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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 25 Documents
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Search results for , issue "Vol 8, No 4 (2024): October" : 25 Documents clear
Dependency Model of the Exchange Rate with the Volume Export of Mining Products in Indonesia Using Copula Rizki, Kurniadi; Budiarti, Retno; Purnaba, I Gusti Putu
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.v8i4.23089

Abstract

This research aims to analyze the dependence of the IDR-USD exchange rate on the volume of mining exports in Indonesia using the copula approach. This dependence is important to understand considering that the exchange rate and mineral exports have a direct impact on the country's economy which depends on foreign exchange from this sector. Mineral exports are one of the country's main sources of foreign exchange, while the exchange rate influences the competitiveness of exports on the international market. The mining products taken are iron and steel, copper and nickel, which are Indonesia's leading commodities. The copula method was chosen because of its ability to capture and model non-linear dependencies between variables, without considering the distribution of each variable. Copula makes it possible to model the marginal distribution of exchange rates and export volumes separately from their dependency structures, which is in line with the complex and dynamic nature of the Indonesian mining sector economy. The results show that there is no significant dependence between the exchange rate and the volume of commodity exports taken. Therefore, this commodity export volume policy will not have a significant effect on fluctuations in the IDR-USD exchange rate and vice versa. This article can be a recommendation for exporters to understand that export volumes do not need to pay attention to exchange rate fluctuations. 
Comparison of Vector Error Correction Model Prediction and Multiresponse Fourier Series, Case Study: Open Unemployment Rate in Indones IA Suliyanto, Suliyanto; Amelia, Dita; Raya, Kezya Bato; Evelyn, Jennifer
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.v8i4.24108

Abstract

Unemployment is someone who has been classified in the active labour force is looking for work at a certain wage level, but not getting the job they want. According to the International Monetary Fund (IMF) 2023, Indonesia is ranked second highest in Southeast Asia, ranked 16th in Asia and ranked 58th in the world with a percentage of 5.45%. The data used in this study is semester data (February and August) regarding the number of open unemployment according to the highest education completed in Indonesia taken from the website of the Central Statistics Agency (BPS) starting from 2000 to 2022. This study using comparison of multi response Fourier series regression with trigonometry method using Gamma and the Vector Error Correction Model (VECM). The result of this study is Fourier series regression method of the cos function with gamma is the best model in predicting because this method has smaller MAPE value compared to VECM method. The MAPE of Fourier Series method is 0.01%, in other hand the MAPE of VECM method is 18.90% which can be categorized as prediction results with the Fourier Series method are very accurate. The results of prediction are expected to be used as reference for government to making ideal future plan to minimalize the rate of open unemployment in Indonesia. 
The Value at Risk Analysis using Heavy-Tailed Distribution on the Insurance Claims Data Mukhaiyar, Utriweni; Dianpermatasari, Aprilia; Dzakiya, Azizah; Widyani, Sasqia Bunga; Syam, Husnul Khatimah
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.v8i4.25053

Abstract

The insurance has often been involved to minimize financial losses. As the product providers, the insurance companies must effectively manage risks to prevent errors in risk measurement. The amount of risk or loss experienced by the policyholder refers to the claim amount. The Value at Risk (VaR) is commonly used to measure risk. The VaR is calculated from the probability function, which can be obtained by evaluating the distribution of claims data. Most claim frequencies are small, but occasionally, huge claims appear. Therefore, the appropriate distribution would be characterized by a heavy-tailed. Thus, this research aims to model and evaluate insurance claims data using exponential, Weibull, Pareto, and lognormal distributions to assess financial risk through VaR. The insurance claims data were collected from a single insurance company and include 1,326 claims. This research specifically examines variables such as gender, diabetic status, smoking status, the number of claims, and the level of confidence. The data were analysed using descriptive statistics, Maximum Likelihood Estimation for parameter estimation, and Goodness of Fit tests to determine the best-fitting distribution, along with VaR calculations based on the results. The suitability of the distribution model is assessed through the VaR and is analysed based on the appropriate distribution of insurance claims data. It is obtained that the Weibull and lognormal distributions appropriately model insurance claims data. The highest VaR is observed in the claim data for female non-diabetic smokers, with a level of confidence of 99.5%. The lowest VaR is obtained from the claim data for male diabetic non-smokers, with a level of confidence of 90%. This approach enhances the prediction of large potential losses for specific demographic groups, aiding more informed decision-making in premium pricing and risk management. The integration of heavy-tailed distributions in risk assessment, with a particular focus on demographic specificity, constitutes a substantial and novel contribution to this research.
Game Chromatic Number of Tadpole Graph, Broom Graph, and Tribune Graph Fran, Fransiskus; Abdurahman, M Luthfi
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.v8i4.25817

Abstract

Graph coloring game is one of application in graph theory. The goal in this article is determine game chromatic number of tadpole graph, broom graph, and tribune graph. The graphs are simple, connected, and undirected and thus eligible for playing graph coloring game. Given two players with the first player is called A and second player is called B coloring vertex of graph G with a set of colors C={c_1,c_2,c_3, ..., c_k}. A must to make sure that all vertex of G has colored and B must try to prevent A coloring of all vertex. The first step was taken by A as first player, two players take turns coloring vertex of graph G, with rule that every vertex have different color from the neighbourhood. If all vertex of graph G have been colored, then A win or B win if some vertex hasn’t colored. The smallest number of k if A has a strategy to win at graph G with k color, then k called game chromatic number which is denoted by χ_g (G). The strategy to win this game is coloring the biggest degree of vertex in graph first. The result obtained from this paper is A win the game with the strategy of first coloring the largest degrees of vertex. So, exact of game chromatic number of tadpole graph is 3, broom graph is 2 or 3 with several conditions, and tribune graph is 3 or 4 with several conditions.
Augmented Reality Learning Media with Ethnomathematic Approach to Grow Students' Mathematics Learning Motivation Rohim, Dhina Cahya; Hana, Fida Maisa; Manggalastawa, Manggalastawa; Saharani, Safira; Himayati, Ade Ima Afifa
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.v8i4.25740

Abstract

The efforts that can be made to increase learning motivation are through the use of learning media integrated with current technology with a culture-based approach that students often find in everyday life. The purpose of this study was to describe the importance of AR in mathematics learning, the use of technology in ethnomathematics, and the effects of AR in fostering student learning motivation. This research method is Systematic Literature Review (SLR) with the PRISMA (Preferred Recording Items for Systematic Review and Meta-analysis) technique. The article search process uses a database from international journals indexed by Scopus and found 287 articles. Then a feasibility study was carried out according to the specified criteria so that 18 final articles were obtained. The results of the study showed that: (1) the use of AR in mathematics learning is very important because it has a positive impact such as improving learning outcomes, increasing learning motivation, improving the quality of learning, creating fun learning, improving learning experiences and improving creative thinking skills; (2) Cultural integration combined with technology provides benefits, namely learning becomes interesting so that it can foster student learning motivation, the form of integration between AR technology and ethnomathematics can be in the form of developing interactive learning media, modules or android-based media; and (3) Several studies using AR-based learning media have provided significant results in increasing students' learning motivation. 
Analysis Stability of the Model SEI_1 I_2 I_3 R on the Spread of TikTok User Bahri, Susila; Afdianti, Sri; Zulakmal, Zulakmal
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.v8i4.25762

Abstract

TikTok addicts, namely content creators (I_1), people who shop (I_2), and people who watch TikTok content (I_3) in Indonesia, continue to increase from year to year. The dynamics of TikTok addicts are analogous to cases of disease transmission. This can be done because TikTok users (S) can gradually increase to become account owners (E), then because there is interaction between account owners and groups of TikTok addicts, TikTok addicts increase, increase or spread. However, TikTok addicts can recover (R) and become vulnerable again over time. Each TikTok addict can have different negative impacts, such as wasting time, getting inaccurate information that can spread people, being deceived, and can disrupt mental health such as depression. Therefore, it is necessary to know which group of TikTok addicts has the greatest influence on the increase in TikTok users in Indonesia so that the government can take action to reduce the increase in TikTok users. In this research, the mathematical dynamics model (〖SEI〗_1 I_2 I_3 R)was first constructed. Analysis of the stability of the model's equilibrium point is carried out by determining the eigenvalues and the Jacobian matrix to obtain an equilibrium point that is free from the influence of Tik Tok addicts, asymptotically stable if R_0=0.941019<1. This means that the influence of TikTok addicts on increasing TikTok users is slowly decreasing and will disappear from the population as time goes by. The endemic equilibrium point is asymptotically stable if R_0=1.011756>1. This means that the influence of TikTok addicts on the increase in TikTok users will remain in the population and will increase over time. Numerical simulations were carried out using MAPLE software.  
A Mathematical Model Analysis of COVID-19 Transmission with Vaccination in Caputo Fractional Derivatives: Case Study in Indonesia Nisardi, Muhammad Rifki; Kasbawati, Kasbawati; Khaeruddin, Khaeruddin
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.v8i4.24711

Abstract

This study aims to investigate a fractional-order mathematical model of COVID-19 transmission using the Caputo derivative definition which suitable to epidemiological cases by its advantage to explain memory effects. The model incorporates compartments for asymptomatic infections and includes a vaccination strategy aimed at mitigating the spread of COVID-19. We derived the disease-free and endemic equilibrium points for the fractional model and computed the basic reproduction number (R_0 )  using the Next-generation Matrix method. Additionally, we conducted sensitivity analyses of parameters affecting R_0. The stability of the fractional model requires specific conditions to be met by the model parameters. To approximate active COVID-19 cases in Indonesia, we utilized the Explicit Grunwald-Letnikov method which well fit with Caputo fractional differential system. Simulation results demonstrate that the fractional-order model offers a flexible approach for modelling active COVID-19 cases in these regions. We found that fractional order for active cases COVID-19 in Indonesia is α=0.9856. The simulation showed that decreasing the vaccination rate and the efficacy of the vaccine would affect the reduction of COVID-19 transmission.
Identifying Poverty Vulnerability Patterns in Indonesia using Cheng and Chruch’s Algorithm Afnan, Irsyifa Mayzela; Wijayanto, Hari; Wigena, Aji Hamim
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.v8i4.25790

Abstract

Poverty remains a significant issue in developing countries, including Indonesia, where in 2022, the number of people living in poverty reached 26.36 million, with a poverty rate of 9.57%. The Central Statistics Agency (BPS) measures poverty using a basic needs approach, defined as the inability to meet essential food and non-food needs through expenditure. Individuals are considered poor if their average monthly per capita expenditure is below the poverty line. Research on poverty has evolved into a more multidimensional understanding, The Multidimensional Poverty Index (MPI), which identifies deprivation across three key dimensions: health, education, and living standards. This study aims to identify patterns of poverty vulnerability by applying the Cheng and Church (CC) algorithm through a biclustering approach using data from BPS. This quantitative method utilizes 13 multidimensional poverty indicators across 34 provinces. The CC algorithm begins by setting a threshold, followed by removing rows and columns with the largest residuals, adding qualifying rows and columns, and substituting elements to prevent overlap. The quality of the bicluster is then evaluated based on the Mean Squared Residue (MSR) value until optimal groups are formed. The results indicate that a threshold of ? = 0.01 generates seven biclusters with the lowest mean squared residual (0.0065), signifying optimal bicluster quality. Further validation using the Liu and Wang index reveals less than 50% similarity with other thresholds, reinforcing the uniqueness of these findings. MSR serves as a measure of homogeneity within the bicluster, similar to how uniform the level of poverty is within a region. If families have similar expenditures and are below the poverty line, they face similar challenges, resulting in a low MSR value. In contrast, the Liu and Wang index compares regions with different poverty alleviation strategies. These findings provide valuable insights for policymakers. For example, in bicluster 7, where specific interventions are needed in Papua and West Kalimantan, which face local challenges such as reliance on agriculture, low education levels, and limited access to sanitation and clean water.
Promoting Computational Thinking through Programming Trends, Tools, and Educational Approaches: a Systematic Review Irawan, Edi; Rosjanuardi, Rizky; Prabawanto, Sufyani
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.v8i4.26407

Abstract

This systematic research aims to provide a comprehensive overview of the development of analysis related to the use of programming in the development of Computational Thinking (CT), especially in the context of education from primary to tertiary levels. This study analyzed 88 articles from empirical studies related to the use of programming to develop CT sourced from the Scopus database. The analysis process followed the PRISMA 2020 guidelines and consisted of three stages: search, selection, and data analysis. Descriptive and thematic statistical approaches were used for data analysis. Instruments used in the selection of articles included Rayyan for screening based on inclusion criteria, as well as Microsoft Excel for coding and thematic analysis. The results showed that articles related to the use of programming to promote CT have appeared since 2011 but have increased significantly since 2016, with an annual growth rate of 17.6%. Most studies used quantitative approaches, followed by qualitative and mixed methods. Overall, 270 authors from 27 countries contributed to the study, with the United States having the highest number of publications. A total of 33 programming tools were identified, with Scratch being the most widely used tool, followed by Blockly, LEGO, Scratch Jr., Code.org, Python, Alice, App Inventor, Kodu, R, MakeCode, and Arduino. Scratch Jr. is most commonly used at the early childhood education level, while programming languages such as Python, R, and MATLAB are more commonly used in higher education. The implications of these findings suggest that the trend of using programming tools such as Scratch and Blockly has the potential to influence CT teaching strategies in the classroom, as well as the importance of using varied programming tools in efforts to integrate CT into the education curriculum.
Analysis of Factor Affecting Tuberculosis Cases in West Java Province Using Panel Data Regression Approach Saifudin, Toha; Aisyah, Arlisya Shafwan; Indrasta, Irma Ayu; Amelia, Dita
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.v8i4.24795

Abstract

Tuberculosis (TB) is a disease that can cause death with the largest number of sufferers after COVID-19. In Indonesia, the number of TB cases reached 724.309 cases in 2022 with the highest number 184.406 cases in West Java Province. Given this situation, Indonesia must try to achieve the health target from SDGs, namely ending the TB epidemic by 2030. Therefore, this research aims to analyze the factors that have a significant influence on the incidence of TB in Indonesia, especially in West Java Province. The research focuses on four variables: percentage of poverty, number of diabetics, number of HIV/AIDS patients, and population density. To provide a more informative analysis, this research uses a combination of cross-section and time series data from 27 regions between 2020 and 2022. So, the method used according to the type of data is panel data regression including common effect, fixed effect, and random effect models. Based on statistical tests, namely through the chow test, hausman test, and lagrange multiplier test, it was found that the best model was fixed effect with an R-squared value of 90%. The research revealed that all the studied factors significantly influence the incidence of TB cases in West Java. The results of this study are expected to help the West Java government in an effort to reduce the number of TB cases and formulate policies by reducing the percentage of poverty and population density in West Java. By ensuring the availability of health facilities such as establishing health centers in densely populated areas and counseling programs also need to be conducted to underscore the importance of TB control in West Java.

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