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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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Process of Proportional Reasoning Students' Errors in Solving Mathematical Problems Irpan, Samsul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33355

Abstract

Proportional reasoning plays a crucial role in mathematical reasoning, yet many students struggle to coordinate multiplicative relationships when solving mathematical problems. This study aimed to examine the processes behind students’ errors in proportional reasoning and to describe the types of incorrect strategies they used when working through a contextual joint‑work problem. Using a qualitative exploratory descriptive design, data were collected from students’ written solutions, think‑aloud explanations, and interview responses to capture their reasoning processes in depth. The participants were 15 first-semester students from the Mathematics Education Department, Universitas Islam Negeri (UIN) Mataram. Results showed four major categories of incorrect reasoning: intuitive reasoning based on misleading but salient information, additive reasoning that relied on differences rather than multiplicative structures, proportion attempts that identified proportional cues but applied them incorrectly, and other incomplete or unsupported strategies. Additive reasoning emerged as the most dominant pattern across students of varying proficiency, indicating a strong tendency to default to non‑proportional interpretations even when the situation required multiplicative thinking. Although some students recognized structural features such as periodic assistance, they struggled to coordinate unit work or rates, leading to systematically flawed conclusions. These findings suggest that students’ proportional reasoning errors stem from entrenched intuitive and additive tendencies. The study highlights the importance of instructional approaches that explicitly develop unit‑rate reasoning, strengthen multiplicative understanding, and support accurate representation of proportional situations.
Learning Trajectory of Whole Numbers using the Context of Muara Enim Melemang Based on Realistic Mathematics Education (PMRI) M., Arbella Sri Marleny; Zulkardi, Zulkardi; Putri, Ratu Ilma Indra; Hartono, Yusuf
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34937

Abstract

Learning whole numbers in the early grades of elementary school often poses challenges because students must understand abstract concepts and represent them symbolically. This study focuses on developing a Local Instructional Theory (LIT) for learning whole numbers using the Muara Enim melemang cultural context within the Pendidikan Matematika Realistik Indonesia (PMRI) framework. The research contributes both to the development of learning theory (LIT) and to improving the effectiveness of culturally based mathematics learning in Indonesian primary schools. The study employed design research (validation study) consisting of three stages: (1) the preliminary design formulated a Hypothetical Learning Trajectory (HLT) through curriculum analysis and contextual task design; (2) the teaching experiment tested the HLT in classroom practice to explore students’ strategies and interactions; and (3) the retrospective analysis compared the HLT and the Actual Learning Trajectory (ALT) to refine the emerging instructional theory. Findings reveal that the predicted HLT aligned with the ALT. Students successfully developed number sense counting, comparing, ordering, and performing simple operations through concrete representations of lemang. Difficulties mainly appeared in symbolic notation, such as using inequality signs and subtraction symbols. The study’s novelty lies in establishing a local culture-based LIT that bridges PMRI principles with ethnomathematics. Practically, it provides a contextual model teachers can adopt to enhance meaningful mathematics learning in early grades.
Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra Yonantha, Krisma; Putra, Dewa Putu Wiadnyana; Rudhito, Marcellinus Andy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33242

Abstract

The transportation system is a crucial infrastructure for supporting connectivity between each National Strategic Tourist Area (NSTA) tourist destination of Yogyakarta. Management of transportation network and scheduling departure of transportation services are not yet optimal. This study aims to design a synchronized DPTT route and schedule that covers the entire service area using max-plus algebra. This type of study is applied research. The scheduling problem will focus on determining the number of fleets serving all routes with departure periods below 60 minutes. This research was conducted through literature review, field observations and online maps using Google Maps, and computation using the Scilab program. The results show that time travel between 8 tourist destinations are organized into a strongly connected directed graph with 20 routes. Departures are modeled as a linear discrete-event system over max-plus algebra. Computation in Scilab produce a baseline departure period of 90 minutes. We evaluate by adding 2, 8, 10, or 12 of buses by reinforcing the longest route. The simulation shows that the addition of 10 and 12 buses in certain section can reduce the departure period to 56 and 48 minutes respectively. The results demonstrate that targeted fleet additions and network reconnection, guided by max-plus synchronization, can substantially improve service regularity and passenger connectivity.
A Daily Transition Analysis of Disaster Events in Riau Islands using Markov Chains: Dominant Disaster Identification and Risk Assessment Hayati, Nahrul; Anggraeni, Andini Setyo; Sulistyono, Eko
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34024

Abstract

Objectives: This study employs a Markov Chain approach to analyze daily disaster transition patterns in the Riau Islands, with the primary objectives of identifying dominant hazards, quantifying long-term disaster risks, and providing evidence-based recommendations for disaster management. Methods: The research utilized daily disaster records from Indonesia’s National Disaster Management Agency (BNPB) for 2024. A dominant state classification approach was applied to handle days with multiple disaster occurrences, followed by the construction of a transition probability matrix and steady-state analysis to determine long-term disaster distribution. Results: The analysis reveals that no disaster conditions represent the most prevalent state in the region. Among actual disasters, wildfires demonstrate the highest persistence, followed by extreme weather events, floods, and landslides. The transition patterns indicate that most disasters occur as isolated events rather than consecutive sequences, though wildfires show a tendency for temporal clustering. Conclusion: The study provides two key contributions. Methodologically, it demonstrates an effective approach for simplifying complex multi disaster daily data. Practically, it offers scientific evidence for prioritizing wildfire management in the Riau Islands while maintaining preparedness for other episodic disasters. These findings support the development of targeted early warning systems and resource allocation strategies for local disaster management agencies.
Statblithz Game Media Development to Train Students' Mathematical Problem-Solving Skills Afifah, Ani; Wulandari, Alya; Darmayanti, Rani; Santiago, Paulo Vitor da Silva; Karim, Samuel
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35179

Abstract

Mathematical problem-solving skills are essential for students to succeed in the 21st century, yet many struggle to apply mathematical concepts in real-life situations. This research addresses the need for innovative learning media by developing Statblithz Game, an educational game designed to train and enhance students’ mathematical problem-solving abilities. The study employed a Research and Development approach using the ADDIE model, involving stages of analysis, design, development, implementation, and evaluation. Participants included middle school students who engaged with the prototype and provided feedback through questionnaires, expert validations, and pre- and post-tests measuring problem-solving performance. The results indicated that Statblithz Game is highly feasible, with expert validation scores averaging 89%. Moreover, students’ problem-solving test scores improved by an average of 25% after using the game. In conclusion, the Statblithz Game effectively enhances mathematical problem-solving skills and offers an engaging alternative to traditional mathematics instruction. The impact of this research lies in providing educators with an innovative and interactive tool that can foster critical thinking and improve student learning outcomes in mathematics.
Can Indonesia Eliminate Tuberculosis by 2030? A Deterministic Epidemic Model Approach Sasmita, Novi Reandy; Ramadani, Maya; Ikhwan, Muhammad; Rahayu, Latifah; Mardalena, Selvi; Suyanto, Suyanto; Safira, Nanda; Huy, Le Ngoc; Myint, Ohnmar
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35252

Abstract

Indonesia, bearing the world’s second-highest tuberculosis (TB) burden, has mandated a national target to eliminate TB by 2030, aiming for an incidence rate of 65 per 100,000 population. This study aims not only to project future transmission dynamics but also to systematically explore the specific epidemiological barriers, namely, drug resistance and relapse mechanisms, that hinder achieving this goal. To address the heterogeneity of TB transmission, we developed a novel deterministic SVE3I3R model. This framework stratifies the population into vaccinated, latent Tuberculosis Infection (LTBI), and infectious compartments, explicitly distinguishing among Drug-Susceptible (DS-TB), Multidrug-Resistant (MDR-TB), and Extensively Drug-Resistant (XDR-TB) strains. The resulting system of ordinary differential equations was solved numerically using the fourth-order Runge-Kutta (RK4) method to ensure stability and accuracy in simulating long-term epidemiological trends from 2023 to 2030. Parameters were calibrated using national reports and literature specific to the Indonesian context. Projections indicate that Indonesia will miss the 2030 elimination target by a significant margin. The model forecasts a TB incidence rate of 321 per 100,000 population by 2030, nearly five times the national benchmark. The analysis reveals that failure to reach the target is mechanistically driven by a "relapse trap" among recovered individuals and an alarming exponential surge in resistant strains (MDR-TB and XDR-TB). These findings suggest that current control strategies are insufficient not merely in scale but in structure. Evidence-based policy must urgently shift from standard intervention to aggressive interruption of resistance pathways and enhanced management of the latent reservoir to prevent the projected demographic resurgence.
Modular Coloring of Comb Graph, Lintang Graph, and Butterfly Graph Pramudya, Deby Debora; Yudhi, Yudhi; Fran, Fransiskus
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34697

Abstract

Given any graph G that contains no isolated vertices, a labeling c is a mapping from its vertex set to the set of integers modulo k (c:V(G)→Z_k) for k≥2, adjacent vertices are allowed to share the same color. The number of color labels of a vertex v (σ(v)), is the number of color labels of the neighborhood of vertex v (N(v)). A labeling c is a modular k-coloring of G if σ(x) ≠ σ(y) in Z_k for all vertices x,y that are neighbors in G. Denoted as mc(G), the modular chromatic number of G is defined as the least integer k that allows for a modular k-coloring of the graph. This research seeks to ascertain the modular chromatic number of the comb graph Cb_n, the lintang graph L_n, and the butterfly graph BF(n). The first step in this research is to define the labeling c, then determine (N(v)). Next, determine the number of color labels from the neighborhood at each vertex with σ(x)≠σ(y) in Z_k for x,y being all neighboring vertices. After the condition σ(x)≠σ(y) in Z_k is satisfied, ascertain mc(G). By performing the same steps on each graph with increasingly larger values of n, a modular coloring pattern will emerge, which is used to formulate the modular coloring formula. This process concludes with the formulation of a modular coloring formula and the determination of the modular chromatic number for comb graph Cb_n, lintang graph L_n, and butterfly graph BF(n). Based on this research, mc(Cb_n)=2, mc(L_n)=2, and mc(BF(n))=3 are obtained.
The Probability Model of Earthquake Frequency in the Enggano Segment using Poisson Mixture Models Yosmar, Siska; Rachmawati, Ramya; Damayanti, Septri; Rizal, Jose
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33446

Abstract

An earthquake is a natural disaster that occurs suddenly resulting in numerous casualties, such as loss of life and property. Bengkulu Province is among the provinces affected by severe earthquakes. Studies on probability models for the frequency of earthquake events in Bengkulu Province are still scarce, as outlined in the 2017 book “Map of Sources and Hazards of Indonesian Earthquakes.” This research uses Poisson mixture models to build a probability model for the frequency of earthquake events in the Enggano segment, located in the coastal area of Bengkulu Province.   ..   The phases of model building are the model diagnosis phase, testing the dispersion state relative to the Poisson distribution, testing the dependence of research data on time variables using the Ljung-Box test, and testing the criteria for selecting the best model using the Bayesian Tests Measures of Information Criterion (BIC) and Akaike Information Criterion (AIC). Annual earthquake frequency data from January 1, 1971, to December 31, 2022, were retrieved from the USGS catalog of data on the frequency of major earthquakes with a magnitude of Mw ≥ 4.40, which occurred a total of 633 times. After completing the model building phase, the AIC and BIC values for each model were determined by determining the number of unobserved groups. Both Poisson mixture models and Poisson hidden Markov models produced the same number of unobserved groups of 3 groups with AIC=302.91 and BIC=324.38.
Analysis of DHF Patients Based on Laboratory Examination Results with Nonparametric Approach Utami, Tiani Wahyu; Haris, M. Al; Salma, Nadia Khoirunnafisa
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33609

Abstract

The dengue virus, which is spread by the Aedes aegypti mosquito, is the cause of Dengue Hemorrhagic Fever (DHF). In the city of Semarang, there was a threefold increase in cases of DHF compared to previous years. This type of research is quantitative research because it produces function that describes the relationship to what extent changes in predictor variable are related to changes in response variable to understand the level of association. Modelling the link between response and predictor factors is the aim of this study. Platelet as the response variable and hemoglobin and leukocyte as the predictor variables, so that the obtained model can be used as a prediction, especially regarding the dynamics of platelet changes influenced by hemoglobin and leukocytes. The pattern of the relationship between platelets and the suspected influencing factors does not form specific pattern, so the Nonparametric Spline method is used in this study. The Spline method is chosen for its flexibility; this model tends to independently seek data estimates, the completion of this study using R software. In the Spline method, there are knot points indicating data changes. The selection of optimum knot points is done by choosing the minimum GCV value The secondary data used came from Roemani Muhammadiyah Hospital's 2023 medical records. The data include platelet count, hemoglobin, and leukocyte. Based on the modeling conducted using truncated spline, the optimum knot points on the linier spline are determined to be 3 knot points with a coefficient determination of 83.58%. The coefficient of determination of 83.58% indicating that 83.58% of the variation in response variable can be explained by predictor variables studied in the regression model. This value indicates that predictor variables have a strong ability to explain changes in response variable.
Analysis Comparison of BiLSTM and BiGRU Models for Aircraft Visibility Prediction Saidah, Nayla Fitriyatus; Ulinnuha, Nurissaidah; Farida, Yuniar
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34698

Abstract

Severe weather conditions such as fog and heavy precipitation pose significant threats to aviation safety. Accurate prediction of aircraft visibility is therefore essential to support operational decision-making and reduce the likelihood of accidents. This study aims to compare and evaluate the performance of two bidirectional deep learning models, BiLSTM and BiGRU, in predicting aircraft visibility using historical meteorological data from BMKG Juanda Sidoarjo. The novelty of this research lies in applying and comparing bidirectional recurrent architectures for visibility prediction, an approach rarely explored in aviation meteorology, to assess their capability in capturing temporal dependencies within time-series visibility patterns. Both models were trained using hyperparameter tuning, with the best configuration obtained from a 24-hour input window, batch size of 32, 64 neurons, a dropout rate of 0.1, and 100–200 epochs. The dataset was divided into training and testing sets (80:20), and model performance was evaluated using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) to assess both predictive accuracy and computational efficiency. The results indicate that while BiLSTM achieved slightly higher accuracy, BiGRU demonstrated superior overall efficiency, obtaining competitive error metrics (MSE = 1.50 × 10⁶, RMSE = 1,223.5, MAPE = 19.35%) compared to BiLSTM (MSE = 1.58 × 10⁶, RMSE = 1,258.1, MAPE = 19.50%). BiGRU’s advantage lies in its simpler structure and faster computation, which reduce training complexity without sacrificing forecast accuracy. Overall, this research contributes to the development of efficient bidirectional time-series models for aviation meteorology, offering a practical framework for real-time visibility forecasting in computationally limited environments. The balance between accuracy, speed, and model simplicity makes BiGRU a more scalable and applicable choice for enhancing flight safety operations.

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