, requires serious handling from the Central Kalimantan Provincial Government. Through the stunting reduction acceleration program, the government is targeting the prevalence of stunting in Central Kalimantan to decrease to 15.38% by 2024. The purpose of this study was to build a mathematical model to determine the dynamics of stunting events in Central Kalimantan with the influence of nutritional interventions. This model will be used to predict changes in stunting prevalence over time, and evaluate the impact of nutritional interventions on reducing stunting. This is a mixed method research that combines quantitative and qualitative approaches. with a mathematical modelling approach. The research method used in this study is a literature study with data collection techniques through semi-structured interviews with sources from the Health Office, Bappedalitbang and BKKBN which are included in the TPPS of Central Kalimantan, and also the BPS of Central Kalimantan. The data collected includes the prevalence of stunting, types and coverage of nutritional interventions, factors that influence stunting in Central Kalimantan, the nutritional status of toddlers, and indicators of nutritional interventions successstunting prevalence. Model simulation with Python programming shows the effectiveness of the intervention in preventing stunting and helping toddlers at risk of stunting to achieve normal nutritional status. Nutritional interventions have successfully reduced the prevalence of stunting in Central Kalimantan by 3.16% and increased the number of toddlers at risk of stunting who managed to achieve normal nutritional status after receiving nutritional interventions by 7%. It can be concluded that early intervention in toddlers at risk of stunting is very important to prevent stunting, and targeted intervention in stunted toddlers is also needed to accelerate recovery and reduce the overall prevalence of stunting.
Implementation of Capital Asset Pricing Model in Optimal Portfolio Formation on IDX High Dividend 20 Auditiyah, Cellyn; Farida, Yuniar; Utami, Wika Dianita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27799

Abstract

The IDX High Dividend 20 (IDX HIDIV20) is an Indonesian stock index known for its high dividend payouts, appealing to passive income investors. However, annual changes and fluctuating stock prices present challenges, necessitating diversification strategies. This study aims to create an optimal portfolio to balance returns and risks amidst market volatility on the IDX High Dividend 20 stock index. This research uses the Capital Asset Pricing Model (CAPM) method. The CAPM determines the relationship between risk and an asset's expected rate of return, especially shares. This model helps in evaluating whether an asset or investment provides sufficient returns commensurate with its risk. In this study. We used weekly stock price data and composite stock prices from Yahoo Finance and BI interest rates taken from Bank Indonesia from January 2020 to December 2023. The research findings found that there were 6 out of 12 samples forming the optimal portfolio, namely ITMG (28.0%), ADRO (16.6%), BMRI (29.2%), BBNI (13.7%), BBCA (11.8%), and BBRI (0.6%) with a portfolio return of 0.41% and a portfolio risk level of 0.16%. The study emphasizes the importance of diversification for investors, particularly in volatile markets, to manage risks and enhance returns. It also highlights the strategic value of investing in high-dividend stocks for consistent income and portfolio stability, offering practical insights for optimizing investment strategies.

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